1000 Sentences With "linearly" | Random Sentence Generator

Rather, I saw pain levels go up linearly with age.

The relationship between SPF and sun protection does not increase linearly.

Moreover, this storm front of data is amassing exponentially, not linearly.

We were layering this idea of a nonlinear experience experienced linearly.

Science doesn't go as linearly as the general public thinks it does.

My whole life, I was thinking linearly, on walls or in books.

Common liquids, such as water, alcohol and oil, respond to force linearly.

Events aren't presented linearly, but Haller's flashbacks and flash-forwards aren't distinct.

Documenting someone's life doesn't necessitate moving from beginning to end, or even linearly.

It's quite a rainbow of things if I look at the mix linearly.

And doesn't that mean their reach is supposed to grow exponentially, not linearly?

This clearly happens with technological progress but also, less linearly, with cultural progress.

It was quiet even when you pushed it, and the torque arrived remarkably linearly.

As that number increases linearly, the possibility for interactions increases at a quadratic rate.

For time to pass means for events to be linearly ordered, by earlier and later.

The game follows a strict series of acts, presented linearly, with a table of contents.

More linearly, Trump's declining public appeal may be a bearish catalyst in and of itself.

It also does this without having the computational cost rise linearly with the security level.

Compounding, for instance, is a mental model that helps us understand how things grow non-linearly.

It's kinda fun to go back and listen linearly—you can see the vision start to unfold.

If you build a business with good competitive advantages, your value grows linearly as you grow revenues.

Conversely, the left hemisphere works linearly and methodically and is all about the past and the future.

It unfolds logically and linearly, and doesn't meander or repeat itself the way a session of gameplay might.

They see the world non-linearly, recognizing the contextual and overlapping features of a given event or situation.

With that much funding, it's time to a way to make the company grow exponentially, not just linearly.

Quantum computers, though, only have to grow linearly when you add atoms, giving them more flex for their size.

But what that did was that it made it so that your advantage went up logarithmically rather than linearly.

Serra and his director of photography, Jonathan Ricquebourg, used three cameras and shot continuously, linearly, in an empty castle.

We either oversimplify things or accept that they're too complex for us to break down linearly, let alone explain fully.

Anonymous uses a more sinuous line and the inkblots are likely to be connected linearly from one vertical series to another.

For far too long, we've been shackled to the normalcy of having gadgets with rectangular displays fitting linearly inside rectangular boxes.

CEO Jeff Lawson stressed that investors can count on growth but shouldn't expect it to occur linearly, on today's earnings call.

As such, seat counts should not need to grow linearly with company growth, as they have in the era of static software.

The first half of the arc will take place linearly, progressing from the beginning in the straightforward humanly experienced direction of time.

And with Y.A., I was just like, how about you have one protagonist and the book goes linearly, in a chronological order.

"Once those "priority" documents are done, I'll start going through the digital folders more linearly and upload files by section," Best said.

In fact, according to his study's findings, the number of required samples scales linearly with the number of microbial species in the system.

Older people like Jim often don't speak clearly or linearly, and those with dementia can't be expected to troubleshoot a machine that misunderstands.

RUSSONELLO "Love Birds, Night Birds, Devil-Birds," from the composer and keyboardist Kelly Moran's new EP "Origin," doesn't seem to move forward linearly.

I think five years in Silicon Valley, it's like we're pretty good at thinking linearly but we're not very good at thinking exponentially.

That's about coverage and adding more content and having an architecture that allows you to add content and increase to understanding faster than linearly.

S|2's more intimate setting seems appropriate for Pettibon's small to medium-sized drawings of American mythos, hung linearly on a singular wall.

"This number has grown—roughly linearly—and this month, for the first time, we saw this '30 day' figure exceed 1 million people," Muffett continues.

"The Temple of Direction" by Geordie Van Der Bosch "is organized linearly" as "linearity also reflects the passage of life," according to the structure's description.

Thirty Flights of Loving, on the other hand, is far more ambitious in its use of the technique, as it jumps non-linearly through the story.

Beyond that, it is critical to find some level of virality since paid channels only scale linearly while organic and word of mouth can grow exponentially.

Their findings show that the relative sizes of entrees, plates, and bread increased linearly over the past millennium, with respective jumps of 23.1%, 65.6%, and 69.2%.

In a typical graph, values on the (vertical) y-axis are plotted linearly: 1, 2, 3, and so on, or 10, 0003, 30, or the like.

To make the challenge even more urgent, while demand for physical assets grows linearly, demand for wireless network capacity has grown — and will continue to grow — exponentially.

The consequences of burning out — a phenomenon that rises linearly as a doctor matures, until it finally dies down at about 60 — can be hard to measure.

Testosterone doesn't drive a single path to athletic performance, nor even a small set of processes that can be linearly traced from more testosterone to more ability.

Samsung is using the same 0.8-micron pixel size from its 48- and 64-megapixel sensors, then linearly increasing the physical surface area to arrive at 108.

We talked about how infectious diseases spread exponentially, not linearly—and how that can make what seems, for weeks, like a small problem suddenly very, very big.

"The only problem was that the ones I know all accelerate linearly and take their sweet time whenever a change in direction occurs," tkuhn writes on their blog.

The amount you get doesn't increase linearly with the amount you pay, and the result is that the larger item appears (as planned) to be the better deal.

These segments were introduced one at a time, and the bacteria systematically integrated them in a linearly coherent manner to reflect the order in which they were introduced.

Even more remarkably, the amount of time it takes the amoeba to reach these nearly optimal solutions grows linearly, even though the number of possible solutions increases exponentially.

Characterization that rock solid barely occurs in the most scripted, linearly structured video games, let alone an open-world shooter, and yet Far Cry 2 avoids easy nihilism.

This unexpected overlap means some species within the Australopithecus genus didn't evolve linearly, with one species tidily following another in an orderly fashion, a process known as anagenesis.

At first glance, each work in a series of color-filled and linearly-appealing artworks seem worked over by the nimblest brushstrokes, producing gauzy dashes that collapse into neat alignment.

I haven't done that that much of that, and the interesting thing about that was, we messed around with a couple different structures, and the movie really didn't work linearly.

Among his powers is that he experiences time non-linearly, and yet he is unable or unwilling to deviate from what he foresees, even at the cost of innocent lives.

In the past, in order to get to all the ideas and variances of a riff, I would have laid out a song really long, and laid it out linearly.

"I would continue to remain cautious, but at the same time, what I would say is that the number of cases so far has only been growing linearly," he said.

You could even play the main levels, called dungeons, in whatever order you wanted — which was nearly unprecedented during the early era of gaming, when games were organized much more linearly.

But the average amount of alcohol someone drank in a lifetime was linearly associated with total risk of cancer, in that risk went up the more someone drank, the data showed.

Told non-linearly, the series ping-pongs between a biographical look at Clinton's life and her final presidential run in a manner that would be resonant if it weren't so confusing.

The founders get this conceptually, but sometimes they can be fixated on making the company grow linearly by getting more "paper" under management, rather than developing a solution that unlocks exponential growth.

As an alternate scenario, it's possible that instead of increasing linearly like the example above, with real net wealth increasing some fixed amount on average every year, that wealth could grow exponentially.

Perhaps the most important thing we've learned about sea level by studying Earth's past is that it doesn't rise linearly—it goes in fits and starts, accelerating dramatically as the ice sheets disintegrate.

Most of the source material I use is from the 40s and 50s, an era that is so far, ideologically, linearly, and imagistically, from the present day as to look like another world.

The researchers were also able to vibrate the nanodumbbell in place by blasting it with a laser that was linearly polarized , with its light confined to a single plane, they wrote in the study.

The most contrived or intentional Vines nevertheless usually had something awkward about their pacing or focus or production, the natural result of being built linearly on the fly, the way being alive is built.

But also because the nature of a lot of that late night content in particular is that it's often viewed — not as it's linearly broadcasted on live channels — but the next day on YouTube.

Thinning out the glass is one of the "two main tricks" to making it bend, says MIT associate professor of materials science Juejun Hu, because physics students learn that tensile strain scales linearly with thickness.

Unlike her characters, who tend to be laconic and aloof, and her narratives, which are elliptical and enigmatic, Denis speaks fluently, linearly, and sometimes at great length, with an instinctual command of pacing, foreshadowing, and suspense.

Whatever the intentions of diplomats and scientists, the fact remains that the science is surging exponentially, popular understanding of it is advancing linearly at best, and the regulatory framework surrounding it is only creeping forward glacially.

Without shirking the mechanics of how time travel works, the novel dwells at length in how time travel feels, both for those who hop back and forth through it and for those who experience it linearly.

Instead of sending players off on a gauntlet of linearly arranged, discrete story missions, the expansion opens up the middle section of its baron-hunting, allowing players to tackle six of the eight barons in any order.

On my first question, Ravi from Hyderabad was first to answer that the next "good year" in Parker's original sense will be 2070, and they occur at gradually (actually, linearly) increasing intervals after that – 92 years, 94 years, etc.

In the experiments they ran, the researchers found that the system, catchily named Decentralized Distributed Proximal Policy Optimization or DD-PPO, appeared to scale almost ideally, with performance increasing nearly linearly to more computing power dedicated to the task.

The implications of decentralized ledger technology (DLT) are astounding: Digital trust is now an ever reasonable possibility; meaning online and offline assets can now be assigned ownership and the transference between those parties can be proven both linearly and cryptographically.

Though the flashbacks unfold somewhat linearly, starting with Elton's childhood as Reginald Kenneth Dwight, born in the working-class London suburb of Pinner, they are used as a way to understand where the music comes from, rather than just hit biographical plot points.

"One of the things you see in these campaigns is that [while] collateral damage is obviously a critical concern, it does not go up with linearly with the intensity of strikes," said Michael Vickers, who was the under secretary from 2011 to 2015.

"One of the things you see in these campaigns is that [while] collateral damage is obviously a critical concern, it does not go up linearly with the intensity of strikes," said Michael Vickers, who was the under secretary from 2011 to 85033.

Here is the reason this is all OK: Lifting progress, or any kind of progress, really, is such that you actually don't need your sessions to be linearly better and better every single time in order to get overall better in the long term.

It's true that comparisons to the Industrial Revolution are not actually comforting, when it comes to jobs; but it's also true that such comparisons are incredibly misleading, because they assume that change and today's all happen linearly, at a constant pace, whereas today's change is nonlinear.

Looking at this ratio over a large number of vertebrate animals, he said, scientists have found that "brain size increases pretty linearly with body size, except for some critical species like Homo sapiens and some cetaceans," the order of mammals that includes whales, dolphins and porpoises.

BitTorrent claims its protocol is cheaper than current methods, with much less lag "Current methods for online live broadcasting over the internet scale linearly with the size of the audience — that means that you have to pay more as additional viewers join your stream," wrote the company in a blog post last year.

Following a rather uninspired- Q&A in which the audience drank up Ashanti's eccentricities while barely probing the intricacies of his craft, Diggs presented a rustic sequence of non-linearly mixed emotive house music, which unfortunately served as an adequate post-recital coolant instead of inspiring further engagement with a modern form of audio sculpting.

" The story of four granddaughters growing up with their extended family on an Ohio farmstead, the novel was "an important debut by a fine new writer," Ms. Atwood wrote, adding that it was "organized musically, with themes recurring in different keys, rather than linearly, along the train-track lines of cause-and-effect plot.

If the main scenario were to prove accurate, the euro zone, Greece's main lender, could achieve Greek debt sustainability through three actions: - the extension of the maximum weighted maturity by 5 years to 37.5 years - a re-profiling of the amortisation scheme by setting loan repayments as 1 percent of GDP until 2050 and linearly amortised after that - a capping of interest charged to Greece at 2 percent, with any interest that would have been payable in excess of the 2 percent being deferred until 2050.

If the main ESM scenario were to prove accurate, the euro zone, Greece's main lender, could achieve Greek debt sustainability through three actions: - the extension of the maximum weighted maturity by 5 years to 37.5 years - a re-profiling of the amortisation scheme by setting loan repayments as 1 percent of GDP until 203 and linearly amortised after that - a capping of interest charged to Greece at 2 percent, with any interest that would have been payable in excess of the 2 percent being deferred until 2050.

In particular, the Y' channels of both are linearly related to each other, both Cb and U are related linearly to (B-Y), and both Cr and V are related linearly to (R-Y).

If we consider n = 2 and v1 = v2 = (1, 0), the set of them consists of only one element and is linearly independent, but the family contains the same element twice and is linearly dependent.

Also note that if altitude is not ignored, it becomes necessary to add a third vector to the linearly independent set. In general, n linearly independent vectors are required to describe all locations in n-dimensional space.

A clothoid has the property that its curvature varies linearly with arclength.

Thus y_2(x) is the second linearly independent solution we were looking for.

Similarly, crystal growth rates have been shown to decrease linearly with increasing reciprocal concentration.

Equivalently, a set of vectors is linearly independent if the only way to express the zero vector as a linear combination of elements of is to take zero for every coefficient a_i. A set of vectors that spans a vector space is called a spanning set or generating set. If a spanning set is linearly dependent (that is not linearly independent), then some element of is in the span of the other elements of , and the span would remain the same if one remove from . One may continue to remove elements of until getting a linearly independent spanning set.

The formation pathway was discovered by Hogness & Lunn in 1925. They also used an early form of mass spectrometry to study hydrogen discharges. They found that as the pressure of hydrogen increased, the amount of increased linearly and the amount of decreased linearly.

Reasonable estimates for organisms' surface area do appear to scale linearly with the metabolic rate.

Circularly polarized light can be converted into linearly polarized light by passing it through a quarter-waveplate. Passing linearly polarized light through a quarter- waveplate with its axes at 45° to its polarization axis will convert it to circular polarization. In fact, this is the most common way of producing circular polarization in practice. Note that passing linearly polarized light through a quarter-waveplate at an angle other than 45° will generally produce elliptical polarization.

Although attitude similarity and attraction are linearly related, attraction may not contribute significantly to attitude change.

The abscissas of Figure 8a,b is RPD values that were linearly quantized using 3 bits.

This equation is descriptive of a Cornu spiral, a spiral whose curvative increases linearly with arclength.

Circular polarizer passing left-handed, counter-clockwise circularly polarized light As shown in the figure, the analyzing filters are constructed of a quarter-wave plate (QWP) and a linearly polarized filter (LPF). The QWP always transforms circularly polarized light into linearly polarized light. However, the angle of polarization of the linearly polarized light produced by a QWP depends on the handedness of the circularly polarized light entering the QWP. In the illustration, the left-handed circularly polarized light entering the analyzing filter is transformed by the QWP into linearly polarized light which has its direction of polarization along the transmission axis of the LPF.

Assuming the equations are consistent and linearly independent, a system of equations describes a flat of dimension .

In more detail: an affine group scheme G of finite type over a field k is called linearly reductive if its finite-dimensional representations are completely reducible. For k of characteristic zero, G is linearly reductive if and only if the identity component Go of G is reductive.Milne (2017), Corollary 22.43. For k of characteristic p>0, however, Masayoshi Nagata showed that G is linearly reductive if and only if Go is of multiplicative type and G/Go has order prime to p.

But the phase of the light leaving the crystal is directly proportional to the length of time it takes that light to pass through it. Therefore, the phase of the laser light exiting an EOM can be controlled by changing the electric field in the crystal. Note that the electric field can be created by placing a parallel plate capacitor across the crystal. Since the field inside a parallel plate capacitor depends linearly on the potential, the index of refraction depends linearly on the field (for crystals where Pockels effect dominates), and the phase depends linearly on the index of refraction, the phase modulation must depend linearly on the potential applied to the EOM.

Rational Mech. Anal., 136 (1996), p. 119-161Ciarlet, P.G. ; Lods, V. ; Miara, B., « Asymptotic analysis of linearly elastic shells. II. Justification of flexural shells », Arch. Rational Mech. Anal., 136 (1996), p. 163-190Ciarlet P.G. ; Lods, V., « Asymptotic analysis of linearly elastic shells : "Generalized membrane shells" », J. Elasticity, 43 (1996), p.

Note that while the coordinated units are not organized hierarchically, they are organized linearly, the one preceding the other.

The Dynamic Energy Budget theory explains why the diameter of crusts grow linearly in time at constant substrate availability.

If S is linearly independent and the span of S equals V, then S is a basis for V.

This shows that ai = 0, which means that the vectors v1 = (1, 1) and v2 = (−3, 2) are linearly independent.

14 Generations of Saint Mary's Presentation nuns are buried in a small, compact and linearly arranged graveyard outside the chapel.

Tubercles on posterior flank are weakly developed. Para vertebral granules linearly arranged. Body short and slender. Head large and depressed.

Tubercles on posterior flank are weakly developed. Para vertebral granules linearly arranged. Body long and slender. Head large and depressed.

Tubercles on posterior flank are well developed. Para vertebral granules linearly arranged. Body short and slender. Head large and depressed.

Tubercles on posterior flank are well developed. Para vertebral granules linearly arranged. Body long and slender. Head small and depressed.

Tubercles on posterior flank are weakly developed. Para vertebral granules linearly arranged. Body short and slender. Head large and depressed.

A half-wave plate rotates polarization by 90° A polarization rotator is an optical device that rotates the polarization axis of a linearly polarized light beam by an angle of choice. Such devices can be based on the Faraday effect, on birefringence, or on total internal reflection.F. J. Duarte, Tunable Laser Optics, 2nd Edition (CRC, New York, 2015) Chapter 5. Rotators of linearly polarized light have found widespread applications in modern optics since laser beams tend to be linearly polarized and it is often necessary to rotate the original polarization to its orthogonal alternative.

In order to ensure at least k keys must be compromised before every shared key can be computed by an attacker, identifiers must be k-linearly independent: all sets of k randomly selected user identifiers must be linearly independent. Otherwise, a group of malicious users can compute the key of any other member whose identifier is linearly dependent to theirs. To ensure this property, the identifiers shall be preferably chosen from a MDS- Code matrix (maximum distance separable error correction code matrix). The rows of the MDS-Matrix would be the identifiers of the users.

Friedrich August Kekulé proposed the term dextrose (from Latin dexter = right), because in aqueous solution of glucose, the plane of linearly polarized light is turned to the right. In contrast, -fructose (a ketohexose) and -glucose turn linearly polarized light to the left. The earlier notation according to the rotation of the plane of linearly polarized light (d and l-nomenclature) was later abandoned in favor of the - and -notation, which refers to the absolute configuration of the asymmetric center farthest from the carbonyl group, and in concordance with the configuration of - or -glyceraldehyde.

If the functions are linearly dependent, then so are the columns of the Wronskian as differentiation is a linear operation, so the Wronskian vanishes. Thus, the Wronskian can be used to show that a set of differentiable functions is linearly independent on an interval by showing that it does not vanish identically. It may, however, vanish at isolated points. A common misconception is that everywhere implies linear dependence, but pointed out that the functions and have continuous derivatives and their Wronskian vanishes everywhere, yet they are not linearly dependent in any neighborhood of .

We have to prove that this leads to a contradiction. By Zorn's lemma, every linearly independent set is contained in a maximal linearly independent set . This maximality implies that spans and is therefore a basis (the maximality implies that every element of is linearly dependent from the elements of , and therefore is a linear combination of elements of ). As the cardinality of is greater than or equal to the cardinality of , one may replace with , that is, one may suppose, without loss of generality, that is a basis.

DBSCAN can find non-linearly separable clusters. This dataset cannot be adequately clustered with k-means or Gaussian Mixture EM clustering.

A lack of links between passengers means that the reader must traverse the story linearly, thereby emphasizing the differences between passengers.

Equivalently is a basis if its elements are linearly independent and every element of is a linear combination of elements of . In more general terms, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.

Riemann further proved the Riemann singularity theorem, identifying the multiplicity of a point p = class(D) on Wg − 1 as the number of linearly independent meromorphic functions with pole divisor dominated by D, or equivalently as h0(O(D)), the number of linearly independent global sections of the holomorphic line bundle associated to D as Cartier divisor on C.

Using negative feedback and identical promoters, linearizer gene circuits can impose uniform gene expression that depends linearly on extracellular chemical inducer concentration.

Several long-distance interactions between linearly well-separated areas of the genome have been identified with functional importance in ensuring efficient replication.

It follows that a=0 too. Therefore, according to the definition of linear independence, e^{t} and e^{2t} are linearly independent.

In mathematics, a parallelization, p. 160 of a manifold M\, of dimension n is a set of n global linearly independent vector fields.

In this case, the second linearly independent solution is then found to be the Bessel function of the second kind, as discussed below.

The amount of electric charge stored in a pseudocapacitance is linearly proportional to the applied voltage. The unit of pseudocapacitance is the farad.

If Σniai is a divisor linearly equivalent to 0, then ΠE(x,ai)ni is a meromorphic function with given poles and zeros.

The proposed model assumes that quality is linearly increased along the capillary tube and the refrigerant does not recondense in the heat exchanger.

He then explained how optical rotation could be understood as a species of birefringence. Linearly-polarized light could be resolved into two circularly-polarized components rotating in opposite directions. If these components propagated at slightly different speeds, the phase difference between them – and therefore the direction of their linearly-polarized resultant – would vary continuously with distance.Buchwald, 1989, pp. 230–32,442.

Its exponents, i. e. solutions of the indicial equation, for expansion around the singular point are and ,corresponding to the two linearly independent solutions,See for precise conditions under which two Frobenius method yields two linearly independent solutions. If the exponents do not differ by an integer, this is always the case. and for expansion around the singular point they are and .

A set of vectors is said to be affinely dependent if at least one of the vectors in the set can be defined as an affine combination of the others. Otherwise, the set is called affinely independent. Any affine combination is a linear combination; therefore every affinely dependent set is linearly dependent. Conversely, every linearly independent set is affinely independent.

The challenges progress linearly - when one challenge is complete, the next is unlocked. The credits are played when all the challenges have been completed.

If there are more vectors than dimensions, the vectors are linearly dependent. This is illustrated in the example above of three vectors in R2.

This diagram linearly (unless otherwise mentioned) tracks the projections of all known structures that allow for touch to their relevant endpoints in the human brain.

Jiménez, J.E., and F.M. Jaksíc. 1990. Historia natural del aguila Geranoaetus melanoleucus: una revision. Hornero 13: 97-110. In the linearly slightly smaller G. m.

Less formally, it is the number of linear combinations included in the sum of squares defining Qi, provided that these linear combinations are linearly independent.

Less commonly used, OpenGL and other APIs support nearest- neighbor sampling from individual mipmaps whilst linearly interpolating the two nearest mipmaps relevant to the sample.

This diagram linearly (unless otherwise mentioned) tracks the projections of all known structures that allow for olfaction to their relevant endpoints in the human brain.

The method is most efficient when many constraints or bounds are active at the solution. For problems with nonlinear constraints, a linearly constrained Lagrangian method is used. This involves a sequence of major iterations, each of which solves (perhaps approximately) a linearly constrained subproblem. The subproblem objective is an augmented Lagrangian, and the subproblem constraints are linearizations of the nonlinear constraints at the current point.

Typically, the bricks are laid also running linearly and extending upwards, forming wythes or leafs. It is as important as with the perpends to bond these leaves together. Historically, the dominant method for consolidating the leaves together was to lay bricks across them, rather than running linearly. Brickwork observing either or both of these two conventions is described as being laid in one or another bond.

It is non-zero (for some x) in a specified interval if and only if the given functions and all their derivatives up to order n−1 are linearly independent. If it can be shown that the Wronskian is zero everywhere on an interval then, in the case of analytic functions, this implies the given functions are linearly dependent. See the Wronskian and linear independence.

A spring type accumulator is similar in operation to the gas-charged accumulator above, except that a heavy spring (or springs) is used to provide the compressive force. According to Hooke's law the magnitude of the force exerted by a spring is linearly proportional to its change of length. Therefore, as the spring compresses, the force it exerts on the fluid is increased linearly.

Circular polarizer passing left-handed, counter-clockwise circularly polarized light. (Left-handed as viewed from the receiver.) The illustration above is identical to the previous similar one with the exception that the left-handed circularly polarized light is now approaching the polarizer from the opposite direction and linearly polarized light is exiting the polarizer toward the right. First note that a quarter- wave plate always transforms circularly polarized light into linearly polarized light. It is only the resulting angle of polarization of the linearly polarized light that is determined by the orientation of the fast and slow axes of the quarter-wave plate and the handedness of the circularly polarized light.

In the illustration, the left-handed circularly polarized light entering the polarizer is transformed into linearly polarized light which has its direction of polarization along the transmission axis of the linear polarizer and it therefore passes. In contrast right-handed circularly polarized light would have been transformed into linearly polarized light that had its direction of polarization along the absorbing axis of the linear polarizer, which is at right angles to the transmission axis, and it would have therefore been blocked. Left-handed/Counter-Clockwise circularly polarized light displayed above linearly polarized light. The blue and green curves are projections of the helix on the vertical and horizontal planes respectively.

Linear polarizing filters were the first types to be used in photography and can still be used for non-reflex and older single-lens reflex cameras (SLRs). However, cameras with through-the-lens metering (TTL) and autofocusing systems – that is, all modern SLR and DSLR – rely on optical elements that pass linearly polarized light. If light entering the camera is already linearly polarized, it can upset the exposure or autofocus systems. Circular polarizing filters cut out linearly polarized light and so can be used to darken skies, improve saturation and remove reflections, but the circular polarized light it passes does not impair through-the-lens systems.

One signal element consists of the phase of the carrier shifted linearly by +1 rad in 25 ms (known as "ramp A"), then shifted linearly by −2 rad over 50 ms ("ramp B"), then shifted linearly again by +1 rad for another 25 ms ("ramp C"), returning the phase to zero. One signal element is always sent at each second between 0 and 58. Two signal elements are sent in sequence to represent a binary one; otherwise it is interpreted as binary zero. During ramp B of the initial signal element, the exact point the signal phase is at zero represents the top of the UTC second.

For example, Y = X + 1 and 2Y = 2X + 2 are linearly dependent equations because the second one can be obtained by taking twice the first one.

More precisely, McVeillance was defined as the ratio (linearly) or difference (logarithmically) of surveillance to sousveillance. McVeillance is one of the topics of the IEEE conference.

The combination of rotating helix and oscillating moving blade, with the till-roll paper moving linearly between them, enabled a raster to be drawn on the paper.

The Burr–Erdős conjecture, published as a conjecture by Burr and Erdős in 1975, solved only in 2015, states that sparse graphs have linearly growing Ramsey numbers.

As a result, SuperDISH-compatible receivers must be able to receive circularly- polarized and linearly-polarized signals at two different frequency ranges from up to four satellites.

A Banach space X is reflexive if it is linearly isometric to its bidual under this canonical embedding J. James' space is an example of a non-reflexive space which is linearly isometric to its bidual. Furthermore, the image of James' space under the canonical embedding J has codimension one in its bidual. A Banach space X is called quasi-reflexive (of order d) if the quotient has finite dimension d.

Systems of this variety are deemed inconsistent. The only cases where the overdetermined system does in fact have a solution are demonstrated in Diagrams #4, 5, and 6. These exceptions can occur only when the overdetermined system contains enough linearly dependent equations that the number of independent equations does not exceed the number of unknowns. Linear dependence means that some equations can be obtained from linearly combining other equations.

A linearly ordered set X is called a set of indiscernibles of a model if the truth of a statement about elements of X depends only on their order. The Ehrenfeucht–Mostowski theorem states that if T is a theory with an infinite model, then there is a model of T containing any given linearly ordered set X as a set of indiscernibles. The proof uses Ramsey's theorem.

The primacy effect extended over the first four serial positions. Serial recall paradigm is a form of free recall where the participants have to list the items presented to them in the correct order they are presented in. Research shows that the learning curve for serial recall increases linearly with every trial. Bruno, Miller, and Zimmerman (1955) in an experiment tested to learn why the serial recall learning curve increases linearly.

We can turn it to a ring by extending linearly (x \otimes u) (y \otimes v) = xy \otimes uv. See also: tensor product of algebras, change of rings.

Lastly, the Eady model assumes that there is constant shear in the zonal component of the mean state wind; the mean state zonal wind varies linearly with altitude.

Let V be the vector space of all differentiable functions of a real variable t. Then the functions e^t and e^{2t} in V are linearly independent.

In particular, a defective matrix has one or more eigenvalues λ with algebraic multiplicity m > 1 (that is, they are multiple roots of the characteristic polynomial), but fewer than m linearly independent eigenvectors associated with λ. If the algebraic multiplicity of λ exceeds its geometric multiplicity (that is, the number of linearly independent eigenvectors associated with λ), then λ is said to be a defective eigenvalue. However, every eigenvalue with algebraic multiplicity m always has m linearly independent generalized eigenvectors. A Hermitian matrix (or the special case of a real symmetric matrix) or a unitary matrix is never defective; more generally, a normal matrix (which includes Hermitian and unitary as special cases) is never defective.

Simplicial maps induce continuous maps between the underlying polyhedra of the simplicial complexes: one simply extends linearly using barycentric coordinates. Simplicial maps which are bijective are called simplicial isomorphisms.

In mathematics, a nullform of a vector space acted on linearly by a group is a vector on which all invariants of the group vanish. Nullforms were introduced by . .

Experiments suggest that the degree of unsaturation increases linearly with pressure for a breathing mixture of fixed composition, and decreases linearly with fraction of inert gas in the breathing mixture. As a consequence, the conditions for maximising the degree of unsaturation are a breathing gas with the lowest possible fraction of inert gas – i.e. pure oxygen, at the maximum permissible partial pressure. This saturation deficit is also referred to as the "Oxygen window".

Rack and pinion animation A rack and pinion is a type of linear actuator that comprises a circular gear (the pinion) engaging a linear gear (the rack), which operate to translate rotational motion into linear motion. Driving the pinion into rotation causes the rack to be driven linearly. Driving the rack linearly will cause the pinion to be driven into a rotation. A rack and pinion drive can use both straight and helical gears.

The main advantages of fabrics are that massive concurrent processing combined with a huge, tightly coupled address space makes it possible to solve huge computing problems (such as those presented by delivery of cloud computing services); and that they are both scalable and able to be dynamically reconfigured. Challenges include a non-linearly degrading performance curve, whereby adding resources does not linearly increase performance which is a common problem with parallel computing and maintaining security.

Project-positions are typically arranged linearly within the project. By correlating project tasks with project positions, the qualifications and availability of personnel assigned to the project positions may be considered.

Multiple inlets also improve sensitivity, with a linearly arranged 19 electrospray emitter coupled to 19 inlets operating at 18 Torr giving a nine-fold increase compared to a single inlet.

By calculus it can be shown that a point load will lead to a linearly varying moment diagram, and a constant distributed load will lead to a quadratic moment diagram.

In higher dimensions, if any two of the indices , ..., are equal, in the same way that the "volume" enclosed by a parallelotope whose edge vectors are linearly dependent is zero.

In step 3 these density estimates are interpolated to any other point, by assuming that inside each Delaunay triangle the density field varies linearly (see figure, lower left-hand frame).

Since Liouville's formula relates the different linearly independent solutions of the system of differential equations, it can help to find one solution from the other(s), see the example application below.

The spin-summed total position-spread is very sensitive to these changes because it increases faster than linearly when electrons start to present mobility (0.0 to 0.5 range of -t/U).

The function is not in (i.e., is not the quotient of two polynomials with complex coefficients). For distinct complex numbers }, the set } is linearly independent over . The function is transcendental over .

Due to the growing of the polarized volume the electric field in the crystal in front of the wave increases linearly, or the driver has to provide a constant current leakage.

Since the Rindler chart is a coordinate chart for Minkowski spacetime, we expect to find ten linearly independent Killing vector fields. Indeed, in the Cartesian chart we can readily find ten linearly independent Killing vector fields, generating respectively one parameter subgroups of time translation, three spatials, three rotations and three boosts. Together these generate the (proper isochronous) Poincaré group, the symmetry group of Minkowski spacetime. However, it is instructive to write down and solve the Killing vector equations directly.

These items create platforms that allow Mega Man to access areas that he otherwise could not. After defeating the eight Robot Masters, the player proceeds to Dr. Wily's fortress, which consists of six levels that are played linearly. As in the first game, the player is required to fight each Robot Master a second time in Dr. Wily's fortress. However, these battles take place in a single room rather than a series of linearly connected rooms.

Light propagating in the direction of the optical axis will not be affected by the birefringence since the refractive index will be no independent of polarization. For other propagation directions the light will split into two linearly polarized beams. For light traveling perpendicularly to the optical axis the beams will have the same direction. This can be used to change the polarization direction of linearly polarized light or to convert between linear, circular and elliptical polarizations with waveplates.

For functions of several variables, a generalized Wronskian is a determinant of an by matrix with entries (with ), where each is some constant coefficient linear partial differential operator of order . If the functions are linearly dependent then all generalized Wronskians vanish. As in the 1 variable case the converse is not true in general: if all generalized Wronskians vanish, this does not imply that the functions are linearly dependent. However, the converse is true in many special cases.

For exogenous susceptibility sources, the susceptibility value is theoretically linearly proportional to the concentration of the contrast agent. This provides a new way for in vivo quantification of gadolinium or SPIO concentrations.

Gas Mark is a temperature scale, predominantly found on British ovens, that scales linearly with Celsius above 135°C (Gas Mark 1) and scales with the log of Celsius below 135°C.

C. Krautschik et al., Proc. SPIE 4343, 392 (2001). For the 34-48 nm pitch range, the best focus position shifts roughly linearly in the opposite direction as a function of pitch.

For multiple manoeuvres, delta-v sums linearly. For interplanetary missions delta-v is often plotted on a porkchop plot which displays the required mission delta-v as a function of launch date.

However, it only converges linearly (that is, with order 1) using the convention for iterative methods. The order of convergence of a discretization method is related to its global truncation error (GTE).

This is because the ripple current rating of a capacitor does not increase linearly with size and there may also be hight limitations. For high current applications banks of capacitors are used instead.

The resulting Kernza crop has traits from both progenitors: uniform orientation and a linearly vertical root system from the domesticated crop, along with increased size and rate of propagation from the wild relatives.

Thus, dynamic processes up to the scope of nano seconds can be resolved and measured. Already from its generation on the radiation is polarized (linearly or circularly); a prerequisite for many experimental applications.

The Fuchsian theory of linear differential equations, which is named after Lazarus Immanuel Fuchs, provides a characterization of various types of singularities and the relations among them. At any ordinary point of a homogeneous linear differential equation of order n there exists a fundamental system of n linearly independent power series solutions. A non-ordinary points is called a singularity. At a singularity the maximal number of linearly independent power series solutions may be less than the order of the differential equation.

These solutions can be shown to be linearly independent, by considering the Vandermonde determinant of the values of these solutions at . Together they form a basis of the vector space of solutions of the differential equation (that is, the kernel of the differential operator). In the case where the characteristic polynomial has only simple roots, the preceding provides a complete basis of the solutions vector space. In the case of multiple roots, more linearly independent solutions are needed for having a basis.

This implies that no vector in the sequence can be represented as a linear combination of the remaining vectors in the sequence. In other words, a sequence of vectors is linearly independent if the only representation of \vec 0 as a linear combination of its vectors is the trivial representation in which all the scalars a_i are zero. Even more concisely, a sequence of vectors is linearly independent if and only if \vec 0 can be represented as a linear combination of its vectors in a unique way. The alternative definition, that a sequence of vectors is linearly dependent if and only if some vector in that sequence can be written as a linear combination of the other vectors, is only useful when the sequence contains two or more vectors.

There are some other instances where "nonlinear model" is used to contrast with a linearly structured model, although the term "linear model" is not usually applied. One example of this is nonlinear dimensionality reduction.

Comparison of creep and stress relaxation for three and four element models This model incorporates viscous flow into the standard linear solid model, giving a linearly increasing asymptote for strain under fixed loading conditions.

Rhaebo olallai are medium-sized toads: males measure and females in snout–vent length. Dorsum is coffee-coloured. The parotoid glands are enlarged and conspicuous. Flanks have conspicuous glands, distributed linearly or irregular patterns.

Thermal expansion data have been reported for a number of fluoride glasses, in the temperature range between ambient and Tg. In this range, as for most glasses, expansion is almost linearly dependent on temperature.

Out of studio shows are non-linearly taped on to Mini DV tapes. SVN offers various production forms to help students have a guideline from the very beginning of production to broadcasting the final product.

With these, samples from outside the pixel being processed are weighted linearly based upon their distance from the centroid of that pixel, with the linear function adjusted based on the wide or narrow filter chosen.

Three types of functional response curves. Adapted from Staddon. For a Type I functional response curve, the rate of prey capture increases linearly with food density. At low prey densities, the search time is long.

Homogeneous circular polarizer passing left-handed, counter-clockwise circularly polarized light. (Left-handed as viewed from the receiver.) A homogeneous circular polarizer passes one handedness of circular polarization unaltered and blocks the other handedness. This is similar to the way that a linear polarizer would fully pass one angle of linearly polarized light unaltered, but would fully block any linearly polarized light that was orthogonal to it. A homogeneous circular polarizer can be created by sandwiching a linear polarizer between two quarter-wave plates.

The reason for Faraday rotation is as follows: When a linearly polarized wave is propagating along a magnetic field line, it is de-composed into left-hand and right-hand circularly polarized components. The phase difference between them as they exit the plasma causes the recombined linearly polarized wave to rotate its polarization direction. In MST, we launch two co-propagating, counter-rotating waves to probe the plasma. We then measure the phase difference between these two beams, which will be twice the Faraday rotation angle.

If the problem is not originally linearly separable, the kernel trick can be used to turn it into a linearly separable one, by increasing the number of dimensions. Thus a general hypersurface in a small dimension space is turned into a hyperplane in a space with much larger dimensions. Neural networks try to learn the decision boundary which minimizes the empirical error, while support vector machines try to learn the decision boundary which maximizes the empirical margin between the decision boundary and data points.

Some of the most important cyclically ordered groups fall into neither previous category: the circle group and its subgroups, such as the subgroup of rational points. Every cyclically ordered group can be expressed as a quotient , where is a linearly ordered group and is a cyclic cofinal subgroup of . Every cyclically ordered group can also be expressed as a subgroup of a product , where is a linearly ordered group. If a cyclically ordered group is Archimedean or compact, it can be embedded in itself.

This similar to how the engineering use of "(\bmod n)" specifically returns the remainder, one of the many elements of the (\bmod n) equivalence class. An element of that can be written in the form is called a pure or simple tensor. In general, an element of the tensor product space is not a pure tensor, but rather a finite linear combination of pure tensors. For example, if and are linearly independent, and and are also linearly independent, then cannot be written as a pure tensor.

The model does have the advantage over small signal however, in that it is equally applicable to signal and dc bias. These can therefore both be analysed in the same operations and will be linearly superimposable.

Ascending concentrations of bafilomycin were found to linearly increase the amount of K+ that traversed the mitochondrial membrane, confirming it acts as an ionophore. Compared to other ionophores, however, bafilomycin has a low affinity for K+.

Earth's energy budget - line thickness is linearly proportional to relative amount of energy Sankey diagrams are often used in fields of science, especially physics. They are used to represent energy inputs, useful output, and wasted output.

In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods.

Multiplicative characters are linearly independent, i.e. if \chi_1, \chi_2, \ldots, \chi_n are different characters on a group G then from a_1\chi_1 + a_2\chi_2 + \cdots + a_n\chi_n = 0 it follows that a_1 = a_2 = \cdots = a_n = 0.

In mathematics, especially in the area of abstract algebra dealing with ordered structures on abelian groups, the Hahn embedding theorem gives a simple description of all linearly ordered abelian groups. It is named after Hans Hahn.

The town is located 138 km from the capital. It is called "Flor da Porcelana" (Porcelain Flower) because of its porcelain related commerce. Pedreira was founded in 1896. It is linearly distributed on Jaguari River banks.

Another significant limitation of the coilgun is the occurrence of magnetic saturation in the ferromagnetic projectile. When the flux in the projectile lies in the linear portion of its material's B(H) curve, the force applied to the core is proportional to the square of coil current (I)—the field (H) is linearly dependent on I, B is linearly dependent on H and force is linearly dependent on the product BI. This relationship continues until the core is saturated; once this happens B will only increase marginally with H (and thus with I), so force gain is linear. Since losses are proportional to I2, increasing current beyond this point eventually decreases efficiency although it may increase the force. This puts an absolute limit on how much a given projectile can be accelerated with a single stage at acceptable efficiency.

A variety V is defined over k if every polynomial in kalg[x1, …, xn] that vanishes on V is the linear combination (over kalg) of polynomials in k[x1, …, xn] that vanish on V. A k-algebraic set is also an L-algebraic set for infinitely many subfields L of kalg. A field of definition of a variety V is a subfield L of kalg such that V is an L-variety defined over L. Equivalently, a k-variety V is a variety defined over k if and only if the function field k(V) of V is a regular extension of k, in the sense of Weil. That means every subset of k(V) that is linearly independent over k is also linearly independent over kalg. In other words those extensions of k are linearly disjoint.

Kerr–Schild perturbations are a special type of perturbation to a spacetime metric which only appear linearly in the Einstein field equations which describe general relativity. They were found by Roy Kerr and Alfred Schild in 1965.

Flow from the high pressure side to the low pressure side of the oar blade is non-Newtonian. (i.e., fluid velocity is not linearly proportional to the square root of the pressure differential over the oar blade).

This distribution allows DW appliances to resolve a relational query by scanning data on each server in parallel. The divide-and-conquer approach delivers high performance and scales linearly as new servers are added into the architecture.

Therefore, (f) is well-defined. Any divisor of this form is called a principal divisor. Two divisors that differ by a principal divisor are called linearly equivalent. The divisor of a meromorphic 1-form is defined similarly.

It only reflects linearly polarized radio waves, with the electric field parallel to the grill elements. This type is often used in radar antennas. Combined with a linearly polarized feed horn, it helps filter out noise in the receiver and reduces false returns. Since a shiny metal parabolic reflector can also focus the sun's rays, and most dishes could concentrate enough solar energy on the feed structure to severely overheat it if they happened to be pointed at the sun, solid reflectors are always given a coat of flat paint.

When one attempts to pass unpolarized light through the linear polarizer, only light that has its electric field at the positive 45° angle leaves the linear polarizer and enters the quarter-wave plate. In the illustration, the three wavelengths of unpolarized light represented would be transformed into the three wavelengths of linearly polarized light on the other side of the linear polarizer. Linearly polarized light, represented using components, entering a quarter-wave plate. The blue and green curves are projections of the red line on the vertical and horizontal planes respectively.

More precisely, find necessary and sufficient conditions on the tuple and separately, so that there is an element of with the property that for all . If is the set of all -module endomorphisms of , then Schur's lemma asserts that is a division ring, and the Jacobson density theorem answers the question on tuples in the affirmative, provided that the are linearly independent over . With the above in mind, the theorem may be stated this way: :The Jacobson Density Theorem. Let be a simple right -module, , and a finite and -linearly independent set.

However, the converse is not necessarily true: it is consistent for there to exist infinite Dedekind-finite sets that are not amorphous.. No amorphous set can be linearly ordered... In particular this is the combination of the implications Ia → II → Δ3 which de la Cruz et al. credit respectively to and . Because the image of an amorphous set is itself either amorphous or finite, it follows that every function from an amorphous set to a linearly ordered set has only a finite image. The cofinite filter on an amorphous set is an ultrafilter.

On early railroads this instant application of lateral force was not an issue since low speeds and wide-radius curves were employed (lateral forces on the passengers and the lateral sway was small and tolerable). As speeds of rail vehicles increased over the years, it became obvious that an easement is necessary, so that the centripetal acceleration increases linearly with the traveled distance. Given the expression of centripetal acceleration , the obvious solution is to provide an easement curve whose curvature, , increases linearly with the traveled distance. This geometry is an Euler spiral.

Then a particular solution of the inhomogeneous equation is :x (t)=\int_0^t x_s (t)\,ds, the result of linearly superposing the infinitesimal homogeneous solutions. There are generalizations to higher order linear differential operators. In practice, variation of parameters usually involves the fundamental solution of the homogeneous problem, the infinitesimal solutions x_s then being given in terms of explicit linear combinations of linearly independent fundamental solutions. In the case of the forced dispersionless spring, the kernel \sin(t-s)=\sin t\cos s - \sin s\cos t is the associated decomposition into fundamental solutions.

3D chirality of anisotropic structures is associated with directionally asymmetric transmission (reflection and absorption) of linearly polarized electromagnetic waves. Different levels of total transmission (reflection and absorption) for the same linearly polarized wave incident on their front and back arise from different, e.g. x-to-y, linear polarization conversion efficiencies for opposite propagation directions of the incident wave and therefore the effect is referred to as linear conversion dichroism. The x-to-y and y-to-x polarization conversion efficiencies are interchanged for opposite directions of wave propagation.

A Cartier divisor is effective if its local defining functions fi are regular (not just rational functions). In that case, the Cartier divisor can be identified with a closed subscheme of codimension 1 in X, the subscheme defined locally by fi = 0. A Cartier divisor D is linearly equivalent to an effective divisor if and only if its associated line bundle O(D) has a nonzero global section s; then D is linearly equivalent to the zero locus of s. Let X be a projective variety over a field k.

The strong electric field of high intensity light (such as output of a laser) may cause a medium's refractive index to vary as the light passes through it, giving rise to nonlinear optics. If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect and causes phenomena such as self-focusing and self-phase modulation. If the index varies linearly with the field (a nontrivial linear coefficient is only possible in materials that do not possess inversion symmetry), it is known as the Pockels effect.

In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems. An n × n defective matrix always has fewer than n distinct eigenvalues, since distinct eigenvalues always have linearly independent eigenvectors.

This shows that the displacement varies as the square root of the time (not linearly), which explains why previous experimental results concerning the velocity of Brownian particles gave nonsensical results. A linear time dependence was incorrectly assumed. At very short time scales, however, the motion of a particle is dominated by its inertia and its displacement will be linearly dependent on time: Δx = vΔt. So the instantaneous velocity of the Brownian motion can be measured as v = Δx/Δt, when Δt << τ, where τ is the momentum relaxation time.

An analogous device, moving linearly rather than rotating, is described as a . These are widely used for refrigeration compressors and ultra-quiet air compressors, where the force motor produces simple harmonic motion in conjunction with a restoring spring.

AUC and Cmax values of valsartan are observed to be approximately linearly dose-dependent over therapeutic dosing range. Owing to its relatively short elimination half life attribution, valsartan concentration in plasma doesn't accumulate in response to repeated dosing.

The period of this beat frequency is linearly proportional to the angular velocity of the ring laser with respect to inertial space. This is the principle of the ring laser gyroscope, widely used in modern inertial navigation systems.

A Finnish study assayed psilocybin concentrations in old herbarium specimens, and concluded that although psilocybin concentration decreased linearly over time, it was relatively stable. They were able to detect the chemical in specimens that were 115 years old.

In robot motion planning, a Pfaffian constraint is a set of k linearly independent constraints linear in velocity, i.e., of the form A(q) \dot q=0 One source of Pfaffian constraints is rolling without slipping in wheeled robots.

An orthogonal probe beam detects the precession using optical rotation of linearly polarized light. In a typical SERF magnetometer, the spins merely tip by a very small angle because the precession frequency is slow compared to the relaxation rates.

Linearization is necessary when sensors produce voltage signals that are not linearly related to the physical measurement. Linearization is the process of interpreting the signal from the sensor and can be done either with signal conditioning or through software.

22, no. 7 (1995), pp. 815-818 Conversely, the low concentration of CFCs allow their effects to increase linearly with mass, so that chlorofluorocarbons are greenhouse gases with a much higher potential to enhance the greenhouse effect than CO2.

Leptin levels vary exponentially, not linearly, with fat mass. Leptin levels in blood are higher between midnight and early morning, perhaps suppressing appetite during the night. The diurnal rhythm of blood leptin levels may be modified by meal-timing.

The two beams follow different paths- one beam (the extraordinary beam) traveling directly to a photomultiplier (PMT), and the other beam (the ordinary beam) passing through a photoelastic modulator (PEM) oriented at 45 degrees to the direction of the ordinary ray polarization. The PMT for the extraordinary beam detects the light intensity of the input beam. The PEM is adjusted to cause an alternating plus and minus 1/4 wavelength shift of one of the two orthogonal components of the ordinary beam. This modulation converts the linearly polarized light into circularly polarized light at the peaks of the modulation cycle. Linearly polarized light can be decomposed into two circular components with intensity represented as I_0 = \frac 12(I_- + I_+) The PEM will delay one component of linearly polarized light with a time dependence that advances the other component by 1/4 λ (hence, quarter-wave shift).

If these components propagated at slightly different speeds (as he had demonstrated for quartz), then the phase difference between them — and therefore the orientation of their linearly-polarized resultant — would vary continuously with distance.Buchwald, 1989, p.442; Fresnel, 1866, p.749.

With the definition as stated, it turns out that the Hermite constant grows linearly in n. Alternatively, the Hermite constant γn can be defined as the square of the maximal systole of a flat n-dimensional torus of unit volume.

Low and Li (2001) showed that a pulse train of linearly increasing magnitude had a significant effect on expulsion processes. Forsman, et al. (2007) demonstrated that a double pulse stream produced increased drilling and cutting rates with significantly cleaner holes.

Thus, constructing the set of Dedekind cuts serves the purpose of embedding the original ordered set S, which might not have had the least-upper-bound property, within a (usually larger) linearly ordered set that does have this useful property.

The lack of a long, central conserved region makes Avsunviroidae harder to identify than Pospiviroidae. A method to detect them is to use their circularity: a computer can piece together many overlapping reads that appear to form repeats when placed linearly.

Because the vectors usually soon become almost linearly dependent due to the properties of power iteration, methods relying on Krylov subspace frequently involve some orthogonalization scheme, such as Lanczos iteration for Hermitian matrices or Arnoldi iteration for more general matrices.

The size of the shell varies between 13 mm and 30 mm. The solid shell has a rather tumidly conical shape. The whorls are slopingly convex, densely strongly grained, here and there linearly engraved. The lines are obliquely minutely crenulated.

The towns of the Upper Calder are situated linearly along the valley, which cuts through the eastern slopes of the Pennines from Portsmouth in the west to Sowerby Bridge, a market town on the outskirts of Halifax, in the east.

As the message grows, however, the compression ratio tends asymptotically to the maximum (i.e., the compression factor or ratio improves on an increasing curve, and not linearly, approaching a theoretical maximum inside a limited time period rather than over infinite time).

Hegel, p. 203. Wang was opposed to the idea that modernity meant developing linearly into something more advanced. "Repressed Modernities," Chapter 1, describes the historical conditions in the Qing Dynasty. Heroldová argued that it was an extension of the introduction.

Figure 2. Cyclic voltammetry waveform. In cyclic voltammetry, the electrode potential ramps linearly versus time in cyclical phases (Figure 2). The rate of voltage change over time during each of these phases is known as the experiment's scan rate (V/s).

O. ingens exhibit sexual dimorphism, with females growing linearly twice as fast as males, and reaching a fully mature size of more than five times that of male counterparts.Bolstad, K. 2003. Spotlight on: Moroteuthis ingens . The Octopus News Magazine Online.

The problem is normally solved using appropriate techniques from the field of optimization. These include gradient- based algorithms, population-based algorithms, or others. Very simple problems can sometimes be expressed linearly; in that case the techniques of linear programming are applicable.

In his 1914 publication, Sounds of the Language, he promotes writing Hangul linearly rather than syllabically. This is one of his few proposals not to have been implemented, although there have been experiments with linear hangul, most notably in Primorsky Krai.

Congregants access a terrace via a 5 step stairway. The portable spruce wall of the synagogue merges with the torah ark. Seats are arranged linearly, similar to church interiors. The mechitza starts in the entrance hall open to the main interior.

It is easy to define Hamming codes for large alphabets of size q. We need to define one H matrix with linearly independent columns. For any word of size q there will be columns who are multiples of each other.

The likelihood of developing substance abuse or dependence increases linearly with the number of sex partners, an effect more pronounced for women. People who have a higher number of sex partners do not have higher rates of anxiety or depression.

The raptors of Europe and the Middle East: a handbook of field identification. London: T & AD Poyser. The common buzzard measures between in length with a wingspan. Females average about 2–7% larger than males linearly and weigh about 15% more.

The sum of these partial pressures (water, oxygen, carbon dioxide and nitrogen) is less than the total pressure of the respiratory gas. This is a significant saturation deficit, and it provides a buffer against supersaturation and a driving force for dissolving bubbles. Experiments suggest that the degree of unsaturation increases linearly with pressure for a breathing mixture of fixed composition, and decreases linearly with fraction of inert gas in the breathing mixture. As a consequence, the conditions for maximising the degree of unsaturation are a breathing gas with the lowest possible fraction of inert gas – i.e.

Mathematically, the simplest kind of transverse wave is a plane linearly polarized sinusoidal one. "Plane" here means that the direction of propagation is unchanging and the same over the whole medium; "linearly polarized" means that the direction of displacement too is unchanging and the same over the whole medium; and the magnitude of the displacement is a sinusoidal function only of time and of position along the direction of propagation. The motion of such a wave can be expressed mathematically as follows. Let d be the direction of propagation (a vector with unit length), and o any reference point in the medium.

For example, the subdirect irreducibles in the variety generated by a finite linearly ordered Heyting algebra H must be just the nondegenerate quotients of H, namely all smaller linearly ordered nondegenerate Heyting algebras. The conditions cannot be dropped in general: for example, the variety of all Heyting algebras is generated by the set of its finite subdirectly irreducible algebras, but there exist subdirectly irreducible Heyting algebras of arbitrary (infinite) cardinality. There also exists a single finite algebra generating a (non- congruence-distributive) variety with arbitrarily large subdirect irreducibles.R. McKenzie, The residual bounds of finite algebras, Int.

No income tax is charged on the basic allowance, which is €9,169 for unmarried persons and €18,338 for married couples who file jointly. Beyond this threshold, the marginal tax rate increases linearly from 14% to 24% for a taxable income of €14,255 (€28,150 for married couples). In the subsequent interval up to a taxable income of €55,961 (€111,922 for married couples), the marginal tax rate increases linearly from 24% to 42%. The last change of rates occurs at a taxable income of €265,327 (€530,654 for married couples) when the marginal tax rate jumps from 42% to 45%.

There are several extra conditions which ensure that the vanishing of the Wronskian in an interval implies linear dependence. Maxime Bôcher observed that if the functions are analytic, then the vanishing of the Wronskian in an interval implies that they are linearly dependent. gave several other conditions for the vanishing of the Wronskian to imply linear dependence; for example, if the Wronskian of functions is identically zero and the Wronskians of of them do not all vanish at any point then the functions are linearly dependent. gave a more general condition that together with the vanishing of the Wronskian implies linear dependence.

In software engineering, basis path testing, or structured testing, is a white box method for designing test cases. The method analyzes the control flow graph of a program to find a set of linearly independent paths of execution. The method normally uses McCabe' cyclomatic complexity to determine the number of linearly independent paths and then generates test cases for each path thus obtained. Basis path testing guarantees complete branch coverage (all edges of the control flow graph), but achieves that without covering all possible paths of the control flow graph—the latter is usually too costly.

All radio (and microwave) antennas used for transmitting or receiving are intrinsically polarized. They transmit in (or receive signals from) a particular polarization, being totally insensitive to the opposite polarization; in certain cases that polarization is a function of direction. Most antennas are nominally linearly polarized, but elliptical and circular polarization is a possibility. As is the convention in optics, the "polarization" of a radio wave is understood to refer to the polarization of its electric field, with the magnetic field being at a 90 degree rotation with respect to it for a linearly polarized wave.

For example, in the Higgs phase the gauge field is Higgsed and so the Wilson loop action is proportional to the length of the loop, which scales linearly with distance. In the confining phase the 't Hooft operator is Higgsed, and so the corresponding action fails as the area of the corresponding (d-3)-dimensional surface, for example linearly in 4 spacetime dimensions. In particular 't Hooft concluded that in 4 dimensions if both the actions of the Wilson and 't Hooft loops scale linearly then both are Higgsed and so there must be massless particles in the spectrum. Today 't Hooft's classication of phases is the bases of the classification of QCD phase diagram, with the Higgs phase manifested at the cold temperatures and low densities usually found on Earth, massless particles and deconfinment existing at high temperature experiments at RHIC and soon the LHC and perhaps mixed phases existing in the cores of neutron stars.

The Stiefel–Whitney classes wi(E) get their name because Eduard Stiefel and Hassler Whitney discovered them as mod-2 reductions of the obstruction classes to constructing everywhere linearly independent sections of the vector bundle restricted to the i-skeleton of X. Here n denotes the dimension of the fibre of the vector bundle . To be precise, provided X is a CW-complex, Whitney defined classes Wi(E) in the i-th cellular cohomology group of X with twisted coefficients. The coefficient system being the (i−1)-st homotopy group of the Stiefel manifold Vn−i+1(F) of linearly independent vectors in the fibres of E. Whitney proved Wi(E) = 0 if and only if E, when restricted to the i-skeleton of X, has linearly- independent sections. Since πi−1Vn−i+1(F) is either infinite-cyclic or isomorphic to Z/2Z, there is a canonical reduction of the Wi(E) classes to classes which are the Stiefel–Whitney classes.

The zone diameter from the ring is linearly related to the log of protein concentration and is compared to zone diameters for known protein standards for quantification. There are kits and serums commercially available for this assay (e.g. The Binding Site Inc.).

The span of is also the intersection of all linear subspaces containing . In other words, it is the (smallest for the inclusion relation) linear subspace containing . A set of vectors is linearly independent if none is in the span of the others.

R-value should not be confused with the intrinsic property of thermal resistivity and its inverse, thermal conductivity. The SI unit of thermal resistivity is K·m/W. Thermal conductivity assumes that the heat transfer of the material is linearly related to its thickness.

Maximum fluorescence between QR and DNA is found within the pH range of 3.2-3.6, with the optimum being a pH 3.5. The amount of fluorescence seen with the use of QR is linearly related to the concentrations of DNA or RNA.

They mine the leaves of their host plant. The mine consists of a straight, narrow corridor, gradually becoming wider and more contorted, in the end almost forming a botch. The frass is dispersed linearly throughout. Pupation takes place outside of the mine.

Gangarampur is located almost in the middle of Dakshin Dinajpur district at . It has spread linearly along the banks of the Punarbhaba River. It has an average elevation of 25 metres (82 feet). The area of the city is 10.29 Sq. km.

The assignment of sub-carriers to users may be changed dynamically, based on the current radio channel conditions and traffic load. Single-carrier FDMA (SC- FDMA), a.k.a. linearly-precoded OFDMA (LP-OFDMA), is based on single-carrier frequency-domain-equalization (SC-FDE).

Charles' law states that under constant pressure, an ideal gas' volume is proportional to its absolute temperature. The volume of a gas at constant pressure increases linearly with the absolute temperature of the gas. The formula he created was V1/T1 = V2/T2.

Volume controlled ventilation is ventilation where both volume and flow are controlled by the ventilator. Normally, flow is set to a fixed amount, meaning volume increases linearly over time. Any mode that relies on flow to control inspiration falls under the VC- category.

For example, if the functions are polynomials and all generalized Wronskians vanish, then the functions are linearly dependent. Roth used this result about generalized Wronskians in his proof of Roth's theorem. For more general conditions under which the converse is valid see .

Circular dichroism causes incident linearly polarized light to become elliptically polarized. The two phenomena are closely related, just as are ordinary absorption and dispersion. If the entire optical rotatory dispersion spectrum is known, the circular dichroism spectrum can be calculated, and vice versa.

The seeds are housed within two valves and are flat, chartaceous and winged on both sides. The trunk is occasionally buttressed and up to in diameter. The heartwood is white-brown coloured, and the pale grey outer bark is scaly and linearly lenticellate.

Because of this characteristic feature, the adjective "lentiginous" is used to describe other skin lesions that similarly proliferate linearly within the basal cell layer.Random House Webster's Unabridged Dictionary. Random House, Inc. 2001. p. 1101. .Robbins and Cotran Pathologic Basis of Disease Elsevier. 2005. p. 1232. .

Introduction to materials science course manual. Madison, Wisconsin: University of Wisconsin-Madison. In glasses, hardness seems to depend linearly on the number of topological constraints acting between the atoms of the network. Hence, the rigidity theory has allowed predicting hardness values with respect to composition.

This illustrates the known relationship between porosity and Young's modulus wherein Young's modulus decreases linearly with increasing porosity. Achievable porosity through the space- holder method is directly related to the type and amount of space-holder utilized (up to a threshold maximum achievable porosity level).

Multidimensional versions of this method exist. Halley's method exactly finds the roots of a linear-over-linear Padé approximation to the function, in contrast to Newton's method or the Secant method which approximate the function linearly, or Muller's method which approximates the function quadratically.

Moreover, the optical rotation of a compound may be non-linearly dependent on its enantiomeric excess because of aggregation in solution. For these reasons other methods of determining the enantiomeric ratio, such as gas chromatography or HPLC with a chiral column, are generally preferred.

The Bernstein polynomials of a fixed degree m are a family of m+1 linearly independent polynomials that are a partition of unity for the unit interval [0,1]. Partition of unity is used to establish global smooth approximations for Sobolev functions in bounded domains.

Bugis pencak silat patterns contains less than 15 percent leg action, and those which are used are more linearly oriented than circular in nature; simple forward stepping movement is, of course, exempt, as it is definitely circular. The Horse riding stance employed suggests Chinese influence.

This diode will emit polarized light. The source is HeNe (632.8 nm) and argon (514 nm). A polarization modulator in this instrument changes the polarization states of the laser output. The linearly polarized beam from the laser then passes through a rotating quarter- wave retarder.

This means that all frequencies have the phase zero. The time origin is arbitrary. If a pulse comes at later times, the phase increases linearly with frequency, but still the zero-frequency phase is zero. This phase at zero frequency is the carrier–envelope offset.

The corresponding a_{i_0} can be expressed as a finite linear combination of b_js, which in turn can be expressed as finite linear combination of a_is, not involving a_{i_0}. Hence a_{i_0} is linearly dependent on the other a_is, which provides the desired contradiction.

Such a linearly independent set that spans a vector space is called a basis of . The importance of bases lies in the fact that there are together minimal generating sets and maximal independent sets. More precisely, if is a linearly independent set, and is a spanning set such that S\subseteq T, then there is a basis such that S\subseteq B\subseteq T. Any two bases of a vector space have the same cardinality, which is called the dimension of ; this is the dimension theorem for vector spaces. Moreover, two vector spaces over the same field are isomorphic if and only if they have the same dimension.

The gradient factor is a percentage of the M-value chosen by the algorithm designer, and varies linearly between the maximum depth of the specific dive and the surface. They are expressed as a two number designation, where the first number is the percentage of the deep M-value, and the second is a percentage of the shallow M-value. The gradient factors are applied to all tissue compartments equally and produce an M-value which is linearly variable in proportion to ambient pressure. :For example: A 30/85 gradient factor would limit the allowed supersaturation at depth to 30% of the designer's maximum, and to 85% at the surface.

Hyperbolic trees employ hyperbolic space, which intrinsically has "more room" than Euclidean space. For instance, linearly increasing the radius of a circle in Euclidean space increases its circumference linearly, while the same circle in hyperbolic space would have its circumference increase exponentially. Exploiting this property allows laying out the tree in hyperbolic space in an uncluttered manner: placing a node far enough from its parent gives the node almost the same amount of space as its parent for laying out its own children. Displaying a hyperbolic tree commonly utilizes the Poincaré disk model of hyperbolic geometry, though the Klein-Beltrami model can also be used.

Inhibition theory is based on the basic assumption that during the performance of any mental task requiring a minimum of mental effort, the subject actually goes through a series of alternating latent states of distraction (non-work 0) and attention (work 1) which cannot be observed and are completely imperceptible to the subject. Additionally, the concept of inhibition or reactive inhibition which is also latent, is introduced. The assumption is made that during states of attention inhibition linearly increases with a slope a1 and during states of distraction inhibition linearly decreases with a slope a0.According to this view the distraction states can be considered a sort of recovery state.

Metacarpal fractures are usually caused by the impact of a clenched fist with a hard, immovable object, such as a skull or a wall. When a punch impacts with improper form, the force occurs at an angle towards the palm, creating a dorsal bend in the bone, ultimately causing the fracture when the bone is bent too far. When a boxer punches with proper form, the knuckles of the second and third metacarpal align linearly with the articulating radius, followed linearly by the humerus. Due to the linear articulation of bones, the force is able to travel freely across these joints and bones and be dissipated without injury.

The transcendence of and are direct corollaries of this theorem. Suppose is a non-zero algebraic number; then is a linearly independent set over the rationals, and therefore by the first formulation of the theorem is an algebraically independent set; or in other words is transcendental. In particular, is transcendental. (A more elementary proof that is transcendental is outlined in the article on transcendental numbers.) Alternatively, by the second formulation of the theorem, if is a non-zero algebraic number, then is a set of distinct algebraic numbers, and so the set is linearly independent over the algebraic numbers and in particular cannot be algebraic and so it is transcendental.

In 1911, Thomas Hunt Morgan argued that genes are on chromosomes, based on observations of a sex-linked white eye mutation in fruit flies. In 1913, his student Alfred Sturtevant used the phenomenon of genetic linkage to show that genes are arranged linearly on the chromosome.

Wintering birds from interior southwestern British Columbia may move south to as far as southwest to Guatemala and northern Nicaragua. Linearly, this relatively large subspecies can seem to run almost contrary to Bergmann's rule, with birds of the Great Basin being longer winged than most Canadian ones.

Mathematically speaking, the normalized floating-point numbers of a given sign are roughly logarithmically spaced, and as such any finite-sized normal float cannot include zero. The denormal floats are a linearly spaced set of values, which span the gap between the negative and positive normal floats.

Since Maxwell's equations are linear, the electric field and magnetic field depend linearly on source distributions. Linearity allows the fields from various multipole moments to be calculated independently and added together to give the total field of the system. This is the well-known principle of superposition.

All the above conjectures and theorems are consequences of the unproven extension of Baker's theorem, that logarithms of algebraic numbers that are linearly independent over the rational numbers are automatically algebraically independent too. The diagram on the right shows the logical implications between all these results.

The number of required lab operations using DNA grows linearly with the number of vertices of the graph. Molecular algorithms have been reported that solves the cryptographic problem in a polynomial number of steps. As known, factoring large numbers is a relevant problem in many cryptographic applications.

The result is a response curve that is a scaled representation of the simple additive model. Typical neural population code. Each color represents a separate, adjacent neuron arranged linearly. X axis shows stimulus, such as head position or sound frequency, and Y axis shows neural response.

The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.

Around the hole, there are considerate eyes, and a round snout linearly decorated. The wolf's mouth is open, showing its enormous teeth. The animal has a tense posture, its front legs are stretched in front, and its back legs are slightly bent. The paws include claws.

A function (blue) and a piecewise linear approximation to it (red) An approximation to a known curve can be found by sampling the curve and interpolating linearly between the points. An algorithm for computing the most significant points subject to a given error tolerance has been published.

From 1985 to 2000, WC points were awarded so that the first four places gave 30, 26, 24, and 22 points, respectively, and then the 5th to 25th place gave 21, 20, ..., down to 1 point. Before this, points were simply awarded linearly from 25 to 1.

The heart rate increases (approximately) linearly up to the deflection point, where the heart rate reaches AT (also known as LT, lactate threshold, in more modern nomenclature). The test continues for a while, under increasing load, until the subject has gone well past the anaerobic threshold.

Figure 1. Typical cyclic voltammogram where i_{pc} and i_{pa} show the peak cathodic and anodic current respectively for a reversible reaction. Cyclic voltammetry (CV) is a type of potentiodynamic electrochemical measurement. In a cyclic voltammetry experiment, the working electrode potential is ramped linearly versus time.

High charge levels and elevated temperatures (whether from charging or ambient air) hasten capacity loss. Carbon anodes generate heat when in use. Batteries may be refrigerated to reduce temperature effects. Pouch and cylindrical cell temperatures depend linearly on the discharge current.. Poor internal ventilation may increase temperatures.

Address into the truncated 16 MSBs, and that plus 1. Linearly interpolate using the 8 MSBs as weights. (One could instead use 3 LUTs instead and quadratically interpolate). This can result in decreased distortion for the same amount of memory at the cost of some multipliers.

This diagram linearly (unless otherwise mentioned) tracks the projections of all known structures that allow for vision to their relevant endpoints in the human brain. Click to enlarge the image. Representation of optic pathways from each of the 4 quadrants of view for both eyes simultaneously.

The two most famous applications of topological -theory are both due to Frank Adams. First he solved the Hopf invariant one problem by doing a computation with his Adams operations. Then he proved an upper bound for the number of linearly independent vector fields on spheres.

German forces had advanced c. 1,700 kilometres, and maintained a linearly-measured front of 3,000 kilometres.Glantz, David, The Soviet-German War 1941–45: Myths and Realities: A Survey Essay, October 11, 2001, page 7 The Red Army put up fierce resistance during the war's early stages.

Location of Kolkata Kolkata is located in the eastern part of India. It has spread linearly along the banks of Hooghly River. The Kolkata Municipal Corporation has an area of 205 square kilometres. The city is near sea level, with the average elevation being 17 feet.

The x- and y-axes are scaled non-linearly by their standard normal deviates (or just by logarithmic transformation), yielding tradeoff curves that are more linear than ROC curves, and use most of the image area to highlight the differences of importance in the critical operating region.

Pollack's Rule states that microprocessor "performance increase due to microarchitecture advances is roughly proportional to [the] square root of [the] increase in complexity". This contrasts with power consumption increase, which is roughly linearly proportional to the increase in complexity. Complexity in this context means processor logic, i.e. its area.

In linear algebra, a basis of a vector space V is a linearly independent subset B such that every element of V is a linear combination of B. The empty sum convention allows the zero- dimensional vector space V={0} to have a basis, namely the empty set.

The problem of determining if a pair of sets is linearly separable and finding a separating hyperplane if they are, arises in several areas. In statistics and machine learning, classifying certain types of data is a problem for which good algorithms exist that are based on this concept.

On the other hand, for integer order , the following relationship is valid (the gamma function has simple poles at each of the non-positive integers):Abramowitz and Stegun, p. 358, 9.1.5. :J_{-n}(x) = (-1)^n J_n(x). This means that the two solutions are no longer linearly independent.

Rather, it allows nutrient prioritisation. For example, if there exists a diet with high carbon but low nitrogen content, then meeting the nitrogen dietary requirement suggests consuming a high level of carbon diet. Since gut volume scales linearly with body mass, larger animals have more capacity to digests food.

The mass of tires and rims must be accelerated linearly and rotationally. It can be shown that the effect of rim and tire mass of typical spoked wheels is effectively doubled. Reducing their mass is thus especially noticeable in the case of sprints and corner "jumps" in a criterium.

Energy diagrams of spontaneous and coherent Raman scattering processes. Coherent Raman scattering is based on Raman scattering (or spontaneous Raman scattering). In spontaneous Raman, only one monochromatic excitation laser is used. Spontaneous Raman scattering's signal intensity grows linearly with the average power of a continuous-wave pump laser.

With a fixed voltage V_{DC} across the junction, the phase will vary linearly with time and the current will be a sinusoidal AC (Alternating Current) with amplitude I_c and frequency K_J V_{DC}. This means a Josephson junction can act as a perfect voltage-to- frequency converter.

Analogously to the Flamant solution for the 2D half-plane, fundamental solutions are known for the linearly elastic 3D half-space as well. These were found by Boussinesq for a concentrated normal load and by Cerruti for a tangential load. See the section on this in Linear elasticity.

American Zoology, (24), 85-94. A notable example is jumping in kangaroos. When hopping at slow speeds, their uses of energy increase linearly, but at high speeds, kangaroos can move as cheaply (from an energetic perspective) as if they were moving at slower speeds.Irschick DJ, Henningsen J. 2009.

If it moves position it moves either circularly or linearly. If it spins in place its outer part revolves around its middle but the one has neither. If it moves its position it moves through something else, which it cannot be inside. Thus the one does not move.

Material for the installation was gathered entirely from retail liquidation sales which occurred in early 2009 within a few blocks of the project. Uniting the project linearly was a brightly lit white section complete with empty shelving, dropped ceiling, shopping carts, surveillance cameras, signage, baskets, pedestals and mannequins.

There are different scales, denoted by a single letter, that use different loads or indenters. The result is a dimensionless number noted as HRA, HRB, HRC, etc., where the last letter is the respective Rockwell scale (see below). When testing metals, indentation hardness correlates linearly with tensile strength.

Weiss used rectangular, constant-current pulses and found that threshold charge required for stimulation increased linearly with pulse duration. He also found that stimulus charge, the product of stimulus current and stimulus duration is proportional to rheobase, so that only two stimulus durations are necessary to calculate rheobase.

Some maps may even be used strictly for cutscenes, with no battles taking place. Maps are progressed through linearly, but it is possible to send the player to maps out of order, enabling multiple/alternate storyline forks. It is also possible to send the player to a previous map.

Based on this argument, the flame height depends non-linearly on the local, time-dependent pressure. The time average of the flow is reduced at the points with oscillating pressure and thus flames are lower.G.W. Ficken, F.C. Stephenson, Rubens flame-tube demonstration, The Physics Teacher, Vol. 17, pp.

The disutility of schedule delay for a late arrival or departure also increase linearly, but Small hypothesises that there can also be a fixed penalty component of schedule delay on the "late" side - e.g. arriving late for work is always bad, even if it is only slightly late.

A Faraday rotator consists of an optical material in a magnetic field. When light propagates in the material, interaction with the magnetic field causes left- and right-handed circularly polarized waves to propagate with slightly different phase velocities. Since a linearly-polarized wave can be described as a superposition of left- and right-handed circularly polarized waves, the difference in phase velocity causes the polarization direction of a linearly-polarized wave to rotate as it propagates through the material. The direction of the rotation depends on whether the light is propagating with or against the direction of the magnetic field: a rotation induced by passing through the material is not undone by passing through it in the opposite direction.

It remains to prove that Lmax is a basis of V. Since Lmax belongs to X, we already know that Lmax is a linearly independent subset of V. If there were some vector w of V that is not in the span of Lmax, then w would not be an element of Lmax either. Let Lw = Lmax ∪ {w}. This set is an element of X, that is, it is a linearly independent subset of V (because w is not in the span of Lmax, and Lmax is independent). As Lmax ⊆ Lw, and Lmax ≠ Lw (because Lw contains the vector w that is not contained in Lmax), this contradicts the maximality of Lmax.

This reverses the fast and slow axes of the wave plate relative to the transmission axis of the linear polarizer reversing which component leads and which component lags. In trying to appreciate how the quarter-wave plate transforms the linearly polarized light, it is important to realize that the two components discussed are not entities in and of themselves but are merely mental constructs one uses to help appreciate what is happening. In the case of linearly and circularly polarized light, at each point in space, there is always a single electric field with a distinct vector direction, the quarter-wave plate merely has the effect of transforming this single electric field.

Theorem 1: The subspace spanned by a non-empty subset S of a vector space V is the set of all linear combinations of vectors in S. This theorem is so well known that at times, it is referred to as the definition of span of a set. Theorem 2: Every spanning set S of a vector space V must contain at least as many elements as any linearly independent set of vectors from V. Theorem 3: Let V be a finite-dimensional vector space. Any set of vectors that spans V can be reduced to a basis for V, by discarding vectors if necessary (i.e. if there are linearly dependent vectors in the set).

In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite or infinite (in the latter case, it is a cardinal number), and defines the dimension of the vector space. Formally, the dimension theorem for vector spaces states that :Given a vector space , any two bases have the same cardinality. As a basis is a generating set that is linearly independent, the theorem is a consequence of the following theorem, which is also useful: :In a vector space , if is a generating set, and is a linearly independent set, then the cardinality of is not larger than the cardinality of .

Note that the linear polarization at 45° can also be viewed as the addition of a horizontally linearly polarized wave (as in the leftmost figure) and a vertically polarized wave of the same amplitude in the same phase. 100px 100px 100px 100px 100px Animation showing four different polarization states and two orthogonal projections. A circularly polarized wave as a sum of two linearly polarized components 90° out of phase Now if one were to introduce a phase shift in between those horizontal and vertical polarization components, one would generally obtain elliptical polarization as is shown in the third figure. When the phase shift is exactly ±90°, then circular polarization is produced (fourth and fifth figures).

T. socranskii is helically coiled and motile using periplasmic flagella. In liquid media, it can move linearly or in a twisting screw-like motion. The cell size ranges from 6-15μm long and 0.16-0.18μm wide. The cells are wider in the center than at the ends and are curved slightly.

A chirp is a sinusoidal signal of frequency increase or decrease over time (often with a polynomial expression for the relationship between time and frequency). In the picture is an example of an upchirp in which the frequency increases linearly over time. Sometimes the frequency of upchirps increase exponentially over time.

In 2000, a large earthquake (M=6.6) occurred in the South Iceland Seismic Zone. During this event, small scale earthquakes concentrated narrowly and linearly around the transform fault planes.Stefánsson, R., Guðmundsson, G. B., & Roberts, M. J. (2006). Long-term and short-term earthquake warnings based on seismic information in the SISZ.

In a linked list, one normally searches linearly for an element by walking from one end to the other. If the linked list is sorted, and we have a reference to some node containing y, then we may find x in O(d) time by starting our search from y.

In general, the conduction velocities of most motor and sensory nerves are positively and linearly associated with body temperature (low temperatures slow nerve conduction velocity and higher temperatures increase conduction velocity). Conduction velocities in the Sural nerve seem to exhibit an especially strong correlation with the local temperature of the nerve.

The resistivity along all three axes increases linearly with temperature from about 30 K to 300 K, as in a metal. This is anomalous since such a law is expected above the Debye temperature (= 400 K for this compound) The resistivity ratios along the three axes are preserved in that range.

The mystery behind the "Black Dawn" is unravelled across multiple mediums in an unprecedented interactive, cross-platform, story-driven experience. Viewers are able to engage with any of the individual components (TV series, video blogs, comic book, etc.) and move through the story non-linearly, in whatever manner they so choose.

The sepals are almost uniform, 1.4 to 2.2 cm long and slowly sharpened linearly. They are hairless to close-fitting, the outer three sepals are lanceolate to broadly lanceolate, and the inner two are narrowly lanceolate. The stamens and the stamp do not protrude beyond the crown. The ovary is hairless.

Example of Mach bands at the ends of gradients where the derivative of the luminance is discontinuous 1\. Actual luminance profile 2\. Perceived luminance profile Mach bands can also appear where the derivative of discontinuity appears, a visual effect common when intensities are linearly interpolated such as in Gouraud shading.

Environmental Science and Technology. 25(3):427. :C_m = Z_m \cdot f where Z is a proportional constant, termed fugacity capacity. This equation does not necessarily imply that C and f are always linearly related. Non-linearity can be accommodated by allowing Z to vary as a function of C or f.

Liquid-crystal polymers are present in melted/liquid or solid form.Callister (2007): "Materials Science and Engineering - An Introduction," 557-558. In solid form the main example of lyotropic LCPs is the commercial aramid known as Kevlar. Chemical structure of this aramid consists of linearly substituted aromatic rings linked by amide groups.

The length of the beak increases linearly for about 50 days. Young birds are fed with earthworms and insects, which are regurgitated by the parents onto the floor of the nest. Older chicks reach into the mouths of parents to obtain food. Chicks fledge 58 to 64 days after hatching.

This fact has had unexpected applications to neural network learning.See Anthony and Bartlett for details. Examples of NIP theories include also the theories of all the following structures:See Simon, Appendix A. linear orders, trees, abelian linearly ordered groups, algebraically closed valued fields, and the p-adic field for any p.

Accuracy depends on both the total number of elements, and the shape of individual elements. The speed of each iteration grows (linearly) with the number of elements, and the number of iterations needed depends on the local solution value and gradient compared to the shape and size of local elements.

The idea of this procedure is that the total concentration of the analyte is the sum of the unknown and the standard, and that the total concentration varies linearly. If the signal response is linear in this concentration range, then a plot similar to what is shown above is generated.

The trouble is for a single transistor parasitic capacitance and gain both scale linearly with the width. For the distributed amplifier the capacitance – that is the width – of the single transistor is chosen based on the highest frequency and the width needed for the current is split across all transistors.

For the coherent addition to be additive, phase-matching must be fulfilled. For tight focusing conditions this is generally not a restriction. Once phase-matching is fulfilled the signal amplitude grows linearly with distance so that the power grows quadratically. This signal forms a collimated beam that is therefore easily collected.

In addition, Stomatopods have a tripartite cornea which contains upper and lower halves, separated by a middle band made up of ommatidia. These photoreceptors include specialized receptors that can detect a wide range of visible and ultraviolet light, as well as being able to detect linearly and circularly polarized light.

Senile plaques can be found in human and animal brains (e.g. mammals and birds). From an age of 60 years (10%) to an age of 80 years (60%), the proportion of people with senile plaques increases linearly. A small proportion of plaques that form can be due to the physiological process of aging.

The naive approach is to write the circuit as a Boolean expression, and use De Morgan's law and the distributive property to convert it to CNF. However, this can result in an exponential increase in equation size. The Tseytin transformation outputs a formula whose size grows linearly relative to the input circuit's.

LD Typical units are g.m−2 for LMA, µm for LTh and g.ml−1 for LD. Both SLA and LMA are frequently used in plant ecology and biology. SLA is one of the components in plant growth analysis, and mathematically scales positively and linearly with the relative growth rate of a plant.

Signal flow graphs can be used to solve sets of simultaneous linear equations."... solving a set of simultaneous, linear algebraic equations. This problem, usually solved by matrix methods, can also be solved via graph theory. " also on-line at The set of equations must be consistent and all equations must be linearly independent.

These three subprovinces lie linearly in southwestern- to northeastern-oriented belts about wide on the southern portion of the Superior Province. The Slave province and portions of the Nain province were also affected. Between about 2,000 and these combined with the Sask and Wyoming cratons to form the first supercontinent, the Kenorland supercontinent.

It seems that people falsely believe that journey time decreases somewhat linearly as driving speed increases, irrespective of the initial speed, causing the time-saving bias. Although it is still unclear what is the dominant heuristic people use to estimate time savings, it is evident that almost none follow the above curvilinear relationship.

A well-known application has been automatic speech recognition, to cope with different speaking speeds. In general, it is a method that allows a computer to find an optimal match between two given sequences (e.g., time series) with certain restrictions. That is, the sequences are "warped" non-linearly to match each other.

If a unipotent group acts on an affine variety, all its orbits are closed, and if it acts linearly on a finite-dimensional vector space then it has a non-zero fixed vector. In fact, the latter property characterizes unipotent groups. In particular, this implies there are no non-trivial semisimple representations.

The ocean is an extensive network of particle transport. Thorium isotopes can help researchers decipher the vertical and horizontal movement of matter. 234Th has a constant, well-defined production rate in the ocean and a half-life of 24 days. This naturally occurring isotope has been shown to vary linearly with depth.

Coverage is not linearly proportional because of the random nature of the process (chaos theory). When 100% coverage is achieved, locations on the surface have been impacted multiple times. At 150% coverage, 5 or more impacts occur at 52% of locations. At 200% coverage, 5 or more impacts occur at 84% of locations.

Although there in no river going through the town, three rivers flow around the town: the Glore River, Yellow River and Pollagh River. The town center sits at the crest of a hill surrounding The High Fort (Mooney's Fort/Lios Ard) in Fortlands and built out linearly on the main road from there.

For dragging, finger input is slower than mouse and stylus. For radial dragging, it was found that task time and movement distance are all linearly correlated with number of items available. Other radial dragging results showed that the stylus is the fastest but had the highest error rate of the three devices.

The Tunbridge Village Historic District encompasses the early 19th-century village center of Tunbridge, Vermont. Stretched linearly along Vermont Route 110, the largely agricultural village reached its peak population around 1820, and was bypassed by the railroads, limiting later development. It was listed on the National Register of Historic Places in 1994.

Quadratic programming (QP) is the process of solving a special type of mathematical optimization problem—specifically, a (linearly constrained) quadratic optimization problem, that is, the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables. Quadratic programming is a particular type of nonlinear programming.

Foraging turtles frequently cross lakes or travel linearly down creeks. Daily crossings of large ponds have been observed. Tag and release studies show that sex also drives turtle movement. Males travel the most, up to , between captures; females the second most, up to , between captures; and juveniles the least, less than , between captures.

Let V be any vector space over some field F. Let X be the set of all linearly independent subsets of V. The set X is nonempty since the empty set is an independent subset of V, and it is partially ordered by inclusion, which is denoted, as usual, by . Let Y be a subset of X that is totally ordered by , and let LY be the union of all the elements of Y (which are themselves certain subsets of V). Since (Y, ⊆) is totally ordered, every finite subset of LY is a subset of an element of Y, which is a linearly independent subset of V, and hence LY is linearly independent. Thus LY is an element of X. Therefore, LY is an upper bound for Y in (X, ⊆): it is an element of X, that contains every element of Y. As X is nonempty, and every totally ordered subset of (X, ⊆) has an upper bound in X, Zorn's lemma asserts that X has a maximal element. In other words, there exists some element Lmax of X satisfying the condition that whenever Lmax ⊆ L for some element L of X, then L = Lmax.

To present a stereoscopic motion picture, two images are projected superimposed onto the same screen through orthogonal polarizing filters (Usually at 45 and 135 degrees).Make Your own Stereo Pictures Julius B. Kaiser The Macmillan Company 1955 page 271 The viewer wears linearly polarized eyeglasses which also contain a pair of orthogonal polarizing filters oriented the same as the projector. As each filter only passes light which is similarly polarised and blocks the orthogonally polarized light, each eye only sees one of the projected images, and the 3D effect is achieved. Linearly polarised glasses require the viewer to keep his or her head level, as tilting of the viewing filters will cause the images of the left and right channels to bleed over to the opposite channel.

Alternatively, it is possible to use Euler's formula to show that the number of cycles in this collection equals the circuit rank of , which is the dimension of the cycle space. Each nonempty subset of cycles has a vector sum that represents the boundary of the union of the bounded faces in the subset, which cannot be empty (the union includes at least one bounded face and excludes the unbounded face, so there must be some edges separating them). Therefore, there is no subset of cycles whose vectors sum to zero, which means that all the cycles are linearly independent. As a linearly independent set of the same size as the dimension of the space, this collection of cycles must form a basis.

This diagram linearly (unless otherwise mentioned) tracks the projections of all known structures that allow for balance and acceleration to their relevant endpoints in the human brain. Another diagram showing neural pathway of vestibular/balance system. Arrows show the direction of information relay. This overview also explains acceleration as its processes are interconnected with balance.

Archimedean groups can be generalised to Archimedean monoids, linearly ordered monoids that obey the Archimedean property. Examples include the natural numbers, the non-negative rational numbers, and the non- negative real numbers, with the usual binary operation + and order <. Through a similar proof as for Archimedean groups, Archimedean monoids can be shown to be commutative.

It had two bastions, and each bastion was equipped with four cannons. Elephant Pass Fort was linearly located with Fort Beschutter and Fort Pass Pyl in the narrow part of the peninsula. During the British rule, the fort was used as a rest house. It was destroyed during the time of Sri Lankan civil war.

Pentenes are alkenes with chemical formula . Each contains one double bond within its molecular structure. There are a total of six different compounds in this class, differing from each other by whether the carbon atoms are attached linearly or in a branched structure, and whether the double bond has a cis or trans form.

Assume a market for nails where the cost of each nail is $0.10. Demand decreases linearly; there is a high demand for free nails and zero demand for nails at a price per nail of $1.10 or higher. The price of $0.10 per nail represents the point of economic equilibrium in a competitive market.

The President Jackson Seamounts are a series of seamounts (underwater volcanoes) located on the Pacific Plate, off of California. It consists of 8 seamounts, 4 independent and 4 morpohologically fused, just west of the northern Gorda Ridge. They are generally very small, and arranged linearly. The assembly consists of 8 seamounts arranged in a chain.

However in this duality the authors are able to cast the dynamics of the quantum foam in the familiar language of a topologically twisted U(1) gauge theory, whose field strength is linearly related to the Kähler form of the A-model. In particular this suggests that the A-model Kähler form should be quantized.

Cyclomatic complexity may also be applied to individual functions, modules, methods or classes within a program. One testing strategy, called basis path testing by McCabe who first proposed it, is to test each linearly independent path through the program; in this case, the number of test cases will equal the cyclomatic complexity of the program.

As it turns out, uniformly distributed measures are very rigid objects. On any "decent" metric space, the uniformly distributed measures form a one-parameter linearly dependent family: Let μ and ν be uniformly distributed Borel regular measures on a separable metric space (X, d). Then there is a constant c such that μ = cν.

The SSIMPLUS index is based on SSIM and is a commercially available tool. It extends SSIM's capabilities, mainly to target video applications. It provides scores in the range of 0–100, linearly matched to human subjective ratings. It also allows adapting the scores to the intended viewing device, comparing video across different resolutions and contents.

PCA was invented in 1901 by Karl Pearson, to transform original dataset into linearly uncorrelated PCA domain. PCA works in the way that principal components with larger possible variance are preserved while discarding low variance components. Image denoising by principal component analysis with local pixel grouping(LPG-PCA) was developed by Lei et. in 2010.

If the number of glass and batch components is not equal, if it is impossible to exactly obtain the desired glass composition using the selected batch ingredients, or if the matrix equation is not soluble for other reasons (i.e., the rows/columns are linearly dependent), the batch composition must be determined by optimization techniques.

Factors affecting coverage density include: number of impacts (shot flow), exposure time, shot properties (size, chemistry), and work piece properties. Coverage is monitored by visual examination to determine the percent coverage (0-100%). Coverage beyond 100% cannot be determined. The number of individual impacts is linearly proportional to shot flow, exposure area, and exposure time.

Exposure to radioactive waste may cause health impacts due to ionizing radiation exposure. In humans, a dose of 1 sievert carries a 5.5% risk of developing cancer, and regulatory agencies assume the risk is linearly proportional to dose even for low doses. Ionizing radiation can cause deletions in chromosomes.Gofman, John W. Radiation and human health.

Water-air interfaces provide another source of circular polarization. Sunlight that gets scattered back up towards the surface is linearly polarized. If this light is then totally internally reflected back down, its vertical component undergoes a phase shift. To an underwater observer looking up, the faint light outside Snell's window therefore is (partially) circularly polarized.

The gamma correction, or contrast selection, is part of the photographic repertoire used to adjust the reproduced image. Analogously, digital cameras record light using electronic sensors that usually respond linearly. In the process of rendering linear raw data to conventional RGB data (e.g. for storage into JPEG image format), color space transformations and rendering transformations will be performed.

In vitro transcription (IVT) linear amplification. Still within the same PCR tube, overnight IVT reaction is assembled, including standard IVT buffer, NTPs, T7 RNA polymerase, RNase inhibitor, DMSO, etc. 6\. Reverse transcription (RT). After overnight IVT, RNAs representing the linearly amplified products of the original genomic DNA are column purified, self primed on the 3′ end, and reverse transcribed.

Some problems encountered by the genetic relationship group of languages include language isolates and mixed, pidgin and creole languages. Mixed languages, pidgins and creole languages constitute special genetic types of languages. They do not descend linearly or directly from a single language and have no single ancestor. Language isolates are languages that are unrelated to other languages.

Marsh woundwort is a perennial plant growing from a horizontal tuberous runner. It has square stems with opposite pairs of leaves that are almost stalkless, linearly lanceolate, slightly cordate at the base and toothed. The calyx has five sharply-pointed lobes. The purplish-red flowers are in terminal spikes, with gaps in the lower part of the spike.

The ideal transfer function of such a monochromator is a triangular shape. The peak of the triangle is at the nominal wavelength selected. The intensity of the nearby colors then decreases linearly on either side of this peak until some cutoff value is reached, where the intensity stops decreasing. This is called the stray light level.

In mathematics, the interval chromatic number X<(H) of an ordered graph H is the minimum number of intervals the (linearly ordered) vertex set of H can be partitioned into so that no two vertices belonging to the same interval are adjacent in H.János Pach, Gabor Tardos, "Forbidden Pattern and Unit Distances",page 1-9,2005,ACM.

The library is optimized for high read concurrency; readers need no locks at all. Readers don't block writers and writers don't block readers, so read performance scales perfectly linearly across arbitrarily many threads and CPUs. Third-party wrappers exist for C++, Erlang and Python. LMDB is distributed by the OpenLDAP Project under the OpenLDAP Public License.

The static friction force adapts to the residual spring force, establishing equilibrium with zero net force and zero velocity. Consider the example of a braking and decelerating car. The brake pads generate kinetic frictional forces and constant braking torques on the disks (or drums) of the wheels. Rotational velocity decreases linearly to zero with constant angular deceleration.

These linear combinations are also known as Bessel functions of the third kind; they are two linearly independent solutions of Bessel's differential equation. They are named after Hermann Hankel. These forms of linear combination satisfy numerous simple-looking properties, like asymptotic formulae or integral representations. Here, "simple" means an appearance of the factor of the form .

In matroid theory, a binary matroid is a matroid that can be represented over the finite field GF(2).. That is, up to isomorphism, they are the matroids whose elements are the columns of a (0,1)-matrix and whose sets of elements are independent if and only if the corresponding columns are linearly independent in GF(2).

Blood plasma concentrations are linearly dependent on the dose up to 1260 mg (the sevenfold daily dose). The metabolite reaches 30–40% of ticagrelor's plasma concentrations. Drug and metabolite are mainly excreted via bile and feces. Plasma concentrations of ticagrelor are slightly increased (12–23%) in elderly patients, women, patients of Asian ethnicity, and patients with mild hepatic impairment.

The film's unit consisted of about 17 people because of budget and time constraints; it was made on a budget of . The film was shot linearly on a non-linear draft. Mehta said it was filmed guerilla style using all "available digital formats without really worrying about which lens was available". The filmmaker used only natural or minimal lighting.

For each event, a first place gives 30 points, a 2nd place 26 pts, a 3rd place 24 pts, a 4th place 22 pts, then linearly decreasing by one point down to the 25th place. Equal placings (ties) give an equal number of points. The sum of all WC points of the season gives the biathlete's total WC score.

The Special Sensor Microwave/Imager (SSM/I) is a seven-channel, four- frequency, linearly polarized passive microwave radiometer system.Hollinger, J.P. 1989: DMSP Special Sensor Microwave/Imager Calibration/Validation. Final Report, Vol. I., Space Sensing Branch, Naval Research Laboratory, Washington D.C. It is flown on board the United States Air Force Defense Meteorological Satellite Program (DMSP) Block 5D-2 satellites.

It was most commonly erected as a linearly-arranged series of vertical posts connected by a series of horizontal crossbeams. The skulls were pierced or threaded laterally along these horizontal stakes. An alternate arrangement, more common in the Maya regions, was for the skulls to be impaled on top of one another along the vertical posts.Nelson et al.

In this contest the notes Sa Re Ga Ma Pa Dha Ni was used for scoring. After every performance of every contestant, every judge independently scored the performance. The scores increased linearly from 'Sa' to 'Ni' and will have values from 'Sa' = 1 to 'Ni' = 7. The result was declared based on the total score from the judges.

Animation of linearly polarized electromagnetic wave, illustrating the directional relationship of the E electric and B magnetic vectors relative to the direction of wave propagation. Electromagnetic waves can have handedness associated with their polarization. Polarization of an electromagnetic wave is the property that describes the orientation, i.e., the time-varying direction and amplitude, of the electric field vector.

In the case that X and Y are both finite-dimensional (i.e. linearly isomorphic to Rm and Rn for some natural numbers m and n) then writing out equation (L) in matrix form shows that λ is the usual Lagrange multiplier vector; in the case n = 1, λ is the usual Lagrange multiplier, a real number.

The authors propose two models which exhibit the power law in the degree distribution while the average shortest path grows linearly with the number of nodes. This proves that not every scale-free network has the small-world property. One of their models shows that this can also be true in the absence of degree correlation.

Germanium-doped core fibers can be radiation hard even at high concentrations of germanium. Such fibers reach saturation, anneal well at higher temperatures and are also responsive to photo-bleaching. In case of phosphorus-doped core fibers, attenuation increases linearly with increasing phosphorus content and these fibers do not reach saturation. Recovery is very difficult even at higher temperatures.

The logistic distribution arises as limit distribution of a finite-velocity damped random motion described by a telegraph process in which the random times between consecutive velocity changes have independent exponential distributions with linearly increasing parameters.A. Di Crescenzo, B. Martinucci (2010) "A damped telegraph random process with logistic stationary distribution", J. Appl. Prob., vol. 47, pp. 84–96.

The simplest form of scene graph uses an array or linked list data structure, and displaying its shapes is simply a matter of linearly iterating the nodes one by one. Other common operations, such as checking to see which shape intersects the mouse pointer are also done via linear searches. For small scene graphs, this tends to suffice.

When particles are larger, scattering increases approximately linearly with wavelength: hence clouds are white since they contain water droplets. This form of scatter is known as Mie scattering and is what occurs in biological tissues. So, although longer wavelengths do scatter less in biological tissues, the difference is not as dramatic as Rayleigh's law would predict.

Once again we find that this equation is not independent of the first two equations. We could also try to compute moments around the clamped end of the beam to get : (10)(50) - (R_a)(40) - (R_b)(25) + (1)(15)(32.5) - 50 + M_c = 0 \,. This equation also turns out not to be linearly independent from the other two equations.

In this particular case, there is a relation of asymmetric c-command between the constituent the King of England and likes apples. Therefore, the first constituent is ordered linearly before the second. Further tests ultimately give rise to linear order for the internal parts of these constituents. The theory of the antisymmetry of syntax has a twofold aims.

Pentacene is a polycyclic aromatic hydrocarbon consisting of five linearly- fused benzene rings. This highly conjugated compound is an organic semiconductor. The compound generates excitons upon absorption of ultra-violet (UV) or visible light; this makes it very sensitive to oxidation. For this reason, this compound, which is a purple powder, slowly degrades upon exposure to air and light.

The expansion coefficients are also numbers. The number of known functions included in the expansion, the same as that of coefficients, is the dimension of the Hamiltonian matrix that will be generated. The statement of the theorem follows. Let an eigenvalue equation be solved by linearly expanding the unknown function in terms of N known functions.

Additionally, due to the measurements always being measured as direct lines from the station, as opposed to hyperbolic curves, the accuracy fell off linearly instead of with the square of distance. Gee-H could this guide the bomber to within 120 yards over Germany, a dramatic improvement over Gee's approximately 1 mile accuracy at the same distance.

Nutrients from human activities tend to accumulate in soils and remain there for years. It has been shown that the amount of phosphorus lost to surface waters increases linearly with the amount of phosphorus in the soil. Thus much of the nutrient loading in soil eventually makes its way to water. Nitrogen, similarly, has a turnover time of decades.

To this solution, any one of the infinite discrete set of eigenfunctions can be added, each of which satisfies the linearly perturbed equation with homogeneous conditions and exponential decay at infinity. The first of these eigenfunctions turns out be the x derivative of the first order Blasius solution, which represents the uncertainty in the effective location of the origin.

470–471 (Macmillan, 2004). Another physical setting for derivation of the wave equation in one space dimension utilizes Hooke's Law. In the theory of elasticity, Hooke's Law is an approximation for certain materials, stating that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress).

CNC plunge milling, also called z-axis milling, is a CNC milling process. In this process, the feed is provided linearly along the tool axis while doing CNC processing. This image shows the material removal in plunge milling. Plunge milling is effective for the rough machining process of complex shape or free form shapes like impeller parts.

Then Nakayama's lemma says that M has a minimal generating set whose cardinality is \dim_k M / mM = \dim_k M \otimes_R k. If M is flat, then this minimal generating set is linearly independent (so M is free). See also: minimal resolution. A more refined information is obtained if one considers the relations between the generators; cf.

A leaky oxide can prevent a charge from building up to the point of causing oxide breakdown. This leads to the somewhat surprising observation that a very thin gate oxide is less likely to be damaged than a thick gate oxide, because as the oxide grows thinner, the leakage goes up exponentially, but the breakdown voltage shrinks only linearly.

Simple function generators usually generate triangular waveform whose frequency can be controlled smoothly as well as in steps. This triangular wave is used as the basis for all of its other outputs. The triangular wave is generated by repeatedly charging and discharging a capacitor from a constant current source. This produces a linearly ascending and descending voltage ramp.

First, given the dual usefulness of this image, begin by imagining the circularly polarized light displayed at the top as still leaving the quarter-wave plate and traveling toward the left. Observe that had the horizontal component of the linearly polarized light been retarded by a quarter of wavelength twice, which would amount to a full half wavelength, the result would have been linearly polarized light that was at a right angle to the light that entered. If such orthogonally polarized light were rotated on the horizontal plane and directed back through the linear polarizer section of the circular polarizer it would clearly pass through given its orientation. Now imagine the circularly polarized light which has already passed through the quarter-wave plate once, turned around and directed back toward the circular polarizer again.

This error will be diffused in the neighboring pixels. In addition, gamma correction may be needed on each of these perceptive channels, if they don't scale linearly with the human vision, so that error diffusion can be accumulated linearly to these gamma-corrected linear channels, before computing the final color channels of the rounded pixel colors, using a reverse conversion to the native non gamma-corrected image format and from which the new residual error will be computed and converted again to be distributed to the next pixels. It should also be noted that, due to limitations of precision during the numeric conversion between color models (notably if this conversion is not linear or uses non integer weights), additional roundoff errors may occur that should be taken into account into the residual error.

In detail, the question applies to the 'round spheres' and to their tangent bundles: in fact since all exotic spheres have isomorphic tangent bundles, the Radon–Hurwitz numbers ρ(N) determine the maximum number of linearly independent sections of the tangent bundle of any homotopy sphere. The case of N odd is taken care of by the Poincaré–Hopf index theorem (see hairy ball theorem), so the case N even is an extension of that. Adams showed that the maximum number of continuous (smooth would be no different here) pointwise linearly-independent vector fields on the (N − 1)-sphere is exactly ρ(N) − 1\. The construction of the fields is related to the real Clifford algebras, which is a theory with a periodicity modulo 8 that also shows up here.

Electromagnetic radiation consists of an electric (E) and magnetic (B) field that oscillate perpendicular to one another and to the propagating direction, a transverse wave. While linearly polarized light occurs when the electric field vector oscillates only in one plane, circularly polarized light occurs when the direction of the electric field vector rotates about its propagation direction while the vector retains constant magnitude. At a single point in space, the circularly polarized- vector will trace out a circle over one period of the wave frequency, hence the name. The two diagrams below show the electric field vectors of linearly and circularly polarized light, at one moment of time, for a range of positions; the plot of the circularly polarized electric vector forms a helix along the direction of propagation (k).

One option is to repeat the test using a different type of assay. Other options include the use of heterophile blocking reagents, steps to remove immunoglobulins, serial dilutions and using non-mammalian capture and/or detection antibodies. Heterophile antibody interference usually doesn't change linearly with serial dilution, but a true result most often will. This is one strategy for heterophile antibody detection.

It is linearly rational and has no grasp of the acoustic. Acoustic Space is multisensory. McLuhan writes about robotism in the context of Japanese Zen Buddhism and how it can offer us new ways of thinking about technology. The Western way of thinking about technology is too much related to the left hemisphere of our brain, which has a rational and linear focus.

Walter H. Schottky and Spenke extended Mott's theory by including a donor ion whose density is spatially constant through the semiconductor surface layer. This changed the constant electric field assumed by Mott to a linearly decaying electric field. This semiconductor space-charge layer under the metal is known as the Schottky barrier. A similar theory was also proposed by Davydov in 1939.

Also, the ring satisfies (and in fact is characterized by) the universal property: for (1) each continuous ring homomorphism A \to B to a linearly topologized ring B, separated and complete and (2) each elements b_1, \dots, b_n in B, there exists a unique continuous ring homomorphism :A \langle x_1, \dots, x_n \rangle \to B, \, x_i \mapsto b_i extending A \to B.

In many applications it is possible to use a quarter-wave plate to produce circularly polarized light, but this is only possible for light of a limited range of wavelengths which is linearly polarized to start with. Other methods have been demonstrated, such as the use of Faraday rotators and liquid crystals. It is also possible to depolarize light using fiber optics.

The top image is left-handed/counter- clockwise circularly polarized, as viewed from the receiver. The bottom image is that of linearly polarized light. The blue and green curves are projections of the red lines on the vertical and horizontal planes respectively. At the top of the illustration toward the right is the circularly polarized light after it leaves the wave plate.

In Finland, the old diplomi-insinööri ("diploma engineer") title was completely replaced by Master of Science (Technology) in the Bologna process. All Finnish academic degrees are awarded both in Finnish and English and therefore the title is still awarded as diplomi-insinööri with Master of Science (Technology) as the official translation. Conversion was straightforward and academic credits were transformed linearly.

Recently, it has been shown that certain promoters are capable of directing transcription inside regions that are otherwise silenced by SIR proteins. Specifically, if an inducible promoter is induced inside a silent chromatin domain, it can achieve ~200x increase in expression levels with little detectable change in covalent histone modifications. SIR spreading is thought to occur linearly from the silencer element.

There are two primary types of imageboard software packages in widespread use: linearly directed imageboards modeled closely after Futaba Channel (in which content is posted through hierarchical subsections of topical interest, usually denoted by a forward slash such as "/f" for female), and nonlinear imageboards modeled after Danbooru (usually indicated by the usage of controlled folksonomic vocabulary for topical tagging and search).

Its output is linearly combined (XORed) with two of the bits of the NLFSR state (bits 0 and 16 on encryption and bits 31 and 15 on decryption) and with a key bit (bit 0 of the key state on encryption and bit 15 of the key state on decryption) and is fed back into the NLFSR state on every round.

Nevertheless, archives were essentially inaccessible to ordinary people. The same applied to other collections (i.e. Johan Theodor Storaker etc.), which were taken care of at the Manuscript Collection in the University Library of Oslo (now the National Library of Norway, Oslo). NFL in particular emphasized folklore genres, beliefs and customs that were linearly passed on from one generation to the next.

Cetirizine is rapidly and extensively absorbed upon oral administration in tablet or syrup form. The oral bioavailability of cetirizine is at least 70% and of levocetirizine is at least 85%. The Tmax of cetirizine is approximately 1.0 hour regardless of formulation. The pharmacokinetics of cetirizine have been found to increase linearly with dose across a range of 5 to 60 mg.

Genes are a fundamental part of DNA that is aligned linearly on a eukaryotic chromosome. Chemical information that is transported and encoded by each gene is referred to as a trait. Many organisms possess two genes for each individual trait that is present within that particular individual. These paired genes that control the same trait is classified as an allele.

Given a linearly ordered set and an order- preserving bijection with unbounded orbits, the orbit space is cyclically ordered by the requirement: :If , then . In particular, one can recover by defining on . There are also -fold coverings for finite ; in this case, one cyclically ordered set covers another cyclically ordered set. For example, the is a double cover of the .

The above variations also appear in adjective form: cyclically ordered set (cyklicky uspořádané množiny, ), circularly ordered set, total cyclically ordered set, complete cyclically ordered set, linearly cyclically ordered set, l-cyclically ordered set, ℓ-cyclically ordered set. All authors agree that a cycle is totally ordered. There are a few different symbols in use for a cyclic relation. uses concatenation: .

The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. One limitation of this model is that it does not predict creep accurately. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time.

Keizan was the author of a number of works including the "Zazen Yōjinki" and, most famously, the Denkōroku "Transmission of the Light", which is a series of fifty-one sermons which details linearly the Sōtō lineage from Gautama Buddha through the Indian Patriarchs, from Bodhidharma and the Chinese Patriarchs, and finally the Japanese patriarchs Dōgen and his immediate successor at Eihei-ji, Ejō.

This diagram linearly (unless otherwise mentioned) tracks the projections of all known structures that allow for taste to their relevant endpoints in the human brain. The glossopharyngeal nerve innervates a third of the tongue including the circumvallate papillae. The facial nerve innervates the other two thirds of the tongue and the cheek via the chorda tympani.Eliav, Eli, and Batya Kamran.

In directions perpendicular to its axis the antenna radiates linearly polarized radio waves (horizontally polarized when the antenna's axis is vertical). This is called normal mode. The radiation pattern, a superposition of the two dipole patterns, is close to omnidirectional but actually "cloverleaf shaped", with four small maxima off the ends of the elements. The pattern departs from omnidirectional by only ±5 percent.

The Sheffield Center Historic District encompasses the historic village center of Sheffield, Massachusetts. The village extends linearly along United States Route 7, roughly between Maple Avenue and Berkshire School Road, and includes the town's major civic and religious buildings. The area's principal period of development was between 1760 and the 1890s. It was listed on the National Register of Historic Places in 1989.

In screw theory angular and linear velocity are combined into one six-dimensional object, called a twist. A similar object called a wrench combines forces and torques in six dimensions. These can be treated as six-dimensional vectors that transform linearly when changing frame of reference. Translations and rotations cannot be done this way, but are related to a twist by exponentiation.

Joule heating (Ohmic heating) is a flash pasteurization (also called "high-temperature short-time" (HTST)) aseptic process that runs an alternating current of 50–60 Hz through food. Heat is generated through the electrical resistance of the food. As the product heats up, electrical conductivity increases linearly. A higher electrical current frequency is best as it reduces oxidation and metallic contamination.

A sensor device embedded on microprocessors used to monitor the temperature of the processor's die is also known as a "thermal diode". This application of thermal diode is based on the property of electrical diodes to change voltage across it linearly according to temperature. As the temperature increases, diodes' forward voltage decreases. Microprocessors having high clock rate encounter high thermal loads.

Seymour Benzer in the late 1950s had developed an assay using phage mutations which provided the first detailed linearly structured map of a genetic region. Crick felt he could use mutagenesis and genetic recombination phage to further delineate the nature of the genetic code. In the Crick, Brenner et al. experiment, using these phages, the triplet nature of the genetic code was confirmed.

Reduction of order is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution y_1(x) is known and a second linearly independent solution y_2(x) is desired. The method also applies to n-th order equations. In this case the ansatz will yield an (n-1)-th order equation for v.

There were (measured linearly) of ship berthing space. Crane capacity ranged from to (portal) and from to (floating). "Herman the German" (YD-171) at Long Beach NSY in 1957. One of the large cranes at Long Beach NSY, YD-171, was nicknamed "Herman the German" based on its origin as a floating crane for the Kriegsmarine (one of four ships in the class).

Assuming the axiom of choice, infinite cardinalities are linearly ordered; no two cardinalities can fail to be comparable. Thus, since by definition no infinite cardinalities are between \aleph_0 and \aleph_1, it follows that :\beth_1 \ge \aleph_1. Repeating this argument (see transfinite induction) yields \beth_\alpha \ge \aleph_\alpha for all ordinals \alpha. The continuum hypothesis is equivalent to :\beth_1=\aleph_1.

Combining multiple depressants can be very dangerous because the central nervous system's depressive properties have been proposed to increase exponentially instead of linearly. This characteristic makes depressants a common choice for deliberate overdoses in the case of suicide. The use of alcohol or benzodiazepines along with the usual dose of heroin is often the cause of overdose deaths in opiate addicts.

It behaves non-linearly at all times. Because it has essentially zero strength in tension, it is almost always used as reinforced concrete, a composite material. It is a mixture of sand, aggregate, cement and water. It is placed in a mould, or form, as a liquid, and then it sets (goes off), due to a chemical reaction between the water and cement.

DASH7 devices operate on a single global frequency and are interoperable regardless of application and by design do not require cumbersome application profiles. Unlike most wireless networks, DASH7 doesn't require a gateway/node controller to operate. DASH7 V1.0 targets scalability : begin with two low cost devices and grow a network linearly. The DASH7 protocol is not built around IP layers.

PEPSIPEPSI – instrument for the LBT is a high-resolution spectrograph for the LBT. It will enable the simultaneous observation of circularly and linearly polarized light with high spectral and temporal resolution. The spectrograph is situated in a temperature- and pressure-stabilized room within the telescope column. The light will be conducted by fiber optics from the telescope to the spectrograph.

Downy mildews are common and widespread pathogens, existing worldwide. P. manshurica exists anywhere soybeans are cultivated. Historically, this pathogen has been rather low risk, because infected crops do not typically exhibit significant yield loss. A 2016 study showed that infected plants did not exhibit decreased numbers of soybean pods or grains per pod, however seed weight decreased linearly with increasing downy mildew severity.

Procedural Model of Cologne Cathedral With procedural models, the model complexity is no longer directly (i.e., linearly) related with the file size. The Procedural Cathedral, a basic model of the Cologne Cathedral, contains 70 tracery windows, and a single window in highest resolution contains about 7 million triangles. These are "unfolded" from only 126 KB of GML code (18 KB zipped).

Pseudocapacitance and double-layer capacitance both contribute inseparably to the total capacitance value. The amount of pseudocapacitance depends on the surface area, material and structure of the electrodes. Pseudocapacitance may contribute more capacitance than double-layer capacitance for the same surface area by 100x. The amount of electric charge stored in a pseudocapacitance is linearly proportional to the applied voltage.

Register files have one word line per entry per port, one bit line per bit of width per read port, and two bit lines per bit of width per write port. Each bit cell also has a Vdd and Vss. Therefore, the wire pitch area increases as the square of the number of ports, and the transistor area increases linearly. Johan Janssen.

The order on the number line Each set on the real number line has a supremum. The real line is a linear continuum under the standard ordering. Specifically, the real line is linearly ordered by , and this ordering is dense and has the least-upper-bound property. In addition to the above properties, the real line has no maximum or minimum element.

The photon energies generated by this process can extend past the 800th harmonic order up to a few KeV. This is called high-order harmonic generation. The laser must be linearly polarized, so that the electron returns to the vicinity of the parent ion. High-order harmonic generation has been observed in noble gas jets, cells, and gas-filled capillary waveguides.

LD is very similar to Circular Dichroism (CD), but with two important differences. (i) CD spectroscopy uses circularly polarized light whereas LD uses linearly polarized light. (ii) In CD experiments molecules are usually free in solution so they are randomly oriented. The observed spectrum is then a function only of the chiral or asymmetric nature of the molecules in the solution.

This road was used as a way to export, through the Unquera inlet, raw materials from Liébana and the La Hermida gorge to England, Belgium and (Germany). In 1881 Unquera is already cited as a village at the bottom of Tina Mayor. Since then Unquera has grown linearly around the road, and also parallel to the estuary, where it has a river walk.

Shot noise is produced by electrons in transit across a discontinuity, which occurs in all detectors. Shot noise is the dominant source in most receivers. There will also be flicker noise caused by electron transit through amplification devices, which is reduced using heterodyne amplification. Another reason for heterodyne processing is that for fixed fractional bandwidth, the instantaneous bandwidth increases linearly in frequency.

The Hosoya index is #P-complete to compute, even for planar graphs.. However, it may be calculated by evaluating the matching polynomial mG at the argument 1.. Based on this evaluation, the calculation of the Hosoya index is fixed-parameter tractable for graphs of bounded treewidth. and polynomial (with an exponent that depends linearly on the width) for graphs of bounded clique-width..

Two datasets are linearly separable if their convex hulls do not intersect. The method may be formulated as a feedforward neural network with weights that are trained via linear programming. Comparisons between neural networks trained with the MSM versus backpropagation show MSM is better able to classify data.Neural Network Training via Linear Programing, Advances in Optimization and Parallel Computing, 1992, p.

Manufacturers of transistors and integrated circuits often divide their product lines into 'linear' and 'digital' lines. "Linear" here means "analog"; the linear line includes integrated circuits designed to process signals linearly, such as op-amps, audio amplifiers, and active filters, as well as a variety of signal processing circuits that implement nonlinear analog functions such as logarithmic amplifiers, analog multipliers, and peak detectors.

Trends do not have to be linear or log-linear. For example, a variable could have a quadratic trend: :Y_t = a \cdot t + c \cdot t^2 + b + e_t. This can be regressed linearly in the coefficients using t and t2 as regressors; again, if the residuals are shown to be stationary then they are the detrended values of Y_t.

Responsivity measures the input–output gain of a detector system. In the specific case of a photodetector, responsivity measures the electrical output per optical input. The responsivity of a photodetector is usually expressed in units of either amperes or volts per watt of incident radiant power. For a system that responds linearly to its input, there is a unique responsivity.

Rather, it is the odds that are doubling: from 2:1 odds, to 4:1 odds, to 8:1 odds, etc. Such a model is a log-odds or logistic model. Generalized linear models cover all these situations by allowing for response variables that have arbitrary distributions (rather than simply normal distributions), and for an arbitrary function of the response variable (the link function) to vary linearly with the predicted values (rather than assuming that the response itself must vary linearly). For example, the case above of predicted number of beach attendees would typically be modeled with a Poisson distribution and a log link, while the case of predicted probability of beach attendance would typically be modeled with a Bernoulli distribution (or binomial distribution, depending on exactly how the problem is phrased) and a log-odds (or logit) link function.

An additive group consists of a set of elements, an associative addition operation that combines pairs of elements and returns a single element, an identity element (or zero element) whose sum with any other element is the other element, and an additive inverse operation such that the sum of any element and its inverse is zero.Additive notation for groups is usually only used for abelian groups, in which the addition operation is commutative. The definition here does not assume commutativity, but it will turn out to follow from the Archimedean property. A group is a linearly ordered group when, in addition, its elements can be linearly ordered in a way that is compatible with the group operation: for all elements x, y, and z, if x ≤ y then (x + z) ≤ (y + z) and (z + x) ≤ (z + y).

The notation na (where n is a natural number) stands for the group sum of n copies of a. An Archimedean group (G, +, ≤) is a linearly ordered group subject to the following additional condition, the Archimedean property: For every a and b in G which are greater than 0, it is possible to find a natural number n for which the inequality b ≤ na holds.. An equivalent definition is that an Archimedean group is a linearly ordered group without any bounded cyclic subgroups: there does not exist a cyclic subgroup S and an element x with x greater than all elements in S.. It is straightforward to see that this is equivalent to the other definition: the Archimedean property for a pair of elements a and b is just the statement that the cyclic subgroup generated by a is not bounded by b.

In algebra, the Hochster–Roberts theorem, introduced by , states that rings of invariants of linearly reductive groups acting on regular rings are Cohen–Macaulay. In other words, :If V is a rational representation of a linearly reductive group G over a field k, then there exist algebraically independent invariant homogeneous polynomials f_1, \cdots, f_d such that k[V]^G is a free finite graded module over k[f_1, \cdots, f_d]. proved that if a variety over a field of characteristic 0 has rational singularities then so does its quotient by the action of a reductive group; this implies the Hochster–Roberts theorem in characteristic 0 as rational singularities are Cohen–Macaulay. In characteristic p>0, there are examples of groups that are reductive (or even finite) acting on polynomial rings whose rings of invariants are not Cohen–Macaulay.

The eigenvectors are used as the basis when representing the linear transformation as Λ. Conversely, suppose a matrix A is diagonalizable. Let P be a non-singular square matrix such that P−1AP is some diagonal matrix D. Left multiplying both by P, AP = PD. Each column of P must therefore be an eigenvector of A whose eigenvalue is the corresponding diagonal element of D. Since the columns of P must be linearly independent for P to be invertible, there exist n linearly independent eigenvectors of A. It then follows that the eigenvectors of A form a basis if and only if A is diagonalizable. A matrix that is not diagonalizable is said to be defective. For defective matrices, the notion of eigenvectors generalizes to generalized eigenvectors and the diagonal matrix of eigenvalues generalizes to the Jordan normal form.

The purpose of the concept of a net, first introduced by E. H. Moore and Herman L. Smith in 1922, is to generalize the notion of a sequence so as to confirm the equivalence of the conditions (with "sequence" being replaced by "net" in condition 2). In particular, rather than being defined on a countable linearly ordered set, a net is defined on an arbitrary directed set. In particular, this allows theorems similar to that asserting the equivalence of condition 1 and condition 2, to hold in the context of topological spaces that do not necessarily have a countable or linearly ordered neighbourhood basis around a point. Therefore, while sequences do not encode sufficient information about functions between topological spaces, nets do, because collections of open sets in topological spaces are much like directed sets in behaviour.

At its simplest, the theory holds that when gravity becomes vanishingly weak—levels seen only at interstellar distances—it diverges from its classically understood nature and its strength begins to decay linearly with distance from a mass. Entropic gravity provides the underlying framework to explain Modified Newtonian Dynamics, or MOND, which holds that at a gravitational acceleration threshold of approximately , gravitational strength begins to vary inversely (linearly) with distance from a mass rather than the normal inverse-square law of the distance. This is an exceedingly low threshold, measuring only 12 trillionths gravity's strength at earth's surface; an object dropped from a height of one meter would fall for 36 hours were earth's gravity this weak. It is also 3,000 times less than exists at the point where crossed our solar system's heliopause and entered interstellar space.

For example, skin effect, proximity effect, and core losses increase R with frequency; winding capacitance and variations in permeability with frequency affect L. At low frequencies and within limits, increasing the number of turns N improves Q because L varies as N2 while R varies linearly with N. Similarly increasing the radius r of an inductor improves (or increases) Q because L varies as r2 while R varies linearly with r. So high Q air core inductors often have large diameters and many turns. Both of those examples assume the diameter of the wire stays the same, so both examples use proportionally more wire. If the total mass of wire is held constant, then there would be no advantage to increasing the number of turns or the radius of the turns because the wire would have to be proportionally thinner.

Models developed by Wright et al. (1998) show radial growth of understorey white spruce increasing almost linearly with increasing light and a continuous decline in radial increment with increasing aspen basal area. When applied to Comeau's (2002) data, the Wright et al. (1998) models suggest that spruce mortality will remain very low until aspen basal area exceeds 20 m²/ha, above which mortality will increase rapidly.

The most important parameter for transistors is usually the forward current gain, h21, in the common emitter configuration. This is designated hfe on data sheets. The small signal equivalent circuit in terms of two-port parameters leads to the concept of dependent generators. That is, the value of a voltage or current generator depends linearly on a voltage or current elsewhere in the circuit.

The density of microcellular plastics has the greatest influence on the behavior and performance. The material tensile strength linearly decreases with the material density as more gas is dissolved into the part. Melting temperature and viscosity also decrease as well. The foam injection process itself introduces surface defects such as swirl marks, streaking, and blistering, which also influence how the part reacts to external forces.

Overall, this causes the transmitted wave to be linearly polarized with an electric field completely perpendicular to the wires. The hypothesis that the waves "slip through" the gaps between the wires is incorrect. For practical purposes, the separation between wires must be less than the wavelength of the incident radiation. In addition, the width of each wire should be small compared to the spacing between wires.

While there is no guarantee that or will not vanish, the complex function will never vanish because two linearly-independent solutions of a regular S-L equation cannot vanish simultaneously as a consequence of the Sturm separation theorem. This trick gives a solution of () for the value . In practice if () has real coefficients, the solutions based on will have very small imaginary parts which must be discarded.

Through computer simulations they studied the asymptotic properties of ICIM in additive QTL mapping as well. The test statistic LOD score linearly increases as the increase in population size. The larger of the QTL effect, the greater the corresponding LOD score increases. When population size is greater than 200, the position estimation of ICIM for QTL explaining more than 5% of the phenotypic variance is unbiased.

The \alpha-perceptron further used a pre-processing layer of fixed random weights, with thresholded output units. This enabled the perceptron to classify analogue patterns, by projecting them into a binary space. In fact, for a projection space of sufficiently high dimension, patterns can become linearly separable. Another way to solve nonlinear problems without using multiple layers is to use higher order networks (sigma-pi unit).

Serial memory processing uses internal representations of the memory set in order to compare them to a target stimulus or item that is being presented. These internal representations are then compared to the target stimulus, one at a time. Reaction time increases linearly with the set size, where the more items in the memory set, the longer it will take to compare.Sternberg, S. (1966).

Modern CMOS image sensors can often capture a high dynamic range from a single exposure. The wide dynamic range of the captured image is non-linearly compressed into a smaller dynamic range electronic representation. However, with proper processing, the information from a single exposure can be used to create an HDR image. Such HDR imaging is used in extreme dynamic range applications like welding or automotive work.

In most cases, sulfate tends to linearly decrease depth, which mostly reflects the diffusion of sulfate downwards. This diffusion is the main source of sulfate to the SMTZ. The sharper decrease in the sulfate that occurs further down is the result of microorganisms using dissimilatory sulfate reduction, which consumes sulfate. Sulfate and methane concentration profiles as observed in the Black Sea by B.B. Jorgensen et al. (2001).

The DKP matrices for spin-1 particles are 10-dimensional. The DKP-algebra can be reduced to a direct sum of irreducible subalgebras for spin‐0 and spin‐1 bosons, the subalgebras being defined by multiplication rules for the linearly independent basis elements.Ephraim Fischbach, Michael Martin Nieto, C. K. Scott: Duffin‐Kemmer‐Petiau subalgebras: Representations and applications, Journal of Mathematical Physics, vol. 14, no.

Parting: The tool is fed radially into the workpiece to cut off the end of a part. Threading: A tool is fed along and across the outside or inside surface of rotating parts to produce external or internal threads. Boring: A single-point tool is fed linearly and parallel to the axis of rotation to create a round hole. Drilling: Feeding the drill into the workpiece axially.

A chirp signal can be generated with analog circuitry via a voltage-controlled oscillator (VCO), and a linearly or exponentially ramping control voltage. It can also be generated digitally by a digital signal processor (DSP) and digital to analog converter (DAC), using a direct digital synthesizer (DDS) and by varying the step in the numerically controlled oscillator. It can also be generated by a YIG oscillator.

Chirp modulation, or linear frequency modulation for digital communication, was patented by Sidney Darlington in 1954 with significant later work performed by Winkler in 1962. This type of modulation employs sinusoidal waveforms whose instantaneous frequency increases or decreases linearly over time. These waveforms are commonly referred to as linear chirps or simply chirps. Hence the rate at which their frequency changes is called the chirp rate.

A small movable induction coil, positioned in the magnetic field of a permanent magnet, is attached to the diaphragm. When sound enters through the windscreen of the microphone, the sound wave moves the diaphragm. When the diaphragm vibrates, the coil moves in the magnetic field, producing a varying current in the coil through electromagnetic induction. A single dynamic membrane does not respond linearly to all audio frequencies.

As a special case, the open interval is defined as the cut . More generally, a proper subset S of K is called convex if it contains an interval between every pair of points: for , either or must also be in S. A convex set is linearly ordered by the cut for any not in the set; this ordering is independent of the choice of .

The ambient pressure in water with a free surface is a combination of the hydrostatic pressure due to the weight of the water column and the atmospheric pressure on the free surface. This increases approximately linearly with depth. Since water is much denser than air, much greater changes in ambient pressure can be experienced under water. Each of depth adds another bar to the ambient pressure.

The term optical activity is derived from the interaction of chiral materials with polarized light. In a solution, the (−)-form, or levorotatory form, of an optical isomer rotates the plane of a beam of linearly polarized light counterclockwise. The (+)-form, or dextrorotatory form, of an optical isomer does the opposite. The rotation of light is measured using a polarimeter and is expressed as the optical rotation.

During the propagation of both temporal solitons and spatial solitons, despite being in a medium with birefringence, the orthogonal polarizations can copropagate as one unit without splitting due to the strong cross-phase modulation and coherent energy exchange between the two polarizations of the vector soliton which may induce intensity differences between these two polarizations. Thus vector solitons are no longer linearly polarized but rather elliptically polarized.

Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain.

Revised version in Information and Control, 68 (1986), 86–104. and Vardi independently showed the descriptive complexity result that the polynomial-time computable properties of linearly ordered structures are definable in FO(LFP), i.e. in first-order logic with a least fixed point operator. However, FO(LFP) is too weak to express all polynomial-time properties of unordered structures (for instance that a structure has even size).

Several bases can span the same space. Of course also dependent vectors span a space, but the linear combinations of the latter can give only rise to the set of vectors lying on a straight line. As we are searching for a \,kdimensional subspace, we are interested in finding \,k linearly independent vectors that span the \,kdimensional subspace we want to project our data on.

Earth's Gravity according to PREM. Green curves show hypothetical Earths with density constant (dashed) and decreasing linearly from center to surface (stippled). The Preliminary reference Earth model (PREM) is a one-dimensional model representing the average Earth properties as a function of planetary radius. It includes a table of Earth properties, including elastic properties, attenuation, density, pressure, and gravity, as a function of planetary radius.

The internal load distribution associated with the deformed shape and stiffness should be used for calculations. Plastic bending begins when an applied moment causes the outside fibers of a cross-section to exceed the material's yield strength. Loaded only by a moment, the peak bending stresses occurs at the outside fibers of a cross-section. The cross-section will not yield linearly through the section.

The yielded areas of the cross-section will vary somewhere between the yield and ultimate strength of the material. In the elastic region of the cross-section, the stress distribution varies linearly from the neutral axis to the beginning of the yielded area. Predicted failure occurs when the stress distribution approximates the material's stress-strain curve. The largest value being that of the ultimate strength.

In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation model corresponding to the group of all automorphisms of the ordered set of rational numbers and the ideal of finite subsets of the rational numbers.

Thus, a transistor is not a thyristor even though it can operate like a switch (ON- OFF). The transistor is not inherently an ON-OFF device, and it is possible for a transistor to operate linearly. Some thyristors can be gated into the ON state. Other thyristors cannot be gated ON, but they can be turned ON when the applied voltage reaches a certain breakover value.

Low-energy surfaces primarily interact with liquids through dispersive (van der Waals) forces. William Zisman produced several key findings: Zisman observed that cos θ increases linearly as the surface tension (γLV) of the liquid decreased. Thus, he was able to establish a linear function between cos θ and the surface tension (γLV) for various organic liquids. A surface is more wettable when γLV and θ is low.

This is because of the size of the intermediate datastructures required during rendering—which can exceed the size of a Z-buffer for a complex scene. Consequently, in contemporary interactive graphics applications, the Z-buffer has become ubiquitous. The Z-buffer allows larger volumes of primitives to be traversed linearly, in parallel, in a manner friendly to modern hardware. Transformed coordinates, attribute gradients, etc.

In CRS microscopy, we can regard SRS and CARS as two aspects of the same process. CARS signal is always mixed with non-resonant four-wave mixing background and has a quadratic dependence on concentration of chemicals being imaged. SRS has much smaller background and depends linearly on the concentration of the chemical being imaged. Therefore, SRS is more suitable for quantitative imaging than CARS.

The major advantage of MALBAC is that DNA is amplified almost linearly. The utilization of specialized primers enables looping of amplicons which then prevents them from being further amplified in subsequent cycles of MALBAC. These primers are 35 nucleotides long, with 8 variable nucleotides that hybridize to the templates and 27 common nucleotides. The common nucleotide sequence is GTG AGT GAT GGT TGA GGT AGT GTG GAG.

Because maglev vehicles essentially fly, stabilisation of pitch, roll and yaw is required. In addition to rotation, surge (forward and backward motions), sway (sideways motion) or heave (up and down motions) can be problematic. Superconducting magnets on a train above a track made out of a permanent magnet lock the train into its lateral position. It can move linearly along the track, but not off the track.

Visco-elastic foam toppers are made from visco- elastic polyurethane, also known as "memory foam". This is a type of material that exhibitst both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. The foam used in the construction of these memory foam toppers reacts to both pressure and temperature.

Its western part contains a regional pattern of east–west-trending wide granitic greenstone and metasedimentary belts (subprovinces). Western Superior province's mantle has remained intact since the 2,700-million-year-ago accretion of the subprovinces. Both folding and faulting can be seen in the Wabigoon, Quetico and Wawa subprovinces. These three subprovinces lie linearly in southwestern- to northeastern-oriented belts of about wide (see figure on right).

Neutron-acceptance diagram shading (NADS) is a beam simulation technique. Unlike Monte-Carlo simulation codes like McStas, NADS does not trace individual neutrons but traces linearly-related bunches in a reduced- dimensionality phase space. Bunches are subdivided where necessary to follow accurately a simplified surface reflectivity model. This makes jnads results equivalent to Monte-Carlo simulations but about 5 orders of magnitude faster for difficult modelling tasks.

In resident-nepotistic intolerant hierarchies, the stable hierarchy is based on kinship and rank can be linearly traced, as it is inherited. In contrast, in resident-nepotistic-tolerant hierarchies, stability is maintained via inter-individual coalitions and tolerance by dominant individuals. In this system, power is not ultimate; it is partially mitigated by cooperation among subordinate individuals. Another form of dominance structure is related to age.

An alternative model assumes that PrPSc exists only as fibrils, and that fibril ends bind PrPC and convert it into PrPSc. If this were all, then the quantity of prions would increase linearly, forming ever longer fibrils. But exponential growth of both PrPSc and of the quantity of infectious particles is observed during prion disease. This can be explained by taking into account fibril breakage.

The relationship between phase shift (φ) and time delay (TD) with angular frequency (ω) is given by the simple relation, : \phi = \omega T_D \, It is required that TD is constant at all frequencies over the band of operation. φ must, therefore, be kept linearly proportional to ω. With a suitable choice of parameters, the network phase shift can be made linear up to about 180° phase shift.

In linear broaching, which is the more common process, the broach is run linearly against a surface of the workpiece to effect the cut. Linear broaches are used in a broaching machine, which is also sometimes shortened to broach. In rotary broaching, the broach is rotated and pressed into the workpiece to cut an axisymmetric shape. A rotary broach is used in a lathe or screw machine.

There are n−3 linearly independent accessory parameters, which can be difficult to determine in practise. For a triangle, when n = 3, there are no accessory parameters. The ordinary differential equation is equivalent to the hypergeometric differential equation and f(z) is the Schwarz triangle function, which can be written in terms of hypergeometric functions. For a quadrilateral the accessory parameters depend on one independent variable λ.

A specific type of phasing, flanging is a similar effect, in which the notches are linearly spaced. In a flanger effect, the notches are created by mixing the signal with a delayed version of itself. Flangers tend to sound more pronounced and natural, like the "jet plane whoosh" effect, whereas phasers tend to sound more subtle and otherworldly. For comparison of the two effects, check .

Students must submit a production proposal form for their idea to be reviewed. If approved, students utilize the SVN studio to tape their show or use the equipment to tape out of the studio. They use the Control room for the postproduction of their show or commercial to finish their project. Shows taped in studio are linearly taped to Final Cut Pro to be edited.

The subject had to identify whether the stimulus was normal or mirror-reversed. Response time increased roughly linearly as the orientation of the letter deviated from upright (0 degrees) to inverted (180 degrees), and then decreases again until it reaches 360 degrees. The authors concluded that the subjects mentally rotate the image the shortest distance to upright, and then judge whether it is normal or mirror-reversed.

In contrast, when MIMO is used with DMT, computational complexity grows log-linearly (i.e., n log n) as data rate is increased. Raleigh subsequently founded Clarity Wireless in 1996 and Airgo Networks in 2001 to commercialize the technology. Clarity developed specifications in the Broadband Wireless Internet Forum (BWIF) that led to the IEEE 802.16 (commercialized as WiMAX) and LTE standards, both of which support MIMO.

A second example is linearly polarized light entering a single-mode optical fiber. Suppose the fiber traces out some path in space and the light exits the fiber in the same direction as it entered. Then compare the initial and final polarizations. In semiclassical approximation the fiber functions as a waveguide and the momentum of the light is at all times tangent to the fiber.

MODFETs can be manufactured by epitaxial growth of a strained SiGe layer. In the strained layer, the germanium content increases linearly to around 40-50%. This concentration of germanium allows the formation of a quantum well structure with a high conduction band offset and a high density of very mobile charge carriers. The end result is a FET with ultra-high switching speeds and low noise.

The tensor \alpha describes the linear magnetoelectric effect, which corresponds to a polarization induced linearly by a magnetic field, and vice versa. The higher terms with coefficients \beta and \gamma describe quadratic effects. For instance, the tensor \gamma describes a linear magnetoelectric effect which is, in turn, induced by an electric field. The possible terms appearing in the expansion above are constrained by symmetries of the material.

In electric circuits, the number of state variables is often, though not always, the same as the number of energy storage elements in the circuit such as capacitors and inductors. The state variables defined must be linearly independent, i.e., no state variable can be written as a linear combination of the other state variables or the system will not be able to be solved.

At higher temperatures, the fluid starts to behave more like an ideal gas, with a more linear density/pressure relationship, as can be seen in Figure 2. For carbon dioxide at 400 K, the density increases almost linearly with pressure. Many pressurized gases are actually supercritical fluids. For example, nitrogen has a critical point of 126.2 K (−147 °C) and 3.4 MPa (34 bar).

Most processes in a streamer discharge are two-body processes, where an electron collides with a neutral molecule. An important example is impact ionization, where an electron ionizes a neutral molecule. Therefore, the mean free path is inversely proportional to the gas number density. If the electric field is changed linearly with the gas number density, then electrons gain on average the same energy between collisions.

The dimension of the row space is called the rank of the matrix. This is the same as the maximum number of linearly independent rows that can be chosen from the matrix, or equivalently the number of pivots. For example, the 3 × 3 matrix in the example above has rank two. The rank of a matrix is also equal to the dimension of the column space.

Earthquakes (M6.0+) since 1900 through 2017 Earthquakes of magnitude 8.0 and greater from 1900 to 2018. The apparent 3D volumes of the bubbles are linearly proportional to their respective fatalities.USGS: Magnitude 8 and Greater Earthquakes Since 1900 One of the most devastating earthquakes in recorded history was the 1556 Shaanxi earthquake, which occurred on 23 January 1556 in Shaanxi province, China. More than 830,000 people died.

The Nemeth Braille Code for Mathematics is a Braille code for encoding mathematical and scientific notation linearly using standard six-dot Braille cells for tactile reading by the visually impaired. The code was developed by Abraham Nemeth. The Nemeth Code was first written up in 1952. It was revised in 1956, 1965, and 1972, and beginning in 1992 was integrated into Unified English Braille.

A Wollaston prism A Wollaston prism is an optical device, invented by William Hyde Wollaston, that manipulates polarized light. It separates light into two separate linearly polarized outgoing beams with orthogonal polarization. The two beams will be polarized according to the optical axis of the two right angle prisms. The Wollaston prism consists of two orthogonal prisms of birefringent material—typically a uniaxial material such as calcite.

Linear potential sweep Linear sweep voltammetry is a voltammetric method where the current at a working electrode is measured while the potential between the working electrode and a reference electrode is swept linearly in time. Oxidation or reduction of species is registered as a peak or trough in the current signal at the potential at which the species begins to be oxidized or reduced.

The orientation of the incident light's polarization with respect to the plane of incidence has an important effect on the strength of the reflection. P-polarized light is incident linearly polarized light with polarization direction lying in the plane of incidence. S-polarized light has polarization perpendicular to the plane of incidence. The s in s-polarized comes from the German word senkrecht, meaning perpendicular.

The nest of O. bicornis consists of an array of partitioned cylindrical cells in holes in wood or reed tubes. These bees accept a diverse range of pre-existing cavities as nest sites. The cells are arranged linearly within a narrow tube. If the internal diameter of the tube exceeds 12 mm, then this linear arrangement may be forced into two rows instead of one.

Let γμ denote a set of four 4-dimensional gamma matrices, here called the Dirac matrices. The Dirac matrices satisfy where } is the anticommutator, is a unit matrix, and is the spacetime metric with signature (+,-,-,-). This is the defining condition for a generating set of a Clifford algebra. Further basis elements of the Clifford algebra are given by Only six of the matrices are linearly independent.

Within Vauban, transport is primarily by foot or bicycle. The development is connected to Freiburg city centre by a tramway and is laid out linearly along the tracks, such that all homes are within easy walking distance from a tram stop. As of 2009, around 70% of the households had chosen to live without a private car. The level of car ownership has fallen over time.

In linear algebra, a branch of mathematics, a k-frame is an ordered set of k linearly independent vectors in a space; thus k ≤ n, where n is the dimension of the vector space, and if k = n an n-frame is precisely an ordered basis. If the vectors are orthogonal, or orthonormal, the frame is called an orthogonal frame, or orthonormal frame, respectively.

For a fixed value of the wavelength they found that the energy increased linearly with the temperature. This was in disagreement with the ruling Wien's radiation law, but consistent with an alternative law proposed by Lord Rayleigh. On 7 October 1900 Rubens and his wife were invited to dinner by Max Planck. Rubens told then his host about the new measurements done at a wavelength 51 μm.

Linear dichroism (LD) or diattenuation is the difference between absorption of light polarized parallel and polarized perpendicular to an orientation axis.Bengt Nordén, Alison Rodger and Timothy Dafforn Linear Dichroism and Circular Dichroism. A Textbook on Polarized-Light Spectroscopy. . The Royal Society of Chemistry – London 2010 It is the property of a material whose transmittance depends on the orientation of linearly polarized light incident upon it.

Haani is a 2013 Punjabi romantic drama film directed by Amitoje Mann and stars Harbhajan Mann, Mehreen Kaleka, Sarbjit Cheema, Anuj Sachdeva, Sonia Mann and Rupan Bal. The film consists of two story lines set in the years 1964 and 2013. The two story lines are told non-linearly and are interwoven with use of match cuts and reflect the themes of love and commitment.

In monochronic cultures, time is experienced linearly and as something to be spent, saved, made up, or wasted. Time orders life, and people tend to concentrate on one thing at a time. In polychronic cultures, people tolerate many things happening simultaneously and emphasize involvement with people. In these cultures, people may be highly distractible, focus on several things at once, and change plans often.

In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order terms) of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.

The reductive steps that FASs use are also optional for the PKSs. By potentially omitting them, there is potential for a more complex pattern of functionalization. There are three main types of polyketides: Type I, type II and type III. Type I is very similar to the FAS type I, in that it contains linearly aligned and covalently fused catalytic domains within large multifunctional enzymes.

Most papers in the cardinal model assume that agents have Quasilinear utility functions - their utility is the room value minus the price. But in reality, agents have budget constraints - if the room price is above their budget, the utility drops much faster than linearly. Procaccia, Velez and YuAriel D. Procaccia, Rodrigo A. Velez and Dingli Yu. "Fair Rent Division on a Budget". AAAI 2018.

Publication-quality physics data was accumulated during multi- weeks runs in the spring months of 2016, 2017, and 2018. The detector is based on a solenoidal hermetic detector optimized for tracking of charged particles (electron, pions, kaons, and protons) and detection of neutral particles (primarily photons). Figure 1 shows the detector. GlueX uses the coherent bremsstrahlung technique to produce a linearly polarized photon beam.

The area also highlights a variety of traditional stone/rock wall and palm grove cutting techniques; many homes have kept these walls up and a variety of linearly-cut coconut palm groves can be seen as home line designations. The Hele-On bus number 6 runs from Hilo town to Waiākea-Uka, and the bus number 7 runs from Waiākea-Uka to Hilo town.

Gillis was born on 3 August 1911 in Great Britain. He studied at Trinity College, Cambridge, completing his doctoral thesis on "Some Geometrical Properties of Linearly Measurable Plane Sets of Points" under A.S. Besicovitch in 1935. During World War II he worked in Bletchley Park as a cryptographer. He was a lecturer at the Maths faculty of Queen's University Belfast between 1937 and 1947.

Data sets are placed within the 4-D space by use of a data descriptor file. GrADS interprets station data as well as gridded data, and the grids may be regular, non-linearly spaced, Gaussian, or of variable resolution. Data from different data sets may be graphically overlaid, with correct spatial and time registration. It uses the ctl mechanism to join differing time group data sets.

Since the NMR signal is intrinsically weak, the observed spectrum suffers from a poor signal-to-noise ratio. This can be mitigated by signal averaging, i.e. adding the spectra from repeated measurements. While the NMR signal is the same in each scan and so adds linearly, the random noise adds more slowly – proportional to the square root of the number of spectra (see random walk).

In any event, the span has a basis of linearly independent vectors that do guarantee exactly one expression; and the number of vectors in that basis (its dimension) cannot be larger than m or n, but it can be smaller. This is important because if we have m independent vectors a solution is guaranteed regardless of the right-hand side, and otherwise not guaranteed.

Adding the first two equations together gives , which can be subtracted from the third equation to yield . Any two of these equations have a common solution. The same phenomenon can occur for any number of equations. In general, inconsistencies occur if the left-hand sides of the equations in a system are linearly dependent, and the constant terms do not satisfy the dependence relation.

To determine the correct number of circuits that are required, telecommunications service providers make use of Traffic Tables. An example of a Traffic Table can be viewed in Figure 1. It follows that in order for a telecommunications network to continue to offer a given Grade of Service, the number of circuits provided in a circuit group must increase (non-linearly) if the traffic intensity increases.

Let the circularly polarized light illustrated at the top now represent that light. Such light is going to travel through the quarter-wave plate a second time before reaching the linear polarizer and in the process, its horizontal component is going to be retarded a second time by one quarter of a wavelength. Whether that horizontal component is retarded by one quarter of a wavelength in two distinct steps or retarded a full half wavelength all at once, the orientation of the resulting linearly polarized light will be such that it passes through the linear polarizer. Had it been right-handed, clockwise circularly polarized light approaching the circular polarizer from the left, its horizontal component would have also been retarded, however the resulting linearly polarized light would have been polarized along the absorbing axis of the linear polarizer and it would not have passed.

During keying operations the output of the cipher is additionally fed-back as linear inputs into both the NLFSR and LFSR update functions. In the original Grain Version 0.0 submission of Grain, one bit of the 80-bit NLFSR and four bits of the 80-bit LFSR are supplied to a nonlinear 5-to-1 Boolean function (that is chosen to be balanced, correlation immune of the first order and has algebraic degree 3) and the output is linearly combined with 1 bit of the 80-bit NLFSR and released as output. In the updated Grain Version 1.0 submission of Grain, one bit of the 80-bit NLFSR and four bits of the 80-bit LFSR are supplied to a (slightly revised) nonlinear 5-to-1 Boolean function and the output is linearly combined with 7 bits of the 80-bit NLFSR and released as output.

The apex consists of 3½ cylindrically globose rounded whorls separated by a linearly impressed suture. They rise to a flattened top, consisting of fully 1½ whorls, in the midst of which lies the very minute and immersed tip. These whorls are coloured of a deep, rich, translucent, faintly ruddy brown.;The earliest ones, perhaps from rubbing, are glossy, but further on they are crossed by crowded, curved, sharpish, almost microscopic riblets.

Very low frequency filters are often designed with crystals to overcome this problem. As the frequency gets higher, into the 600 MHz and higher range, the inductors in the tank circuit become too small to be practical. Since the electrical reactance of an inductor of a certain inductance increases linearly with respect to frequency, at higher frequencies, to achieve the same reactance, a prohibitively low inductance may be required.

Thus this shows that Lmax spans V. Hence Lmax is linearly independent and spans V. It is thus a basis of V, and this proves that every vector space has a basis. This proof relies on Zorn's lemma, which is equivalent to the axiom of choice. Conversely, it has been proved that if every vector space has a basis, then the axiom of choice is true.Blass, Andreas (1984).

Onyx 3000 refers to Origin 3000 systems that are sold with graphics hardware as standard. The graphics hardware is contained within G-bricks hosting InfiniteReality3 or InfiniteReality4 graphics pipes, or V-bricks hosting InfinitePerformance (VPro) graphics. The number of G-bricks or V-bricks a system supports scales linearly with the number of C-bricks present. Systems must use either G-bricks or V-bricks, as these options cannot be mixed.

Beyond a certain distance, the energy of the flux tube binding two quarks increases linearly. At a large enough distance, it becomes energetically more favorable to pull a quark-antiquark pair out of the vacuum rather than increase the length of the flux tube. Gluons also share this property of being confined within hadrons. One consequence is that gluons are not directly involved in the nuclear forces between hadrons.

Old Vatia is a prehistoric village site on the north side of Tutuila, the largest island of American Samoa. The site is located on the Faiga ridge, above the modern village of Vatia in the National Park of American Samoa. It is stretched linearly along the ridge, with terraced areas that have features such as stone house foundations and pavement. The site, believed to have been occupied c.

The system will begin to have a structure of thermal conductivity: the temperature, and the density and pressure with it, will vary linearly between the bottom and top plane. A uniform linear gradient of temperature will be established. (This system may be modelled by statistical mechanics). Once conduction is established, the microscopic random movement spontaneously becomes ordered on a macroscopic level, forming Benard convection cells, with a characteristic correlation length.

Spiral antennas transmit circularly polarized radio waves, and will receive linearly polarized waves in any orientation, but will drastically attenuate circularly polarized signals received with the opposite-rotation. A spiral antenna will reject circularly polarized waves of one type, while receiving perfectly well waves having the other polarization. One application of spiral antennas is wide-band communications. Another application of spiral antennas is monitoring of the frequency spectrum.

Following Gelman and Hill, the assumptions of the ANOVA, and more generally the general linear model, are, in decreasing order of importance: # the data points are relevant with respect to the scientific question under investigation; # the mean of the response variable is influenced additively (if not interaction term) and linearly by the factors; # the errors are independent; # the errors have the same variance; # the errors are normally distributed.

Maximum Variance Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefinite programming to perform non-linear dimensionality reduction of high-dimensional vectorial input data. It is motivated by the observation that kernel Principal Component Analysis (kPCA) does not reduce the data dimensionality, as it leverages the Kernel trick to non-linearly map the original data into an inner-product space.

This F-statistic follows the F-distribution with degrees of freedom d_1=p-1 and d_2=N-p under the null hypothesis. If the variances are indeed heterogeneous, techniques that allow for this (such as the Welch one-way ANOVA) may be used instead of the usual ANOVA. Good [1994,2005], noting that the deviations are linearly dependent, has modified the test so as to drop the redundant deviations.

In algebra, a linear topology on a left A-module M is a topology on M that is invariant under translations and admits a fundamental system of neighborhood of 0 that consists of submodules of M. If there is such a topology, M is said to be linearly topologized. If A is given a discrete topology, then M becomes a topological A-module with respect to a linear topology.

Zift's plot unfolds non-linearly: although the main story after Moth's release from prison is told chronologically, the events leading to his imprisonment are revealed by means of numerous relatively long and not necessarily chronological flashbacks. The story is presented chronologically here. Moth is an ordinary guy from Sofia, the capital of Bulgaria. At school, he falls in love with the beautiful Ada (Tanya Ilieva), later nicknamed "Mantis".

PVLAS uses a high-finesse Fabry-Perot optical cavity. The first setup, used until 2005, sent a linearly polarized laser beam through vacuum with 5T magnetic field from a superconducting magnet to an ellipsometer. After upgrades to avoid fringe fields, several runs were done at 2.3T and 5T, excluding a prior claim of axion detection. It was determined that an optimized optical setup was needed for discovery potential.

Compassion fade contradicts the traditional model for valuing life that assumes all lives should be valued equally. Empirical data on charitable giving found that donations are not linearly related to the number of victims but rather decrease as the number of victims increase. This concept termed "psychophysical" or “psychic numbing”. A psychophysical numbing function depicts the number of lives at risk as a function of the value of life saving.

The level of RANKL expression does not linearly correlate to the effect of this ligand. High protein expression of RANKL is commonly detected in the lungs, thymus and lymph nodes. Low protein expression is found in bone marrow, the stomach, peripheral blood, the spleen, the placenta, leukocytes, the heart, the thyroid, and skeletal muscle. While bone marrow expresses low levels of RANKL, RANKL plays a critical role for adequate bone metabolism.

For each event, a first place gives 30 points, a 2nd place 26 pts, a 3rd place 24 pts, a 4th place 22 pts, then linearly decreasing by one point down to the 25th place. Equal placings (ties) give an equal number of points. The sum of all WC points of the season, minus the two worst results in each of the two disciplines, gives the biathlete's total WC score.

For a given set of n beads, all distinct, the number of distinct necklaces made from these beads, counting rotated necklaces as the same, is = (n − 1)!. This is because the beads can be linearly ordered in n! ways, and the n circular shifts of such an ordering all give the same necklace. Similarly, the number of distinct bracelets, counting rotated and reflected bracelets as the same, is , for n ≥ 3\.

The folds of garments were depicted less linearly, thus appearing more plastic. The manner of presenting scenes also changed substantially. Firstly, the paintings ceased to focus on the moment of a particular event, but rather, with dramatic tension, showed the situation immediately before the action, thus implying and contextualising the event proper. Also, some of the other new achievements of Athenian democracy began to show an influence on vase painting.

The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field. The field requirement means that the Berlekamp–Massey algorithm requires all non-zero elements to have a multiplicative inverse. Reeds and Sloane offer an extension to handle a ring.

Most of the proposed algorithms have asymptotic output size O(n); i.e., the size of the resulting signature increases linearly with the size of input (number of public keys). That means that such schemes are impracticable for real use cases with sufficiently large n (for example, an e-voting with millions of participants). But for some application with relatively small median input size such estimate may be acceptable.

Stronger gradients allow for faster imaging, or for higher resolution; similarly, gradient systems capable of faster switching can also permit faster scanning. However, gradient performance is limited by safety concerns over nerve stimulation. Some important characteristics of gradient amplifiers and gradient coils are slew rate and gradient strength. As mentioned earlier, a gradient coil will create an additional, linearly varying magnetic field that adds or subtracts from the main magnetic field.

CRS normally use lasers with narrow bandwidth lasers, whose bandwidth < 1 nm, to maintain good spectral resolution ~ 15 cm−1. Lasers with sub 1 nm bandwidth are picosecond lasers. In spectral-focusing CRS, femtosecond pump and Stokes lasers are equally linearly chirped into picosecond lasers. The effective bandwidth become smaller and therefore, high spectral resolution can be achieved this way with femtosecond lasers which normally have a broad bandwidth.

Projective texture mapping is a method of texture mapping that allows a textured image to be projected onto a scene as if by a slide projector. Projective texture mapping is useful in a variety of lighting techniques and it is the starting point for shadow mapping. Projective texture mapping is essentially a special matrix transformation which is performed per-vertex and then linearly interpolated as standard texture mapping.

Recently, researchers have been using nanotechnology to link molecules together to increase the nonlinear susceptibility. Since the connected molecules have more electrons, collective motions of these electrons yield enhanced nonlinear response. Since calculations show that the Kuzyk limit increases faster than linearly, it is best to link together as many molecules as possible. Researchers have made a material of interconnected fullerenes that appear to breach the Kuzyk quantum gap.

A sequence profile represents a multiple alignment of homologous sequences and describes what amino acids are likely to occur at each position in related sequences. With this method substitution matrices are unnecessary. In addition, there is no need for transition probabilities as a result of the fact that context information is encoded within the context profiles. This makes computation simpler and allows for runtime to be scaled linearly instead of quadratically.

For each event, a first place gives 30 points, a 2nd place 26 pts, a 3rd place 24 pts, a 4th place 22 pts, then linearly decreasing by one point down to the 25th place. Equal placings (ties) give an equal number of points. The sum of all WC points of the season, minus the two worst results in each of the two disciplines, gives the biathlete's total WC score.

Flashbacks are often confused with true narratives which are not linear, but the concept is fundamentally linear. An example would be Citizen Kane by Orson Welles. Although some films appear to open (very briefly) with the ending, flashback movies almost immediately jump back to the very beginning of the story to proceed linearly from there, and usually proceed past the supposed "ending" shown at the beginning of the movie.

The CP- ENDOR technique makes use of circularly polarized rf fields. Two linearly polarized fields are generated by rf currents in two wires which are oriented parallel to the magnetic field. The wires are then connected into half loops which then cross at a 90 degree angle. This technique was developed by Schweiger and Gunthard so that the density of ENDOR lines in a paramagnetic spectrum could be simplified.

There is no other known example of Olmec drawing, much less writing, on a serpentine slab. #All other Mesoamerican writing systems are written either vertically or linearly. The glyphs on the block are arranged in neither format but instead "randomly bunch". #As pointed out by the original authors, some of the glyphs do appear on other Olmec artifacts, but have never been heretofore identified as writing, only as decorative motifs.

Since the total flight-time difference between "fast" and "slow" lightsignals would be expected to scale linearly with distance in simple emission theory, and the study would (statistically) have included stars with a reasonable spread of distances and orbital speeds and orientations, de Sitter concluded that the effect should have been seen if the model was correct, and its absence meant that the emission theory was almost certainly wrong.

Lafevre (1746–1818) was a descendant of the original New Paltz Huguenots. He was granted 500 acres (2 km²) of the Huguenot's original patent and built the house there in 1772. In 1798 he added a third room, following in the Ulster County tradition of expanding the house linearly rather than on the back. His son Matthew (1774–1851) altered the interior and may have added the rear addition.

The second is to plot the density of individuals in habitat A vs. the density of individuals in habitat B when the fitness of all individuals is equal. The line in this second graph is an isodar line. Ideal free isodars predict that a species density in habitat A will increase linearly with its density in habitat B so that each individual in the species has the same fitness.

Inboard the wing chord reduced linearly by about 30% to the root. The outer wing had 3° of dihedral, though the narrowing centre section curved downwards strongly to the roots. The Delanne 20 was an all wood aircraft and each wing was built around two spruce and plywood box spars. The trailing edges carried ailerons and camber changing flaps, coupled to slats on the corresponding sections of the leading edges.

Vackář analyzes the circuit and explains how to get an approximately constant amplitude response. The circuit's transconductance increases linearly with frequency, but that increase is offset by the tuning inductor's increasing . This circuit has become known as the Vackář VFO. Vackář referred to the circuit as "our circuit" and states that O. Landini independently discovered the circuit and published it (without an analysis) in Radio Rivista in 1948.

If the symmetry is specially dx2-y2 then the penetration depth should vary linearly with T at low temperatures. This technique is increasingly being used to study superconductors and is limited in application largely by the quality of available single crystals. Photoemission spectroscopy also could provide information on the HTS symmetry. By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons.

In some situations, the equations can be simplified by assuming a field that is nearly independent of position. For instance, in a region close to the surface of the Earth, the gravitational acceleration, g, can be considered constant. In that case, the difference in potential energy from one height to another is, to a good approximation, linearly related to the difference in height: :\Delta U \approx mg \Delta h.

Earthquakes of magnitude 8.0 and greater from 1900 to 2018. The apparent 3D volumes of the bubbles are linearly proportional to their respective fatalities. This list of 20th-century earthquakes is a global list of notable earthquakes that occurred in the 20th century. After 1900 most earthquakes have some degree of instrumental records and this means that the locations and magnitudes are more reliable than for earlier events.

Instrument landing system ground stations provide radio frequency signals that vary linearly in the depth of modulation from the centre or course line at a rate of 0.145% per meter . The two individual audio modulation frequencies and their associated sidebands are 150Hz and 90Hz. The DDM for a localizer at the outer extremity of the course sector is 15.5% or an electric current equivalent of 150 microamperes full scale deflection.

In mathematics, the cylindrical harmonics are a set of linearly independent functions that are solutions to Laplace's differential equation, abla^2 V = 0, expressed in cylindrical coordinates, ρ (radial coordinate), φ (polar angle), and z (height). Each function Vn(k) is the product of three terms, each depending on one coordinate alone. The ρ-dependent term is given by Bessel functions (which occasionally are also called cylindrical harmonics).

The number of steps of this approach grows linearly with b, or exponentially in the number of digits. Another inefficient approach is to find the prime factors of one or both numbers. As noted above, the GCD equals the product of the prime factors shared by the two numbers a and b. Present methods for prime factorization are also inefficient; many modern cryptography systems even rely on that inefficiency.

Circular plot of the bipartite mouse X chromosome, generated by the Epigenome Browser. Image from The different 3C-style experiments produce data with very different structures and statistical properties. As such, specific analysis packages exist for each experiment type. Hi-C data is often used to analyze genome-wide chromatin organization, such as topologically associating domains (TADs), linearly contiguous regions of the genome that are associated in 3-D space.

Wang, and P. Hänggi that allows for system-bath interaction to play a role in equilibrium differing from the KMS state. In 1981, Amir Caldeira and Anthony J. Leggett proposed a simplifying assumption in which the bath is decomposed to normal modes represented as harmonic oscillators linearly coupled to the system.A. Caldeira and A. J. Leggett, Influence of dissipation on quantum tunneling in macroscopic systems, Physical Review Letters, vol. 46, p.

The resources required for a brute-force attack grow exponentially with increasing key size, not linearly. Although U.S. export regulations historically restricted key lengths to 56-bit symmetric keys (e.g. Data Encryption Standard), these restrictions are no longer in place, so modern symmetric algorithms typically use computationally stronger 128- to 256-bit keys. There is a physical argument that a 128-bit symmetric key is computationally secure against brute-force attack.

Maypole Dancers in East City Park. Picnic table with squirrel in East City Park There are seventeen neighborhood parks located throughout the town offering a wide variety of venues for outdoor activities. These parks fall under the jurisdiction of the Moscow Parks and Recreation Department. The Moscow Pathways Commission (formerly Paradise Path Task Force) is a citizen committee seeking to develop a system of linearly connected parks throughout the area.

For modern cameras, a circular polarizer (CPL) is typically used; this comprises firstly a linear polarizer which performs the artistic function just described, followed by a quarter-wave plate which further transforms the now-linearly polarized light into circularly-polarized light before entering the camera. This additional step avoids problems with autofocus and light-metering sensors within some cameras, which otherwise may not function reliably with a simple linear polarizer.

Didactic art became more prevalent, as well as moralising subjects – including many depictions of devils in mural art. On the whole, Late Gothic paintings are more narrative and less decorative than earlier Gothic murals. Humans are depicted more linearly, with sharper contours and more solid volumes, and the ornamentation is more varied, detailed and richer. The entire church, including both the walls and the vaults, was typically decorated.

The radiation pattern can be distorted from an isotropic dipole pattern into an extremely forward-pointing cone of radiation. Synchrotron radiation is the brightest artificial source of X-rays. The planar acceleration geometry appears to make the radiation linearly polarized when observed in the orbital plane, and circularly polarized when observed at a small angle to that plane. Amplitude and frequency are however focused to the polar ecliptic.

AUC is a method by which for a given peptide spectrum in an LC-MS run, the area under the spectral peak is calculated. AUC peak measurements are linearly proportional to the concentration of protein in a given analyte mixture. Quantification is achieved with through ion counts, the measurement of the amount of an ion at a specific retention time. Discretion is required for the standardization of the raw data.

For a linearly-polarized antenna, this is the plane containing the electric field vector (sometimes called the E aperture) and the direction of maximum radiation. The electric field or "E" plane determines the polarization or orientation of the radio wave. For a vertically polarized antenna, the E-plane usually coincides with the vertical/elevation plane. For a horizontally polarized antenna, the E-Plane usually coincides with the horizontal/azimuth plane.

For a Type II functional response curve, the rate of prey capture negatively accelerates as it increases with food density. This is because it assumes that the predator is limited by its capacity to process food. In other words, as the food density increases, handling time increases. At the beginning of the curve, rate of prey capture increases nearly linearly with prey density and there is almost no handling time.

However, at low prey densities (the bottom of the curve) the rate of prey capture increases faster than linearly. This means that as the predator feeds and the prey type with the higher E/h becomes less abundant, the predator will start to switch its preference to the prey type with the lower E/h, because that type will be relatively more abundant. This phenomenon is known as prey switching.

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together. Electrodynamics is the physics of electromagnetic radiation, and electromagnetism is the physical phenomenon associated with the theory of electrodynamics.

Dark pulses are characterized by being formed from a localized reduction of intensity compared to a more intense continuous wave background. Scalar dark solitons (linearly polarized dark solitons) can be formed in all normal dispersion fiber lasers mode-locked by the nonlinear polarization rotation method and can be rather stable. Vector dark solitons and references therein. are much less stable due to the cross-interaction between the two polarization components.

In mathematics, the Chevalley–Iwahori–Nagata theorem states that if a linear algebraic group G is acting linearly on a finite-dimensional vector space V, then the map from V/G to the spectrum of the ring of invariant polynomials is an isomorphism if this ring is finitely generated and all orbits of G on V are closed . It is named after Claude Chevalley, Nagayoshi Iwahori, and Masayoshi Nagata.

Both circular and linear polarization of sunlight has been measured. Circular polarization is mainly due to transmission and absorption effects in strongly magnetic regions of the Sun's surface. Another mechanism that gives rise to circular polarization is the so-called "alignment-to-orientation mechanism". Continuum light is linearly polarized at different locations across the face of the Sun (limb polarization) though taken as a whole, this polarization cancels.

Similarly, if IIN,2 > IIN,1, we get IOUT,1 = 0 and IOUT,2 = IBIAS. Simulation of the two-input CMOS winner- take-all circuit A SPICE-based DC simulation of the CMOS winner-take-all circuit in the two-input case is shown on the right. As shown in the top subplot, the input IIN,1 was fixed at 6nA, while IIN,2 was linearly increased from 0 to 10nA.

SWI is uniquely suited to take advantage of higher field systems, as the contrast in the phase image is linearly proportional to echo time (TE) and field strength. Higher fields thus allow shorter echo times without a loss of contrast which can reduce scan time and motion related artifacts. The high signal-to-noise available at higher fields also increases scan quality and allows for higher resolution scans..

Mitchell, Don P., "Generating Antialiased Images at Low Sampling Densities." Computer Graphics, volume 21, number 4, July 1987. Retinal cells are arranged in a blue-noise- like pattern which yields good visual resolution. Cherenkov radiation is a naturally occurring example of almost perfect blue noise, with the power density growing linearly with frequency over spectrum regions where the permeability of index of refraction of the medium are approximately constant.

Models for time series data can have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. These three classes depend linearly on previous data points. Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models.

Sacred writings were also used as dedicatory devices in ritual structures. The art of writing was controlled by the elite in Mesoamerica, and the skill passed down linearly. An example of this can be seen in Classic Maya Chichen Itza, in which elite women created architectural texts dedicating structures to their female ancestors and patron deities.McAnany, Patricia (2008) Shaping social difference: Political and ritual economy of Classic Maya royal courts.

180–181 Tapers can provide transitions between lines in different media, especially different forms of planar media. Tapers commonly change shape linearly, but a variety of other profiles may be used. The profile that achieves a specified match in the shortest length is known as a Klopfenstein taper and is based on the Chebychev filter design. Tapers can be used to match a transmission line to an antenna.

The hyperelastic material is a special case of a Cauchy elastic material. For many materials, linear elastic models do not accurately describe the observed material behaviour. The most common example of this kind of material is rubber, whose stress-strain relationship can be defined as non-linearly elastic, isotropic, incompressible and generally independent of strain rate. Hyperelasticity provides a means of modeling the stress–strain behavior of such materials.

In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology of signal processing, a frame provides a redundant, stable way of representing a signal. Frames are used in error detection and correction and the design and analysis of filter banks and more generally in applied mathematics, computer science, and engineering.

The q and u input. The angle of polarization can be unwrapped into the Q and U Stokes parameters. Q and U are defined as the linearly polarized intensities along the position angles 0° and 45° respectively; -Q and -U are along the position angles 90° and −45°. If the sun is located on the horizon due west, the degree of polarization is then along the North-Zenith-South plane.

The numbers are binned based on the first significant digit, and within each stack binned again based on the second significant digit. On the other hand, Q-Q plots compare two probability distributions by graphing quantiles against each other. This allows the viewer to see if the plot values are similar and if the two are linearly related. SPLOM is a technique that represents the relationships among multiple variables.

It has been found that the F number linearly correlates with the log k' value (logarithm of the retention factor) in aqueous reversed- phase liquid chromatography. This relationship can be used to understand the significance of different aspects of molecular architecture on their separation using different stationary phases. This size analysis is complementary to the length-to-breadth (L/B) ratio, which classifies molecules according to their "rodlike" or "squarelike" shape.

Simple polarimeters have been used since this time to measure the concentrations of simple sugars, such as glucose, in solution. In fact one name for D-glucose (the biological isomer), is dextrose, referring to the fact that it causes linearly polarized light to rotate to the right or dexter side. In a similar manner, levulose, more commonly known as fructose, causes the plane of polarization to rotate to the left.

From the inception of show, back in 2007, Pakistan Idol faces many problems and immense negative response by audience which leads to stop the production of franchise, it then took six years to handle all the problems and show finally went on air in late 2013. Owing to the production with linearly, shows became icon of the year, all the perceptions went wrong and series garnered millions views.

The Wilkinson ADC was designed by D. H. Wilkinson in 1950. The Wilkinson ADC is based on the comparison of an input voltage with that produced by a charging capacitor. The capacitor is allowed to charge until its voltage is equal to the amplitude of the input pulse (a comparator determines when this condition has been reached). Then, the capacitor is allowed to discharge linearly, which produces a ramp voltage.

Bicalutamide is extensively and well-absorbed following oral administration, and its absorption is not affected by food. The absolute bioavailability of bicalutamide in humans is unknown due to its very low water solubility and hence lack of an assessable intravenous formulation. However, the absolute bioavailability of bicalutamide has been found to be high in animals at low doses (72% in rats at 1 mg/kg; 100% in dogs at 0.1 mg/kg), but diminishes with increasing doses such that the bioavailability of bicalutamide is low at high doses (10% in rats at 250 mg/kg; 31% in dogs at 100 mg/kg). In accordance, absorption of (R)-bicalutamide in humans is slow and extensive but saturable, with steady-state levels increasing linearly at a dosage of up to 150 mg/day and non-linearly at higher dosages. At higher dosages of 100 to 200 mg/day, absorption of bicalutamide is approximately linear, with a small but increasing departure from linearity above 150 mg/day.

A blade representing of one of this class of object may be found as the outer product of linearly independent vectors representing points on the object. In the base space, this linear independence manifests as each point lying outside the object defined by the other points. So, for example, a fourth point lying on the generalized circle defined by three distinct points cannot be used as a fourth point to define a sphere.

Forced convection is type of heat transport in which fluid motion is generated by an external source like a (pump, fan, suction device, etc.). Heat transfer through porus media is very effective and efficiently. Porous medium is defined as a material volume consisting of solid matrix with an interconnected void. Flow in porous media have revealed the Darcy law< which relates linearly the flow velocity to the pressure gradient across the porous medium.

Oxford University Press. . p. 81. Faraday also discovered that the plane of polarization of linearly polarized light can be rotated by the application of an external magnetic field aligned with the direction in which the light is moving. This is now termed the Faraday effect. In Sept 1845 he wrote in his notebook, "I have at last succeeded in illuminating a magnetic curve or line of force and in magnetising a ray of light".

Fresnel, 1866, pp.737–9. Cf. Whewell, 1857, ; Jenkins & White, 1976, . Thus, although we now think of the Fresnel rhomb primarily as a device for converting between linear and circular polarization, it was not until the memoir of December 1822 that Fresnel himself could describe it in those terms. In the same memoir, Fresnel explained optical rotation by noting that linearly-polarized light could be resolved into two circularly-polarized components rotating in opposite directions.

This allowed easier conversion to many other formats, including LilyPond.NWCTXT2Ly converter and manual Freygish scale A feature of the user interface is that notation is displayed during editing. Each staff proceeds linearly from left to right, without being wrapped to the screen, like the galley view in other software. Staff systems are visually broken to fit margins during page layout, allowing many possibilities at "print time", when parts and scores can be laid out.

When an attacker makes N forgery attempts the probability of getting one or more tags right increases linearly to less than N/260 or N/2120. In an applied implementation of VMAC, using AES to produce keys and pads, these forgery probabilities increase by a small amount related to the security of AES. As long as AES is secure, this small additive term is insignificant for any practical attack. See specification for more details.

As the complexity of GCD computations and divisions increase more than linearly with the degree, it follows that the total running time of the "repeat" loop is less than the running time of the first line of the algorithm, and that the total running time of Yun's algorithm is upper bounded by twice the time needed to compute the GCD of f and f' and the quotient of f and f' by their GCD.

The game progresses linearly from one story event to the next, usually presented as a cutscene, though there are numerous side quests available that provide benefits to the characters. Players may also choose the order in which they tackle some areas. Most of the gameplay occurs on interconnected field maps where battles take place. Combat in Kingdom Hearts occurs in real time and involves pressing buttons to initiate attacks by the on-screen character.

Single layer perceptrons are only capable of learning linearly separable patterns. For a classification task with some step activation function a single node will have a single line dividing the data points forming the patterns. More nodes can create more dividing lines, but those lines must somehow be combined to form more complex classifications. A second layer of perceptrons, or even linear nodes, are sufficient to solve a lot of otherwise non-separable problems.

Above the equivalence point, A_{T} and A are again linearly related. In vivo, the synthesis of A and B as well as the degradation of all three components complicates generation of ultrasensitivity. If the synthesis rates of A and B are equal this system still exhibits ultrasensitivity at the equivalence point. One example of a buffering mechanism is protein sequestration, which is a common mechanism found in signalling and regulatory networks.

That is, it is the only matrix such that: # When multiplied by itself, the result is itself # All of its rows and columns are linearly independent. The principal square root of an identity matrix is itself, and this is its only positive-definite square root. However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots.Mitchell, Douglas W. "Using Pythagorean triples to generate square roots of I2".

In other cases, the vibration is applied after the horn came in contact with the part and some pressure has been created. The force is then continues to increase linearly until some predefined value. The power rises at the same time as ultrasonic energy is being applied in order to accommodate the stack vibration. After some period of time a steady-state process, which indicate sufficient melting at the interface, is reached.

There is also a strong five exponentials conjecture formulated by Michel WaldschmidtWaldschmidt, (1988). It would imply both, the strong six exponentials theorem and the sharp five exponentials conjecture. This conjecture claims that if x1, x2 and y1, y2 are two pairs of complex numbers, with each pair being linearly independent over the algebraic numbers, then at least one of the following five numbers is not in L∗: :x_1y_1,\,x_1y_2,\,x_2y_1,\,x_2y_2,\,x_1/x_2.

By analogy with an Archimedean linearly ordered group, one can define an Archimedean cyclically ordered group as a group that does not contain any pair of elements such that for every positive integer . Since only positive are considered, this is a stronger condition than its linear counterpart. For example, no longer qualifies, since one has for every . As a corollary to Świerczkowski's proof, every Archimedean cyclically ordered group is a subgroup of itself.

FPN is commonly suppressed by flat-field correction (FFC) that uses DSNU and PRNU to linearly interpolate and reduce the local photo response (non-uniform PRNL) to the array average. Hence, two exposures with an equal illumination across the array are necessary (one without light and one close to saturation) to obtain the values. Note that this correction usually is very sensitive to modifications of the system parameters (i.e., exposure time, temperature).

Depiction of the simple model where the circle map arises 'naturally'. The red line is y(t) and is reset every time it reaches the sinusoidal black line. Another way to view the circle map is as follows. Consider a function y(t) that decreases linearly with slope a. Once it reaches zero, its value is reset to a certain oscillating value, described by a function z(t) = c + b \sin(2 \pi t).

As a linearly independent set of enough cycles, it necessarily forms a cycle basis., pp. 105–106. It is always a weakly fundamental cycle basis, and is fundamental if and only if the embedding of the graph is outerplanar. For graphs properly embedded onto other surfaces so that all faces of the embedding are topological disks, it is not in general true that there exists a cycle basis using only face cycles.

Prior to 1980, the species designation was uncertain. It was sometimes referred to as either Halophila decipiens or H. baillonis Ascherson, despite most closely resembling H. ovalis. > Morphologically, Johnson's seagrass is recognized by the presence of pairs > of linearly shaped foliage leaves, each with a petiole formed on the node of > a horizontally creeping rhizome. The rhizome is located at or just below the > sediment surface and is anchored to unconsolidated substrate by unbranched > roots.

Brushed DC motors develop a maximum torque when stationary, linearly decreasing as velocity increases. Some limitations of brushed motors can be overcome by brushless motors; they include higher efficiency and lower susceptibility to mechanical wear. These benefits come at the cost of potentially less rugged, more complex, and more expensive control electronics. A typical brushless motor has permanent magnets that rotate around a fixed armature, eliminating problems associated with connecting current to the moving armature.

The effect of a passing polarized gravitational plane wave on the relative positions of a cloud of (initially static) test particles will be qualitatively very similar. We might mention here that in general, the motion of test particles in pp-wave spacetimes can exhibit chaos. The fact that Einstein's field equation is nonlinear is well known. This implies that if you have two exact solutions, there is almost never any way to linearly superimpose them.

As entanglement density increases, the optimum particle size decreases linearly, ranging between 0.1 and 3 micrometers. The effect of particle size on toughening is dependent on the type of test performed. This can be explained because for different test conditions, the failure mechanism changes. For impact strength testing on PMMA where failure occurs by shear-yielding, the optimum size of filler PBA-core PMMA-shell particle was shown in one case to be 250 nm.

To convert this into direct current (DC), the AC must be rectified, which is typically done with a diode. The resulting DC current can then be used to power an external load. The resonant frequency of antennas (frequency which results in lowest impedance and thus highest efficiency) scales linearly with the physical dimensions of the antenna according to simple microwave antenna theory. The wavelengths in the solar spectrum range from approximately 0.3-2.0 μm.

The DLX architecture does not force single clock cycle execution, and is therefore immune to this problem. In the DLX design a more modern approach to handling long instructions was used: data-forwarding and instruction reordering. In this case the longer instructions are "stalled" in their functional units, and then re-inserted into the instruction stream when they can complete. Externally this design behaviour makes it appear as if execution had occurred linearly.

The list ranking problem was posed by , who solved it with a parallel algorithm using logarithmic time and O(n log n) total steps (that is, O(n) processors). Over a sequence of many subsequent papers, this was eventually improved to linearly many steps (O(n/log n) processors), on the most restrictive model of synchronous shared-memory parallel computation, the exclusive read exclusive write PRAM (; ;). This number of steps matches the sequential algorithm.

In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non- standard model is one that has additional elements outside this initial segment.

The main data structures using the various facilities of the program are in doubly linked list, which facilitates their movement. The maximum number of entries is limited only by available memory. Search operations in most of the facilities are carried out linearly, a fact that causes a mild but almost imperceptible impact. Because of the speed with which tends to increase the traffic monitor IPs, it use a hash table to perform searches more efficiently.

A miniature electro- mechanical goniometer stage. This type of stage is used primarily in the field of lasers and optics. A positioning goniometer or goniometric stage is a device that rotates an object precisely about a fixed axis in space. It is similar to a linear stage— however, rather than move linearly relative to its base, the stage platform rotates partially about a fixed axis above the mounting surface of the platform.

The magnitude of the current is controlled by how much of the target gas is oxidized at the working electrode. Sensors are usually designed so that the gas supply is limited by diffusion and thus the output from the sensor is linearly proportional to the gas concentration. This linear output is one of the advantages of electrochemical sensors over other sensor technologies, (e.g. infrared), whose output must be linearized before they can be used.

The most sensitive detector accomplished the task possessing a sensitivity measurement of about one part in () provided by the LIGO and VIRGO observatories. A space based observatory, the Laser Interferometer Space Antenna, is currently under development by ESA. Linearly polarised gravitational wave Gravitational waves can penetrate regions of space that electromagnetic waves cannot. They allow the observation of the merger of black holes and possibly other exotic objects in the distant Universe.

Brown, Leslie and Amadon, Dean (1986) Eagles, Hawks and Falcons of the World. The Wellfleet Press. . Although otherwise outwardly similar, the species displays reverse sexual dimorphism as do most birds of prey, in which males are usually smaller than the females. For the eastern imperial eagle, females are up to 10% larger linearly and 40% heavier in body mass in some cases.Katzner, T. E., Jackson, D. S., Ivy, J., Bragin, E. A., & DeWoody, A. (2014).

The slightly curved, near vertical, lines on the main part of the map are the (constant rotational) corrected speed lines. They are a measure of rotor blade tip Mach number. Note on the illustration that the speed lines are not distributed linearly with flow. This is because this particular compressor is fitted with variable stators, which open progressively as speed increases, causing an exaggerated increase in flow in the medium to high speed region.

Earthquakes of magnitude 8.0 and greater from 1900 to 2018. The apparent 3D volumes of the bubbles are linearly proportional to their respective fatalities. Animated Map of all world earthquakes from 2001-2015 The following is a summary of significant earthquakes during the 21st century. In terms of fatalities, the 2010 Haiti earthquake was the most destructive event, followed by the 2004 Indian Ocean earthquake, 2005 Pakistan earthquake and 2008 Sichuan earthquake.

Light composite aircraft Composite materials are used increasingly in vehicles and aircraft structures, and to some extent in other structures. They are increasingly used in bridges, especially for conservation of old structures such as Coalport cast iron bridge built in 1818. Composites are often anisotropic (they have different material properties in different directions) as they can be laminar materials. They most often behave non- linearly and will fail in a brittle manner when overloaded.

Mehrstellen discretization, which is shorter ranged than the commonly used than central difference discretization, is used to represent the kinetic energy operator. This decreases the cost of processor-to-processor communication, which is advantageous for the use on massively parallel supercomputers. Domain decomposition is used to assign different regions of space to individual CPU cores or nodes. RMG scales nearly linearly up to 100k processor cores and 20k GPUs on Cray XK6.

The eyes have a tendency to "refixate" on a target to refresh the memory of its shape, or to update for changes in its shape or geometry in drawing tasks that involve the relating of visual input and hand movement to produce a copy of what was perceived. In high accuracy tasks, when acting on greater amounts of visual stimuli, the time it takes to plan and execute movement increases linearly, per Fitts's law.

We refer to these two trajectories as the short trajectory (which are emitted first), and the long trajectory. Some interesting limits on the HHG process which are explained by this model show that HHG will only occur if the driving laser field is linearly polarised. Ellipticity on the laser beam causes the returning electron to miss the parent nucleus. Quantum mechanically, the overlap of the returning electron wavepacket with the nuclear wavepacket is reduced.

The main strength of Chinese Whispers lies in its time linear property. Because the processing time increases linearly with the number of nodes, the algorithm is capable of identifying communities in a network very fast. For this reason Chinese Whispers is a good tool to analyze community structures in graph with a very high number of nodes. The effectiveness of the method increases further if the network has the small world property.

After oral administration of 50 mg of buformin to volunteers, almost 90% of the applied quantity was recovered in the urine; the rate constant of elimination was found to be 0.38 per hr. Buformin is a strong base (pKa = 11.3) and not absorbed in the stomach. After intravenous injection of about 1 mg/kg buformin-14-C, the initial serum concentration is 0.2-0.4 µg/ml. Serum level and urinary elimination rate are linearly correlated.

Since some wavelengths of fluorescence are beyond the range of the human eye, charged- coupled devices (CCD) are used to accurately detect light and image the emission. This typically occurs in the 300 – 800 nm range. One of the advantages of fluorescent signaling is that intensity of emitted light behaves rather linearly in regards to the quantity of fluorescent molecules provided. This is obviously contingent that the absorbed light intensity and wavelength are constant.

Detecting pressure changes inside an artery from the outside is difficult, whereas volume and flow changes of the artery can well be determined by using e.g. light, echography, impedance, etc. But unfortunately these volume changes are not linearly correlated with the arterial pressure– especially when measured in the periphery, where the access to the arteries is easy. Thus, noninvasive devices have to find a way to transform the peripheral volume signal to arterial pressure.

They will use this to gain entry into the substrate. After the structure of the nest has been formed, females linearly layer the walls with pollen and nectar and then put an egg into the food mass. Finally, the nest is sealed off. The location of nests may vary from dead branches on the ground or cut wood that was hung above the ground; however, they are normally found in partially shaded areas.

Initially, for a given radius and pressure, stiffness of the material increases linearly. At a certain point, the stiffness of the arterial wall starts to decrease with increasing load. At higher strain values, the area under the curve increases, thus increasing the impact on the material that would promote crack propagation. The differences in the mechanical properties of the aneurysmal blood vessels and the healthy blood vessels stem from the compositional differences of the vessels.

A spouted bed is used in drying and coating. It involves spraying a liquid into a bed packed with the solid to be coated. A fluidizing gas fed from the bottom of the bed causes a spout, which causes the solids to circle linearly around the liquid. Work has been undertaken to model the minimum velocity of gas required for spouting in a spouted bed, including the use of artificial neural networks.

By contrast, finite element matrices are typically banded (elements are only locally connected) and the storage requirements for the system matrices typically grow quite linearly with the problem size. Compression techniques (e.g. multipole expansions or adaptive cross approximation/hierarchical matrices) can be used to ameliorate these problems, though at the cost of added complexity and with a success-rate that depends heavily on the nature of the problem being solved and the geometry involved.

As opposed to Arnold Schoenberg, Vermeulen did not choose to build a new regulatory system, but proceeded purely in terms of thematic information and its logical and psychological development. His symphonies and chamber works consequently differ greatly as far as construction is concerned. But he always succeeded in creating architectonic cohesion. The Third Symphony is in a large A-B-A form, in which A develops linearly and B is reminiscent of a Classical rondo.

As an erasure code, it can correct up to d − 1 known erasures. A rank code is an algebraic linear code over the finite field GF(q^N) similar to Reed–Solomon code. The rank of the vector over GF(q^N) is the maximum number of linearly independent components over GF(q). The rank distance between two vectors over GF(q^N) is the rank of the difference of these vectors.

ECD is often open-source, non-structured, moves horizontally and non-linearly. For example, virtual sit-ins may be announced on the internet and participants may have no formal connection with each other, not knowing each other's identity. ECD actors can participate from home, from work, from the university, or from other points of access to the Net. Electronic civil disobedience generally involves large numbers of people and may use legal and illegal techniques.

For a given capacitor charging current, the amplitude of the output waveform will decrease linearly with frequency. In musical terms, this means a waveform an octave higher in pitch is of half the amplitude. In order to produce a constant amplitude over the full range of the oscillator, some compensation scheme must be employed. This is often done by controlling the charging current from the same microprocessor that controls the counter reset value.

It uses magnetic deflection, where current passing through a coil placed in the magnetic field of a permanent magnet causes the coil to move. The modern form of this instrument was developed by Edward Weston, and uses two spiral springs to provide the restoring force. The uniform air gap between the iron core and the permanent magnet poles make the deflection of the meter linearly proportional to current. These meters have linear scales.

The 3-D organization of the genome can also be analyzed via eigendecomposition of the contact matrix. Each eigenvector corresponds to a set of loci, which are not necessarily linearly contiguous, that share structural features. A significant confounding factor in 3C technologies is the frequent non-specific interactions between genomic loci that occur due to random polymer behavior. An interaction between two loci must be confirmed as specific through statistical significance testing.

In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line. Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered, i.e., between any two distinct elements there is another (and hence infinitely many others), and complete, i.e., which "lacks gaps" in the sense that every non-empty subset with an upper bound has a least upper bound.

The common ostrich has no sweat glands, and under heat stress they rely on panting to reduce their body temperature. Panting increases evaporative heat (and water) loss from its respiratory surfaces, therefore forcing air and heat removal without the loss of metabolic salts. Panting allows the common ostrich to have a very effective respiratory evaporative water loss (REWL). Heat dissipated by respiratory evaporation increases linearly with ambient temperature, matching the rate of heat production.

The hierarchical structure through which DNA is packaged into chromosomes. The first level of genome organization concerns how DNA is arranged linearly, and how it is packaged into chromosomes. DNA is composed of two antiparallel strands of nucleic acids, with two bound and opposing nucleic acids referred to as DNA base pairs. In order for DNA to pack inside the tiny cell nucleus, each strand is wrapped around histones, forming nucleosome structures.

He held positions at the University of Minnesota and Purdue University before joining the faculty at Michigan in 1977. Hochster's work is primarily in commutative algebra, especially the study of modules over local rings. He has established classic theorems concerning Cohen–Macaulay rings, invariant theory and homological algebra. For example, the Hochster–Roberts theorem states that the invariant ring of a linearly reductive group acting on a regular ring is Cohen–Macaulay.

It contains a linearly-arranged catalytic triad of Asp153, His154, and Cys156. It runs on a ping-pong mechanism, where the cysteine attacks the acyl-CoA to form an S-acylated DHHC, and then the acyl group is transferred to the substrate. DHHR enzymes exist, and it (as well as some DHHC enzymes) may use a ternary complex mechanism instead. An inhibitor of S-palmitoylation by DHHC is 2-Bromopalmitate (2-BP).

Several structures of the DHHC domain has been solved, and it is known to run on a linearly-arranged catalytic triad of Asp153, His154, and Cys156. It runs on a ping-pong mechanism, where the cysteine attacks the acyl-CoA to form an S-acylated DHHC, and then the acyl group is transferred to the substrate. DHHR enzymes exist exist, and it (as well as some DHHC enzymes) may use a ternary complex mechanism instead.

The first stage is the region of the stress-strain curve where both fiber and the matrix are elastically deformed. This linearly elastic region can be expressed in the following form. \sigma_c - E_c \epsilon_c = \epsilon_c (V_f E_f + V_m E_m) where \sigma is the stress, \epsilon is the strain, E is the elastic modulus, and V is the volume fraction. The subscripts c, f, and m are indicating composite, fiber, and matrix, respectively.

This operation merges two adjacent terminal nodes into one morphological word. In other words, it allows for two heads which are adjacent to merge into one word without syntactic head movement – the operation is post-syntactic. This operation is doing the work of, say, affix lowering of the past tense morpheme in English in early generative syntax. For the operation to apply, what is crucial is that the morphemes to be merged are linearly adjacent.

In optimal control, problems of singular control are problems that are difficult to solve because a straightforward application of Pontryagin's minimum principle fails to yield a complete solution. Only a few such problems have been solved, such as Merton's portfolio problem in financial economics or trajectory optimization in aeronautics. A more technical explanation follows. The most common difficulty in applying Pontryagin's principle arises when the Hamiltonian depends linearly on the control u, i.e.

Mass-shell hyperboloids are 'squashed' into a cylinder. The momentum generators p_i commute among themselves but addition of momenta, reflected in the quantum group structure, is deformed (momentum space becomes a non-abelian group). Meanwhile, the Lorentz group generators enjoy their usual relations among themselves but act non-linearly on the momentum space. The orbits for this action are depicted in the figure as a cross-section of p_0 against one of the p_i.

In the case of the same linearly polarized antenna, this is the plane containing the magnetic field vector (sometimes called the H aperture) and the direction of maximum radiation. The magnetizing field or "H" plane lies at a right angle to the "E" plane. For a vertically polarized antenna, the H-plane usually coincides with the horizontal/azimuth plane. For a horizontally polarized antenna, the H-plane usually coincides with the vertical/elevation plane.

A last physical principle useful to design isolators is the Faraday rotation. When a linearly polarized wave propagates through ferrite having a magnetization aligned with the direction of propagation of the wave, the polarization plane will rotate along the propagation axis. This rotation may be used to create microwave devices as isolators, circulators, gyrators, etc. In rectangular waveguide topology, it also requires the implementation of circular waveguide sections which come out of the device plane.

Chessmetrics is a weighted average of past performance.Chessmetrics formulas page The score considers a player's win percentage against other players weighted by the ratings of the other players and the time elapsed since the match. A 10% increase in performance is equivalent to an increase of 85 rating points. The weighting of previous matches digresses linearly from 100% for just-finished matches to zero for matches conducted more than two years ago.

Almost as complex as PostScript itself is its handling of fonts. The font system uses the PS graphics primitives to draw glyphs as curves, which can then be rendered at any resolution. A number of typographic issues had to be considered with this approach. One issue is that fonts do not scale linearly at small sizes and features of the glyphs will become proportionally too large or small and start to look displeasing.

A. koschevnikovi is very long-tongued (5.870 mm) and slender, with narrow tomenta. Apis koschevnikovi is larger than its sympatric A. cerana, consistently being 10 to 15% larger linearly. Apis koschevnikovi also has two distinct characteristics which are species specific – its drones have a secondary sex characteristic of a hairy fringe on the margin of the tibia of the hind leg, and worker bee forewing venation shows a cubital index which is large and varied.

CARS spectroscopy can be used for temperature measurements; because the CARS signal is temperature dependent. The strength of the signal scales (non-linearly) with the difference in the ground state population and the vibrationally excited state population. Since the population of states follows the temperature dependent Boltzmann distribution, the CARS signal carries an intrinsic temperature dependence as well. This temperature dependence makes CARS a popular technique for monitoring the temperature of hot gases and flames.

Linear polarization in spectral lines is usually created by anisotropic scattering of photons on atoms and ions which can themselves be polarized by this interaction. The linearly polarized spectrum of the Sun is often called the second solar spectrum. Atomic polarization can be modified in weak magnetic fields by the Hanle effect. As a result, polarization of the scattered photons is also modified providing a diagnostics tool for understanding stellar magnetic fields.

Kernel matrix defines the proximity of the input information. For example, in Gaussian Radial basis function, determines the dot product of the inputs in a higher-dimensional space, called feature space. It is believed that the data become more linearly separable in the feature space, and hence, linear algorithms can be applied on the data with a higher success. The kernel matrix can thus be analyzed in order to find the optimal number of clusters .

The polarization of the emitted radiation can be controlled by using permanent magnets to induce different periodic electron trajectories through the undulator. If the oscillations are confined to a plane the radiation will be linearly polarized. If the oscillation trajectory is helical, the radiation will be circularly polarized, with the handedness determined by the helix. If the electrons follow the Poisson distribution a partial interference leads to a linear increase in intensity.

The example tree in the first section of this article is in accordance with X-bar theory (with the exception that [Spec,CP] is treated as an adjunct). It can be seen that removing any of the structure in the tree (e.g. deleting the C dominating the 'c' terminal, so that the complement of A is [CP c]) will destroy the asymmetric c-command relations necessary for linearly ordering the terminals of the tree.

The isoforms affect the protein's N-terminal region, which extends linearly out from the cell and bears the O-linked glycan chains. CD45 isoforms show cell-type and differentiation-stage specific expression, a pattern which is quite well conserved in mammals. These isoforms are often used as markers that identify and distinguish between different types of immune cells. Naive T lymphocytes are typically positive for CD45RA, which includes only the A protein region.

Traditional approaches to QC tend toward quadratic O(n^2), while solutions in deep learning are necessarily linearly limited due to scale and complexity: O(n). With the possible exception of exponent distance-based quantum clustering algorithms, many QC solutions still required data preprocessing (primarily, cleaning to resolve noise, artifacting, column gapping and interchange). This preprocessing step, even when successful, would introduce inherent data bias by corrupting the full richness of the data set.

Comparison of average female and male life expectancy as defined in the 2018 CIA Factbook, with selected bubbles labelled. The dotted line corresponds to equal female and male life expectancy. The apparent 3D volumes of the bubbles are linearly proportional to their population. (In the SVG file, hover over a bubble to highlight it and show its data.) The article documents lists of countries by average life expectancy at birth by various sources of estimates.

Given a fixed price for the feedstock (e.g. the price per barrel of crude oil), the product cost can be decreased using a larger scale process because the capital investment and operational costs do not normally increase linearly with scale. For example, the capacity or volume of a cylindrical vessel used to produce a product increases proportional to the square of the radius of the cylinder, so cost of materials per unit volume decreases.

Climate change has and will continue to harm rice yields. A study by Okayama University in Japan found that grain yield declines when the average daily temperature exceeds , and grain quality continues to decline linearly as temperatures rise. Another study found that each increasing in global mean temperature would, on average, reduce yields of rice by 3.2%. Traditional rice cultivation is the second largest agricultural source of greenhouse gas (GHG) after livestock.

In the short-range correlations hypothesis, the EMC effect stems from large modification of these high-momentum SRC nucleons. This is supported by the observation that the size of the EMC effect in different nuclei correlates linearly with the density of SRC pairs. This hypothesis predicts increasing modification as a function of nucleon momentum, which was tested using recoil-tagging techniques in experiments at Jefferson Lab. The results showed definitive evidence in favor of SRC.

This section further heats the plasma to greater than —about 173 times the temperature of the Sun's surface. The path of ions and electrons through the engine approximates lines parallel to the engine walls; however, the particles actually orbit those lines while traveling linearly through the engine. The final, diverging, section of the engine contains an expanding magnetic field that ejects the ions and electrons from the engine at velocities as great as .

However, cartesian complex number representation is often more powerful for circuit analysis purposes. The notion of impedance is useful for performing AC analysis of electrical networks, because it allows relating sinusoidal voltages and currents by a simple linear law. In multiple port networks, the two-terminal definition of impedance is inadequate, but the complex voltages at the ports and the currents flowing through them are still linearly related by the impedance matrix.Callegaro, Sec.

RNase digestion is carried out to convert the double-stranded DNA-RNA hybrids into single-stranded DNA. 7\. Second strand synthesis (SSS). Taking advantage of the 19-bp specific sequence on the 3' end of each single-stranded DNA, SSS step is performed by specific priming and DNA polymerase extension. The resulting double-stranded DNA fragments are LIANTI amplicons linearly amplified from the original single-cell genomic DNA, with unique molecular barcodes attached on each amplicon. 8\.

Flow around an airfoil All fluids are viscous, meaning that they exert some resistance to deformation: neighbouring parcels of fluid moving at different velocities exert viscous forces on each other. The velocity gradient is referred to as a strain rate; it has dimensions T^{-1}. Isaac Newton showed that for many familiar fluids such as water and air, the stress due to these viscous forces is linearly related to the strain rate. Such fluids are called Newtonian fluids.

There are a variety of methods available for calculating the energy release rate given material properties, specimen geometry, and loading conditions. Some are dependent on certain criteria being satisfied, such as the material being entirely elastic or even linearly-elastic, and/or that the crack must grow straight ahead. The only method presented that works arbitrarily is that using the total potential energy. If two methods are both applicable, they should yield identical energy release rates.

In the middle of July, the progeny of the first brood begin to emerge. The emergence of larvae continues to rise linearly through the last week of August. A majority of these new progeny have already dispersed to lay new eggs and died off by early September. The few members of the new progeny that remain continue laying eggs for another two weeks, but will die by October, likely due to changes in climate around that time.

Ten pairs of caudal papillae are found towards the tail region of the body, and they are arranged linearly in well- defined groups such as precloacal (three pairs), cloacal (one pair), postcloacal (one pair), and subterminal (three pairs) papillae. Eggs found in the feces of infected birds are oval with smooth shells and measure 73-92 by 45-57 microns.Soulsby, EJL (1982) Helminths, arthropods and protozoa of domesticated animals. 7th Ed. Lea & Febiger, Philadelphia pg. 164.

Circular polarizer creating left-handed circularly polarized light. It is considered left-handed as viewed from the receiver and right-handed as viewed from the source. There are several ways to create circularly polarized light, the cheapest and most common involves placing a quarter-wave plate after a linear polarizer and directing unpolarized light through the linear polarizer. The linearly polarized light leaving the linear polarizer is transformed into circularly polarized light by the quarter wave plate.

FAST TCP has been shown to be promising in terms of system stability, throughput and fairness. However, it requires buffering which increases linearly with the number of flows bottlenecked at a link. The paper proposes a new TCP algorithm that extends FAST TCP to achieve (α, n)-proportional fairness in steady state, yielding buffer requirements which grow only as the nth power of the number of flows. The authors call the new algorithm Generalized FAST TCP.

Yield is inversely proportional to grind size – a smaller grain size produces more surface area, and faster extraction – and increases roughly linearly with brewing time. Thus, for a given temperature and grind size, an ideal brewing time can be determined. A French press is associated with a large grain size in conventional brewing, and a comparatively long brew time, commonly 3–4 minutes. Filter coffee is associated with a smaller grain size and shorter brew time.

Theoretically predicted phase diagram of carbon The equilibrium pressure and temperature conditions for a transition between graphite and diamond is well established theoretically and experimentally. The pressure changes linearly between at and at (the diamond/graphite/liquid triple point). However, the phases have a wide region about this line where they can coexist. At normal temperature and pressure, and , the stable phase of carbon is graphite, but diamond is metastable and its rate of conversion to graphite is negligible.

Common to all these arrangements is the need to ensure that the two beams recombine exactly as the system scans. The simplest systems have a plane mirror that moves linearly to vary the path of one beam. In this arrangement the moving mirror must not tilt or wobble as this would affect how the beams overlap as they recombine. Some systems incorporate a compensating mechanism that automatically adjusts the orientation of one mirror to maintain the alignment.

Permutations, when considered as arrangements, are sometimes referred to as linearly ordered arrangements. In these arrangements there is a first element, a second element, and so on. If, however, the objects are arranged in a circular manner this distinguished ordering no longer exists, that is, there is no "first element" in the arrangement, any element can be considered as the start of the arrangement. The arrangements of objects in a circular manner are called circular permutations.

In a differential scanning calorimeter (DSC), heat flow into a sample—usually contained in a small aluminium capsule or 'pan'—is measured differentially, i.e., by comparing it to the flow into an empty reference pan. In a heat flux DSC, both pans sit on a small slab of material with a known (calibrated) heat resistance K. The temperature of the calorimeter is raised linearly with time (scanned), i.e., the heating rate : dT/dt = β is kept constant.

Groups that cannot be linearly ordered, such as the finite groups, are not Archimedean. For another example, see the p-adic numbers, a system of numbers generalizing the rational numbers in a different way to the real numbers. Non- Archimedean ordered groups also exist; the ordered group (G, +, ≤) defined as follows is not Archimedean. Let the elements of G be the points of the Euclidean plane, given by their Cartesian coordinates: pairs (x, y) of real numbers.

Schematic setup of an ellipsometry experiment Electromagnetic radiation is emitted by a light source and linearly polarized by a polarizer. It can pass through an optional compensator (retarder, quarter wave plate) and falls onto the sample. After reflection the radiation passes a compensator (optional) and a second polarizer, which is called an analyzer, and falls into the detector. Instead of the compensators, some ellipsometers use a phase-modulator in the path of the incident light beam.

PEEK has a glass transition temperature of around 143 °C (289 °F) and melts around 343 °C (662 °F). Some grades have a useful operating temperature of up to 250 °C (482 °F). The thermal conductivity increases nearly linearly with temperature between room temperature and solidus temperature.J. Blumm, A. Lindemann, A. Schopper, "Influence of the CNT content on the thermophysical properties of PEEK-CNT composites", Proceedings of the 29th Japan Symposium on Thermophysical Properties, October 8–10, 2008, Tokyo.

Another historical turnpoint can be traced back to 1895, when Georg Cantor proved in a theorem that if a binary relation is linearly ordered, then it is also isomorphically embeddable in the ordered real numbers. This notion would become very influential for the theory of preferences in economics: by the 1940s prominent authors such as Paul Samuelson, would theorize about people having weakly ordered preferences.Fishburn, Peter (1994). "Utility and subjective probability", in: Robert Aumann and Sergiu Hart (eds).

However, studies on the concentrations of ptaquiloside in Danish bracken by Rasmussen et al. showed that the concentrations of ptaquiloside in the rhizomes were significantly higher than the previously reported values. Ptaquiloside can pass into the milk produced by bracken-fed cows and sheep. In 1996, Alonso-Amelot, Smith and co-workers found that ptaquiloside was excreted in milk at a concentration of 8.6 ± 1.2% of the amount ingested by a cow from bracken, and was linearly dose-dependent.

Cassandra is designed as a distributed system, for deployment of large numbers of nodes across multiple data centers. Key features of Cassandra’s distributed architecture are specifically tailored for multiple- data center deployment, for redundancy, for failover and disaster recovery. ; Scalability : Designed to have read and write throughput both increase linearly as new machines are added, with the aim of no downtime or interruption to applications. ; Fault-tolerant : Data is automatically replicated to multiple nodes for fault-tolerance.

BaseN is a global full stack Internet of Things (IoT) operator, headquartered in Helsinki, Finland. BaseN was established in 2001 to provide extremely scalable and fault-tolerant network and service management systems for telecom operators and large multinational enterprises. BaseN develops and markets a software as a service (SaaS) suite, BaseN Platform, for public and private infrastructures. BaseN Platform is built on a redundant computing grid due to which BaseN is linearly scalable, flexible and resilient.

The first term in these expressions comes from Debye-Hückel theory. The second term shows how the contributions from "interaction" are dependent on concentration. Thus, the interaction coefficients are used as corrections to Debye-Hückel theory when concentrations are higher than the region of validity of that theory. The activity coefficient of a neutral species can be assumed to depend linearly on ionic strength, as in :\log \gamma = k_m I\, where km is a Sechenov coefficient.

Mathematically, a wallpaper group or plane crystallographic group is a type of topologically discrete group of isometries of the Euclidean plane that contains two linearly independent translations. Two such isometry groups are of the same type (of the same wallpaper group) if they are the same up to an affine transformation of the plane. Thus e.g. a translation of the plane (hence a translation of the mirrors and centres of rotation) does not affect the wallpaper group.

The Evil Eye is divided into six separate episodes, which do not need to be played linearly. The first episode can be set anywhere in any campaign, and serves as a door into the world of Ravenloft and an introduction to the mysterious Vistani. Once in Ravenloft, the player characters meet the principal characters, each of which is pursuing his or her own hidden agenda. The central plot involves Gabrielle Aderre, lord of Invidia, mother of Molocchio.

The zeros of two linearly independent solutions of the Airy equation y - xy = 0 alternate, as predicted by the Sturm separation theorem. In mathematics, in the field of ordinary differential equations, Sturm separation theorem, named after Jacques Charles François Sturm, describes the location of roots of solutions of homogeneous second order linear differential equations. Basically the theorem states that given two linear independent solutions of such an equation the zeros of the two solutions are alternating.

The phase of the contributions of the individual wavelets in the aperture varies linearly with position in the aperture, making the calculation of the sum of the contributions relatively straightforward in many cases. With a distant light source from the aperture, the Fraunhofer approximation can be used to model the diffracted pattern on a distant plane of observation from the aperture (far field). Practically it can be applied to the focal plane of a positive lens.

In case 2, we say that A1 is consistency-wise stronger than A2 (vice versa for case 3). If A2 is stronger than A1, then ZFC+A1 cannot prove ZFC+A2 is consistent, even with the additional hypothesis that ZFC+A1 is itself consistent (provided of course that it really is). This follows from Gödel's second incompleteness theorem. The observation that large cardinal axioms are linearly ordered by consistency strength is just that, an observation, not a theorem.

These are the rankings for the 1990-91 Biathlon World Cup for men. For each event, first place gives 30 points, 2nd place 26 pts, 3rd place 24 pts, 4th place 22 pts, then linearly decreasing by one point down to 25th place. Equal placings (ties) give an equal number of points. The sum of all WC points of the season minus the two worst results in each of the disciplines gives the biathlete's total WC score.

Careful comparison of the random initiation approach to principal component initialization for one-dimensional SOM (models of principal curves) demonstrated that the advantages of principal component SOM initialization are not universal. The best initialization method depends on the geometry of the specific dataset. Principal component initialization is preferable (in dimension one) if the principal curve approximating the dataset can be univalently and linearly projected on the first principal component (quasilinear sets). For nonlinear datasets, however, random initiation performs better.

Notice that you can also launch waves on the string by moving your hand to the right and left instead of up and down. This is an important point. There are two independent (orthogonal) directions that the waves can move.(This is true for any two directions at right angles, up and down and right and left are chosen for clarity.) Any waves launched by moving your hand in a straight line are linearly polarized waves.

In general, adult extracellular Nematopsis (sporadins) are milky-white in color, and associate as groups of two caudo-frontally, with one cell's anterior side entacting the other's posterior (Prasadan and Janardana, 2001). The two cells are associated linearly and range from around 150-200 μm in length (Prasadan and Janardana 2001). Nuclei are generally spherical to ovoid and each associated cell possesses a single nucleus (Prasadan and Janardana 2001). Apicomplexan parasites such as Nematopsis have specialized organelles called rhoptries.

High Hopes is a first for Springsteen: a studio album composed entirely of covers, outtakes and reimagined versions of songs from past albums and tours. "The best way to describe this record," Springsteen said, "is that's it's a bit of an anomaly but not much. I don't really work linearly like a lot of people do." The album's title track and first single, "High Hopes", was originally recorded in 1995 and released on the Blood Brothers (EP).

As well as these time-varying phenomena, there is a frequency domain ripple that arises in some classes of filter and other signal processing networks. In this case the periodic variation is a variation in the insertion loss of the network against increasing frequency. The variation may not be strictly linearly periodic. In this meaning also, ripple is usually to be considered an incidental effect, its existence being a compromise between the amount of ripple and other design parameters.

The Bode plot of a first-order Butterworth low-pass filter The frequency response of the Butterworth filter is maximally flat (i.e. has no ripples) in the passband and rolls off towards zero in the stopband. When viewed on a logarithmic Bode plot, the response slopes off linearly towards negative infinity. A first-order filter's response rolls off at −6 dB per octave (−20 dB per decade) (all first-order lowpass filters have the same normalized frequency response).

He also proposed that other, distant genes might also influence the amount of white present.WL Pulos & FB Hutt (1969). "Odriozola added no new data on dominant white, but ... suggested that different forms of W arranged linearly in the chromosome might be responsible for the differing degrees of white ... and that the expression of white is also influenced by modifying genes." The embryonic lethality hypothesis was originally supported by Pulos and Hutt's 1969 study of Mendelian progeny ratios.

Yield strength testing involves taking a small sample with a fixed cross-section area and then pulling it with a controlled, gradually increasing force until the sample changes shape or breaks. This is called a Tensile Test. Longitudinal and/or transverse strain is recorded using mechanical or optical extensometers. Indentation hardness correlates roughly linearly with tensile strength for most steels, but measurements on one material cannot be used as a scale to measure strengths on another.

The Italian Air Force (Aeronautica Militare Italiana) also conducted experiments for their pilots. In schedules involving night shifts and fragmentation of duty periods through the entire day, a sort of polyphasic sleeping schedule was studied. Subjects were to perform two hours of activity followed by four hours of rest (sleep allowed), this was repeated four times throughout the 24-hour day. Subjects adopted a schedule of sleeping only during the final three rest periods in linearly increasing duration.

When using this radar projection the Cartesian radar video pixels can directly displayed on a computer screen (only being linearly transformed according to the current position on the screen and e.g. the current zoom level). A problem now arises if e.g. also a satellite map shall be shown together with the radar video data. The ‘natural’ geographical projection of a satellite image would be a satellite projection which depends on the satellite orbit, position and further parameters.

3D-chiral materials can exhibit optical activity, which manifests itself as circular birefringence, causing polarization rotation for linearly polarized waves, and circular dichroism, causing different attenuation of left- and right-handed circularly polarized waves. The former can be exploited to realize polarization rotators, while the latter can be used to realize circular polarizers. Optical activity is weak in natural chiral materials, but it can be enhanced by orders of magnitude in an artificial chiral materials, i.e., chiral metamaterials.

Auditory phonetics studies how humans perceive speech sounds. Due to the anatomical features of the auditory system distorting the speech signal, humans do not experience speech sounds as perfect acoustic records. For example, the auditory impressions of volume, measured in decibels (dB), does not linearly match the difference in sound pressure. The mismatch between acoustic analyses and what the listener hears is especially noticeable in speech sounds that have a lot of high-frequency energy, such as certain fricatives.

Any remaining pressure at the muzzle or at the end of the engine's power stroke represents lost energy. To extract the maximum amount of energy, then, the swept volume is maximized. This can be done in one of two ways -- increasing the length of the barrel or increasing the diameter of the projectile. Increasing the barrel length will increase the swept volume linearly, while increasing the diameter will increase the swept volume as the square of the diameter.

The main objective of the office was to acquire cheap Tamil labour for the Ceylon tea plantations. Girls typically follow their mothers, grandmothers and older sisters on the plantations, and the women are expected to perform most of the domestic duties. They live in housing known as "lines", a number of linearly attached houses with one or two rooms. This housing system and the environmental sanitation conditions are generally poor for labourers in the plantation sector.

Gouraud-shaded triangle mesh using the Phong reflection model Gouraud shading, named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces represented by polygon meshes. In practice, Gouraud shading is most often used to achieve continuous lighting on Triangle meshes by computing the lighting at the corners of each triangle and linearly interpolating the resulting colours for each pixel covered by the triangle. Gouraud first published the technique in 1971.

The alphabetic principle is closely tied to phonics, as it is the systematic relationship between spoken words and their visual representation (letters). The alphabetic principle does not underlie logographic writing systems like Chinese or syllabic writing systems such as Japanese kana. Korean was formerly written partially with Chinese characters, but is now written in the fully alphabetic Hangul system, in which the letters are not written linearly, but arranged in syllabic blocks which resemble Chinese characters.

A study that asked participants to count each act of kindness they performed for one week significantly enhanced their subjective happiness. It is important to note that, while research supports the idea that altruistic acts bring about happiness, it has also been found to work in the opposite direction—that happier people are also kinder. The relationship between altruistic behavior and happiness is bidirectional. Studies have found that generosity increases linearly from sad to happy affective states.

In each Landau level the cyclotron and Zeeman energies and the number of electron states (eB/h) all increase linearly with increasing magnetic field. Thus, as the magnetic field increases, the spin-split Landau levels move to higher energy. As each energy level passes through the Fermi energy, it depopulates as the electrons become free to flow as current. This causes the material's transport and thermodynamic properties to oscillate periodically, producing a measurable oscillation in the material's conductivity.

If the VFO frequency is then adjusted, the gain may increase substantially; the result is more gain compression is needed, and that affects both the output amplitude of the VFO and its frequency stability. Vackář reviewed several existing circuits for their amplitude stability. In his analysis, Vackář made several assumptions. He assumed the tuned circuit has a constant quality factor () over the VFO's frequency range; this assumption implies that the tank's effective resistance increases linearly with frequency ().

Even after experiments showed that Einstein's equations for the photoelectric effect were accurate, resistance to the idea of photons continued. Einstein's work predicted that the energy of individual ejected electrons increases linearly with the frequency of the light. Perhaps surprisingly, the precise relationship had not at that time been tested. By 1905 it was known that the energy of photoelectrons increases with increasing frequency of incident light and is independent of the intensity of the light.

They completed the certification process in March 1998 as the OE600A. The OE600's "natural" target was the PT6, the most popular turboprop engine of all time. Although a turboprop has a superb power-to- weight ratio, it has high fuel consumption, and its performance drops off linearly with altitude. The OE600 offered better fuel economy, as well as considerably improved climb rates (even though it was heavier) and cruise speeds, all suggesting a lower overall cost of operation.

The forces that cause the adhesion of solvent molecules in the IHP are physical forces rather than chemical bonds. Chemical bonds exist within the adsorbed molecules, but they are polarized. The magnitude of the electric charge that can accumulate in the layers corresponds to the concentration of the adsorbed ions and the electrodes surface. Up to the electrolyte's decomposition voltage, this arrangement behaves like a capacitor in which the stored electrical charge is linearly dependent on the voltage.

If one of the adjunct processors failed during operation, the system could detect and restart programs that had been running on the failed element. The 3B4000 was capable of significant expansion; one test system (including storage) occupied 17 mid-height cabinets. Generally, the performance of the system increased linearly with additional processing elements, however the lack of a true shared memory capability required rewriting applications that relied heavily on this feature to avoid a severe performance penalty.

Visibility in a natural haze declines exponentially, not linearly, with distance, due to scattering. The colour of the light being scattered into the viewing path affects the colour of the haze; blue under blue skies, reddish near sunset, as with alpenglow. These more subtle details are represented in some graphics. "Fogging" is another use of distance fog in mid-to-late 1990s games, when processing power was not enough to render far viewing distances, and clipping was employed.

In nonresonant TPA the transition occurs without the presence of the intermediate state. This can be viewed as being due to a "virtual" state created by the interaction of the photons with the molecule. The "nonlinear" in the description of this process means that the strength of the interaction increases faster than linearly with the electric field of the light. In fact, under ideal conditions the rate of TPA is proportional to the square of the field intensity.

See for an experimental comparison with a preliminary version of the Boyer and Myrvold planarity test. Furthermore, the Boyer–Myrvold test was extended to extract multiple Kuratowski subdivisions of a non-planar input graph in a running time linearly dependent on the output size.. The source code for the planarity test and the extraction of multiple Kuratowski subdivisions is publicly available. Algorithms that locate a Kuratowski subgraph in linear time in vertices were developed by Williamson in the 1980s.

The story opens with the village hearing the news of Zein's upcoming nuptials. Because Zein is regarded as the village idiot, the people as a whole are greatly surprised that any family agreed to give their daughter to him. The rest of the story unfolds non-linearly. The first section is an account of Zein's childhood and young adulthood, focusing on his strange ability to draw attention to village girls by falling in love with them.

Comparison of male and female life expectancy at birth for countries and territories as defined in the 2011 CIA Factbook, with selected bubbles labelled. The green dotted line corresponds to equal female and male life expectancy. The apparent 3D volumes of the bubbles are linearly proportional to their population. (In the SVG file, hover over a bubble to highlight it and show its data.) The word "longevity" is sometimes used as a synonym for "life expectancy" in demography.

The results didn't support the Elkind's claim that adolescent egocentrism emerges in early adolescence and decreases linearly throughout middle and late adolescence. In other words, adolescents aged 11 or 12 could experience adolescent egocentrism of the same magnitude as those aged 15 or 16 do. Another study by Frankenberger (2000) also provides evidence that adolescent egocentrism is not age-related. In this study, a survey was conducted for data collection from 223 adolescents and 131 adults.

The Gardner–Salinas braille codes are a method of encoding mathematical and scientific notation linearly using braille cells for tactile reading by the visually impaired. The most common form of Gardner–Salinas braille is the 8-cell variety, commonly called GS8. There is also a corresponding 6-cell form called GS6. The codes were developed as a replacement for Nemeth Braille by John A. Gardner, a physicist at Oregon State University, and Norberto Salinas, an Argentinian mathematician.

Theoretically predicted phase diagram of carbon The equilibrium pressure and temperature conditions for a transition between graphite and diamond are well established theoretically and experimentally. The pressure changes linearly between at and at (the diamond/graphite/liquid triple point). However, the phases have a wide region about this line where they can coexist. At normal temperature and pressure, and , the stable phase of carbon is graphite, but diamond is metastable and its rate of conversion to graphite is negligible.

Cooper's hawks are fairly variable in size. There is usually minimal to no overlap in dimensions between the sexes, with females being considerably larger than males. On average, she may be about 20% larger linearly and around 40% heavier (though can be up to 125% more massive). More westerly Cooper's hawks (roughly west of the Rocky mountains) show slightly less pronounced sexual dimorphism than hawks of the species elsewhere.Smith, J. P., Hoffman, S. W., & Gessaman, J. A. (1990).

The key to neuroaesthetics is the investigation of apparatuses in which a network of heterogeneous discourses is administered. As the world and technology change, so to the apparatuses which organize it, and the cognitive strategies with which one can understand it. This is especially true of the information age, which distributes such apparatuses non-linearly and profusely. Neidich's work is inspired by Michael Snow, Stan Brakhage, Jean-Luc Godard and the Apparatus Theory of Stephen Heath.

One proof of the theorem uses the properties of Minkowski sums. If K is a body of constant width w, then the Minkowski sum of K and its 180° rotation is a disk with radius w and perimeter 2πw. However, the Minkowski sum acts linearly on the perimeters of convex bodies, so the perimeter of K must be half the perimeter of this disk, which is πw as the theorem states.The Theorem of Barbier (Java) at cut-the-knot.

Non-birefringent methods, to rotate the linear polarization of light beams, include the use of prismatic polarization rotators which use total internal reflection in a prism set designed for efficient collinear transmission. A polariser changing the orientation of linearly polarised light. In this picture, θ1 – θ0 = θi. Media that reduce the amplitude of certain polarization modes are called dichroic, with devices that block nearly all of the radiation in one mode known as polarizing filters or simply "polarisers".

The principal yards were arranged linearly, with the eastern limits of the Departure Yard in Lowellville. The Hump Yard was located in Struthers in the center of the facility, and the Receiving Yard was to the west. The special purpose yards were "Diesel Servicing Facilities", "Gorilla Park" and "Interchange" yards. The "Interchange" yard was made up of six tracks, four were for interchange to and from the B&O; Railroad and two of which were for general use.

Attention is then directed to items depending on their level of activation, starting with those most activated. This explains why search times are longer when distractors share one or more features with the target stimuli. In contrast, during inefficient search, the reaction time to identify the target increases linearly with the number of distractor items present. According to the guided search model, this is because the peak generated by the target is not one of the highest.

Laws of fluid dynamics do not provide good approximations for the behavior of individual, highly separated, non-interacting gas molecules, like those found in high vacuum environments. The maximum compression varies linearly with circumferential rotor speed. In order to obtain extremely low pressures down to 1 micropascal, rotation rates of 20,000 to 90,000 revolutions per minute are often necessary. Unfortunately, the compression ratio varies exponentially with the square root of the molecular weight of the gas.

Tests of the D-38 showed it was not large enough to cope with hot and high environments, so a version with an envelope linearly enlarged by 9.4% and a volume of 50,000 cu ft (1,416 m³) was produced, designated the D-50. As well as being larger, the D-50 had a revised tail, with four almost rectangular, low aspect ratio surfaces, two vertical and two horizontal. The D-50 first flew on 2 September 1981.

For sinusoidal signals, when the phase difference \varphi(t) is 180° (\pi radians), one says that the phases are opposite, and that the signals are in antiphase. Then the signals have opposite signs, and destructive interference occurs. When the phase difference \varphi(t) is a quarter of turn (a right angle, or ), sinusoidal signals are sometimes said to be in quadrature. If the frequencies are different, the phase difference \varphi(t) increases linearly with the argument t.

In reversed-phase chromatography, solvent A is often water or an aqueous buffer, while B is an organic solvent miscible with water, such as acetonitrile, methanol, THF, or isopropanol. In isocratic elution, peak width increases with retention time linearly according to the equation for N, the number of theoretical plates. This leads to the disadvantage that late-eluting peaks get very flat and broad. Their shape and width may keep them from being recognized as peaks.

0800, 0820, 0840) and a person wishes to begin their journey between those intervals (e.g. at 0815), they incur a schedule delay through having to retime their departure from the desired 0815 point to the bus departure time of 0820. Schedule delay can be measured as a utility (or, rather, a disutility). The Small model of scheduling has the disutility of schedule delay decrease linearly towards zero as the actual arrival (or departure) time approaches the desired time.

Dependence logic is a logic of imperfect information, like branching quantifier logic or independence-friendly logic: in other words, its game theoretic semantics can be obtained from that of first-order logic by restricting the availability of information to the players, thus allowing for non-linearly ordered patterns of dependence and independence between variables. However, dependence logic differs from these logics in that it separates the notions of dependence and independence from the notion of quantification.

A fireproof herbarium was also constructed based on plans from Kew. King also altered the garden design from one segregated linearly on the basis of taxonomy to one based on regions with combinations of species showing the natural plant associations. He began the journal, the Annals of the Royal Botanic Garden, Calcutta In 1873 King was also associated with the creation of the Calcutta Zoological Garden. He was also associated with setting up a botanical garden at Darjeeling.

The car was designed to be powered by an engine that can burn both gasoline and natural gas. The series hybrid no-transmission layout uses an electric generator that feeds its power directly into the car's two rear electric motors, unlike parallel hybrid cars like the Toyota Prius. A super capacitor would provide a small but powerful energy buffer. It was planned to install a rotary vane type engine, with the pistons moving in a circle, rather than linearly.

CIE 1931 XYZ color space was one of the first attempts to produce a color space based on measurements of human color perception (earlier efforts were by James Clerk Maxwell, König & Dieterici, and Abney at Imperial College)William David Wright, 50 years of the 1931 CIE Standard Observer. Die Farbe, 29:4/6 (1981). and it is the basis for almost all other color spaces. The CIERGB color space is a linearly-related companion of CIE XYZ.

Since the amplitude at these reflections grows linearly with the number N of scatterers, the observed intensity of these spots should grow quadratically, like N2. In other words, using a crystal concentrates the weak scattering of the individual unit cells into a much more powerful, coherent reflection that can be observed above the noise. This is an example of constructive interference. In a liquid, powder or amorphous sample, molecules within that sample are in random orientations.

In signal processing, each vector is interpreted as a signal. In this interpretation, a vector expressed as a linear combination of the frame vectors is a redundant signal. Using a frame, it is possible to create a simpler, more sparse representation of a signal as compared with a family of elementary signals (that is, representing a signal strictly with a set of linearly independent vectors may not always be the most compact form). Frames, therefore, provide robustness.

In analyzing the performance of binary search, another consideration is the time required to compare two elements. For integers and strings, the time required increases linearly as the encoding length (usually the number of bits) of the elements increase. For example, comparing a pair of 64-bit unsigned integers would require comparing up to double the bits as comparing a pair of 32-bit unsigned integers. The worst case is achieved when the integers are equal.

They found that when the cells were released and concurrently treated with nocodazole, a G2/M phase cell cycle inhibitor, telomere length increased for the first few hours and then remained constant. In comparison, when cells were released and allowed to cycle, telomere length increased linearly with time. These data suggest that telomere elongation occurs only in S phase. Additional experiments with greater time resolution support this hypothesis and narrow the timeframe to late S phase.

Thus is circular polarization created in practice, starting with linearly polarized light and employing a quarter-wave plate to introduce such a phase shift. The result of two such phase-shifted components in causing a rotating electric field vector is depicted in the animation on the right. Note that circular or elliptical polarization can involve either a clockwise or counterclockwise rotation of the field. These correspond to distinct polarization states, such as the two circular polarizations shown above.

The word relative is critical: as the wavelength is very small compared with the dimensions of typical apparatus, the individual phase advances suffered by the s and p components are not readily observable, but the difference between them is easily observable through its effect on the state of polarization of the emerging light. If the incoming light is linearly polarized (plane-polarized), the s and p components are initially in phase; hence, after two reflections, "the p component is 90° ahead in phase", so that the polarization of the emerging light is elliptical with principal axes in the s and p directions (Fig.1). Similarly, if the incoming light is elliptically polarized with axes in the s and p directions, the emerging light is linearly polarized. In the special case in which the incoming s and p components not only are in phase but also have equal magnitudes, the initial linear polarization is at 45° to the plane of incidence and reflection, and the final elliptical polarization is circular.

The test image is only valid when displayed "raw", i.e. without scaling (1:1 pixel to screen) and color adjustment, on the screen. It does, however, also serve to point out another widespread problem in software: many programs perform scaling in a color space with gamma, instead of a physically-correct linear space. In a sRGB color space with an approximate gamma of 2.2, the image should show a "2.2" result at 50% size, if the zooming is done linearly.

Therefore, initial cost should be minimized by considering the whole system. Furthermore, not only the initial cost but also the operational costs should be considered during the optimization of the system overall costs. This requires the long term predictions of HTR value of a GHE. Results show that the average HTR values linearly increase with the value of D and Lp. These linear dependencies are due to the increment of peripheral surface area and heat capacity of ground per turn.

Through the pre-verse interludes and instrumental bridge, "Over the Hills and Far Away" stands out as an example of Jones and Bonham's tight interplay. Following the final verse, the rhythm section fades out, gradually replaced by the echo returns from Page's electric guitar and a few chords played by Jones on Clavinet. In the final 8 bars, Page executes a linearly descending/ascending sequence and then concludes with the idiomatic V-I cadence on synth imitating a pedal steel guitar.

A software taggant is a form of code signing somewhat similar to Microsoft's Authenticode. The key differences between a software taggant and Authenticode are that the transparent and free addition of a software taggant for the end user of a runtime packer. Also, a software taggant may cover small critical areas of the program to minimize the cost of software integrity checking. To contrast, Authenticode always covers nearly the entire file so the cost of checking linearly depends on the file size.

The linear polarizer sandwiched between the quarter wave plates is oriented so that it will pass one linear polarization and block the other. The second quarter-wave plate then takes the linearly polarized light that passes and retards the orthogonal component that was not retarded by the previous quarter-wave plate. This brings the two components back into their initial phase relationship, reestablishing the selected circular polarization. Note that it does not matter in which direction one passes the circularly polarized light.

Stretching of the sheet during manufacture causes the PVA chains to align in one particular direction. Valence electrons from the iodine dopant are able to move linearly along the polymer chains, but not transverse to them. So incident light polarized parallel to the chains is absorbed by the sheet; light polarized perpendicularly to the chains is transmitted. The durability and practicality of Polaroid makes it the most common type of polarizer in use, for example for sunglasses, photographic filters, and liquid crystal displays.

Since these specular highlights are absent from the polygon's vertices and Gouraud shading interpolates based on the vertex colors, the specular highlight will be missing from the polygon's interior. This problem is fixed by Phong shading. Unlike Gouraud shading, which interpolates colors across polygons, in Phong shading a normal vector is linearly interpolated across the surface of the polygon from the polygon's vertex normals. The surface normal is interpolated and normalized at each pixel and then used in a reflection model, e.g.

Whenever index notation is used the indexed objects form a family. For example, consider the following sentence: Here (vi)i ∈ {1, ..., n} denotes a family of vectors. The i-th vector vi only makes sense with respect to this family, as sets are unordered and there is no i-th vector of a set. Furthermore, linear independence is only defined as the property of a collection; it therefore is important if those vectors are linearly independent as a set or as a family.

Every linearly ordered field contains (an isomorphic copy of) the rationals as an ordered subfield, namely the subfield generated by the multiplicative unit 1 of , which in turn contains the integers as an ordered subgroup, which contains the natural numbers as an ordered monoid. The embedding of the rationals then gives a way of speaking about the rationals, integers, and natural numbers in . The following are equivalent characterizations of Archimedean fields in terms of these substructures. 1\. The natural numbers are cofinal in .

This design is commonly referred to as a LPCSA configuration. The orientation of the angles of P and C are chosen in such a way that the elliptically polarized light is completely linearly polarized after it is reflected off the sample. For simplification of future calculations, the compensator can be fixed at a 45 degree angle relative to the plane of incidence of the laser beam. This set up requires the rotation of the analyzer and polarizer in order to achieve null conditions.

Fig. 7: This schematic figure illustrates the notion of radar distance between a ring-riding observer and a static central observer (with the same Z coordinate). Even in flat spacetime, it turns out that accelerating observers (even linearly accelerating observers; see Rindler coordinates) can employ various distinct but operationally significant notions of distance. Perhaps the simplest of these is radar distance. Consider how a static observer at R=0 might determine his distance to a ring riding observer at R = R0.

Full mixing is the simplest representation of CBL in some global models. Fluxes within this layer are assumed to decrease linearly with height, and the mean variables keep their vertical profile at each simulation time step. All mean variables are uniformly distributed throughout the whole CBL and have a jump at the top of CBL. This simple model has been used in meteorology for a long time, and continues to be a popular approach in some global course resolution models.

The southeastern volcanoes also have low-level parallel faults arranged linearly against the Juan de Fuca Ridge. The construction of the cones left a lot of debris scattered across the ocean surface, much of which is aligned parallel to the ridge axis. The largest of these cones are nearly across, whereas the smallest appear to be only a few hundred meters in diameter. In 2006, an expedition was conducted by the Monterey Bay Aquarium Research Institute on the seamount formations.

The rigidity matroid of the given framework is a linear matroid that has as its elements the edges of the graph. A set of edges is independent, in the matroid, if it corresponds to a set of rows of the rigidity matrix that is linearly independent. A framework is called generic if the coordinates of its vertices are algebraically independent real numbers. Any two generic frameworks on the same graph G determine the same rigidity matroid, regardless of their specific coordinates.

Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-based clusters in spatial data. It was presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander. Its basic idea is similar to DBSCAN, but it addresses one of DBSCAN's major weaknesses: the problem of detecting meaningful clusters in data of varying density. To do so, the points of the database are (linearly) ordered such that spatially closest points become neighbors in the ordering.

The method then gives the familiar formula for the volume of a sphere. By scaling the dimensions linearly Archimedes easily extended the volume result to spheroids. Archimedes argument is nearly identical to the argument above, but his cylinder had a bigger radius, so that the cone and the cylinder hung at a greater distance from the fulcrum. He considered this argument to be his greatest achievement, requesting that the accompanying figure of the balanced sphere, cone, and cylinder be engraved upon his tombstone.

Walter 2007 In 1907 Einstein came to the conclusion that to achieve this a successor to special relativity was needed. From 1907 to 1915, Einstein worked towards a new theory, using his equivalence principle as a key concept to guide his way. According to this principle, a uniform gravitational field acts equally on everything within it and, therefore, cannot be detected by a free-falling observer. Conversely, all local gravitational effects should be reproducible in a linearly accelerating reference frame, and vice versa.

Print (text, still photos, graphics) and television (video, audio, animated graphics) tell stories linearly. Both these mediums are one-way systems because they offer the reader or viewer little opportunity for feedback. Both are also temporal – "the newspaper becomes fishwrap; television's news disappears into the ether." Multimedia storytelling – the heart of backpack journalism – uses a combination of text, still photos, animated graphics, video and audio presented in a nonlinear format in which all of the information in the elements are non-redundant.

Little of the maritime infrastructure associated with these activities has survived. After the American Civil War, and with the decline in demand for wooden ships, the area's economic focus changed to one as a seaside resort and vacation area. The historic district extends along Main Road, the principal historic thoroughfare on the point prior to the construction of Massachusetts Route 88 in the 1960s. The district extends linearly along Main Road for about a mile, ending roughly at Charles Street.

The tooling consists of two pressure Chambers and a counter punch, which is linearly displaceable. Similar to the cavity forming technology, at the process beginning, the firmly clamped blank is bulged by gas pressure. The second phase of the process involves the material being formed over the punch surface by applying a pressure against the previous forming direction. Due to a better material use, which is caused by process conditions, blanks with a smaller initial thickness compared to cavity forming can be used.

The first specimens observed would later come to be known as single-walled carbon nanotubes (SWNTs). Endo, in his early review of vapor-phase-grown carbon fibers (VPCF), also reminded us that he had observed a hollow tube, linearly extended with parallel carbon layer faces near the fiber core. This appears to be the observation of multi-walled carbon nanotubes at the center of the fiber. The mass-produced MWCNTs today are strongly related to the VPGCF developed by Endo.

Fort Beschutter ( Beshshatar Balakotuwa) or Fort Pass Beschutter (; Beshshatar Pas Balakotuwa) was a small fort, which was linearly located between Elephant Pass Fort and Fort Pass Pyl in the narrow part of the Jaffna peninsula. The strategic fort was used to protect Jaffna peninsula from the forces of mainland (Vanniyas and Sinhalese) as well as illegal access, smuggling, etc. Fort Beschutter was built as square-shaped fort like other two in the Elephant Pass area. It was completely destroyed and nothing found today.

By contrast, finite element matrices are typically banded (elements are only locally connected) and the storage requirements for the system matrices typically grow linearly with the problem size. Compression techniques (e.g. multipole expansions or adaptive cross approximation/hierarchical matrices) can be used to ameliorate these problems, though at the cost of added complexity and with a success-rate that depends heavily on the nature and geometry of the problem. BEM is applicable to problems for which Green's functions can be calculated.

The scenes are not represented linearly; they do not always read from left to right. Each shows a comatose man, collapsed or dead near the hotel room's lavatory seat. In most, Dyer is followed by black horizontal fleshy winged creatures, raw and red/pink blobs of dying flesh, or by painterly arrows. These devices act both as pointers to the depravity and tragedy of the scene and as manifestations of Bacon's guilt at the death of an emotionally dependent friend.

The target-centric approach to intelligence is a method of intelligence analysis that Robert M. Clark introduced in his book "Intelligence Analysis: A Target-Centric Approach" in 2003 to offer an alternative methodology to the traditional intelligence cycle. Its goal is to redefine the intelligence process in such a way that all of the parts of the intelligence cycle come together as a network. It is a collaborative process where collectors, analysts and customers are integral, and information does not always flow linearly.

Motions of a bike can be roughly grouped into those out of the central plane of symmetry: lateral; and those in the central plane of symmetry: longitudinal or vertical. Lateral motions include balancing, leaning, steering, and turning. Motions in the central plane of symmetry include rolling forward, of course, but also stoppies, wheelies, brake diving, and most suspension activation. Motions in these two groups are linearly decoupled, that is they do not interact with each other to the first order.

The rank of the matrix A is the largest number of columns which are linearly independent, i.e., none of the selected columns can be written as a linear combination of the other selected columns. It is not true that adding nonnegativity to this characterization gives the nonnegative rank: The nonnegative rank is in general less than or equal to the largest number of columns such that no selected column can be written as a nonnegative linear combination of the other selected columns.

Subcortical arteriosclerotic encephalopathy (SAE), also called lower-body parkinsonism, and cerebellar ataxia are two other gait disorders whose symptoms seem to closely resemble that of Parkinson's. However, through regression analysis studies have revealed that in Parkinson's, increasing the velocity of walking changes the stride length linearly (which resembles that of controls). However, in SAE and cerebellar ataxia stride length had a disproportionate contribution to increasing velocity, indicating that SAE and cerebellar ataxia have common underlying mechanisms different from those of Parkinson's.

The hardware Creamware created was among the first linearly scalable DSP systems, with expansion DSP boards being offered to increase the processing power of the platform. As a real time DSP platform, there was no processing (waiting) time for changes to take effect. The software made by Creamware offered better visual handling of audio 'samples', sometimes called 'clips' or 'items' in similar software. A user could easily drag samples up and down virtual digital multi-tracks in a window called the 'arranger'.

The authors found that when temperatures first increased above ~15 °C in the spring, the population dynamics crossed a Hopf bifurcation from stability to repeated outbreak cycles, until stabilization again in the fall. Above the Hopf threshold, population-cycle amplitude increased roughly linearly with temperature. This study affirmed the classic concept of temperature as a "pacemaker of all vital rates." Understanding life-cycle dynamics is relevant for pest control because some insecticides only work at one or two life stages of the insect.

The particular sequence of shots was unimportant: the individual guns could have fired in a completely different pattern from the way they actually did, but the sound produced would still have been the same. These ideas combined to form the basis of Metastaseis. As Newtonian views of time show it flowing linearly, Einsteinian views show it as a function of matter and energy; change one of those quantities and time too is changed. Xenakis attempted to make this distinction in his music.

The CEBus standard includes such things as spread spectrum modulation on the power line. Spread spectrum involves starting a modulation at one frequency, and altering the frequency during its cycle. The CEBus power line standard begins each burst at 100 kHz, and increases linearly to 400 kHz during a 100 microsecond duration. Both the bursts (referred to as "superior" state) and the absence of burst (referred to as the "inferior" state) create similar digits, so a pause in between is not necessary.

The magnetic field of a linear motor sweeping to the left, past an aluminium block. Coloured by induced electric current. In this electric motor design, the force is produced by a linearly moving magnetic field acting on conductors in the field. Any conductor, be it a loop, a coil, or simply a piece of plate metal, that is placed in this field will have eddy currents induced in it thus creating an opposing magnetic field in accordance with Lenz's law.

Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the amplitude of the analog signal is sampled regularly at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps. Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform.

The energy needed per unit distance increases by the square of the velocity and the time decreases linearly. For example, 2.5 times as much power is needed to travel at than . Aircraft take advantage of lower air pressure and lower temperatures by cruising at altitude to reduce energy consumption but unlike trains need to carry fuel on board. This has led to the suggestion of conveying maglev vehicles through partially evacuated tubes or tunnels with the possibility of supplying energy from renewable sources.

In other words, with these cardiomyopathies, as LV filling decreases, ejection fraction decreases directly, yet non-linearly and with a negative concavity (negative first and second derivatives). Similarly with tamponade, the degree of diastolic dysfunction is inversely proportional to the LV end-diastolic volume. So during inspiration, since LV filling is lesser relative to that during expiration, the diastolic dysfunction is also proportionally greater, so the systolic pressure drops >10 mmHg. This mechanism is also likely with pericarditis, where diastolic function is chastened.

Anodizing can also be performed in borate or tartrate baths in which aluminium oxide is insoluble. In these processes, the coating growth stops when the part is fully covered, and the thickness is linearly related to the voltage applied. These coatings are free of pores, relative to the sulfuric and chromic acid processes. This type of coating is widely used to make electrolytic capacitors because the thin aluminium films (typically less than 0.5 μm) would risk being pierced by acidic processes.

An example is the p–n junction diode (curve at right). As seen in the figure, the current does not increase linearly with applied voltage for a diode. One can determine a value of current (I) for a given value of applied voltage (V) from the curve, but not from Ohm's law, since the value of "resistance" is not constant as a function of applied voltage. Further, the current only increases significantly if the applied voltage is positive, not negative.

In addition, the eardrum itself moves in a very chaotic fashion at frequencies >3 kHz. The linear attachment of the eardrum to the malleus actually smooths out this chaotic motion and allows the ear to respond linearly over a wider frequency range than a point attachment. The auditory ossicles can also reduce sound pressure (the inner ear is very sensitive to overstimulation), by uncoupling each other through particular muscles. The middle ear efficiency peaks at a frequency of around 1 kHz.

The game plays out linearly, requiring input from the player in the form of short minigames which help mimic or reveal Florence's thoughts and actions. These games include: Florence brushing her teeth, Florence following the sound of a cello to find Krish, Krish cleaning his room before Florence visits, and Florence packing up her things when Krish moves in—and giving Krish's things back to him when he moves out—among others. A single play-through of Florence takes approximately 30 minutes.

Alisport Silent 2 The fuselage is carbon and glass fiber composite with epoxy resin. The wings have an elliptical planform, vertical or elliptical design winglets. The wing structure includes extensive use of carbon fiber, both in the sandwich skins and in the tapered I-beam wing spar which uses pultruded carbon rods for the spar caps. The wing geometry is notable in that it varies non-linearly from the root to the tip, both in overall planform shape and in wing section profile.

The four basis vectors stem from the center of a regular tetrahedron and go to its four corners. Their coordinate addresses are (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0) and (0, 0, 0, 1) respectively. These may be scaled and linearly combined to span conventional XYZ space, with at least one of the four coordinates unneeded (set to zero) in any given quadrant. The normalization scheme is somewhat unusual in keeping all coordinates non- negative.

The cosmic microwave background contains a small linearly-polarized component attributed to Thomson scattering. That polarized component mapping out the so-called E-modes was first detected by DASI in 2002. The solar K-corona is the result of the Thomson scattering of solar radiation from solar coronal electrons. The ESA and NASA SOHO mission and the NASA STEREO mission generate three-dimensional images of the electron density around the sun by measuring this K-corona from three separate satellites.

Trajectories of projectiles launched at different elevation angles but the same speed of 10 m/s in a vacuum and uniform downward gravity field of 10 m/s2. Points are at 0.05 s intervals and length of their tails is linearly proportional to their speed. t = time from launch, T = time of flight, R = range and H = highest point of trajectory (indicated with arrows). The range, R, is the greatest distance the object travels along the x-axis in the I sector.

The dimension of the column space is called the rank of the matrix. The rank is equal to the number of pivots in the reduced row echelon form, and is the maximum number of linearly independent columns that can be chosen from the matrix. For example, the 4 × 4 matrix in the example above has rank three. Because the column space is the image of the corresponding matrix transformation, the rank of a matrix is the same as the dimension of the image.

The rate for the hydrolysis of cobalt(III) ammine (NH3-containing) halide complexes are deceptive, appearing to be associative but proceeding by a pathway that is dissociative in character. The hydrolysis of [Co(NH3)5Cl]2+ follows second order kinetics: the rate increases linearly with concentration of hydroxide as well as the starting complex. Studies show, however, that in the hydroxide deprotonates one NH3 ligand to give the conjugate base of the starting complex, i.e., [Co(NH3)4(NH2)Cl]+.

When entering the sacred space of the cathedral, its mass is arranged linearly based on a vertical axis, with two main arcades of stone. The two main arcades consists of ivory piers with patterned spandrels of blue and red, however, string courses outline the decorated triforium. The first three piers closest to the altar are topped with red abacuses to define the sacred space. The left and right aisles begin with ribbed vaults and then transition into an exposed beam ceiling.

Many voltage-controlled oscillators for electronic music are based on a capacitor charging linearly in an op-amp integrator configuration. When the capacitor charge reaches a certain level, a comparator generates a reset pulse, which discharges the capacitor and the cycle begins again. This produces a rising ramp (or sawtooth) waveform, and this type of oscillator core is known as a ramp core. A common DCO design uses a programmable counter IC such as the 8253 instead of a comparator.

In 2012, ARM contributed a new `udelay` implementation allowing the system timer built into many ARMv7 CPUs to be used instead of a busy-wait loop. This implementation was released in Version 3.6 of the Linux kernel. Timer-based delays are more robust on systems that use frequency scaling to dynamically adjust the processor's speed at runtime, as `loops_per_jiffies` values may not necessarily scale linearly. Also, since the timer frequency is known in advance, no calibration is needed at boot time.

The story features several loosely-interconnected narratives. Most individual narratives are linear, but the story jumps between them non-linearly. Early parts of the story focus on two main narratives: # The first one deals with attempts to create, understand and control interdimensional portals with the form of tunnels lined with human flesh, named "flesh interfaces", created by subjecting people to large doses of LSD. Flesh interfaces are first created in 1944 in Treblinka, and research about them is abandoned around the year 2020.

The magnitude of the electrochemical potential across the glass bulb is linearly related to the pH according to the Nernst equation. The reference electrode is insensitive to the pH of the solution, being composed of a metallic conductor, which connects to the display. This conductor is immersed in an electrolyte solution, typically potassium chloride, which comes into contact with the test solution through a porous ceramic membrane. The display consists of a voltmeter, which displays voltage in units of pH.

The notation is arranged linearly on the page and can be written with a typewriter that has the proper font installed. Unlike SignWriting or the Hamburg Notation System, it is based on the Latin alphabet and is phonemic, being restricted to the symbols needed to meet the requirements of ASL (or extended to BSL, etc.) rather than accommodating all possible signs. For example, there is a single symbol for circling movement, regardless of whether the plane of the movement is horizontal or vertical.

The depression is followed by linearly extended folded ridges and dome-shaped elevations substituting with wide synclinal valleys and constitutes in plan to the eastern part of the Shamakhy-Gobustan syncline. The northwestern section of the Jeyrankechmez corresponds to the topography of the Baku age alluvial- proluvial plain. The southeastern part of the depression characterized by younger abrasion-accretion marine plain and relief composed of the large brachyanticline elevations and broken by lengthwise ruptures. Mud volcanoes are typical for there.

The design of the distributed amplifiers was first formulated by William S. Percival in 1936.W. S. Percival, “Thermionic Valve Circuits,” British Patent Specification no. 460,562, filed 24 July 1936, granted January 1937. In that year Percival proposed a design by which the transconductances of individual vacuum tubes could be added linearly without lumping their element capacitances at the input and output, thus arriving at a circuit that achieved a gain-bandwidth product greater than that of an individual tube.

Researchers look at how luminance contrasts are spatially distributed in an image: the luminance contrasts are highly correlated the closer they are in measurable distance and less correlated the farther apart the pixels are. Independent component analysis (ICA) is an algorithm system that attempts to "linearly transform given (sensory) inputs into independent outputs (synaptic currents) ". ICA eliminates the redundancy by decorrelating the pixels in a natural image. Thus the individual components that make up the natural image are rendered statistically independent.

The inner disk within a radius of has a typical composition gradient that decreases linearly from the core. Beyond this radius, out to about , the gradient is much flatter. This suggests a different star formation history between the inner disk and the outer disk and halo, and may be explained by a scenario of "inside-out" galaxy formation. This occurs when gas is accumulated at large radii later in a galaxy's life space, while the gas at the core becomes exhausted.

The greater the aggregate distribution of the data, the more benefit there is in parallel processing of the data. Data-intensive processing requirements normally scale linearly according to the size of the data and are very amenable to straightforward parallelization. The fundamental challenges for data-intensive computing are managing and processing exponentially growing data volumes, significantly reducing associated data analysis cycles to support practical, timely applications, and developing new algorithms which can scale to search and process massive amounts of data.

For example, the solution space for the above equation is generated by . These two functions are linearly independent over , so the dimension of this space is two, as is the degree of the equation. A field extension over the rationals can be thought of as a vector space over (by defining vector addition as field addition, defining scalar multiplication as field multiplication by elements of , and otherwise ignoring the field multiplication). The dimension (or degree) of the field extension over depends on .

The Zhegalkin monomials, being linearly independent, span a 2n-dimensional vector space over the Galois field GF(2) (NB: not GF(2n), whose multiplication is quite different). The 22n vectors of this space, i.e. the linear combinations of those monomials as unit vectors, constitute the Zhegalkin polynomials. The exact agreement with the number of Boolean operations on n variables, which exhaust the n-ary operations on {0,1}, furnishes a direct counting argument for completeness of the Zhegalkin polynomials as a Boolean basis.

Let be a vector space, be a linearly independent set of elements of , and be a generating set. One has to prove that the cardinality of is not larger than that of . If is finite, this results from the Steinitz exchange lemma. (Indeed, the Steinitz exchange lemma implies every finite subset of has cardinality not larger than that of , hence is finite with cardinality not larger than that of .) If is finite, a proof based on matrix theory is also possible.

The classic traditional forms were emanating from and could be described by using Euclidean geometry for instance in relation to the cartesian triedre (one perpendicular axe for three "dimensions"). These forms can have material realisations (cubes, balls..). Many natural objects however cannot be satisfactorily described using the Euclidean geometry. Many of them are for instance fractals (Mandelbrot, 1983), because they are branched, have holes, or are too anfractuous, etc.. In their case the three dimensions are no more linked linearly.

The increasing thermal gradient counters the effect of the growing thermal buffer imposed by the growing ice front. It has been shown that a linearly decreasing temperature on one side of a freeze-cast will result in near-constant solidification velocity, yielding ice crystals with an almost constant thickness along the SSZ of an entire sample. However, as pointed out by Waschkies et al. even with constant solidification velocity, the thickness of the ice crystals does increase slightly over the course of freezing.

An adjoint solver allows one to compute the gradient of the quantity of interest with respect to all design parameters at the cost of one additional solve. This, potentially, leads to a linear speedup: the computational cost of constructing an accurate surrogate decrease, and the resulting computational speedup s scales linearly with the number d of design parameters. The reasoning behind this linear speedup is straightforward. Assume we run N primal solves and N adjoint solves, at a total cost of 2N.

Dissolution of sucrose and other sugars in water changes not only its specific gravity but its optical properties, in particular its refractive index and the extent to which it rotates the plane of linearly polarized light. The refractive index, nD, for sucrose solutions of various percentage by mass has been measured and tables of nD vs. °Bx published. As with the hydrometer, it is possible to use these tables to calibrate a refractometer so that it reads directly in °Bx.

For some purposes it is important to know that any linear combination of sine waves of the same period or frequency but different phase shifts is also a sine wave with the same period or frequency, but a different phase shift. This is useful in sinusoid data fitting, because the measured or observed data are linearly related to the and unknowns of the in-phase and quadrature components basis below, resulting in a simpler Jacobian, compared to that of and .

Every operational ice concentration algorithm is predicated on this principle or a slight variation. The NASA team algorithm, for instance, works by taking the difference of two channels and dividing by their sum. This makes the retrieval slightly nonlinear, but with the advantage that the influence of temperature is mitigated. This is because brightness temperature varies roughly linearly with physical temperature when all other things are equal—see emissivity—and because the sea ice emissivity at different microwave channels is strongly correlated.

The reason is that the attenuation coefficient also depends on concentration and density, even in the absence of any interactions. These changes are, however, usually negligible except for high concentrations and large oscillator strength. For high concentrations and/or oscillator strengths, it is the integrated absorbance which is linearly depending on concentration, at least as long as there are no local field effects. If there are local field effects, they can be approximately taken into account by applying the Lorentz-Lorenz relation.

Many simulation codes may be formulated naturally as ISLs. Since computing time and memory consumption grow linearly with the number of array elements, parallel implementations of ISLs are of paramount importance to research.Datta, Kaushik (2009) Auto-tuning Stencil Codes for Cache-Based Multicore Platforms , Ph.D. Thesis This is challenging since the computations are tightly coupled (because of the cell updates depending on neighboring cells) and most ISLs are memory bound (i.e. the ratio of memory accesses to calculations is high).

By design, the NDVI itself thus varies between -1.0 and +1.0. NDVI is functionally, but not linearly, equivalent to the simple infrared/red ratio (NIR/VIS). The advantage of NDVI over a simple infrared/red ratio is therefore generally limited to any possible linearity of its functional relationship with vegetation properties (e.g. biomass). The simple ratio (unlike NDVI) is always positive, which may have practical advantages, but it also has a mathematically infinite range (0 to infinity), which can be a practical disadvantage as compared to NDVI.

For amplitudes up to 15 or 20°, the velocity of a saccade linearly depends on the amplitude (the so-called saccadic main sequence, a term borrowed from astrophysics; see Figure). For amplitudes larger than 20°, the peak velocity starts to plateau (nonlinearly) toward the maximum velocity attainable by the eye at around 60°. For instance, a 10° amplitude is associated with a velocity of 300°/s, and 30° is associated with 500°/s."Sensory Reception: Human Vision: Structure and function of the Human Eye" vol.

It is important to note that \partial_if(a) is a linear transformation from V_i into W . Heuristically, if f has an i-th partial differential at a , then \partial_if(a) linearly approximates the change in the function f when we fix all of its entries to be a_j for j eq i , and we only vary the i-th entry. We can express this in the Landau notation as : f(a_1, \dots, a_i+h, \dots a_n) - f(a_1, \dots, a_n) = \partial_if(a)(h) + o(h).

Fig.1:Cross-section of a Fresnel rhomb (blue) with graphs showing the p component of vibration (parallel to the plane of incidence) on the vertical axis, vs. the s component (square to the plane of incidence and parallel to the surface) on the horizontal axis. If the incoming light is linearly polarized, the two components are in phase (top graph). After one reflection at the appropriate angle, the p component is advanced by 1/8 of a cycle relative to the s component (middle graph).

Implementing service-oriented provisioning requires the network operator to re-engineer the way services are created and distributed into a network. This re-engineering is a result of extensive usage of profile-oriented provisioning which technically is similar to service-oriented provisioning except that a profiles based approach does not scale properly. In a profile-oriented system the number of required profiles grows exponentially with the number of services provided by a network. In a service-oriented system the number of required "profiles" grows linearly.

Total binding energy provided by the strong interaction increases linearly with the number of nucleons, whereas electrostatic repulsion increases with the square of the atomic number, i.e. the latter grows faster and becomes increasingly important for heavy and superheavy nuclei. Superheavy nuclei are thus theoretically predicted and have so far been observed to predominantly decay via decay modes that are caused by such repulsion: alpha decay and spontaneous fission. Almost all alpha emitters have over 210 nucleons, and the lightest nuclide primarily undergoing spontaneous fission has 238.

For example, when people are motivated to donate money to altruistic causes, the quantity they are willing to give does not increase linearly with the magnitude of the issue: people are roughly as concerned about 200,000 birds getting stuck in oil as they are about 2,000.Desvousges, W.H., Johnson, F.R., Dunford, R.W., Boyle, K.J., Hudson, S.P., and Wilson, N. 1993, Measuring natural resource damages with contingent valuation: tests of validity and reliability. In Hausman, J.A. (ed), Contingent Valuation:A Critical Assessment, pp. 91–159 (Amsterdam: North Holland).

This leads to the total size required being (number of processors)×number of cache lines, having a storage overhead ratio of (number of processors)/(cache block size×8). It can be observed that directory overhead scales linearly with the number of processors. While this may be fine for a small number of processors, when implemented in large systems the size requirements for the directory becomes excessive. For example, with a block size of 32 bytes and 1024 processors, the storage overhead ratio becomes 1024/(32×8) = 400%.

Both linearly and circularly polarized X-rays will be available. Contrast due to polarization is invaluable in distinguishing fluorescence and diffraction signals and imaging magnetic domain structure by using techniques such as linear and circular dichroism and magnetic diffraction. Tomography. In X-ray tomography, one of these modes is combined with sample rotation to produce a series of two-dimensional projection images, to be used for reconstructing the sample’s internal three-dimensional structure. This will be particularly important for observing the morphology of complex nanostructures.

However, absorbance is linearly related to concentration, and so absorbance is often preferred for plotting a standard curve. This type of standard curve relates the concentration of the solution (on the x-axis) to measures of its absorbance (y-axis). To obtain such a curve, a series of dilutions of known concentration of a solution are prepared and readings are obtained for each of the dilutions (see plot at left). In this plot, the slope of the line is the product ε x l.

Atomic magnetometer principle of operation, depicting alkali atoms polarized by a circularly polarized pump beam, precessing in the presence of a magnetic field and being detected by optical rotation of a linearly polarized probe beam. Alkali metal vapor of sufficient density is obtained by simply heating solid alkali metal inside the vapor cell. A typical SERF atomic magnetometer can take advantage of low noise diode lasers to polarize and monitor spin precession. Circularly polarized pumping light tuned to the D_1 spectral resonance line polarizes the atoms.

This relationship can be exploited to measure the wall shear stress. If a sensor could directly measure the gradient of the velocity profile at the wall, then multiplying by the dynamic viscosity would yield the shear stress. Such a sensor was demonstrated by A. A. Naqwi and W. C. Reynolds. The interference pattern generated by sending a beam of light through two parallel slits forms a network of linearly diverging fringes that seem to originate from the plane of the two slits (see double-slit experiment).

If one replaces the field occurring in the definition of a vector space by a ring, one gets the definition of a module. For modules, linear independence and spanning sets are defined exactly as for vector spaces, although "generating set" is more commonly used than that of "spanning set". Like for vector spaces, a basis of a module is a linearly independent subset that is also a generating set. A major difference with the theory of vector spaces is that not every module has a basis.

Directly below it, for comparison purposes, is the linearly polarized light that entered the quarter-wave plate. In the upper image, because this is a plane wave, each vector leading from the axis to the helix represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the direction of travel. All the electric field vectors have the same magnitude indicating that the strength of the electric field does not change. The direction of the electric field however steadily rotates.

In linear problems, for example, a family of linearly independent solutions can be used to construct general solutions through the superposition principle. A good example of this is one-dimensional heat transport with Dirichlet boundary conditions, the solution of which can be written as a time-dependent linear combination of sinusoids of differing frequencies; this makes solutions very flexible. It is often possible to find several very specific solutions to nonlinear equations, however the lack of a superposition principle prevents the construction of new solutions.

How does FIR polarimetry work? A plasma is also an optically active media, meaning when a linearly polarized electromagnetic wave is propagating parallel (or anti-parallel) to the magnetic field, the polarization of the wave exiting the plasma will rotate a small angle. This is called Faraday rotation, and the angle is called the Faraday rotation angle. The FIR system measures the Faraday rotation, which is proportional to the line average of the electron density times the magnetic field component parallel to the beam path.

In 1853 he showed that an electrical double layer (DL) is essentially a molecular dielectric and stores charge electrostatically. Below the electrolyte's decomposition voltage, the stored charge is linearly dependent on the voltage applied. This early model predicted a constant differential capacitance independent from the charge density depending on the dielectric constant of the electrolyte solvent and the thickness of the double-layer.Srinivasan S. (2006) Fuel cells, from Fundamentals to Applications, Springer eBooks, , Chapter 2, Electrode/electrolyte interfaces: Structure and kinetics of charge transfer.

When a linearly polarized EM wave is propagating perpendicular to the magnetic field, the refractive index depends on whether the wave polarization is parallel or perpendicular to the magnetic field direction. Why choose FIR lasers? For plasma polarimetry-interferometry, the wavelength we chose is sufficiently long to provide measurable plasma induced phase changes, but sufficiently short to avoid complicated plasma-wave interactions, including the bending of the beam. There are many high power molecular laser lines available in this wavelength range, and many commercially available detectors.

Such a model is termed an exponential-response model (or log- linear model, since the logarithm of the response is predicted to vary linearly). Similarly, a model that predicts a probability of making a yes/no choice (a Bernoulli variable) is even less suitable as a linear-response model, since probabilities are bounded on both ends (they must be between 0 and 1). Imagine, for example, a model that predicts the likelihood of a given person going to the beach as a function of temperature.

The notion of group velocity is based on a linear approximation to the dispersion relation \omega(k) near a particular value of k. Equation 4.24 In this approximation, the amplitude of the wave packet moves at a velocity equal to the group velocity without changing shape. This result is an approximation that fails to capture certain interesting aspects of the evolution a free quantum particle. Notably, the width of the wave packet, as measured by the uncertainty in the position, grows linearly in time for large times.

The Maxover algorithm (Wendemuth, 1995) is "robust" in the sense that it will converge regardless of (prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if desired, even with optimal stability (maximum margin between the classes). For non-separable data sets, it will return a solution with a small number of misclassifications. In all cases, the algorithm gradually approaches the solution in the course of learning, without memorizing previous states and without stochastic jumps.

In these experiments, the strain of a stretched rubber sample was held fixed as the temperature was varied between 10 and 70 degrees Celsius. For each value of fixed strain, it is seen that the tensile stress varied linearly (to within experimental error). These experiments provide the most compelling evidence that entropy changes are the fundamental mechanism for rubber elasticity. The positive linear behavior of the stress with temperature sometimes leads to the mistaken notion that rubber has a negative coefficient of thermal expansion, i.e.

When counting is not feasible because the clock rate would be too high, analog methods can be used. Analog methods are often used to measure intervals that are between 10 and 200 ns. These methods often use a capacitor that is charged during the interval being measured. Initially, the capacitor is discharged to zero volts. When the start event occurs, the capacitor is charged with a constant current I1; the constant current causes the voltage v on the capacitor to increase linearly with time.

Intel Display Power Saving Technology or Intel DPST is an Intel backlight control technology. Intel claims that display take up most power in mobile devices and reducing backlight linearly affects energy footprint. Intel DPST technology aims to adaptively reduce backlight brightness while maintaining satisfactory visual performance. The Intel DPST subsystem analyzes the image to be displayed and it uses a set of algorithms to change the chroma value of pixels while reducing the brightness of backlight simultaneously such that there is minimum perceived visual degradation.

Economics of Education Review, 19(2), pp. 131-147. Together with Oosterbeek, he observes health, wealth or happiness among Dutch not to increase linearly in education: individuals with only a non-vocational secondary school degree are generally healthier, wealthier and happier than TVET or university graduates; moreover, they find IQ to increase health, social background to increase wealth, and being a woman to increase happiness.Hartog, J., Oosterbeek, H. (1998). Health, wealth and happiness: Why pursue a higher education? Economics of Education Review, 17(3), pp. 245-256.

Instead, all the variables are linearly scanned to determine their live range, represented as an interval. Once the live ranges of all variables have been figured out, the intervals are traversed chronologically. Although this traversal could help identifying variables whose live ranges interfere, no interference graph is being built and the variables are allocated in a greedy way. The motivation for this approach is speed; not in terms of execution time of the generated code, but in terms of time spent in code generation.

Diaz, (2001), section 4. This conjecture states that if x1 and x2 are two positive real algebraic numbers, neither of them equal to 1, then π² and the product are linearly independent over the rational numbers. This corresponds to the special case of the four exponentials conjecture whereby y1 = iπ, y2 = −iπ, and x1 and x2 are real. Perhaps surprisingly, though, it is also a corollary of Bertrand's conjecture, suggesting there may be an approach to the full four exponentials conjecture via the modular function j.

The Oscar Crow House is a historic house at 404 Washington Street in Star City, Arkansas. The single story wood-frame house was built in 1929 by Robert and Doug Verdue for Oscar Crow, owner of a local drug store. The Craftsman style house resembles a shotgun house, but does not exactly follow that form, because its rooms do not progress linearly from the front. The front of the house has a recessed porch supported by box columns, with a vent placed in the gable-end pediment.

In mathematics, a cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order. Cyclically ordered groups were first studied in depth by Ladislav Rieger in 1947. They are a generalization of cyclic groups: the infinite cyclic group and the finite cyclic groups . Since a linear order induces a cyclic order, cyclically ordered groups are also a generalization of linearly ordered groups: the rational numbers , the real numbers , and so on.

Individual cells are capable of taking up many DNA molecules, but the presence of multiple plasmids does not significantly affect the occurrence of successful transformation events. A number of factors may affect the transformation efficiency: Plasmid size – A study done in E. coli found that transformation efficiency declines linearly with increasing plasmid size, i.e. larger plasmids transform less well than smaller plasmids. Forms of DNA – Supercoiled plasmid have a slightly better transformation efficiency than relaxed plasmids – relaxed plasmids are transformed at around 75% efficiency of supercoiled ones.

As x increases from 0 to , the function 2x increases almost linearly from to . The exponential cent scale can therefore be accurately approximated as a piecewise linear function that is numerically correct at semitones. That is, n cents for n from 0 to 100 may be approximated as 1 + n instead of 2. The rounded error is zero when n is 0 or 100, and is about 0.72 cents high when n is 50, where the correct value of 2 = is approximated by 1 + × 50 = 1.02973.

In computer science, particularly the study of approximation algorithms, an L-reduction ("linear reduction") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preserving reduction. L-reductions in studies of approximability of optimization problems play a similar role to that of polynomial reductions in the studies of computational complexity of decision problems. The term L reduction is sometimes used to refer to log-space reductions, by analogy with the complexity class L, but this is a different concept.

In accelerator physics, a kinematically complete experiment is an experiment in which all kinematic parameters of all collision products are determined. If the final state of the collision involves n particles 3n momentum components (3 Cartesian coordinates for each particle) need to be determined. However, these components are linked to each other by momentum conservation in each direction (3 equations) and energy conservation (1 equation) so that only 3n-4 components are linearly independent. Therefore, the measurement of 3n-4 momentum components constitutes a kinematically complete experiment.

Hexacene is an aromatic molecule consisting of six linearly-fused benzene rings. It is one of a series of linear polycyclic molecules created by such aromatic ring fusions, a series termed acenes—the previous in the series being pentacene (with five fused rings) and the next being heptacene (with seven). The CAS registry number for hexacene is , and it has a molecular weight of 328 g/mol. It and other acenes and their derivatives have been investigated in potential applications related to organic semiconductors.

This ordering of is called the universal cover of . Its order type is independent of the choice of , but the notation is not, since the integer coordinate "rolls over" at . For example, although the cyclic order of pitch classes is compatible with the A-to-G alphabetical order, C is chosen to be the first note in each octave, so in note-octave notation, B3 is followed by C4. The inverse construction starts with a linearly ordered set and coils it up into a cyclically ordered set.

Discrete dynamical systems on cyclically ordered spaces have also been studied. The interval topology forgets the original orientation of the cyclic order. This orientation can be restored by enriching the intervals with their induced linear orders; then one has a set covered with an atlas of linear orders that are compatible where they overlap. In other words, a cyclically ordered set can be thought of as a locally linearly ordered space: an object like a manifold, but with order relations instead of coordinate charts.

A cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order. Cyclically ordered groups were first studied in depth by Ladislav Rieger in 1947. They are a generalization of cyclic groups: the infinite cyclic group and the finite cyclic groups . Since a linear order induces a cyclic order, cyclically ordered groups are also a generalization of linearly ordered groups: the rational numbers , the real numbers , and so on.

Diagonal matrices occur in many areas of linear algebra. Because of the simple description of the matrix operation and eigenvalues/eigenvectors given above, it is typically desirable to represent a given matrix or linear map by a diagonal matrix. In fact, a given n-by-n matrix A is similar to a diagonal matrix (meaning that there is a matrix X such that X−1AX is diagonal) if and only if it has n linearly independent eigenvectors. Such matrices are said to be diagonalizable.

Quark forcibly takes Zek back to the wormhole to ask the Prophets what they did to him. The Prophets, being immaterial creatures who do not experience time linearly, found Zek's obsession with accumulation of material wealth to be strange and adversarial. They "de-evolved" him to a more primitive state resembling the less greedy ancestors of the Ferengi. They threaten to de-evolve Quark as well, but Quark warns them that if he is also changed, more curious Ferengi will visit the wormhole looking for answers.

Three related terms are used in this context: ;Late-life mortality deceleration :Hazard rate increasing at a decreasing rate (rather than increasing log-linearly as in the Gompertz law). ; :More strongly, hazard rate eventually stops increasing (or rather, asymptotes towards a limit), and then proceeds at a constant rate (or rather, approaches a constant rate), yielding (slightly sub-) exponential decay, as in radioactive decay. ; This is used synonymously with "mortality leveling-off", or rather to refer to the region where hazard rate is approximately constant.

An oligodendrocyte seen myelinating several axons. Mammalian nervous systems depend crucially on myelin sheaths, which reduce ion leakage and decrease the capacitance of the cell membrane, for rapid signal conduction. Myelin also increases impulse speed, as saltatory propagation of action potentials occurs at the nodes of Ranvier in between Schwann cells (of the PNS) and oligodendrocytes (of the CNS). Furthermore, impulse speed of myelinated axons increases linearly with the axon diameter, whereas the impulse speed of unmyelinated cells increases only with the square root of the diameter.

The round- shaped dunes (dots) were formed when the winds that caused the linearly-shaped accumulations were interrupted. The round dunes are classified as "barchanoid dunes". However, the exact mechanism of either formation is still unknown and this is the reason the area was chosen for imaging by the HiRISE mission. Veronica Bray, HiRISE camera targeting specialist, commented that there are similarly shaped dunes in other locations on Mars, but the Hagal field provides better images of these shapes due to the uncommon characteristics of its topography.

In a homogeneous elastic medium, complex oscillations (vibrations in a material or light flows) can be described as the superposition of many simple sinusoidal waves, either transverse (linearly polarized) or longitudinal. The vibrations of a violin string, for example, can be analyzed as the sum of many transverse waves of different frequencies, that displace the string either up or down or left to right. The ripples in a pond can be analyzed as a combination of transverse and longitudinal waves (gravity waves) that propagate together.

According to the recoding interference hypothesis, verbalizing non-verbal memory makes the visual representations less accurate. The recoding interference hypothesis predicts that verbal overshadowing will occur more readily if participants generate less accurate verbal descriptions. A computational model detected core processing principles of the recoding interference hypothesis to simulate facial recognition, and it reproduced these behavioral phenomena as well as verbal overshadowing, providing an account as to why target description accuracy does not linearly predict recognition accuracy. The study addressed the replicability issues in verbal overshadowing.

The light-like vectors of Minkowski space are null vectors. The four linearly independent biquaternions , , , and are null vectors and } can serve as a basis for the subspace used to represent spacetime. Null vectors are also used in the Newman–Penrose formalism approach to spacetime manifolds.Patrick Dolan (1968) A Singularity-free solution of the Maxwell-Einstein Equations, Communications in Mathematical Physics 9(2):161–8, especially 166, link from Project Euclid A composition algebra splits when it has a null vector; otherwise it is a division algebra.

The most immediate case is to apply polynomial functions to a square matrix, extending what has just been discussed. In the finite-dimensional case, the polynomial functional calculus yields quite a bit of information about the operator. For example, consider the family of polynomials which annihilates an operator T. This family is an ideal in the ring of polynomials. Furthermore, it is a nontrivial ideal: let n be the finite dimension of the algebra of matrices, then {I, T, T2...Tn} is linearly dependent.

A Finnish study assayed psilocybin concentrations in old herbarium specimens, and concluded that although psilocybin concentration decreased linearly over time, it was relatively stable. They were able to detect the chemical in specimens that were 115 years old. Michael Beug and Jeremy Bigwood, analyzing specimens from the Pacific Northwest region of the United States, reported psilocybin concentrations ranging from 0.62% to 1.28%, averaging 1.0 ±0.2%. They concluded that the species was one of the most potent, as well as the most constant in psilocybin levels.

The rate for the hydrolysis of cobalt(III) ammine halide complexes are deceptive, appearing to be associative but proceeding by an alternative pathway. The hydrolysis of [Co(NH3)5Cl]2+ follows second order kinetics: the rate increases linearly with concentration of hydroxide as well as the starting complex. Based on this information, the reactions would appear to proceed via nucleophilic attack of hydroxide at cobalt. Studies show, however, that the hydroxide deprotonates one NH3 ligand to give the conjugate base of the starting complex, i.e.

Just like in marching cubes, the intersections of these edges with the isosurface are approximated by linearly interpolating the values at the grid points. Adjacent cubes share all edges in the connecting face, including the same diagonal. This is an important property to prevent cracks in the rendered surface, because interpolation of the two distinct diagonals of a face usually gives slightly different intersection points. An added benefit is that up to five computed intersection points can be reused when handling the neighbor cube.

More generally, a TUF allows downward (and upward) step functions to have any pre- and post-critical time utilities. Tardiness represented as a TUF is a special case whose non-zero utility is the linear function C - d, where C is the action's completion time—either current, expected, or believed. More generally, a TUF allows non-zero earliness and tardiness to be non- linear—e.g., increasing tardiness may result in non-linearly decreasing utility (greater "penalty" or "cost"), such as when detecting a threat.

Shunting is an event in the neuron which occurs when an excitatory postsynaptic potential and an inhibitory postsynaptic potential are occurring close to each other on a dendrite, or are both on the soma of the cell.Kandel, E. R., Schwartz, J. H., Jessell, T. M. (2000) [1981]. Principles of Neural Science (Fourth ed.). New York: McGraw-Hill. pp. 217, 223-225 According to temporal summation one would expect the inhibitory and excitatory currents to be summed linearly to describe the resulting current entering the cell.

RRS can be used because the change in this was linearly correlated to the concentration of ethion (Range: 10.0–900.0 mg/L). Furthermore, it has as advantages over general detection methods that ethion can be measured in just 3 minutes and that no pretreatment of the sample is required before the measurement. From interference tests it became clear that the method has a very good selectivity for ethion. The limit of detection (LOD) was 3.7 mg/L and limit of quantification (LOQ) was 11.0 mg/L.

Taxes may be changed by the government or policymakers at different levels. For instance, when a low tax is levied, the deadweight loss is also small (compared to a medium or high tax). An important consideration is that the deadweight loss resulting from a tax increases more quickly than the tax itself; the area of the triangle representing the deadweight loss is calculated using the area (square) of its dimension. Where a tax increases linearly, the deadweight loss increases as the square of the tax increase.

The energy of the selected ions is increased by application of a supplemental resonance excitation voltage applied to all segments of two rods located on the X-axis. This increase of energy causes dissociation of the selected ions due to collisions with damping gas. The product ions formed are retained in the trapping field. Scanning the contents of the trap to produce a mass spectrum is accomplished by linearly increasing the RF voltage applied to all sections of the trap and utilizing a supplemental resonance ejection voltage.

One uses the technique of separation of variables to extract the corresponding solutions for the radial dependencies. In practice, many fields can be well approximated with a finite number of multipole moments (although an infinite number may be required to reconstruct a field exactly). A typical application is to approximate the field of a localized charge distribution by its monopole and dipole terms. Problems solved once for a given order of multipole moment may be linearly combined to create a final approximate solution for a given source.

As the content can vary widely, zoned editions are often produced in parallel. Editioning occurs in the main sections as news is updated throughout the night. The advertising is usually the same in each edition (with the exception of zoned regionals, in which it is often the 'B' section of local news that undergoes advertising changes). As each edition represents the latest news available for the next press run, these editions are produced linearly, with one completed edition being copied and updated for the next edition.

The core of the Andromeda Galaxy is called 2C 56 in the 2C radio astronomy catalog. In 2009, the first planet may have been discovered in the Andromeda Galaxy. This was detected using a technique called microlensing, which is caused by the deflection of light by a massive object. Observations of linearly polarized radio emission with the Westerbork Synthesis Radio Telescope, the Effelsberg 100-m telescope, and the Very Large Array revealed ordered magnetic fields aligned along the "10-kpc ring" of gas and star formation.

The "Nanos" of Reus. The principal Reus festivity is Sant Pere on June 29, declared of National Touristic Interest. One of the most characteristic and popular acts of these festivities is the so-called tronada, which is a series of 29 little mortars masclets with bangers interleaved, arranged linearly around the Mercadal square (where the city hall is located), united by a hand craft gunpowder line. This line ends in a square shape in front of the city hall, with more bangers and 9 more masclets.

The Aberth method, or Aberth–Ehrlich method, named after Oliver Aberth and Louis W. Ehrlich, is a root-finding algorithm developed in 1967 for simultaneous approximation of all the roots of a univariate polynomial. This method converges cubically, an improvement over the Durand–Kerner method, another algorithm for approximating all roots at once, which converges quadratically. (However, both algorithms converge linearly at multiple zeros.) This method is used in MPSolve, which is the reference software for approximating all roots of a polynomial to an arbitrary precision.

Startlight intensity has been observed to be a function of its polarization. Starlight becomes partially linearly polarized by scattering from elongated interstellar dust grains whose long axes tend to be oriented perpendicular to the galactic magnetic field. According to the Davis–Greenstein mechanism, the grains spin rapidly with their rotation axis along the magnetic field. Light polarized along the direction of the magnetic field perpendicular to the line of sight is transmitted, while light polarized in the plane defined by the rotating grain is blocked.

This disorder is caused by the deletion of the long arm of chromosome 13, which can either be deleted linearly or as a ring chromosome. It is typically not hereditary— the loss of a portion of the chromosome typically occurs during gametogenesis, making it a de novo mutation. When it is hereditary, it is usually caused by a parent having mosaicism or a balanced translocation. The severity of the disorder is correlated with the size of the deletion, with larger deletions causing more severe manifestations.

Throughout time, the Hawaiian Islands formed linearly from northwest to the southeast. A study was conducted to determine the approximate ages of the Hawaiian Islands using K–Ar dating of the oldest found igneous rocks from each island. Kauai was determined to be about 5.1 million years old, Oahu about 3.7 million years old and the youngest island of Hawaii about 0.43 million years old. By determining the maximum age of the islands, inferences could be made about the maximum possible age of organisms inhabiting the island.

Another graph shows that performance on these games scales nearly linearly with the number of cores up to 32 cores. At 48 cores the performance drops to 90% of what would be expected if the linear relationship continued. A June 2007 PC Watch article suggested that the first Larrabee chips would feature 32 x86 processor cores and come out in late 2009, fabricated on a 45 nanometer process. Chips with a few defective cores due to yield issues would be sold as a 24-core version.

Magnetic amplifiers were widely studied during the 1950s as a potential switching element for mainframe computers. Mag amps could be used to sum several inputs in a single core, which was useful in the arithmetic logic unit (ALU). Custom tubes could do the same, but transistors could not, so the mag amp was able to combine the advantages of tubes and transistors in an era when the latter were expensive and unreliable. The principles of magnetic amplifiers were applied non linearly to create magnetic digital logic gates.

Since a nontrivial quadratic equation has at most two solutions, this line actually lies in the Lie quadric, and any point [q] on this line defines a cycle incident with [x], [y] and [z]. Thus there are infinitely many solutions in this case. If instead x, y and z are linearly independent then the subspace V orthogonal to all three is 2-dimensional. It can have signature (2,0), (1,0), or (1,1), in which case there are zero, one or two solutions for [q] respectively.

The times needed for lanthanites to fully crystallize increase linearly with the ionic potential of the trivalent rare- earth ion (La3+, Ce3+, Pr3+, Nd3+) present in their structure. The differences in these ion sizes and ionic potential as well as differences in dehydration energy of the trivalent rare-earth ions control the lifetime of the poorly ordered precursor and thus also the crystallization kinetics of the lanthanites. Furthermore, they also affect the structural characteristics (e.g. unit-cell dimensions and standard shape) of the crystals.

The plot is not told linearly, but is composed of individual report fragments and flashbacks.Rudolf Hermes: "Muß man gesehen haben...", review of the 2018 staging in Hagen 2018, in: Der Opernfreund, May 6, 2018, accessed July 6, 2018.In addition, there are always interjections from the choir in the form of comments, questions, echoes or time information. At the end of the opera it becomes clear that the choir is composed of the souls of the many victims of the mountain who are waiting for "another name".

The Johnson-Lindenstrauss lemma states that large sets of vectors in a high-dimensional space can be linearly mapped in a space of much lower (but still high) dimension n with approximate preservation of distances. One of the explanations of this effect is the exponentially high quasiorthogonal dimension of n-dimensional Euclidean space. There are exponentially large (in dimension n) sets of almost orthogonal vectors (with small value of inner products) in n–dimensional Euclidean space. This observation is useful in indexing of high-dimensional data.

The best focus for a given feature size varies as a strong function of pitch, polarity, and orientation under a given illumination. At 36 nm pitch, horizontal and vertical darkfield features have more than 30 nm difference of focus. The 34 nm pitch and 48 nm pitch features have the largest difference of best focus regardless of feature type. In the 48-64 nm pitch range, the best focus position shifts roughly linearly as a function of pitch, by as much as 10-20 nm.

An m x n matrix () where the row index varies from 1 to m and column index from 1 to n,aij denotes the number in the ith row and the jth column. In the computer memory, all elements are stored linearly using contiguous addresses. Therefore,in order to store a two-dimensional matrix a, two dimensional address space must be mapped to one-dimensional address space. In the computer's memory matrices are stored in either Row-major order or Column-major order form.

Cyclomatic complexity is a software metric used to indicate the complexity of a program. It is a quantitative measure of the number of linearly independent paths through a program's source code. It was developed by Thomas J. McCabe, Sr. in 1976. Cyclomatic complexity is computed using the control flow graph of the program: the nodes of the graph correspond to indivisible groups of commands of a program, and a directed edge connects two nodes if the second command might be executed immediately after the first command.

The ACV frequency is used to monitor the Faradaic current, which quantifies target binding. The generation of signal has been reported to be insensitive to ACV frequency as long as the ACV is in a sensible range, therefore, not too low to be detected or too fast. The ACV frequency is used instead of a single-directional current to protect the degradation of the electrodes. Square wave voltammetry is applied and measured to analyze the change in current as the voltage is swept linearly across an electrode.

Cross-section of a Fresnel rhomb (blue) with graphs showing the p component of vibration (parallel to the plane of incidence) on the vertical axis, vs. the s component (square to the plane of incidence and parallel to the surface) on the horizontal axis. If the incoming light is linearly polarized, the two components are in phase (top graph). After one reflection at the appropriate angle, the p component is advanced by 1/8 of a cycle relative to the s component (middle graph).

This then corresponds to the second derivative of a function which, when positive, indicates a curvature that is 'lower at the centre' i.e. sagging. When defining moments and curvatures in this way calculus can be more readily used to find slopes and deflections. Critical values within the beam are most commonly annotated using a bending moment diagram, where negative moments are plotted to scale above a horizontal line and positive below. Bending moment varies linearly over unloaded sections, and parabolically over uniformly loaded sections.

The wavelength of the writing laser is chosen such that it is not linearly absorbed by the medium, and therefore it does not interact with the medium except at the focal point. At the focal point two-photon absorption becomes significant, because it is a nonlinear process dependent on the square of the laser fluence. Writing by two-photon absorption can also be achieved by the action of two lasers in coincidence. This method is typically used to achieve the parallel writing of information at once.

Similarly, the exponents for are and for the two solutions. One has thus where the condition (sometimes called Riemann's identity) :\alpha + \alpha' + \beta + \beta' + \gamma + \gamma' = 1 on the exponents of the solutions of Riemann's differential equation has been used to define . The first set of constants on the left hand side in , denotes the regular singular points of Riemann's differential equation. The second set, , are the corresponding exponents at for one of the two linearly independent solutions, and, accordingly, are exponents at for the second solution.

Also termed data cache block touch, the effect is to request loading the cache line associated with a given address. This is performed by the `PREFETCH` instruction in the x86 instruction set. Some variants bypass higher levels of the cache hierarchy, which is useful in a 'streaming' context for data that is traversed once, rather than held in the working set. The prefetch should occur sufficiently far ahead in time to mitigate the latency of memory access, for example in a loop traversing memory linearly.

A full-wave plate introduces a phase difference of exactly one wavelength between the two polarization directions, for one wavelength of light. In optical mineralogy, it is common to use a full-wave plate designed for green light (wavelength = 540 nm). Linearly polarized white light which passes through the plate becomes elliptically polarized, except for 540 nm light which will remain linear. If a linear polarizer oriented perpendicular to the original polarization is added, this green wavelength is fully extinguished but elements of the other colors remain.

The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric field instead of varying linearly with it. All materials show a Kerr effect, but certain liquids display it more strongly than others. The Kerr effect was discovered in 1875 by John Kerr, a Scottish physicist.

This is not to be confused with a meter per second (m/s), a unit of velocity, the time-derivative of position. For example, opening the gate of a gate valve (of rectangular cross section) by 1 mm for 10 seconds yields the same absement of 10 mm·s as opening it by 5 mm for 2 seconds. The amount of water having flowed through it is linearly proportional to the absement of the gate, so it is also the same in both cases.Maya Burhanpurkar.

Marx & Van Muffling (1922) Radio Reception, p.96-101 The smaller coil was mounted on a rack so it could be slid linearly in or out of the larger coil. If radio interference was encountered, the smaller coil would be slid further out of the larger, loosening the coupling, narrowing the bandwidth, and thereby rejecting the interfering signal. The antenna coupling transformer also functioned as an impedance matching transformer, that allowed a better match of the antenna impedance to the rest of the circuit.

A system being acted upon by Coulomb damping is nonlinear because the frictional force always opposes the direction of motion of the system as stated earlier. And because there is friction present, the amplitude of the motion decreases or decays with time. Under the influence of Coulomb damping, the amplitude decays linearly with a slope of ±((2μmgωn)/(πk)) where ωn is the natural frequency. The natural frequency is the number of times the system oscillates between a fixed time interval in an undamped system.

The strength of the magnetic field is not linearly related to the ampere-turns when a magnetic material is used as a part of the system. Also, the material within the magnet carrying the magnetic flux "saturates" at some point, after which adding more ampere- turns has little effect. The ampere-turn is equal to gilberts, the equivalent CGS unit. Alternatively, NI (the product of the number of turns, N, and the current [in amperes], I) has been used in industry, specifically, US-based coil-making industries.

If a system is cooled at any non-zero rate (e.g. linearly) through a continuous phase transition, the time to reach the transition will eventually become shorter than the correlation time of the critical fluctuations. At this time, the fluctuations are too slow to follow the cooling rate; the system has fallen out of equilibrium and ceases to be adiabatic. A "fingerprint" of critical fluctuations is taken at this fall-out time and the longest-length scale of the domain size is frozen out.

Thus the line is a parametric curve with the parameter which is the number of the interval for the quantile. If the two distributions being compared are similar, the points in the Q–Q plot will approximately lie on the line . If the distributions are linearly related, the points in the Q–Q plot will approximately lie on a line, but not necessarily on the line . Q–Q plots can also be used as a graphical means of estimating parameters in a location-scale family of distributions.

KTP crystal, viewed down b axis, used in second harmonic generation. Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (values of atomic electric fields, typically 108 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear.

The approach is strongly related to density networks which use importance sampling and a multi-layer perceptron to form a non-linear latent variable model. In the GTM the latent space is a discrete grid of points which is assumed to be non- linearly projected into data space. A Gaussian noise assumption is then made in data space so that the model becomes a constrained mixture of Gaussians. Then the model's likelihood can be maximized by EM. In theory, an arbitrary nonlinear parametric deformation could be used.

The effects of rosuvastatin on low-density lipoprotein (LDL) cholesterol are dose- related. Higher doses were more efficacious in improving the lipid profile of patients with hypercholesterolemia than milligram-equivalent doses of atorvastatin and milligram-equivalent or higher doses of simvastatin and pravastatin. Meta-analysis showed that rosuvastatin is able to modestly increase levels of high-density lipoprotein (HDL) cholesterol as well, as with other statins. A 2014 Cochrane review determined there was good evidence for rosuvastatin lowering non-HDL levels linearly with dose.

Stochastic effects are those that occur randomly, such as radiation-induced cancer. The consensus of nuclear regulators, governments and the UNSCEAR is that the incidence of cancers due to ionizing radiation can be modeled as increasing linearly with effective dose at a rate of 5.5% per sievert. This is known as the Linear no-threshold model (LNT model). Some commentators such as the French Academy of Sciences (2005, Dose- effect relationships and...Tubiana, M. and Aurengo, A. Académie des Sciences & Académie Nationale de Médecine.

"Bulk reading" is a strategy for interrogating multiple tags at the same time, but lacks sufficient precision for inventory control. A group of objects, all of them RFID tagged, are read completely from one single reader position at one time. Bulk reading is a possible use of HF (ISO 18000-3), UHF (ISO 18000-6) and SHF (ISO 18000-4) RFID tags. However, as tags respond strictly sequentially, the time needed for bulk reading grows linearly with the number of labels to be read.

Fig.1:Field vectors (E,D,B,H) and propagation directions (ray and wave-normal) for linearly-polarized plane electromagnetic waves in a non-magnetic birefringent crystal. The plane of vibration, containing both electric vectors (E & D) and both propagation vectors, is sometimes called the "plane of polarization" by modern authors. Fresnel's "plane of polarization", traditionally used in optics, is the plane containing the magnetic vectors (B & H) and the wave-normal. Malus's original "plane of polarization" was the plane containing the magnetic vectors and the ray.

The initial derivation of SEA arose from independent calculations made in 1959 by Richard LyonLYON, R.H.; MAIDANIK, G.: Power Flow Between Linearly Coupled Oscillators, Journal of the Acoustical Society of America; 34, pp.623-639, 1962 and Preston SmithSmith, P. W. "Response and radiation of structural modes excited by sound." The Journal of the Acoustical Society of America 34.5 (1962): 640-647. as part of work concerned with the development of methods for analyzing the response of large complex aerospace structures subjected to spatially distributed random loading.

Around 1975 she was the chairman of the local Cologne chapter of Deutscher Akademikerinnenbund ("Association of German women academics"). With her doctoral advisor Fritz Goos, Hänchen discovered the Goos-Hänchen effect, which is an optical phenomenon in which linearly polarized light undergoes a small lateral shift when totally internally reflected. In 1946 she married physicist Albert Hermann Lindberg (born 1914), who before his retirement in 1979 served as the Vice President and Development Director of Leybold AG. They had three daughters - Renate, Claudia, and Dorothea.

227 show fusees. The earliest existing clock with a fusee, also the earliest spring-powered clock, is the Burgunderuhr (Burgundy clock), a chamber clock whose iconography suggests that it was made for Phillipe the Good, Duke of Burgundy about 1430, now in the Germanisches Nationalmuseum The word fusee comes from the French fusée and late Latin fusata, 'spindle full of thread'. The torque provided by a mainspring decreases linearly as the spring unwinds during a clock's running period. The fusee's purpose is to even out this torque.

Valve disc A disc or valve member is a movable obstruction inside the stationary body that adjustably restricts flow through the valve. Although traditionally disc-shaped, discs come in various shapes. Depending on the type of valve, a disc can move linearly inside a valve, or rotate on the stem (as in a butterfly valve), or rotate on a hinge or trunnion (as in a check valve). A ball is a round valve member with one or more paths between ports passing through it.

In contrast to positively curved varieties such as del Pezzo surfaces, a complex algebraic K3 surface X is not uniruled; that is, it is not covered by a continuous family of rational curves. On the other hand, in contrast to negatively curved varieties such as surfaces of general type, X contains a large discrete set of rational curves (possibly singular). In particular, Fedor Bogomolov and David Mumford showed that every curve on X is linearly equivalent to a positive linear combination of rational curves.Huybrechts (2016), Corollary 13.1.5.

The E-plane and H-plane are reference planes for linearly polarized waveguides, antennas and other microwave devices. In waveguide systems, as in the electric circuits, it is often desirable to be able to split the circuit power into two or more fractions. In a waveguide system, an element called a junction is used for power division. In a low frequency electrical network, it is possible to combine circuit elements in series or in parallel, thereby dividing the source power among several circuit components.

The total amount of nectar foraged increases linearly with time spent in a patch. However, the weight of the nectar adds a significant cost to the bee's flight between flowers and its trip back to the hive. Wolf and Schmid-Hempel showed, by experimentally placing varying weights on the backs of bees, that the cost of heavy nectar is so great that it shortens the bees' lifespan. The shorter the lifespan of a worker bee, the less overall time it has to contribute to its colony.

To endow the Grassmannian with the structure of a differentiable manifold, choose a basis for . This is equivalent to identifying it with with the standard basis, denoted (e_1, \dots, e_n) , viewed as column vectors. Then for any -dimensional subspace , viewed as an element of , we may choose a basis consisting of linearly independent column vectors (W_1, \dots, W_k) . The homogeneous coordinates of the element consist of the components of the rectangular matrix of maximal rank whose th column vector is W_i, \quad i=1, \dots, k .

A high pressure grinding roll, often referred to as HPGRs or roller press, consists out of two rollers with the same dimensions, which are rotating against each other with the same circumferential speed. The special feeding of bulk material through a hopper leads to a material bed between the two rollers. The bearing units of one roller can move linearly and are pressed against the material bed by springs or hydraulic cylinders. The pressures in the material bed are greater than 50 MPa (7,000 PSI).

Magnetic media are inherently non-linear, but AC bias was the means whereby the magnetisation of the recording tape was made linearly proportional to the electrical signal which represents the audio component. The Magnetophon became a 'high fidelity' recording system because in so many respects, it outperformed gramophone recording (which was the 78 rpm system of the time). Many speeches, concerts, and operatic performances were recorded. Since many of the recordings survived World War II they were later issued on LPs and compact discs.

The left end, −1, is never replaced (it does not change at first and after the first three iterations, is negative on the interval) and thus the width of the bracket never falls below 1. Hence, the right endpoint approaches 0 at a linear rate (the number of accurate digits grows linearly, with a rate of convergence of 2/3). For discontinuous functions, this method can only be expected to find a point where the function changes sign (for example at for or the sign function).

The other significant invariant of D is its degree d, which is the sum of all its coefficients. A divisor is called special if ℓ(K − D) > 0, where K is the canonical divisor.Hartshorne p.296 Clifford's theorem states that for an effective special divisor D, one has: :\ell(D)- 1 \le d/2, and that equality holds only if D is zero or a canonical divisor, or if C is a hyperelliptic curve and D linearly equivalent to an integral multiple of a hyperelliptic divisor.

In the linear approximation we find: Fnorm=1+(∂F/∂T-ST)ΔT. Due to the linearity of the fluorescence intensity and the thermophoretic depletion, the normalized fluorescence from the unbound molecule Fnorm(A) and the bound complex Fnorm(AT) superpose linearly. By denoting x the fraction of molecules bound to targets, the changing fluorescence signal during the titration of target T is given by: Fnorm=(1-x) Fnorm(A)+x Fnorm(AT). Quantitative binding parameters are obtained by using a serial dilution of the binding substrate.

The Interpolated Spread or I-spread or ISPRD of a bond is the difference between its yield to maturity and the linearly interpolated yield for the same maturity on an appropriate reference yield curve. The reference curve may refer to government debt securities or interest rate swaps or other benchmark instruments, and should always be explicitly specified. If the bond is expected to repay some principal before its final maturity, then the interpolation may be based on the weighted-average life, rather than the maturity.

Atlantic multidecadal oscillation spatial pattern obtained as the regression of monthly HadISST sea surface temperature anomalies (1870-2013). Atlantic Multidecadal Oscillation Index according to the methodology proposed by van Oldenborgh et al. 1880-2018. Atlantic Multidecadal Oscillation index computed as the linearly detrended North Atlantic sea surface temperature anomalies 1856-2013. The Atlantic Multidecadal Oscillation (AMO), also known as Atlantic Multidecadal Variability (AMV), is a climate cycle that affects the sea surface temperature (SST) of the North Atlantic Ocean based on different modes on multidecadal timescales.

This discovery marked the first concerted effort towards frame theory. The frame condition was first described by Richard Duffin and Albert Charles Schaeffer in a 1952 article on nonharmonic Fourier series as a way of computing the coefficients in a linear combination of the vectors of a linearly dependent spanning set (in their terminology, a "Hilbert space frame"). In the 1980s, Stéphane Mallat, Ingrid Daubechies, and Yves Meyer used frames to analyze wavelets. Today frames are associated with wavelets, signal and image processing, and data compression.

The Special Sensor Microwave Imager / Sounder (SSMIS) is a 24-channel, 21-frequency, linearly polarized passive microwave radiometer system. The instrument is flown on board the United States Air Force Defense Meteorological Satellite Program (DMSP) F-16, F-17, F-18 and F-19 satellites, which became operational in November 2005, March 2008 March 2016 and May 2016, respectively. It is the successor to the Special Sensor Microwave/Imager (SSM/I). The SSMIS on the F19 satellite stopped producing useful data in February 2016.

The Goldreich-Kylafis (GK) effect is a quantum mechanical effect with applications in Astrophysics. The theoretical background of the work was published by Peter Goldreich and - his postdoc at the time - Nick Kylafis in a series of two papers in The Astrophysical Journal. The GK effect predicts that, under special conditions, the spectral lines emitted by interstellar molecules should be linearly polarized and the linear polarization vector should reveal the magnetic field direction in the molecular cloud. Even a μG magnetic field is enough for this effect.

These military and civilian specialists are concerned with protecting aircrew and patients who are transported by AirEvac aircraft (helicopters or fixed-wing airplanes). Atmospheric physics potentially affect all air travelers regardless of the aircraft. As humans ascend through the first 9100-12,300 m (30,000-40,000 ft), temperature decreases linearly at an average rate of 2 °C (3.6 °F) per 305 m (1000 ft). If sea-level temperature is 16 °C (60 °F), the outside air temperature is approximately −57 °C (−70 °F) at 10,700 m (35,000 ft).

A system of equations whose left-hand sides are linearly independent is always consistent. Putting it another way, according to the Rouché–Capelli theorem, any system of equations (overdetermined or otherwise) is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If, on the other hand, the ranks of these two matrices are equal, the system must have at least one solution. The solution is unique if and only if the rank equals the number of variables.

A laser diode is used to generate an optical signal that is modulated by a linearly- chirped low frequency signal. This modulated optical signal is then split, with one part immediately converted to an electronic signal at 4 times the frequency of the original modulating signal. This waveform is then amplified, emitted via a standard antenna, and then received again via another standard antenna. The second half of the modulated optical signal is further modulated by the reflected signal, and then converted to an electronic signal.

The electro-optic effect is a change in the optical properties of an optically active material due to interaction with light. This interaction usually results in a change in the birefringence, and not simply the refractive index of the medium. In a Kerr cell, the change in birefringence is proportional to the square of the optical electric field, and the material is usually a liquid. In a Pockels cell, the change in birefringence varies linearly with the electric field, and the material is usually a crystal.

A sweep generator is a piece of electronic test equipment similar to, and sometimes included on, a function generator which creates an electrical waveform with a linearly varying frequency and a constant amplitude. Sweep generators are commonly used to test the frequency response of electronic filter circuits. These circuits are mostly transistor circuits with inductors and capacitors to create linear characteristics. Sweeps are a popular method in the field of audio measurementLet's Clear Up Some Things About Sweeps to describe the change in a measured output value over a progressing input parameter.

Some inverse problems have a very simple solution, for instance, when one has a set of unisolvent functions, meaning a set of functions such that evaluating them at distinct points yields a set of linearly independent vectors. This means that given a linear combination of these functions, the coefficients can be computed by arranging the vectors as the columns of a matrix and then inverting this matrix. The simplest example of unisolvent functions is polynomials constructed, using the unisolvence theorem, so as to be unisolvent. Concretely, this is done by inverting the Vandermonde matrix.

The experiment was designed to measure how long it would take each subject to determine whether the pair of objects were indeed the same object or two different objects. Their research showed that the reaction time for participants to decide if the pair of items matched or not was linearly proportional to the angle of rotation from the original position. That is, the more an object has been rotated from the original, the longer it takes an individual to determine if the two images are of the same object or enantiomorphs.

The interior spaces of the three blocks are linearly arranged, with almost all classrooms and offices leading off verandah spaces. On the first floor, Block A contains three classrooms of a similar size; Block B has six classrooms; and Block C has four classrooms, with two withdrawal rooms separating the outermost classrooms from innermost classrooms. Blocks B and C are each terminated at the eastern end by a store and staircase. The classroom spaces generally have plastered walls, timber picture rails, and plastered ceilings with painted timber battens, and ceiling vents.

AM Herculis was first cataloged in 1923 by Max Wolf and was listed at the time as Veränderlicher 28.1923, which is now AN 28.1923 in the General Catalogue of Variable Stars. It was observed to be an irregular variable star ranging from 12 to 14 in apparent magnitude. In 1976, the astronomer S. Tapia discovered that light from the star is both linearly and circularly polarized, showing that there was a strong magnetic field surrounding the system and revealing that the system was more complex than previously thought.

Water is drawn into a small tube by surface tension. Water pressure, u, is negative above and positive below the free water surfaceIf there is no pore water flow occurring in the soil, the pore water pressures will be hydrostatic. The water table is located at the depth where the water pressure is equal to the atmospheric pressure. For hydrostatic conditions, the water pressure increases linearly with depth below the water table: :u = \rho_w g z_w where \rho_w is the density of water, and z_w is the depth below the water table.

This area is also where the town's early churches were built, and it thus developed as a small commercial center as well. The district extends along Boston Post Road from Westbrook Town Hall in the west to the Oxford Academy campus in the east. A major lobe extends linearly along Old Clinton Road, which is primarily residential in character, while properties are also include on South Main Street (an old alighnment of the post road). The district includes 195 historically significant buildings spread over , most of which are residential.

F210 Honda tiller 1949 Farmall C with C-254-A two-row cultivator A tractor- mounted tiller Tines close-up A cultivator pulled by a tractor in Canada in 1943 A cultivator is any of several types of farm implement used for secondary tillage. One sense of the name refers to frames with teeth (also called shanks) that pierce the soil as they are dragged through it linearly. Another sense refers to machines that use rotary motion of disks or teeth to accomplish a similar result. The rotary tiller is a principal example.

The motion depicted in the animation is for the idealized situation that the force exerted by the spring increases linearly with the distance to the center of rotation. Also, the animation depicts what would occur if there would not be any friction. In rotational-vibrational coupling there is an oscillation of the angular velocity. In pulling the circling masses closer to the center of rotation, the force exerted by the spring (a centripetal force) is doing work, converting stored strain energy in the spring into kinetic energy of the masses.

The guess is adjusted to reduce the discrepancy between the simulated field and the measured field. This process is iterated until convergence. Another common technique is beamforming, wherein a theoretical model of the magnetic field produced by a given current dipole is used as a prior, along with second-order statistics of the data in the form of a covariance matrix, to calculate a linear weighting of the sensor array (the beamformer) via the Backus-Gilbert inverse. This is also known as a linearly constrained minimum variance (LCMV) beamformer.

Carbonylation of a cysteine residue via hydroxyl radical, analogous to how SBPase is inactivated by ROS. Moreso than other enzymes in the Calvin cycle, SBPase levels have a significant impact on plant growth, photosynthetic ability, and response to environmental stresses. Small decreases in SBPase activity result in decreased photosynthetic carbon fixation and reduced plant biomass. Specifically, decreased SBPase levels result in stunted plant organ growth and development compared to wild-type plants, and starch levels decrease linearly with decreases in SBPase activity, suggesting that SBPase activity is a limiting factor to carbon assimilation.

For Bangladesh, which is a historically agrarian country, the agricultural sector has shrunk from over 30% in the 1980s to under 20% a decade into the millennium. On the other hand, industry is growing from under 20% in the 1980s to over 30% currently. With highly industry national economy, the generation of electricity will be linearly related to the national GDP. With lesser agriculture and more industry, not only more emissions will be given off to the atmosphere but lack of trees and plants will hinder any chance of carbon sequestration.

Every electrode has a range of scan rates called the linear region. The response to a reversible redox couple in the linear region is a "diffusion controlled peak" which can be modeled with the Cottrell equation. The upper limit of the useful linear region is bound by an excess of charging current combined with distortions created from large peak currents and associated resistance. The charging current scales linearly with scan rate while the peak current, which contains the useful information, scales with the square root of scan rate.

Modo's renderer is multi-threaded and scales nearly linearly with the addition of processors or processor cores. That is, an 8-core machine will render a given image approximately eight times as fast as a single-core machine with the same per-core speed. Modo runs on up to 32 cores and offers the option of network rendering. In addition to the standard renderer, which can take a long time to run with a complex scene on even a fast machine, Modo has a progressive preview renderer which renders to final quality if left alone.

They are composed mostly of iron oxides, with smaller proportion of aluminium oxide, and uranium and plutonium oxides. Particles larger than 1–2 micrometers are very spherical, corresponding to vaporized material condensing into droplets and then solidifying. The radioactivity is evenly distributed throughout the particle volume, making total activity of the particles linearly dependent on particle volume.Radioactive fallout after nuclear explosions and accidents, Volume 3, I. A. Izraėl, Elsevier, 2002 About 80% of activity is present in more volatile elements, which condense only after the fireball cools to considerable degree.

The price per carat does not increase linearly with increasing size. Instead, there are sharp jumps around milestone carat weights, as demand is much higher for diamonds weighing just more than a milestone than for those weighing just less. As an example, a 0.99-carat diamond may have a significantly lower price per carat than a comparable 1.01-carat diamond, because of differences in demand. A weekly diamond price list, the Rapaport Diamond Report is published by Martin Rapaport, CEO of Rapaport Group of New York, for different diamond cuts, clarity and weights.

This is the only natural context in which individual chromosomes are visible with an optical microscope. Mitotic metaphase chromosomes are best described by a linearly organized longitudinally compressed array of consecutive chromatin loops. During mitosis, microtubules grow from centrosomes located at opposite ends of the cell and also attach to the centromere at specialized structures called kinetochores, one of which is present on each sister chromatid. A special DNA base sequence in the region of the kinetochores provides, along with special proteins, longer-lasting attachment in this region.

His artillery were themselves different—in addition to the usual complements of heavy cannon, he introduced light mobile guns for the first time into the Renaissance battlefield. These were grouped in batteries supporting his more linearly deployed formations, replacing the cumbersome and unmaneuverable traditional deep squares (such as the Spanish tercios that were up to 50 ranks deep) used in other pike and shot armies of the day. In consequence, his forces could redeploy and reconfigure very rapidly, confounding his enemies.Boyd L. Dastrup, The Field Artillery: History and Sourcebook (1994) p 11.

From the above definitions, a new quantity, M, the mean anomaly can be defined :M = n(t - \tau), which gives an angular distance from the pericenter at arbitrary time t, with dimensions of radians or degrees. Because the rate of increase, n, is a constant average, the mean anomaly increases uniformly (linearly) from 0 to 2 radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, radians (180°) at the apocenter, and 2 radians (360°) after one complete revolution.Meeus (1991), p.

However, the folding in the brain continues to become more complex until the late teens. The biggest changes in the folds during this time occur in the parts of the cortex that process cognitive and emotional information. Over the course of adolescence, the amount of white matter in the brain increases linearly, while the amount of grey matter in the brain follows an inverted-U pattern. Through a process called synaptic pruning, unnecessary neuronal connections in the brain are eliminated and the amount of grey matter is pared down.

It behaves as if the string had constant tension, so that separating out the ends (quarks) would give a potential energy increasing linearly with the separation. When the energy is higher than that of a meson, the string breaks and the two new ends become a quark-antiquark pair, thus describing the creation of a meson. Thus confinement is incorporated naturally into the model. In the form of the Lund model Monte Carlo program, this picture has had remarkable success in explaining experimental data collected in electron-electron and hadron-hadron collisions.

Transitional metals like Cu, Au and Ag adsorb single molecules linearly on their surface due to weak van der Waals forces. This linear projection of single molecules allows interactions of the terminal atoms of the tip with the atoms of the substrate resulting in Pauli repulsion for single molecule or atom mapping studies. Gaseoss deposition on the tip is carried out in an ultrahigh vacuum (5 x 10−8 mbar) chamber at a low temperature (10K). Depositions of Xe, Kr, NO, CH4 or CO on tip have been successfully prepared and used for imaging studies.

There are cases in which uncorrelatedness does imply independence. One of these cases is the one in which both random variables are two-valued (so each can be linearly transformed to have a Bernoulli distribution).Virtual Laboratories in Probability and Statistics: Covariance and Correlation, item 17. Further, two jointly normally distributed random variables are independent if they are uncorrelated, although this does not hold for variables whose marginal distributions are normal and uncorrelated but whose joint distribution is not joint normal (see Normally distributed and uncorrelated does not imply independent).

In fact the value of δ can even be allowed to decrease linearly with time to accommodate Moore's Law. The Actor event timed diagrams form a partially ordered set . The diagrams are partial computation histories representing "snapshots" (relative to some frame of reference) of a computation on its way to being completed. For d1, d2εTimedDiagrams, d1≤d2 means d1 is a stage the computation could go through on its way to d2 The completed elements of TimedDiagrams represent computations that have terminated and nonterminating computations that have become infinite.

The boring process can be executed on various machine tools, including (1) general-purpose or universal machines, such as lathes (/turning centers) or milling machines (/machining centers), and (2) machines designed to specialize in boring as a primary function, such as jig borers and boring machines or boring mills, which include vertical boring mills (workpiece rotates around a vertical axis while boring bar/head moves linearly; essentially a vertical lathe) and horizontal boring mills (workpiece sits on a table while the boring bar rotates around a horizontal axis; essentially a specialized horizontal milling machine).

Liquid-crystal displays, the most common sort of flat-panel display, cause their pixels to become lighter or darker through rotation of the polarization (circular birefringence) of linearly polarized light as viewed through a sheet polarizer at the screen's surface. Similarly, light modulators modulate the intensity of light through electrically induced birefringence of polarized light followed by a polarizer. The Lyot filter is a specialized narrowband spectral filter employing the wavelength dependence of birefringence. Waveplates are thin birefringent sheets widely used in certain optical equipment for modifying the polarization state of light passing through it.

Viscosity may be added back by using Langevin dynamics instead of Hamiltonian mechanics and choosing an appropriate damping constant for the particular solvent. In practical bimolecular simulations one can often speed-up conformational search significantly (up to 100 times in some cases) by using much lower collision frequency \gamma. Recent work has also been done developing thermostats based on fluctuating hydrodynamics to account for momentum transfer through the solvent and related thermal fluctuations. One should keep in mind, though, that the folding rate of proteins does not depend linearly on viscosity for all regimes.

Transportability: The performance and functional literacy studies both illustrated how g is transportable across life situations and it represents a set of largely generalizable reasoning and problem-solving skills. G appear to be linearly linked to performance in school, jobs and achievements. Generality: Studies show that IQ measured at the age of 11 predicted longevity, premature death, lung and stomach cancers, dementia, loss of functional independence, more than 60 years later. Research has shown that higher IQ at age 11 is significantly related to higher social class in midlife.