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291 Sentences With "smallest possible"

How to use smallest possible in a sentence? Find typical usage patterns (collocations)/phrases/context for "smallest possible" and check conjugation/comparative form for "smallest possible". Mastering all the usages of "smallest possible" from sentence examples published by news publications.

type: All Declarative Interrogative Exclamative

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length: All <=10 words 10-20 words 20-30 words 30-50 words

Antic told reporters the price hike was the "smallest possible".
For an ordinary jump, creating the smallest possible splash scores points.
To put in the smallest possible way, she's not there for you.
SNPs are the smallest possible differences between individuals' DNA—single genetic letters.
It's crazy speedy and writes at the smallest possible read/write level: the byte level.
The basic unit of classical computing is the bit, the smallest possible chunk of information.
The video shows the behavior of space-time at the Planck scale, the smallest possible area.
The 4chan proof outlines how to find the smallest possible number of episodes for the solution.
"This is the smallest possible increase, half the amount the IMF asked for," Antic told reporters.
Throw it into the smallest possible yellow/orange/red circle to maximize throw bonus (more XP!)
Liberals have their own history of avoiding leading intellectuals for those with the smallest possible intellectual footprints.
Scientists want to bring MRI to the smallest possible length scales to better understand tiny things like proteins.
Their atoms have an innate property called spin, which turns each one into the smallest possible bar magnets.
If she can't do that, she'll at least try to ease them down to the smallest possible dose.
A bit represents the smallest possible dollop of information: on or off; yes or no; 1 or 0.
Imagine—the smallest possible blip of light, but with the energy of a baseball thrown by a Major League pitcher.
Print the slides at the smallest possible size, so that the type becomes unreadable while the images are still visible.
Quantum mechanics, the theory that governs the smallest possible spaces, forces our human brains to accept some really wacky, uncomfortable realities.
Meaning that censured content (such as nazi hate tweets) would only be blocked for the smallest possible number of Twitter users.
"The system is designed to ensure that the smallest possible number of those who are accused are found guilty," she said.
Cram the flows and cycles necessary for life into the smallest possible volume and they have neither elegance nor any visual logic.
Aleksandar Antic said the increase is the smallest possible and there has been no adjustment to inflation for the past two years.
The task is of finding values for those variables that result in the smallest possible number on the ride side of the equation.
Although the tweaks are essentially the smallest possible changes, that was enough to send the euro EUR= up half a percent and bank shares .
"We decided to try and tell the smallest possible story in the biggest possible tapestry... The tiny becomes the universal," director James Gray said.
These are ads that appear right when you open a site, take over the whole page and have the smallest possible button for dismissing them.
Urging the audience to come closer instead of forcing the show to grow bigger, he made you enter its world through the smallest possible door.
It is likely to continue moving by the smallest possible increments, fearing that anything bigger might set off market turbulence and unravel years of work.
But I -- I want to – my objective for policy should be that we -- we have the smallest possible balance sheet in an ample reserves regime.
Rather than create a fully fleshed out space station before lunar landings begin, now NASA is focused on getting the smallest possible outpost ready by 2024.
A morsel of information, the smallest possible thing, and the mind, always seeking narrative and order, tries to slot it into a world we can imagine.
The problem they have to solve is this: Divide the state into groups including an equal number of people with the smallest possible perimeters defining them.
Simply place your items inside the designated bags, and the Dr. Save Pump will remove the air inside and compress it to the smallest possible size.
Weisberg and Fields have turned the smallest possible stakes (will this marriage survive?) into the largest possible ones through narrative sleight of hand, and it's brilliant.
Though Chakrabarti may consider it the "smallest possible thing," anyone who glances at Ocasio-Cortez's document will realize that it is far from small or easy.
A client would then test each combination "against the smallest possible audience" on Facebook, with the one generating the most engagement being scaled to a full audience.
Those assessment areas, which will be determined by the bank and validated by the regulator, should be the smallest possible area where 5 percent of deposits originate.
Hundreds of hours of stroking rich women's egos as they stuffed themselves into the smallest possible size, while letting me know how I could lose weight by skipping meals.
To this end, he developed what is arguably the smallest possible executable code (code that can be read by a machine) that can be represented by a prime number.
"The biggest advantage of a [negative income tax] is that it requires the smallest possible bureaucracy to implement," Guy Sorman, a right-leaning French philosopher, wrote in City Journal.
LIDAR presented a similar challenge to speakers: how do you measure the world around you and, with the smallest possible delay, and use that data to adjust your input signal?
This is what allows scientists to create a new definition for the kilogram: measuring the fundamentals of the physical world down to what is essentially the smallest possible physical action.
If you're looking for the smallest possible computer that can still run modern games and handle heavier tasks, the HiGame is smaller and less expensive than Intel's niche-focused NUC.
A significant part of the Galaxy Note 7 battery fiasco last year was Samsung dragging its feet and trying to take the smallest possible steps to make the situation go away.
In a follow-up essay, Hurwitz defends his thinking: Men who are proposing to women are going to buy the smallest possible diamond that will still "ensure" their proposal is accepted.
Merely reducing complexity by, for example, breaking up user stories into the smallest possible bits, keeping turnover of team members to a minimum and reducing external dependencies is not good enough.
Commonwealth Fusion expects to have its smallest possible reactor built by 2025 thanks to the research that MIT has done on proprietary magnet technology that the company uses to confine its nuclear reaction.
"It appears that Samsung made the changes at a smallest possible scale in order to ensure that its business operations keep running," said Park Ju-gun, head of corporate analysis firm CEO Score.
"The idea is that we, as clinicians and engineers, need to become obsessed with how we provide the best outcomes for patients while having the smallest possible footprints on their lives," he says.
The idea is this: If you just can't motivate yourself to get started on something today, slice it up into the smallest possible units of progress and attack them one at a time.
So she will either upload a 10GB RAW that no email server would ever try to deliver, or she will send me the smallest possible image her computer can downgrade the original photo into.
At their smallest-possible size, disc drives take up a lot of space and would force Nintendo to make the Switch's standalone mobile screen much bulkier — not a positive trait on a mobile system.
The coach, among the best in college history, preaches "the process," one that takes apart complex goals, such as winning a game or a national title, into their smallest possible units and perfects them.
Pardon the gimmicky phrase, but the idea goes like this: For any task you have to complete, break it down into the smallest possible units of progress and attack them one at a time.
It's about trying to understand climate change and motherhood — concepts so big that the mind can't quite look at them dead on — by looking at them slantwise, through the smallest possible unit of thought.
It's unfortunate that oil development occurs here, but if it must, BLM must ensure that any future decisions for development in the Reserve result in the smallest possible environmental footprint and minimize cumulative impacts.
On the Democratic side, the debates were obviously scheduled by the Democratic National Committee to reach the smallest possible audience, a ridiculous proposition with Clinton now refusing to do press conferences on any normal basis.
Because it is impossible for researchers to determine what is the largest and smallest possible weight and length for babies, designers begin the charts at the fifth percentile and end them at the 95th percentile.
But the form paradoxically has its eye on the big picture — the grand sweep of the entire series — alongside the smallest possible unit of on-screen time, the scene, without much regard for everything in between.
"They should state precisely what law they are complying with, what piece of content is being removed, and what steps they're taking to ensure the action has the smallest possible impact on human rights," he says.
Under this approach, taxes are less an issue of economic engineering and more an issue of personal freedom: The government should spend as little as it reasonably can in order to take the smallest possible slice from citizens.
Scientists think these black holes are dense masses of the smallest possible length, surrounded by a far-out point-of-no-return of warped space from which light can't escape, based on Albert Einstein's theory of general relativity.
"We all know that this is the smallest possible majority you can have in Althingi (parliament) and so it is important to go thoroughly through the matters upfront and that is why this has taken time," Benediktsson said.
Jean-Baptiste Colbert, the finance minister of Louis XIV of France, famously compared the art of raising tax to "plucking the goose so as to obtain the largest possible amount of feathers with the smallest possible amount of hissing".
My phone is always in my pocket with the hole exposed—I believe in minimal-to-no casing for the smallest possible phone profile—and when I charge it at night, it's in my bed—a breeding ground of lint.
In his infamous deposition, he managed to get "sex" defined as intercourse, and then said that he had not had sex with Monica Lewinsky, which as we all know is true in the smallest possible sense of anything being true.
On the other hand, splitting objectives up into their smallest possible form as a way of accomplishing a big task is the most efficient and least stressful way to accomplish that larger project Builders 2 excels at combining these two things.
When Jon prattles on about all his connections to the Mormonts, she cuts him off with the declaration that she's had "enough small talk," and when he asks for an army to support his efforts, she agrees, but makes roughly the smallest possible commitment of just 62 men.
We put together the money we would have had to come up with for a security deposit and first and last month's rent and put it instead toward the smallest possible down payment for a little house in Athens, Georgia, a 1950s cottage that was modest even back in its day.
Should you insist on spending the smallest possible amount, on the other hand, be prepared to compromise on the sound quality and / or accepting a wired connection instead of Bluetooth, the latter of which has been growing in popularity (and necessity, thanks to the new breed of phones without headphone jacks).
Perhaps finding a smaller five-color graph — or the smallest possible five-color graph — would give researchers further insight into the Hadwiger-Nelson problem, allowing them to prove that exactly five shades (or six, or seven) are enough to color a graph made from all the points of the plane.
The best action now would be to revise the tariffs to include the smallest possible list of countries (zero is best) and to refocus the any trade action toward those countries that committed offences for which an economic and legal case can be made in an appropriate forum such as the WTO.
The universe's particles are represented as phonons, the smallest possible units of vibrational energy (sound) traveling through the atoms, according to the paper published yesterday in Physical Review X.It might sound completely different, but it appears the two systems—the early expanding universe and the super-cold atoms—are governed by some very similar math.
Today, theoretical physicists are trying to reconcile these mysteries by examining the structure of so-called "spacetime" in the universe at the smallest possible scale, with surprising findings: spacetime might not be the trampoline-like plane scientists once envisioned—it might be a foamy mess of bubbles all containing mini-universes living and dying inside our own.
The punishment for annoying interstitials — those annoying ads and announcements that take over the whole page and have the smallest possible button for dismissing them, which inevitably leads you to accidentally clicking on the ad even though you really didn't want to buy a new car — will likely be bemoaned by bad marketers, but for users, it can't come too early.
It is not still, of course; it is moving in increments of time we can't even imagine, portions of millions of a second quicker than the moment of recognition of a single leaf on a tree somewhere off in the distance of your mind, smaller than the smallest possible thought, the dunk still happening in front of you, still the truest two points imaginable, but the machinations of time keeping it from ever counting in the true "two points" sense of the word.
Light from certain types of laser has the smallest possible beam divergence.
An Atom of time or "a-tom" (“indivisible” in Greek), refers to the smallest possible unit of time.
Need- to-know also aims to discourage "browsing" of sensitive material by limiting access to the smallest possible number of people.
Vk is the volume in k-space whose wavevectors are smaller than the smallest possible wavevectors decided by the characteristic spacing of the system.
This CPAP-10 has the smallest possible common difference, 7# = 210. The only other known CPAP-10 as of 2018 was found by the same people in 2008.
The smallest possible binary "square" de Bruijn torus, depicted above right, denoted as (4,4;2,2)2 de Bruijn torus (or simply as B2), contains all 2×2 binary matrices.
The convex sets with the smallest possible Kovner–Besicovitch measure are the triangles, for which the measure is 2/3. The result that triangles are the minimizers of this measure is known as Kovner's theorem or the Kovner–Besicovitch theorem, and the inequality bounding the measure above 2/3 for all convex sets is the Kovner–Besicovitch inequality. The curve of constant width with the smallest possible Kovner–Besicovitch measure is the Reuleaux triangle.
The shapes of minimum Estermann measure are the triangles, for which this measure is 1/2. The curve of constant width with the smallest possible Estermann measure is the Reuleaux triangle.
8064 is the smallest possible volume (and 6384 is the smallest possible surface area) of a perfect tetrahedron. The integral edge lengths of a Heronian tetrahedron with this volume and surface area are 25, 39, 56, 120, 153 and 160. In 1943, E. P. Starke published another example, in which two faces are isosceles triangles with base 896 and sides 1073, and the other two faces are also isosceles with base 990 and the same sides.
This small response (~0.4mV) is called a miniature end plate potential (MEPP) and is generated by one acetylcholine-containing vesicle. It represents the smallest possible depolarization which can be induced in a muscle.
"Uncertainty principle on 3-dimensional manifolds of constant curvature," Found. Phys. 48, 716-725. doi:10.1007/s10701-018-0173-0 arxiv:1804.02551. The Planck length may represent the diameter of the smallest possible black hole.
After gaining the support of the Greens and three independents on confidence and supply votes, Labor was able to form a minority government with 76 seats, the smallest possible margin in the 150-seat House.
SMO is an iterative algorithm for solving the optimization problem described above. SMO breaks this problem into a series of smallest possible sub-problems, which are then solved analytically. Because of the linear equality constraint involving the Lagrange multipliers \alpha_i, the smallest possible problem involves two such multipliers. Then, for any two multipliers \alpha_1 and \alpha_2, the constraints are reduced to: :0 \leq \alpha_1, \alpha_2 \leq C, :y_1 \alpha_1 + y_2 \alpha_2 = k, and this reduced problem can be solved analytically: one needs to find a minimum of a one-dimensional quadratic function.
One of the earliest occurrences of the word “atom” to mean the smallest possible unit of measuring time is found in the Greek text of the New Testament in Paul's . The text compares the length of time of the “atom” to the time needed for “the twinkling of an eye.” The text reads: “en atomo, en repe ophthamou” – the word "atom" is usually translated "a moment" - “In a moment, in the twinkling of an eye”. With that meaning it was later referred to in Medieval philosophical writings as the smallest possible division of time.
Two graphs are called cospectral or isospectral if the adjacency matrices of the graphs have equal multisets of eigenvalues. enneahedra, the smallest possible cospectral polyhedral graphs Cospectral graphs need not be isomorphic, but isomorphic graphs are always cospectral.
Branko Grünbaum has conjectured that every configuration that can be realized by irrational but not rational numbers has at least nine points; if so, the Perles configuration would be the smallest possible irrational configuration of points and lines..
Several of them may be panmagic squares. A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main triagonals summing correctly. (No broken triagonals have the correct sum.) Order 7 is the smallest possible pandiagonal magic cube.
A cycloparaphenylene can be considered as the smallest possible armchair carbon nanotube, and is a type of carbon nanohoop. Cycloparaphenylenes are challenging targets for chemical synthesis due to the ring strain incurred from forcing benzene rings out of planarity.
The requirement for trucks far exceeded Pershing's initial order and Clydesdale struggled to keep up with demand.Middleton & Semon, p. 24 Trucks were shipped to Europe in kit form to reduce shipping tonnage. Clydesdale were particularly good at getting trucks into the smallest possible crate.
According to ISO/IEC 11172-3:1993, Section 2.4.2.3: To provide the smallest possible delay and complexity, the (MPEG audio) decoder is not required to support a continuously variable bit rate when in layer I or II.TwoLAME: MPEG Audio Layer II VBR, retrieved on 2009-07-11.
Substituting into the identity and removing common factors gives the numerical example cited above. In 1988, Roger Frye found the smallest possible counterexample :: for by a direct computer search using techniques suggested by Elkies. This solution is the only one with values of the variables below 1,000,000.
Falls and hip fractures are frequently reported. The combination with alcohol increases these impairments. Partial but incomplete tolerance develops to these impairments. The smallest possible effective dose should be used in elderly or very ill patients, as a risk of apnea and/or cardiac arrest exists.
Cayley graph with permutations of a triangle Cycle graph with matrices of permutations of 3 elements (The generators a and b are the same as in the Cayley graph shown above.) Cayley table as multiplication table of the permutation matrices abelian. general (and special) linear group GL(2, 2) In mathematics, D3 (sometimes alternatively denoted by D6) is the dihedral group of degree 3, or, in other words, the dihedral group of order 6. It is isomorphic to the symmetric group S3 of degree 3. It is also the smallest possible non-abelian group.. For the identification of D3 with S3, and the observation that this group is the smallest possible non-abelian group, see p. 49.
Areas of research include smallest possible population sizes and current population sizes. Also, the genetic diversity between populations is important to study. Restoring Hine's emeralds to lasting population sizes allows the ESA to downgrade the species from endangered to threatened. To do this, however, up-to-date population data is crucial.
Glycolaldehyde is the organic compound with the formula HOCH2-CHO. It is the smallest possible molecule that contains both an aldehyde group and a hydroxyl group. It is a highly reactive molecule that occurs both in the biosphere and in the interstellar medium. It is normally supplied as a white solid.
The coordinate-wise mean of a point set is the centroid, which solves the same variational problem in the plane (or higher-dimensional Euclidean space) that the familiar average solves on the real line -- that is, the centroid has the smallest possible average squared distance to all points in the set.
Since the radial distance r cannot be a negative number, neither can its inverse u; therefore, u2 must be a positive number. If u1 is also positive, it is the smallest possible value of u, which corresponds to the largest possible value of r, the distance of furthest approach (apoapsis). If u1 is zero or negative, then the smallest possible value of u is zero (the orbit goes to infinity); in this case, the only relevant values of φ are those that make u positive. For an attractive force (α < 0), the orbit is an ellipse, a hyperbola or parabola, depending on whether u1 is positive, negative, or zero, respectively; this corresponds to an eccentricity e less than one, greater than one, or equal to one.
Another fairly common fullerene has empirical formula , but fullerenes with 72, 76, 84 and even up to 100 carbon atoms are commonly obtained. The smallest possible fullerene is the dodecahedral . There are no fullerenes with 22 vertices. The number of different fullerenes C2n grows with increasing n = 12, 13, 14, ..., roughly in proportion to n9 .
Two people having this imbalance often have difficulty resolving it by themselves. To stabilize the relationship, the couple often seek the aid of a third party to help re-establish closeness. A triangle is the smallest possible relationship system that can restore balance in a time of stress. The third person assumes an outside position.
The original definition is applicable only to magic cubes, not tesseracts, dimension 5 cubes, etc. Example: A perfect magic cube of order 8 has 244 correct lines by the old definition, but 832 correct lines by this new definition. Order 8 is the smallest possible perfect magic cube. None can exist for double odd orders.
The disambiguation is thus context- sensitive. Advanced semantic analysis has resulted in a sub-distinction. A word sense corresponds either neatly to a seme (the smallest possible unit of meaning) or a sememe (larger unit of meaning), and polysemy of a word of phrase is the property of having multiple semes or sememes and thus multiple senses.
The band gets thicker, and this would increase its volume. But it also gets shorter in circumference, and this would decrease its volume. The two effects exactly cancel each other out. In the extreme case of the smallest possible sphere, the cylinder vanishes (its radius becomes zero) and the height h equals the diameter of the sphere.
Figure-eight knot of practical knot-tying, with ends joined In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure- eight knot is a prime knot.
The geometric median is the point to which the population has the smallest possible sum of distances (or equivalently, the smallest average distance). Because of this property, it is also known as the point of minimum aggregate travel. Unfortunately, there is no direct closed-form expression for the geometric median; it is typically computed using iterative methods.
The confined Gaussian window yields the smallest possible root mean square frequency width for a given temporal width . These windows optimize the RMS time-frequency bandwidth products. They are computed as the minimum eigenvectors of a parameter-dependent matrix. The confined Gaussian window family contains the and the in the limiting cases of large and small , respectively.
The dynamic sessile drop is similar to the static sessile drop but requires the drop to be modified. A common type of dynamic sessile drop study determines the largest contact angle possible without increasing its solid–liquid interfacial area by adding volume dynamically. This maximum angle is the advancing angle. Volume is removed to produce the smallest possible angle, the receding angle.
With respect to the membership issue, former US President Barack Obama noted the difficulty of pleasing everyone: "Everybody wants the smallest possible group that includes them. So, if they're the 21st largest nation in the world, they want the G21, and think it's highly unfair if they have been cut out."Kelly Chernenkoff. "Obama to Usher In New World Order at G-20".
There is a natural map from Teichmüller space to the curve complex, which takes a marked hyperbolic structures to the collection of closed curves realising the smallest possible length (the systole). It allows to read off certain geometric properties of the latter, in particular it explains the empirical fact that while Teichmüller space itself is not hyperbolic it retains certain features of hyperbolicity.
Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities. In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes. Claim of efficacy is demonstrated that the gene - unit of classical heredity - is the deoxyribonucleic acid (DNA), a macro-molecule.
The golden ratio, on the other hand, is the number requiring the most coefficients for each digit. A prominent example of a number not exhibiting this behavior is the golden ratio—sometimes known as the "most irrational" number—whose continued fraction terms are all ones, the smallest possible in canonical form. On average it requires approximately 2.39 continued fraction terms per decimal digit.
The smallest possible crystalline wires with cross-section as small as a single atom can be engineered in cylindrical confinement. Carbon nanotubes, a natural semi-1D nanostructure, can be used as a template for synthesis. Confinement provides mechanical stabilization and prevents linear atomic chains from disintegration; other structures of 1D nanowires are predicted to be mechanically stable even upon isolation from the templates.
For example, consider the smallest possible truly quantum system S, as shown in the illustration. This describes for instance, the spin-state of an electron. Considering a specific axis (say the z-axis) the north pole represents spin "up" and the south pole, spin "down". The superposition states of the system are described by a sphere called the Bloch sphere.
Tony Clarke and Richard Wadman established the specifications for the Dragon."The Computer that Roared" by Fernleigh Edmonson. "Microcomputing" magazine 1983 May. The units had a robust motherboard in a spacious case, reminiscent of the BBC Micro, and so were more tolerant of home-modification than some of their contemporaries, which often had their components crammed into the smallest possible space.
Constructed in less than five weeks at a cost of under $5,000 USD, the Gee Bee (for "Granville Brothers") Model Z, named City of Springfield, was a small, tubby airplane. It was essentially the smallest possible airframe constructed around the most powerful available engine,Donald 1997, pp. 466–467. a supercharged Pratt & Whitney R-985 "Wasp Junior" radial engine, producing .
It is a Leyland number since 25 \+ 52 = 57. 57 is a repdigit in base 7 (111). There are 57 vertices and 57 hemi-dodecahedral facets in the 57-cell, a 4-dimensional abstract regular polytope. The Lie algebra E has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E8 is also 57-dimensional.
The rn-r+1 is the smallest possible: the extremal case is when n=r-1 is a prime power, and all colors are edges of the truncated projective plane of order n. So each color has n2=rn-r+1 edges and a fractional matching of size n, but any fractional matching of that size requires all rn-r+1 edges.
A primitive element, α, of Fpn is an element that generates this group. Representing the non-zero field elements as powers of α allows multiplication in the field to be performed efficiently. The primitive polynomial for α is the monic polynomial of smallest possible degree with coefficients in Fp that has α as a root in Fpn (the minimal polynomial for α). It is necessarily irreducible.
Typical utility functions are also included: POS returns the column of the print head POS(X) returns the position in a file TAX(X) moves the print head to column X TAX(X,N) the same in file number N DATE TIME SUPER BASIC also included pseudo-variables for and , the later being double-precision, as well as the previously mentioned to represent the smallest possible value.
Webber, pp. 42–43. Surrey had made much of the running in the title race but their challenge faded after defeats by Kent at Rectory Field and by Yorkshire at Bramall Lane. These results left only Kent and Yorkshire in contention. Yorkshire were the favourites but, in a tense match at Bristol, they lost to Gloucestershire by one run, the smallest possible margin of victory.
A hand shadow being thrown The hands and fingers are exercised and different finger positions are practiced to help aid in forming shadows. The light source to be used should be small and bright. The best shadows come from light proceeding from the smallest possible point. Albert Almoznino suggests a candle, a flashlight (with the lens and reflector removed) or any very small light.
Wire braiding functions on the lazy tongs principle. When axial tension is applied to the hose, the braid reaches its extension limit. This means that the wires lie tightly spaced with the smallest crossing angle, creating a hose braiding of the smallest possible diameter and the largest possible length. When the hose is axially compressed, the crossing angle and diameter increase to maximum values.
Biochemical Journal 240 289–292. Beta hairpins are broken into four distinct classes as depicted in the publication's Figure 1. Each class begins with the smallest possible number of loop residues and progressively increases the loop size by removing hydrogen bonds in the beta sheet. The primary hairpin of class 1 is a one-residue loop where the bound residues share two hydrogen bonds.
The law courts in ancient Athens (4th and 5th centuries BC) were a fundamental organ of democratic governance. According to Aristotle, whoever controls the courts controls the state. These courts were jury courts and very large ones: the smallest possible had 200 members (+1 to avoid ties) and sometimes 501, 1000 or 1500. The annual pool of jurors, whose official name was Heliaia, comprised 6000 members.
The horizontal cross section of the tower is kidney-shaped, which offers the maximum defensive view of the wall while occupying the smallest possible space inside the wall. The ground and first floors probably date from the reign of Henry III. The upper floors were probably added in the fifteenth century to accommodate small guns and cannons.Eamon McEneaney, Discover Waterford, (O'Brien Press), 2001, p.
A typical RHEED source has a focal length around 50 cm. The beam is focused to the smallest possible point at the detector rather than the sample surface so that the diffraction pattern has the best resolution. Phosphor screens that exhibit photoluminescence are widely used as detectors. These detectors emit green light from areas where electrons hit their surface and are common to TEM as well.
Approximate Inspiration Mars Trajectory (not to scale) Artist's Concept of Inspiration Mars Capsule and Hab. Inspiration Mars Periapsis. They proposed a free return trajectory to allow the spacecraft to use the smallest possible amount of propellant to flyby Mars and return to Earth. They stated that the January 2018 launch window offered a rare orbit opportunity to travel to Mars and return to Earth in 501 days.
However, patients may require intervention during childhood, because 50% of IH leave residual fibrofatty tissue, redundant skin, or damaged structures after involution. Waiting until involution is completed, ensures that the least amount of fibro fatty residuum and excess skin is resected, giving the smallest possible scar. Another option for treatment is the pulsed- dye laser. After involution residual telangiectasias can be treated with laser therapy.
When a larger block is split, it is divided into two smaller blocks, and each smaller block becomes a unique buddy to the other. A split block can only be merged with its unique buddy block, which then reforms the larger block they were split from. Starting off, the size of the smallest possible block is determined, i.e. the smallest memory block that can be allocated.
Hironaka's variety is a smooth 3-dimensional complete variety but is not projective as it has a non-trivial curve algebraically equivalent to 0. Any 2-dimensional smooth complete variety is projective, so 3 is the smallest possible dimension for such an example. There are plenty of 2-dimensional complex manifolds that are not algebraic, such as Hopf surfaces (non Kähler) and non-algebraic tori (Kähler).
This also means that at the smallest possible volume, there will be the greatest surface area to volume ratio, giving a greater surface area for reactions. The use of inert gas is favored because it prevents oxidation, and therefore deterioration of the aroma compounds. Black tea contains compounds that have low solubilities, which tend to bind together. The solution becomes cloudy and changes color to pale brown.
In 1992, Urban Müller, a Swiss physics student, took over a small online archive for Amiga software. The archive grew more popular, and was soon mirrored around the world. Today, it is the world's largest Amiga archive, known as Aminet. Müller designed Brainfuck with the goal of implementing it with the smallest possible compiler, inspired by the 1024-byte compiler for the FALSE programming language.
This resulted in slower growth of routing tables in routers. The smallest possible individual allocation is a subnet for 264 hosts, which is the square of the size of the entire IPv4 Internet. At these levels, actual address utilization ratios will be small on any IPv6 network segment. The new design also provides the opportunity to separate the addressing infrastructure of a network segment, i.e.
Let G be a graph with vertex set V. Let F be a field, and f a function from V to Fk such that xy is an edge of G if and only if f(x)·f(y) ≥ t. This is the dot product representation of G. The number t is called the dot product threshold, and the smallest possible value of k is called the dot product dimension.
An extremal hypergraph to Ryser's conjecture is a hypergraph in which the conjecture holds with equality, i.e., \tau(H) = (r-1)\cdot u(H). The existence of such hypergraphs show that the factor r-1 is the smallest possible. An example of an extremal hypergraph is the truncated projective plane - the projective plane of order r-1 in which one vertex and all lines containing it is removed.
The smallest possible number of vertices for a non-hamiltonian polyhedral graph is 11. Therefore, the Goldner–Harary graph is a minimal example of graphs of this type. However, the Herschel graph, another non-Hamiltonian polyhedron with 11 vertices, has fewer edges. As a non-Hamiltonian maximal planar graph, the Goldner–Harary graph provides an example of a planar graph with book thickness greater than two.. See in particular Figure 9.
The permutation representation on 11 points gives a complex irreducible representation in 10 dimensions. This is the smallest possible dimension of a faithful complex representation, though there are also two other such representations in 10 dimensions forming a complex conjugate pair. M11 has two 5-dimensional irreducible representations over the field with 3 elements, related to the restrictions of 6-dimensional representations of the double cover of M12.
More recently Popescu's interest is in the thermodynamics of quantum systems. In collaboration with Noah Linden and Paul Skrzypczyk, he described the smallest possible refrigerator, and together with Skrzypczyk and Anthony J. Short, extended the laws of thermodynamics to individual quantum systems. Popescu is co-editor and co-author of the first textbook on quantum information and computation. In 2015, Popescu appeared on Science Channel's Through the Wormhole with Morgan Freeman.
The surface tension of a liquid tends to assume the smallest possible size, acting as a membrane under tension. Any portion of the liquid surface exerts a tension upon adjacent portions or upon other objects that it contacts. This force is in the plane of the surface, and its amount per unit of length is surface tension. The value for water is about 0.073 N/m at 21 °C.
The raft extended well past the sides of the lower, more traditionally shaped lower hull. A small armoured pilot house was fitted on the upper deck towards the bow, however, its position prevented Monitor from firing her guns straight forward. One of Ericsson's prime goals in designing the ship was to present the smallest possible target to enemy gunfire. The turret's rounded shape helped to deflect cannon shot.
Additionally the enumerations do not leak, so they have to be used with Enumeration `Type::enumeration`. This is specified by the phrase "enum class". For example: enum class Color {Red, Green, Blue}; The underlying type is an implementation-defined integral type that is large enough to hold all enumerated values (it doesn't have to be the smallest possible type!). In C++ you can specify the underlying type directly.
Asmutils is a rewrite of the standard Unix commands in x86 assembly language aimed to have smallest possible size of ELF executables. All standard Unix commands (ls, cat, sh, etc.) executables are less than one kilobyte in size. Asmutils is available for Linux, UnixWare, Solaris, FreeBSD, OpenBSD and AtheOS and is licensed under the GNU GPL version 2. Linux mini distributions based entirely on asmutils are a-Linux and SAMEL Linux.
In sociology, a dyad (from the Greek: dyás, "pair") is a group of two people, the smallest possible social group. As an adjective, "dyadic" describes their interaction. The pair of individuals in a dyad can be linked via romantic interest, family relation, interests, work, partners in crime, and so on. The relation can be based on equality, but may be based on an asymmetrical or hierarchical relationship (master–servant).
The smallest possible domains have those variables that can only have two values, also called binary (or dichotomous) variables. Bigger domains have non-dichotomous variables and the ones with a higher level of measurement. (See also domain of discourse.) Semantically, greater precision can be obtained when considering an object's characteristics by distinguishing 'attributes' (characteristics that are attributed to an object) from 'traits' (characteristics that are inherent to the object).
Hello world is used to give a very small example of the syntax used by a programming language and is often the smallest possible program for any given programming language. Here is an example of a PBCC hello world program. By default PBCC creates a console window at runtime for displaying output. The only purpose of Waitkey$ in this example is to keep the console up so you can read the output.
The stall has a longitudinal passage with a door at the gable and only a small threshing place. The farmhouses are built on an east–west axis in order to present the smallest possible surface area to the prevailing westerly winds. The entrances to the stall and living areas are on the leeward southern side. Because the size of the house is necessarily restricted due to its design, there are often adjacent animal sheds.
If all these sub-tiles are of different sizes then the tiling is additionally described as perfect. A shape that is rep-n or irrep-n is trivially also irrep-(kn − k + n) for any k > 1, by replacing the smallest tile in the rep-n dissection by n even smaller tiles. The order of a shape, whether using rep-tiles or irrep-tiles is the smallest possible number of tiles which will suffice.
The book thickness of a graph is the smallest possible number of half-planes for any book embedding of the graph. Book thickness is also called pagenumber, stacknumber or fixed outerthickness. Book embeddings have also been used to define several other graph invariants including the pagewidth and book crossing number. Every graph with vertices has book thickness at most \lceil n/2\rceil, and this formula gives the exact book thickness for complete graphs.
Perphenazine has sedating and anxiolytic properties, making the drug useful for the treatment of agitated psychotic patients. A valuable off-label indication is the short-time treatment of hyperemesis gravidarum, in which pregnant women experience violent nausea and vomiting. This problem can become severe enough to endanger the pregnancy. As perphenazine has not been shown to be teratogenic and works very well, it is sometimes given orally in the smallest possible dose.
A maximal matching can be found with a simple greedy algorithm. A maximum matching is also a maximal matching, and hence it is possible to find a largest maximal matching in polynomial time. However, no polynomial-time algorithm is known for finding a minimum maximal matching, that is, a maximal matching that contains the smallest possible number of edges. A maximal matching with k edges is an edge dominating set with k edges.
In theoretical physics, an extremal black hole is a black hole with the minimal possible mass that can be compatible with a given charge and angular momentum. In other words, this is the smallest possible black hole that can exist while rotating at a given fixed constant speed. The concept of an extremal black hole is theoretical and none have thus far been observed in nature. However, many theories are based on their existence.
The Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle. A possible Hamiltonian path is shown. Any Hamiltonian cycle can be converted to a Hamiltonian path by removing one of its edges, but a Hamiltonian path can be extended to Hamiltonian cycle only if its endpoints are adjacent. All Hamiltonian graphs are biconnected, but a biconnected graph need not be Hamiltonian (see, for example, the Petersen graph).
This algorithm usually produces small trees, but it does not always produce the smallest possible decision tree. ID3 is harder to use on continuous data than on factored data (factored data has a discrete number of possible values, thus reducing the possible branch points). If the values of any given attribute are continuous, then there are many more places to split the data on this attribute, and searching for the best value to split by can be time consuming.
With each successive reprint, the publisher needs to instruct the printer to change the impression number. In practice, if the plates (in offset printing) have been kept, a number can be erased, but nothing can be added. In this arrangement, all the printer must do is "rub off" the last number in sequence. Changing only the outer number requires the fewest possible changes to the page of characters, which means the smallest possible charge to the publisher.
Schematic picture of a 2-bridge knot. In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given by the z-coordinate has only two maxima and two minima as critical points. Equivalently, these are the knots with bridge number 2, the smallest possible bridge number for a nontrivial knot. Other names for 2-bridge knots are rational knots', 4-plats, and ''''' ().
The choice above, however, is typical because it has two useful properties. First, it consists of sinusoids whose frequencies have the smallest possible magnitudes: the interpolation is bandlimited. Second, if the x_n are real numbers, then p(t) is real as well. In contrast, the most obvious trigonometric interpolation polynomial is the one in which the frequencies range from 0 to N-1 (instead of roughly -N/2 to +N/2 as above), similar to the inverse DFT formula.
The mean center, or centroid, is the point on which a rigid, weightless map would balance perfectly, if the population members are represented as points of equal mass. Mathematically, the centroid is the point to which the population has the smallest possible sum of squared distances. It is easily found by taking the arithmetic mean of each coordinate. If defined in the three-dimensional space, the centroid of points on the Earth's surface is actually inside the Earth.
He also collaborated with Shanghai-based Stellar Works to a create a recycled leather chair and table for the collection. The table and chair were designed as flat-pack pieces so that they could be transported with the smallest possible carbon footprint. At the Milan Design Week 2016, Marone Cinzano unveiled Dondolo, a rocking chair made from salvaged Alfa Romeo car parts. The chair was sourced and made in Turin and inspired by his hometown’s industrial roots.
After Campbell's achievement of the 300 mph land speed record with Blue Bird in 1935 he retired from the land speed record. Shortly afterwards he switched his attentions to the water speed record, at that time dominated by the American Gar Wood.Harris, Skimming the Surface Blue bird was designed by Fred Cooper and built by Fred Goatley of Saunders-Roe. The design was intended to be the smallest possible hull capable of carrying the Rolls-Royce R racing engine.
The design of the YO-51 Dragonfly was typical for aircraft of its type, being optimised for the observation and liaison role, with emphasis on the ability to operate out of the smallest possible airfields.Penfield 1941, p.31. The Dragonfly was a high-wing braced parasol monoplane with fixed tailwheel landing gear, a two-seat open cockpit, and full-span slots and Fowler flaps for STOL capability. It was powered by a single Pratt & Whitney R-985-21 Wasp Junior radial engine.
A Fitting chain' (or Fitting series or ') for a group is a subnormal series with nilpotent quotients. In other words, a finite sequence of subgroups including both the whole group and the trivial group, such that each is a normal subgroup of the previous one, and such that the quotients of successive terms are nilpotent groups. The Fitting length or nilpotent length of a group is defined to be the smallest possible length of a Fitting chain, if one exists.
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator an integer) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical". Minimizing the number of radicals that appear underneath other radicals in an expression is called denesting radicals.
H0e scale A pizza layout is a model railway laid out as a circle of the smallest workable radius of curve, on the smallest possible square or circular baseboard. This baseboard can be so small as to look as if it would fit into a pizza box, hence the name. Pizza layouts are not serious scale models, but are to provide a little humour. Despite their simplicity, they are rarely built by beginners but are usually light relief for an experienced modeller.
Bădoiu et al. presented a 1+\varepsilon approximation to the bounding sphere problem, where a 1+\varepsilon approximation means that the constructed sphere has radius at most (1+\varepsilon)r, where r is the smallest possible radius of a bounding sphere. A coreset is a small subset, that a 1+\varepsilon expansion of the solution on the subset is a bounding sphere of the whole set. The coreset is constructed incrementally by adding the farthest point into the set in each iteration.
103 The most prominent feature on the vessel was a large cylindrical gun turret mounted amidships above the low-freeboard upper hull, also called the "raft". This extended well past the sides of the lower, more traditionally shaped hull. A small armored pilot house was fitted on the upper deck towards the bow, however, its position prevented Monitor from firing her guns straight forward. One of Ericsson's prime goals in designing the ship was to present the smallest possible target to enemy gunfire.
One method is to define a minimum district to convex polygon ratio . To use this method, every proposed district is circumscribed by the smallest possible convex polygon (its convex hull; think of stretching a rubberband around the outline of the district). Then, the area of the district is divided by the area of the polygon; or, if at the edge of the state, by the portion of the area of the polygon within state boundaries. Minimal convex polygon, showing how to rate district shape irregularity.
1782 Henry Seymour Conway, a veteran of both the War of the Austrian Succession and Seven Years' War made a motion against the war. Wrottesley voted for it but it was defeated by the smallest possible margin: 194 votes to 193. Five days later Conway moved a similar motion, again with Wrottesley's endorsement, which was approved by 234 to 215. On 15 March Wrottesley also voted for the motion of no confidence in North’s administration made by Sir John Rous, which finally ended the government.
One of Ericsson's prime goals in designing the ship was to present the smallest possible target to enemy gunfire. The turret's rounded shape helped to deflect cannon shot. A pair of donkey engines rotated the turret through a set of gears; a full rotation was made in 22.5 seconds during testing on 9 February 1862. Fine control of the turret proved to be difficult as the engine would have to be placed in reverse if the turret overshot its mark or another full rotation could be made.
The Panasonic Lumix DMC-GM5 is a Micro Four Thirds rangefinder-styled digital mirrorless camera announced by Panasonic on September 15, 2014. The camera was designed to provide maximum usability and image quality in the smallest possible body. It is slightly larger than the earlier GM1, as it adds a flash hot shoe, an electronic viewfinder and a rear scroll-wheel for adjusting settings. However, with a body roughly the same size as a pack of playing cards, it is still extremely small for a system camera.
The dihedral angle of a Euclidean regular dodecahedron is ~116.6°, so no more than three of them can fit around an edge in Euclidean 3-space. In hyperbolic space, however, the dihedral angle is smaller than it is in Euclidean space, and depends on the size of the figure; the smallest possible dihedral angle is 60°, for an ideal hyperbolic regular dodecahedron with infinitely long edges. The dodecahedra in this dodecahedral honeycomb are sized so that all of their dihedral angles are exactly 72°.
The 2008 event was due to take place from 11–13 January, but was postponed due to a 15-day period of national mourning for the King of Thailand's sister, and was ultimately cancelled. The third edition took place in January 2009 with the Asian team winning for the first time. In 2010, Europe regained the trophy, winning by the smallest possible margin, 8½–7½. Europe won again in 2011 but Asia won the trophy again in 2012 after a sudden-death play-off.
It is the smallest possible snark, and was the only known snark from 1898 until 1946. The snark theorem, a result conjectured by W. T. Tutte and announced in 2001 by Robertson, Sanders, Seymour, and Thomas, states that every snark has the Petersen graph as a minor. Additionally, the graph has fractional chromatic index 3, proving that the difference between the chromatic index and fractional chromatic index can be as large as 1. The long-standing Goldberg- Seymour Conjecture proposes that this is the largest gap possible.
Eastlake, writing in 1872, noted that the quality of construction in Pugin's buildings was often poor, and believed he was lacking in technical knowledge, his strength lying more in his facility as a designer of architectural detail.Eastlake, 1872, pp152 Pugin's legacy began to fade immediately after his death. This was partly due to the hostility of John Ruskin. In his appendix to The Stones of Venice (1851), Ruskin wrote of Pugin, "he is not a great architect but one of the smallest possible or conceivable architects".
In early control system design it was discovered that having same value of components makes design easier and faster. One way to implement passive components with same value or in practice with smallest possible distribution is to place them on the same substrate near to each other. Earliest form of integrated passive devices were resistor networks in the 1960s when four to eight resistors were packaged in form of Single-in-line package (SIP) by Vishay Intertechnology. Many other type of packages like DILs, DIPs etc.
The \lceil r\cdot n\rceil is the smallest possible when n is an integer. An r-partite hypergraph is an r-uniform hypergraph in which the vertices are partitioned into r disjoint sets and each hyperedge contains exactly one vertex of each set (so a 2-partite hypergraph is a just bipartite graph). Let n be any positive integer. Any family of rn-r+1 fractional-matchings (=colors) of size at least n in an r-partite hypergraph has a rainbow-fractional-matching of size n.
Close inspection reveals the central mark left by the pin. In several earlier works Escher explored the limits of infinitesimal size and infinite number, for example the Circle Limit series, by actually carrying through the rendering of smaller and smaller figures to the smallest possible sizes. By contrast, in Snakes, the infinite diminution of size – and infinite increase in number – is only suggested in the finished work. Nevertheless, the print shows very clearly how this rendering would have been carried out to the limits of human visibility.
In Skyrme's model, reproduced in the large N or string approximation to quantum chromodynamics (QCD), the proton and neutron are fermionic topological solitons of the pion field. Whereas Skyrme's example involved pion physics, there is a much more familiar example in quantum electrodynamics with a magnetic monopole. A bosonic monopole with the smallest possible magnetic charge and a bosonic version of the electron will form a fermionic dyon. The analogy between the Skyrme field and the Higgs field of the electroweak sector has been used to postulate that all fermions are skyrmions.
Giddings resigned after Labor and the Greens lost government at the 2014 election and long-serving minister and former deputy leader Bryan Green assumed the Labor leadership in opposition. After consistently trailing the Liberal government of Will Hodgman in the polls, Green abruptly resigned from the leadership and from parliament in March 2017. He was succeeded as Labor and Opposition Leader by Rebecca White, who led Labor to a narrow election loss at the 2018 Tasmanian state election, winning 3 seats back and reducing the Liberals to the smallest possible majority.
An Arri Alexa camera, a prime lens, and Scorpio and Strada cranes were used for the principal photography, while a probe lens and high-intensity lighting were used for the macro photography. Senthil Kumar had to use a special lens with a minimum f-stop of f8.0; the wide apertures required high-intensity lighting to get acceptable shots. He used GoPro cameras as they were the smallest possible ones that offered close to professional resolution. Phantom Cam was used to film extreme slow motion sequences; certain scenes were shot at 2,000 frames per second.
Pair production is also the mechanism behind the hypothesized pair-instability supernova type of stellar explosion, where pair production suddenly lowers the pressure inside a supergiant star, leading to a partial implosion, and then explosive thermonuclear burning. Supernova SN 2006gy is hypothesized to have been a pair production type supernova. Pair production does not occur in X-ray imaging because the machines are usually rated ~150 kV (photons with energy 150 keV) which is much smaller than the minimum of 1022 keV needed to create the smallest possible particle pair, the electron and positron.
The software interface was similarly unforgiving, with very strict syntaxes meant to be parsed by the smallest possible compilers and interpreters. Holes are punched in the card according to a prearranged code transferring the facts from the census questionnaire into statistics Once the cards were punched, one would drop them in a job queue and wait. Eventually, operators would feed the deck to the computer, perhaps mounting magnetic tapes to supply another dataset or helper software. The job would generate a printout, containing final results or an abort notice with an attached error log.
For example, the first four terms add to 1805/1806, and therefore any Egyptian fraction for a number in the open interval (1805/1806,1) requires at least five terms. It is possible to interpret the Sylvester sequence as the result of a greedy algorithm for Egyptian fractions, that at each step chooses the smallest possible denominator that makes the partial sum of the series be less than one. Alternatively, the terms of the sequence after the first can be viewed as the denominators of the odd greedy expansion of 1/2.
Breaking the Magician's Code: Magic's Biggest Secrets Finally Revealed, Fox Television, Original broadcast date: November 24, 1997. The trick hinges on two things: that people will not suspect the woman is key for the trick to work, and that the box is larger than it appears. Details are as follows: # Unlike more conventional magic tricks, this illusion relies on the skill of the woman inside, while the magician outside is a demonstrator. The success of the illusion rests on the woman's ability to fit into the smallest possible space.
In the context of differentiable dynamical systems, the notion of integrability refers to the existence of invariant, regular foliations; i.e., ones whose leaves are embedded submanifolds of the smallest possible dimension that are invariant under the flow. There is thus a variable notion of the degree of integrability, depending on the dimension of the leaves of the invariant foliation. This concept has a refinement in the case of Hamiltonian systems, known as complete integrability in the sense of Liouville (see below), which is what is most frequently referred to in this context.
When Alan Turing came up with the idea of a universal machine he had in mind the simplest computing model powerful enough to calculate all possible functions that can be calculated. Claude Shannon first explicitly posed the question of finding the smallest possible universal Turing machine in 1956. He showed that two symbols were sufficient so long as enough states were used (or vice versa), and that it was always possible to exchange states for symbols. Marvin Minsky discovered a 7-state 4-symbol universal Turing machine in 1962 using 2-tag systems.
An associated concept is the utilization distribution which examines where the animal is likely to be at any given time. Data for mapping a home range used to be gathered by careful observation, but nowadays, the animal is fitted with a transmission collar or similar GPS device. The simplest way of measuring the home range is to construct the smallest possible convex polygon around the data but this tends to overestimate the range. The best known methods for constructing utilization distributions are the so- called bivariate Gaussian or normal distribution kernel density methods.
Jainism speaks of karmic "dirt", as karma is thought to be manifest as very subtle and sensually imperceptible particles pervading the entire universe. They are so small that one space-point—the smallest possible extent of space—contains an infinite number of karmic particles (or quantity of karmic dirt). It is these karmic particles that adhere to the soul and affect its natural potency. This material karma is called dravya karma; and the resultant emotions—pleasure, pain, love, hatred, and so on—experienced by the soul are called bhava karma, psychic karma.
Formally, an edge cover of a graph G is a set of edges C such that each vertex in G is incident with at least one edge in C. The set C is said to cover the vertices of G. The following figure shows examples of edge coverings in two graphs. :File:Edge-cover.svg A minimum edge covering is an edge covering of smallest possible size. The edge covering number \rho(G) is the size of a minimum edge covering. The following figure shows examples of minimum edge coverings. :File:Minimum-edge-cover.
Atoms were thought to be the smallest possible division of matter until 1897 when J. J. Thomson discovered the electron through his work on cathode rays. A Crookes tube is a sealed glass container in which two electrodes are separated by a vacuum. When a voltage is applied across the electrodes, cathode rays are generated, creating a glowing patch where they strike the glass at the opposite end of the tube. Through experimentation, Thomson discovered that the rays could be deflected by an electric field (in addition to magnetic fields, which was already known).
Minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. This term is commonly used in the fields of biology, ecology, and conservation biology. MVP refers to the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" is defined as a group of interbreeding individuals in similar geographic area that undergo negligible gene flow with other groups of the species.
Another important factor is the length of the cables used to connect the antennas with the radio beacons at the shore, for example placed on lighthouses, or on oil rig platforms and the cable(s) to connect the antenna with the transmitter at the vessel. Normally the antenna will be placed at the top of the mast and the transmitter wil be placed in the wheelhouse, where the captain and the mate can see the displays of the transmitter. Those cables has to be calibrated in order to obtain the smallest possible measurement uncertainty.
Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as Holevo entropy and the conditional quantum entropy. Unlike classical digital states (which are discrete), a qubit is continuous-valued, describable by a direction on the Bloch sphere. Despite being continuously valued in this way, a qubit is the smallest possible unit of quantum information, and despite the qubit state being continuously-valued, it is impossible to measure the value precisely. Five famous theorems describe the limits on manipulation of quantum information.
As telegrams have been traditionally charged by the word, messages were often abbreviated to pack information into the smallest possible number of words, in what came to be called "telegram style". The average length of a telegram in the 1900s in the US was 11.93 words; more than half of the messages were 10 words or fewer. According to another study, the mean length of the telegrams sent in the UK before 1950 was 14.6 words or 78.8 characters. For German telegrams, the mean length is 11.5 words or 72.4 characters.
In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities). Optimal BSTs are generally divided into two types: static and dynamic. In the static optimality problem, the tree cannot be modified after it has been constructed. In this case, there exists some particular layout of the nodes of the tree which provides the smallest expected search time for the given access probabilities.
Distances smaller than that are similarly described in reference to the equine body with terms such as a "neck", and a "head", a "short head" or "nose", the smallest possible named advantage by which a horse can win. In Ireland a margin of more than 30 lengths is described as a "distance". In the United Kingdom, the maximum recognised distance is 99 lengths, with anything over this being referred to as "99+ lengths". In France the term "short neck" is used for a margin intermediate between a head and a neck.
This means that if the air temperature is higher and the aircraft has a higher altitude, the force of the operative engine will be lower, the rudder will have to provide less counteractive force, and so the VMCA will be lower. The bank angle also influences the minimum control speed. A small bank angle away from the inoperative engine is required for smallest possible sideslip and therefore lower VMCA. Finally, if the P-factor of the working engine increases, then its yawing moment increases, and the aircraft's VMCA increases as a result.
Main articles: Homeopathy Homeopathy and natural medicine were the focus of the studies of the students at MSM. Two main principles guide the use of medicine in homeopathy: the Similia Principle and the Dose. The Similia Principle states that a substance that can cause a symptom complex in a healthy person can be used to treat similar symptoms in a sick person. The Dose states that the quantity of medicine used should be the smallest possible to affect a cure and should not be repeated as long as improvement lasts.
A beam compass and a regular compass Using a compass A compass with an extension accessory for larger circles A bow compass capable of drawing the smallest possible circles A compass, also known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, they can also be used as tools to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation and other purposes. Prior to computerization, compasses and other tools for manual drafting were often packaged as a seta current vendor's product with interchangeable parts.
Questair Inc was founded by Ed MacDonough in the mid 1980s. The Venture was designed by Jim Griswold, an engineer with Piper Aircraft, and used technology from the Piper Malibu. The layout of the design was intended to combine a large two-seat side-by-side cabin with rear baggage space in the smallest possible airframe, having a highly streamlined design. Questair Venture Questair Spirit with fixed undercarriage at Sun N' Fun Lakeland, Florida in April 2009 The aircraft is of all-metal construction using pre-formed multi-curvature panels and is supplied as a kit to homebuilders.
More generally, the hyperbolic volume may be defined for any hyperbolic 3-manifold. The Weeks manifold has the smallest possible volume of any closed manifold (a manifold that, unlike link complements, has no cusps); its volume is approximately 0.9427.. Thurston and Jørgensen proved that the set of real numbers that are hyperbolic volumes of 3-manifolds is well-ordered, with order type .. The smallest limit point in this set of volumes is given by the knot complement of the figure-eight knot, and the smallest limit point of limit points is given by the complement of the Whitehead link.
As stated by the Gabor limit, an uncertainty principle, the product of the width of the frequency function and the width of the impulse response cannot be smaller than a specific constant. This implies that if a specific frequency function is requested, corresponding to a specific frequency width, the minimum width of the filter in the signal domain is set. Vice versa, if the maximum width of the response is given, this determines the smallest possible width in the frequency. This is a typical example of contradictory requirements where the filter design process may try to find a useful compromise.
When on the defensive, they wait in prepared positions or use any natural terrain elements (such as small hills) for cover. A tank sitting just behind a hill crest ("hull-down") exposes only the top of its turret, with the gun and sensors, to the enemy, leaving the smallest possible target while allowing it to engage the enemy on the other side of the hill. Tanks are usually able to depress the main gun below the horizontal since modern kinetic energy (KE) rounds have nearly flat trajectories. Without this they would be unable to exploit such positions.
For many years the proof of the four-vertex theorem remained difficult, but a simple and conceptual proof was given by , based on the idea of the minimum enclosing circle.. This is a circle that contains the given curve and has the smallest possible radius. If the curve includes an arc of the circle, it has infinitely many vertices. Otherwise, the curve and circle must be tangent at at least two points. At each tangency, the curvature of the curve is greater than that of the circle (else the curve would continue from the tangency outside the circle rather than inside).
The T.K.4 was built by students at Stag Lane Aerodrome in 1937 with the aim of building the smallest possible aircraft around the 140 hp (104 kW) de Havilland Gipsy Major II.Jackson 1974, page 323 It was a low-wing monoplane with a conventional retractable tailwheel landing gear and had a De Havilland PD30 variable-pitch propeller and was fitted with slots and flaps. The only T.K.4, registered G-AETK, was first flown on 30 July 1937. It was 9th in the 1937 Kings Cup Race at a speed of 230.5 mph.Lewis 1972, p.191.
Bradman's outfit managed to fall short of the victory by the smallest possible margin, ending one run short of their target with one wicket remaining at the end of the final over. Hassett continued his liking for the Queensland attack, scoring 104 and 205 in Victoria's two matches against their northern opponents for the year. Victoria did not do so well as a team, winning two and losing one of the six matches in which Hassett played, as New South Wales took the title. The summer finished with Hassett captaining a team against an eleven led by Morris.
The technology behind AWOMO is based on the principle that a player does not need to hold all of the game data locally in order to run and start playing the game. Instead, when the user logs into AWOMO, the server checks the reliable connection speed between server and user. It then calculates the smallest possible 'stub' of data that will enable the player to launch the game and continue playing with no interruption, with the rest of the data downloading as a background task. This technique was employed by Exent, Triton,SteamReview comparison of AWOMO with other services at SteamReview.
The smallest cubic semi-symmetric graph (that is, one in which each vertex is incident to exactly three edges) is the Gray graph on 54 vertices. It was first observed to be semi-symmetric by . It was proven to be the smallest cubic semi-symmetric graph by Dragan Marušič and Aleksander Malnič.. All the cubic semi-symmetric graphs on up to 768 vertices are known. According to Conder, Malnič, Marušič and Potočnik, the four smallest possible cubic semi-symmetric graphs after the Gray graph are the Iofinova-Ivanov graph on 110 vertices, the Ljubljana graph on 112 vertices,.
The automorphism group of the Gray graph is a group of order 1296. It acts transitively on the edges the graph but not on its vertices : there are symmetries taking every edge to any other edge, but not taking every vertex to any other vertex. The vertices that correspond to points of the underlying configuration can only be symmetric to other vertices that correspond to points, and the vertices that correspond to lines can only be symmetric to other vertices that correspond to lines. Therefore, the Gray graph is a semi-symmetric graph, the smallest possible cubic semi- symmetric graph.
The minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. More specifically MVP is the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" refers to the population of a species in the wild. As a reference standard, MVP is usually given with a population survival probability of somewhere between ninety and ninety-five percent and calculated for between one hundred and one thousand years into the future.
The line graph of the Petersen graph, another graph of this type, has a property analogous to the cages in that it is the smallest possible graph in which the largest clique has three vertices, each vertex is in exactly two edge-disjoint cliques, and the shortest cycle with edges from distinct cliques has length five. A more complicated expansion process applies to planar graphs. Let G be a planar graph embedded in the plane in such a way that every face is a quadrilateral, such as the graph of a cube. Necessarily, if G has n vertices, it has n-2 faces.
By several numerical measures it is the farthest from being centrally symmetric. It provides the largest constant-width shape avoiding the points of an integer lattice, and is closely related to the shape of the quadrilateral maximizing the ratio of perimeter to diameter. It can perform a complete rotation within a square while at all times touching all four sides of the square, and has the smallest possible area of shapes with this property. However, although it covers most of the square in this rotation process, it fails to cover a small fraction of the square's area, near its corners.
These can all be applied to natural and man-made sources. For man-made sources the use of Containment is a major tool in reducing dose uptake and is effectively a combination of shielding and isolation from the open environment. Radioactive materials are confined in the smallest possible space and kept out of the environment such as in a hot cell (for radiation) or glove box (for contamination). Radioactive isotopes for medical use, for example, are dispensed in closed handling facilities, usually gloveboxes, while nuclear reactors operate within closed systems with multiple barriers that keep the radioactive materials contained.
In contrast to a basis of a vector space in linear algebra, a base need not be maximal; indeed, the only maximal base is the topology itself. In fact, any open set generated by a base may be safely added to the base without changing the topology. The smallest possible cardinality of a base is called the weight of the topological space. An example of a collection of open sets which is not a base is the set S of all semi-infinite intervals of the forms (−∞, a) and (a, ∞), where a is a real number.
One is that the electrical grids are charged to the point where there is a strong mechanical force pulling them together, which limits how small the grid materials can be. This results in a minimum rate of collisions between the ions and the grids, removing energy from the system. Additionally, these collisions spall off metal into the fuel, which causes it to rapidly lose energy through radiation. It may be that the smallest possible grid material is still large enough that collisions with the ions will remove energy from the system faster than the fusion rate.
Extradition was therefore rational since "It is often better that a crime be prosecuted where its harmful impact is felt and where the witnesses and the persons most interested in bringing the criminal to justice reside." Even if extradition may not be the smallest possible limit on the right, the government was allowed some flexibility and extradition simply did not strike at the primary values of section 6. This conclusion was reinforced by the fact that extradition has long been practiced in Canada, and Re Burley (1865) showed that criminals should receive "little leniency" in extradition cases.
Because of the way arguments are typically passed, each format specifier moves closer to the top of the stack frame. Eventually, the return pointer and stack frame pointer can be extracted, revealing the address of a vulnerable library and the address of a known stack frame; this can completely eliminate library and stack randomization as an obstacle to an attacker. One can also decrease entropy in the stack or heap. The stack typically must be aligned to 16 bytes, and so this is the smallest possible randomization interval; while the heap must be page-aligned, typically 4096 bytes.
Kenneth Waltz, the founder of Neorealism, in his epochal Theory of International Politics (1979) precluded the possibility of unipolarity. Two, he stated (1979: 136), is the smallest possible number of poles in a system. Within twelve years, unipolarity emerged. In two papers of 1993--“Structural Realism after the Cold War” and "The Emerging Structure of International Politics"—Waltz defends the neorealist theory against a cascade of criticism that emerged after the Cold War. First of all, he stresses that unipolarity is “the least durable of international configurations.”"Structural Realism After the Cold War," International Security, 25/1, (2000): p 27.
Because screwmen were skilled laborers, they received higher wages than stevedores or ship hands and were considered to be at the top of societal ladder. Working in gangs of five, many of them exclusively Irish, the screwmen went into the holds of the cotton ships where they used large jackscrews to compress the bales into the smallest possible size. This was a dangerous way of earning a living, for in the cramped quarters below deck a screwman had little space to dodge a wayward bale. Broken limbs were common and occasionally a heavy bale crushed the life out of a worker.
The following year, Lee crewed for Art Biehi in Lee's first Transpacific Yacht Race where he was exposed to the conditions of the race and the expectations for victory. Lee is quoted reflecting to Biehi on how to win, "I told him that to win the Transpac (under the old conditions) you needed the smallest possible boat, the lowest possible rating, and the lightest possible boat, for little boats can surf when the bigger boats can't." With this insight, Biehi hired Lee to build his next boat. Bill Lee built Witchcraft for Biehi, which launched in April, 1972.
In contrast to other Hough transform-based approaches for analytical shapes, Fernandes' technique does not depend on the shape one wants to detect nor on the input data type. The detection can be driven to a type of analytical shape by changing the assumed model of geometry where data have been encoded (e.g., euclidean space, projective space, conformal geometry, and so on), while the proposed formulation remains unchanged. Also, it guarantees that the intended shapes are represented with the smallest possible number of parameters, and it allows the concurrent detection of different kinds of shapes that best fit an input set of entries with different dimensionalities and different geometric definitions (e.g.
Since the fleet had no vessels of the type, and thus no experience designing cruisers to fit his requirements, offers were extended to five British shipyards, with the only design requirements being a speed of at least , an armament of guns, on the smallest possible displacement. The Austro- Hungarian Navy established a commission to examine the designs submitted by the British firms; Armstrong received the contract in part because they could build the ships more cheaply. The commission requested the ventilation for the boilers be improved, and requested that the armament consist of four deck- mounted torpedo tubes, two 12 cm guns, and ten Hotchkiss revolver cannon.Bilzer, pp.
Görgi and his family were left behind for their safety when Webern fled on foot with his family to Mittersill, about 75 km. away, for safety of their own in light of the coming Russian invasion; Amalie, one of Webern's daughters, wrote of '17 persons pressed together in the smallest possible space' upon their arrival. Ironically, the Russians pronounced Görgi a "Nazi spy" when he was discovered due to the Nazi munitions and propaganda in the Weberns' basement store-room. Görgi is said to have saved himself from execution by protesting and drawing attention to his clothes, sewn as specified by the Nazis with the yellow Star of David.
Following a naming competition that drew 3500 proposals, the ship was named Birka Paradise to reflect its design, reminiscent of a Caribbean cruise ship. The ship was designed with various environmentally friendly innovations; in addition to exhaust and closed sewage treatment systems already used on the company's Birka Princess, Birka Paradise was built to fulfill Det Norske Veritas' Clean Design rule relating to environmentally friendly structural solutions. Her hull form was optimised for smallest possible impact on the sensitive archipelago routes on which she sails. The keel of Birka Paradise was laid on 19 October 2003 and she was launched on 15 April 2004.
The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, who published the Hardy–Ramanujan number Ta(2) = 1729. This particular example of 1729 was made famous in the early 20th century by a story involving Srinivasa Ramanujan. In 1938, G. H. Hardy and E. M. Wright proved that such numbers exist for all positive integers n, and their proof is easily converted into a program to generate such numbers. However, the proof makes no claims at all about whether the thus-generated numbers are the smallest possible and thus it cannot be used to find the actual value of Ta(n).
Alice knows that Bob will end the game on his last move, so she decides to end the game one step before then. However, Bob knows that Alice will end early, so he decides to end just before she does. This process repeats until Alice is confronted with her decision on the first round; knowing that Bob will end the game at the first opportunity, Alice ends the game on the first round, and they walk home with the smallest possible total payoff. Thus, standard analytic methods predict that all players will defect as soon as they have the opportunity, despite the higher payoffs that would accrue to more cooperative play.
Electric power distribution systems include circuit breakers to disconnect power in case of a fault, but to maximize reliability, they wish to disconnect the smallest possible portion of the network. This means that even the smallest circuit breakers, as well as all wiring to them, must be able to disconnect large fault currents. A problem arises if the electricity supply is upgraded, by adding new generation capacity or by adding cross- connections. Because these increase the amount of power that can be supplied, all of the branch circuits must have their bus bars and circuit breakers upgraded to handle the new higher fault current limit.
Burnup is one of the key factors determining the isotopic composition of spent nuclear fuel, the others being its initial composition and the neutron spectrum of the reactor. Very low fuel burnup is essential for the production of weapons-grade plutonium for nuclear weapons, in order to produce plutonium that is predominantly 239Pu with the smallest possible proportion of 240Pu and 242Pu. Plutonium and other transuranic isotopes are produced from uranium by neutron absorption during reactor operation. While it is possible in principle to remove plutonium from used fuel and divert it to weapons usage, in practice there are formidable obstacles to doing so.
An object moves with different speeds in different frames of reference, depending on the motion of the observer. This implies the kinetic energy, in both Newtonian mechanics and relativity, is frame dependent, so that the amount of relativistic energy, and therefore the amount of relativistic mass, that an object is measured to have depends on the observer. The rest mass or invariant mass (typically denoted as just mass) is defined as the mass that an object has when it is not moving (as observed from an inertial frame of reference). The invariant mass is the smallest possible value of the relativistic mass of the object or system.
In order to pinpoint the position of the relevant arteries, a three-dimensional CT scan is done, which allows accurate visualization of the course of each artery. This is necessary, as the course of the arteries varies from person to person, and even from side to side in the same individual. During surgery, the position of the artery is further verified by means of a Doppler Flowmeter, with which one can hear the blood flowing through the vessel. Use of the three-dimensional CT scan and the Doppler Flowmeter allows the surgeon to make use of the smallest possible incision, so the procedure is minimally invasive.
Today many designers have moved previously "external" stores into internal multifunction "weapons bays" capable of carrying air-to-air missiles, air-to-ground missiles, drop tanks, and other military "stores" and deploying them rapidly in a battle. The principal reason for the change is to use stealth technology to make aircraft more difficult to detect on radar. Military fighters are now designed to have the smallest possible radar cross- section, which has decreased very substantially since attention was paid to this feature. Large racks of missiles and bombs hanging below the wings return very distinct radar signatures which can be eliminated by bringing the weapons inside the fuselage.
If the four-color conjecture were false, there would be at least one map with the smallest possible number of regions that requires five colors. The proof showed that such a minimal counterexample cannot exist, through the use of two technical concepts:; ; # An unavoidable set is a set of configurations such that every map that satisfies some necessary conditions for being a minimal non-4-colorable triangulation (such as having minimum degree 5) must have at least one configuration from this set. # A reducible configuration is an arrangement of countries that cannot occur in a minimal counterexample. If a map contains a reducible configuration, the map can be reduced to a smaller map.
In 1935, two designers from GAZ-21 (Gosoodarstvenny Aviatsiya Zavod – state aviation plant/factory), at Gor'ky began work on a new high-speed biplane fighter design. Borovkov and Florov drew heavily on their experience working in the Polikarpov I-16 program, producing 'Prototype No.7211' (Izdeliye 7, Zavod 21, Samolyet 1 – article 7, factory 21, aircraft 1). The goal was the smallest possible aircraft with the most powerful engine then available in the Soviet Union, the Mikulin M-85 14-cylinder radial, a licensed-built Gnome-Rhône K14 Mistral Major. The No.7211 was a sleek biplane with fully cantilever outer wings, the upper centre-section being supported by four well-streamlined cabane struts.
Minilateralism does falls only loosely into the category of the bottom-up framework as it is against integrating nongovernmental actors and governmental actors in approaching the problem. Aside from this main difference, minilateralism encourages the smallest possible break from the current top-down UNFCCC-led approach where the UNFCCC is still employed but other intergovernmental bodies are also incorporated. Possible intergovernmental bodies to be utilized include the OECD, the G20, or other international leading bodies that could address the issue further. This encourages the UNFCCC to not completely stop working on addressing the issue from a top-down approach, but in the interim these other bodies are important in furthering the cause.
The Dewoitine D.500 was an all-metal low-wing cantilever monoplane.NACA 1933 p. 1. It featured a sharp fuselage, complete with a streamlined nose section that housed the aircraft's powerplant, a single Hispano-Suiza 12Xbrs V-12 liquid-cooled piston engine capable of generating up to . Underneath the fuselage was a relatively large- volume radiator, which was designed to present the smallest possible frontal area while still conforming with the cooling requirements of the Hispano-Suiza engine.NACA 1933 pp. 1, 3. The cockpit of the D.500 was located directly above the trailing edge of the wing. The pilot was provided with a vertically- adjustable chair, which can be raised in-flight to improve visibility for landing.
The unknown steamer was USS Yankee, a 6,888-ton auxiliary cruiser under Commander Willard H. Brownson armed with 10 5-inch guns, 6 6-pound guns and two Colt machine guns. Yankee was carrying out blockade tasks off the port, and was in fact waiting for the arrival of El Purísima Concepción in order to intercept it.Dictionary of American Naval Fighting Ships At about 1,400 meters range, the American ship put her helm over, unmasked her port battery, and opened fire. Diego Velázquez opted for a running fight, presenting the smallest possible target and only allowing Yankee to bring one or two of her guns to bear without turning away from her target's course.
The Fano plane In finite geometry, the Fano plane (after Gino Fano) is the finite projective plane of order 2. It is the finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. The standard notation for this plane, as a member of a family of projective spaces, is where stands for "projective geometry", the first parameter is the geometric dimension and the second parameter is the order. The Fano plane is an example of a finite incidence structure, so many of its properties can be established using combinatorial techniques and other tools used in the study of incidence geometries.
The specifications for the Casco class originally called for a vessel with a light draft, not exceeding six feet, and a low freeboard to present the smallest possible target to Confederate guns. For the design of the new class, the Navy turned once again to John Ericsson, designer of USS Monitor. Diagram of USS Nausett, showing the large wooden "raft" surrounding the iron hullEricsson came up with a design for a -long vessel with a single revolving turret containing two guns, an armored upper deck, and twin screw propellers giving a top speed of around eight knots. Around the hull of the vessel, a large wooden "raft" was to be constructed, which would help increase buoyancy.
A small armoured pilot house was fitted on the upper deck towards the bow; however, its position prevented Monitor from firing her guns straight forward. Like Coles's, one of Ericsson's goals in designing the ship was to present the smallest possible target to enemy gunfire. The turret's rounded shape helped to deflect cannon shot. A pair of donkey engines rotated the turret through a set of gears; a full rotation was made in 22.5 seconds during testing on 9 February 1862 but fine control of the turret proved to be difficult as the engine would have to be placed in reverse if the turret overshot its mark or another full rotation could be made.
Collimated laser beams of visible and near-infrared light are especially dangerous at relatively low powers because the lens focuses the light onto a tiny spot on the retina. Light sources with a smaller degree of spatial coherence than a well- collimated laser beam, such as high-power LEDs, lead to a distribution of the light over a larger area on the retina. For such sources, the MPE is higher than for collimated laser beams. In the MPE calculation, the worst-case scenario is assumed, in which the eye lens focuses the light into the smallest possible spot size on the retina for the particular wavelength and the pupil is fully open.
Thus, any activity of production (which distributism holds to be the most important part of any economy) ought to be performed by the smallest possible unit. This helps support distributism's argument that smaller units, families if possible, ought to be in control of the means of production, rather than the large units typical of modern economies. In Quadragesimo anno, Pope Pius XI further stated that "every social activity ought of its very nature to furnish help to the members of the body social, and never destroy and absorb them". To prevent large private organizations from thus dominating the body politic, distributism applies this principle of subsidiarity to economic as well as to social and political action.
The important concept of pressure lubrication of engine bearings began with high-speed steam engines and is now a vital part of internal combustion engines. This is both reliable as a lubrication system and also allows the use of hydrodynamic bearings ('oil wedge') that can support greater loads. The first patents for this were issued to Belliss & Morcom in 1890, from the work of their draughtsman Albert Charles Pain. Belliss & Morcom preferred double-acting cylinders, so as to produce the smallest possible engines for a given power; one of their major markets, like Peter Brotherhood, was in supplying generator sets to the Royal Navy for use in the confines of a warship engine room.
An example known to Leonhard Euler is a Heronian birectangular tetrahedron, a tetrahedron with a path of three edges parallel to the three coordinate axes and with all faces being right triangles. The lengths of the edges on the path of axis-parallel edges are 153, 104, and 672, and the other three edge lengths are 185, 680, and 697, forming four right triangle faces described by the Pythagorean triples (153,104,185), (104,672,680), (153,680,697), and (185,672,697). Eight examples of Heronian tetrahedra were discovered in 1877 by Reinhold Hoppe. 117 is the smallest possible length of the longest edge of a perfect tetrahedron with integral edge lengths. Its other edge lengths are 51, 52, 53, 80 and 84.
According to William Safire, the term "dog whistle" in reference to politics may have been derived from its use in the field of opinion polling. Safire quotes Richard Morin, director of polling for The Washington Post, as writing in 1988, > "subtle changes in question-wording sometimes produce remarkably different > results ... researchers call this the 'Dog Whistle Effect': Respondents hear > something in the question that researchers do not". He speculates that campaign workers adapted the phrase from political pollsters. In her 2006 book, Voting for Jesus: Christianity and Politics in Australia, academic Amanda Lohrey writes that the goal of the dog-whistle is to appeal to the greatest possible number of electors while alienating the smallest possible number.
Since the 2011 parliamentary elections Michelsen has been a controversial politician on several occasions. The coalition parties had the smallest possible majority with only 17 of 33 members of the Løgting. But after only a few days Sonja Jógvansdóttir who was the first openly homosexual person who was elected to the Løgting chose to leave the Social Democratic Party, because she did not wish to be a part of a party which she deemed was ruled by a few homophobic men. In March 2016 the proposal from four female members of the Løgting which was a proposal to implement the Danish law which allows same-sex marriage in the Faroe Islands got the second reading.
The concept of intercept point is based on the assumption of a weakly nonlinear system, meaning that higher- order nonlinear terms are small enough to be negligible. In practice, the weakly nonlinear assumption may not hold for the upper end of the input power range, be it during measurement or during use of the amplifier. As a consequence, measured or simulated data will deviate from the ideal slope of n. The intercept point according to its basic definition should be determined by drawing the straight lines with slope 1 and n through the measured data at the smallest possible power level (possibly limited towards lower power levels by instrument or device noise).
Given the transient nature of most reality TV ventures, many believe that as viewership declines, funding could significantly decrease, thereby harming the entire expedition. Further, contestants have reported that they were ranked based on their donations and funds raised. In February 2013, the US nonprofit Inspiration Mars Foundation announced a plan to send a married couple on a 2018 mission to travel to Mars and back to Earth on a 501-day round trip, with no landing planned on Mars. The mission would have taken advantage of an infrequently occurring free return trajectory—a unique orbit opportunity which occurs only once every fifteen years—and will allow the space capsule to use the smallest possible amount of fuel to get it to Mars and back to Earth.
TSRs are no exception, and take chunks from that 640 KB that are thus unavailable to other applications. This meant that writing a TSR was a challenge of achieving the smallest possible size for it, and checking it for compatibility with a lot of software products from different vendors—often a very frustrating task. In the late 1980s and early 1990s, many video games on the PC platform pushed up against this limit and left less and less space for TSRs—even essential ones like CD-ROM drivers—and arranging things so that there was enough free RAM to run the games, while keeping the necessary TSRs present, became a black art. Many gamers had several boot disks with different configurations for different games.
To compete in the August 1941 Osoaviakhim all-union air race Chyeranovskii followed the successful recipe he used in the BICh-20, building the smallest possible aircraft to house the Renault 6 in-line MV-6 engine and the cockpit in the leading edge of the fin. The inverted gull wings allowed a shorter, pneumatically retracted tail-wheel undercarriage, to be fitted at the junction of the inner and outer wings. The aircraft was completed in 1940 but flight tests were not carried out till June 1941. The BICh-21 was a firm favourite to win the all-union air race but Operation Barbarossa intervened, with the start of the Great Patriotic War, further work on the BICh-21 was stopped..
Total radiation doses from 3D dental CBCT exams are 96% lower than conventional CT exams, but deliver more radiation than standard dental 2D x-ray (OPG). The time of exposure in CBCT is also comparatively less when compared to conventional CT. CBCT use is only lightly regulated in the US. The recommended standard of care is to use the smallest possible field of view (FOV), the smallest voxel size, the lowest mA setting and the shortest exposure time in conjunction with a pulsed exposure mode of acquisition. International organisations such as the World Health Organization and ICRP, as well as many local bodies and legislation, encourage the idea of justification for all medical exposures, where risks and benefits must be weighed up before a procedure goes ahead.
The 2,5-diketopiperazines (2,5-DKPs) are the smallest possible cyclic peptides, which are peptidomimetic in nature and bear resemblance with a constrained protein beta turn. These cyclic dipeptides incorporate both donor and acceptor groups for hydrogen bonding and are small, conformationally constrained heterocyclic scaffolds in which diversity can be introduced at up to six positions and stereochemistry controlled at up to four positions, and they are stable to proteolysis. These characteristics enable them to bind to a wide range of receptors which result in a widespread class of biologically active natural compounds. They have a rigid backbone, which can mimic a preferential peptide conformation and contain constrained amino acids embedded within their structures without the unwanted physical and metabolite properties of peptides.
The effect that windshield wipers have on a vehicle's airflow varies between vehicles; however, they are often omitted from race vehicles and high efficiency concepts in order to maintain the smallest possible coefficient of drag. A much more common option is to replace the windshield wipers with lower profile wipers, or to only remove the windshield wiper on the passenger side of the vehicle, and even to fabricate a deflector to deflect the air up and over the wipers. Another alternative is to equip the vehicle with a single wiper placed in the centre of the windshield, allowing it to cover both sides of the windshield. This mitigates the amount of drag by decreasing the frontal area of the blade.
The unitary mytheme, by contrast, is the equivalent in myth of the phonemes, morphemes, and sememes into which structural linguistics divides language, the smallest possible units of sound, structure, and meaning (respectively) within a language system. In the 1950s Claude Lévi-Strauss first adapted this technique of language analysis to analytic myth criticism. In his work on the myth systems of primitive tribes, working from the analogy of language structure, he adopted the French term mythème, with the assertion that the system of meaning within mythic utterances parallels closely that of a language system. Roman Jakobson varies this idea, treating mythemes as concepts or phonemes which have no significance in themselves but whose significance might be shown by sociological analysis.
Based on their 1939 civilian pre-war design, the prototype had a right hand brake and was fitted with an Amal carburettor and had a low-mounted toolbox. The trials went well and led to some modifications, including fitting a twin-box exhaust system to help silence the noisy two stroke engine, a Villiers carburettor (indicated by a 'V' on the engine), raising the toolbox and fitting a folding kick-start, footrests and even folding handlebars, so that it could be packed into the smallest possible space. A Miller lighting system was added, together with a sealed vent on the fuel filler to prevent spillage when the motorcycle was packed in a drop carrier. The foot brake was also relocated to the left side.
In a game of less than 5 players, the best possible hand would score 29 points (besides 5 for full hand): Double Khanhoo (15 points), any Double Triplet (10 points) and any one of the Royal Groups (4 points) equals 29 points. The smallest possible score would be 2: Two sequences of 9 and 6 cards or two of 8 and 7 cards respectively. Though sequences score so little they are of great use in filling a hand. Not only does a long sequence take up a large proportion of the 15 cards, but a sequence of more than 3 cards is exceedingly useful, as either a card can be thrown away in order to declare full hand, or used in a triplet, without spoiling the sequence.
His simple and elegant model was refined and developed by Carl Friedrich von Weizsäcker and, after the discovery of the neutron, by Werner Heisenberg in 1935 and Niels Bohr in 1936, it agreed closely with observations. In the model, the nucleons were held together in the smallest possible volume (a sphere) by the strong nuclear force, which was capable of overcoming the longer ranged Coulomb electrical repulsion between the protons. The model remained in use for certain applications in the 21st century, when it attracted the attention of mathematicians interested in its properties, but in its 1934 form it confirmed what physicists thought they already knew: that nuclei were static, and that the odds of a collision chipping off more than an alpha particle were practically zero.
If the two radii are equal to half the cavity length (R1 = R2 = L / 2), a concentric or spherical resonator results. This type of cavity produces a diffraction-limited beam waist in the centre of the cavity, with large beam diameters at the mirrors, filling the whole mirror aperture. Similar to this is the hemispherical cavity, with one plane mirror and one mirror of radius equal to the cavity length. A common and important design is the confocal resonator, with mirrors of equal radii to the cavity length (R1 = R2 = L). This design produces the smallest possible beam diameter at the cavity mirrors for a given cavity length, and is often used in lasers where the purity of the transverse mode pattern is important.
SI defines the second as 9,192,631,770 cycles of the radiation that corresponds to the transition between two electron spin energy levels of the ground state of the 133Cs atom. Today, the Global Positioning System in coordination with the Network Time Protocol can be used to synchronize timekeeping systems across the globe. In medieval philosophical writings, the atom was a unit of time referred to as the smallest possible division of time. The earliest known occurrence in English is in Byrhtferth's Enchiridion (a science text) of 1010–1012, where it was defined as 1/564 of a momentum (1½ minutes),"atom", Oxford English Dictionary, Draft Revision September 2008 (contains relevant citations from Byrhtferth's Enchiridion) and thus equal to 15/94 of a second.
For example the light orange line spreads to produce the color spreading effect. (8) If the lines were reversed and the orange was on the outside than the orange hue would appear to be penetrating outward of the object while the purple line would be on the inside. Some other properties are the following: (9) the coloration extends about 45 visual degrees (found in experiments listed above); (10) the coloration is complete by 100 millisecond the smallest possible measurable unit due to the experiment equipment; (11) the line width that produces the best coloration effect is 6 arc minutes; (12) the color also spreads in directions other than the line; (13) and lastly it can induce a complementary color when one of the lines is achromatic and the other is chromatic.
In 1895 he persuaded the other judges of the Queen's Bench Division, in which Lord Russell of Killowen had just been appointed Chief Justice, to assent to the formation of a special list for commercial cases to be heard in a particular court, presided over by the same judge sitting continuously and with a free hand as to his own procedure. Of this office Mathew was the first and by far the most successful occupant. He swept away written pleadings, narrowed the issues to the smallest possible dimensions, and allowed no dilatory excuses to interfere with the speedy trial of the action. His own judgments, ‘concise and terse, free from irrelevancies and digression,’ won the approval of all who practised in the court, and the confidence of the mercantile community.
The Gray graph, arranged to show its construction from a 3d grid In 1930 she was appointed to the post of assistant engineer at the Department of Development and Research of the American Telephone and Telegraph Company in New York. While working there she discovered an unusual cubic semi-symmetric graph with 54 vertices, representing the 27 points and 27 lines in a 3 × 3 × 3 three-dimensional grid, with an edge for each pair of a point and a line that meet each other. Here, "cubic" means that each vertex is the endpoint of three edges, and "semi-symmetric" means that every two edges are symmetric to each other but the same is not true for the vertices. This graph is the smallest possible cubic semi-symmetric graph.
Sorby works as a guide and historian of Antarctica, having visited the continent more than 100 times and also having skied across the Greenland icecap, across King George Island, Antarctica, and skied to the South Pole. Her journey to the South Pole, which she reached on 14 January 1993, was as a member of the first women’s team (under the leadership of Ann Bancroft) to do so. Sorby co-founded Hearts in the Ice, a social media project aimed at engagement on climate change and together with Norwegian Hilde Fålun Strøm, is the first woman to over-winter in Svalbard without men. Focusing on the smallest possible carbon footprint while overwintering on Svalbard, Sorby and Strøm intend to pioneer the use of an electric snowmobile, and keep packaging of supplies to a minimum.
The internal state variables are the smallest possible subset of system variables that can represent the entire state of the system at any given time. The minimum number of state variables required to represent a given system, n, is usually equal to the order of the system's defining differential equation, but not necessarily. If the system is represented in transfer function form, the minimum number of state variables is equal to the order of the transfer function's denominator after it has been reduced to a proper fraction. It is important to understand that converting a state-space realization to a transfer function form may lose some internal information about the system, and may provide a description of a system which is stable, when the state-space realization is unstable at certain points.
They are named after Franz Reuleaux,. a 19th- century German engineer who pioneered the study of machines for translating one type of motion into another, and who used Reuleaux triangles in his designs.. However, these shapes were known before his time, for instance by the designers of Gothic church windows, by Leonardo da Vinci, who used it for a map projection, and by Leonhard Euler in his study of constant-width shapes. Other applications of the Reuleaux triangle include giving the shape to guitar picks, pencils, and drill bits for drilling square holes, as well as in graphic design in the shapes of some signs and corporate logos. Among constant-width shapes with a given width, the Reuleaux triangle has the minimum area and the sharpest (smallest) possible angle (120°) at its corners.
This could be broken down even further when required, with each of the three tank platoons of a medium tank company being assigned to one of the regiment's three infantry battalions. When breaking out of the Bocage in Normandy, the smallest possible combination—a single tank operating with a nine-man infantry squad—was often used. The light tank company was seldom used in direct infantry support missions, and usually served in a screening role or to augment the division's cavalry reconnaissance troop in their operations. This was due to the severe limitations of the M5 Stuart light tank, which, by 1944, was under-gunned and too lightly armored to be effective in anything but reconnaissance missions (the 752nd Tank Battalion referred to the 37mm gun as a "peashooter").
The instrumentation suggested in the commission was: eight solo trumpeters, one extra soloist, 104 trumpets divided into four equal sections, 32 horns divided into four sections, 32 mixed tenor and baritone horns in four sections, 64 trombones in four sections, and 8 tubas in two sections . Stockhausen accommodated this request with a flexible scoring for four tutti groups of instruments (two of treble and two of bass instruments), a group of solo instruments, and synthesizers ad lib. There is no upper limit on the size of this ensemble, but the groups should be balanced in size. The smallest possible option is for twelve parts: four soloists, four tutti treble and four tutti bass instruments (divided 2 + 2), but when synthesizers are included, each player can cover two parts (one with each hand).
After a lucid explanation of the state and prospects of the > company, the Chairman, the Earl of Elgin, who said he had not the smallest > possible trust in the promises of the North British directors, moved the > approval and confirmation of the memorandum of amalgamation... [and] > ultimately the heads of agreement were, by a majority, approved of.Falkirk > Herald: Thursday 22 February 1877 Elgin's view was hardly balanced: shareholders got 3% preference shares, and the NBR took the whole of the escalated debt of the D&QR.;E F Carter, An Historical Geography of the Railways of the British Isles, Cassell, London, 1959 The NBR now hastened the completion of the D&QR;, and it opened on 2 November 1877.Thomas, volume 1, page 242, says 1 April 1878; Brotchie and Jack say 1 November 1877.
Campbell had already used this engine in his Blue Bird car, and they had also been used in pairs in Segrave and Kaye Don's Miss England boats. Of the three individual R engines used by K3, one had previously run in Blue Bird and one in Miss England II. The most compact layout placed the engine behind the driver and relied on a front-mounted v-drive gearbox to reverse the direction of the drive shaft and increase the shaft revolutions 1:3 to 9,000 rpm. This gearbox, along with much of the mechanical design, was designed by Reid Railton who had previously designed cars for Campbell. Unlike Gar Wood's multi-engined monsters, Blue Bird was designed for a single engine, and the smallest possible craft to carry it.
Behind Russian Prime Minister Dmitry Medvedev at the June 2016 roll-out In February 2017, it passed 90% of the static ultimate load test (150% of the highest load in operation) at the TsAGI but failed the 100% test for which the wingbox will need 25kg reinforcements: this is common for new airliners like the Airbus A380, Boeing 787 or Mitsubishi MRJ, aiming for the smallest possible margin to avoid excess weight; it passed the limit load test (highest load during flight) which enables flight testing which should start in April. Cracks developed at the point of contact between the titanium beam and the composite wing skin in the wingbox. The reinforced wingbox withstood a load exceeding specifications without damage in mid-November at TsAGI Moscow. In May 2017, it was undergoing systems ground testing including its auxiliary power unit and taxiing tests.
For propellants to oxidize and burn rapidly and effectively, the combustible ingredients must be reduced to the smallest possible particle sizes, and be as thoroughly mixed as possible. Once mixed, however, for better results in a gun, makers discovered that the final product should be in the form of individual dense grains that spread the fire quickly from grain to grain, much as straw or twigs catch fire more quickly than a pile of sawdust. Because the dry powdered ingredients must be mixed and bonded together for extrusion and cut into grains to maintain the blend, size reduction and mixing is done while the ingredients are damp, usually with water. After 1800, instead of forming grains by hand or with sieves, the damp mill-cake was pressed in molds to increase its density and extract the liquid, forming press-cake.
If K is given inside an algebraically closed field C, then the conjugates can be taken inside C. If no such C is specified, one can take the conjugates in some relatively small field L. The smallest possible choice for L is to take a splitting field over K of pK,α, containing α. If L is any normal extension of K containing α, then by definition it already contains such a splitting field. Given then a normal extension L of K, with automorphism group Aut(L/K) = G, and containing α, any element g(α) for g in G will be a conjugate of α, since the automorphism g sends roots of p to roots of p. Conversely any conjugate β of α is of this form: in other words, G acts transitively on the conjugates.
Tobacco virtovirus 1, informally called Tobacco mosaic satellite virus, Satellite tobacco mosaic virus, or tobacco mosaic satellivirus, is a satellite virus first reported in Nicotiana glauca from southern California, U.S.. Its genome consists of linear positive-sense single-stranded RNA. Tobacco virtovirus 1 is a small, icosahedral plant virus which worsens the symptoms of infection by Tobacco mosaic virus (TMV). Satellite viruses are some of the smallest possible reproducing units in nature; they achieve this by relying on both the host cell and a host virus (in this case, TMV) for the machinery necessary for them to reproduce. The entire Tobacco virtovirus 1 particle consists of 60 identical copies of a single protein that make up the viral capsid (coating), and a 1063-nucleotide single-stranded RNA genome which codes for the capsid and one other protein of unknown function.
The design of the self-sealing suction cup was initially inspired by the suckers of the octopus and its ability to pick up different sized items by individually actuating its suction cups based on the item's size and physical features. The internal geometry of the self-sealing suction cup was designed to the smallest possible size and features a minimum wall thickness of 1.02 mm, a tube diameter of 1.59 mm, and minimum part spacing of 0.13 mm. The suction cup incorporates a mix of rubber and plastic components, where the cup lip, base, tube, springs, and plug are made out of soft rubber while the cup side, collar, hinges, and flange are made out of plastic. As part of its design, a central vacuum pump can be used to maximize the suction force of the suction cup.
The half-ton Expedition EL/Max competes with the half-ton Chevrolet Suburban 1500 and GMC Yukon XL 1500 in the towing segment. Since its introduction, the Expedition's braked trailer towing capacity has grown from 8,100 lbs (3,674 kg or 4.05 tons) to a current rating of 9,200 lbs (4,173 kg or 4.6 tons) when properly equipped. The list of towing features is also ever growing. Towing features common to all generations of the Expedition include: smallest possible turning radius for increased trailer maneuverability, large side view mirrors to improve rearward visibility, rearward-facing lane departure indicators which are helpful to other motorist when the Expedition is towing a long trailer providing added visual safety, heavy-duty flashers, heavy-duty large disc brakes to withstand prolonged braking while towing, and an available heavy- duty trailer towing package which includes necessary additions for heavy-duty towing.
To achieve the smallest distance between the mids and tweeters requires the drivers to have the smallest possible size - but there are design limitations to this (lowest mid-range frequency, for example, will place a lower limit to the mid's diameter). Another problem with the MTM configuration is the interaction between the two midwoofers. For any frequency (over the operating range of the midwoofers), the off-axis response exhibits different lobing patterns because of the vertical distance between the midwoofers, and as a function of the frequency and horizontal distance from the speaker. At any off-axis listening position, although both midwoofers operate in phase (are time-aligned), the waves from each reach the listening position at different times (and therefore have a relative phase difference) - at frequencies where the time displacement between the two midwoofers corresponds to one-half of one wavelength, the outputs of the two midwoofers will null.
The approach that he selected was to build the smallest possible aircraft around the intended powerplant, thereby minimizing weight and drag — the philosophy of the light fighter. As specified, the aircraft was to be capable of reaching 670 km/h (417 mph). In August 1939, Polikarpov fell out of favor with Joseph Stalin and as a result, when Polikarpov went in November 1939 to tour Germany's aviation works, the Soviet authorities decided to scatter his construction team and create a new Experimental Construction Section (OKO), headed by Artem Mikoyan and Mikhail Gurevich, which remained formally subordinated to the Polikarpov bureau until June 1940. Further work upon the I-200 design was assigned to Mikoyan and Gurevich, who later became recognized — not with full justice — as its designers.Gordon (2008), pp. 95–96 The MiG-1 was a low-wing monoplane with a tailwheel undercarriage of mixed construction.
In a standard English auction, the winner pays the amount of their bid—regardless of competitors' bids—and it is therefore desirable to place a bid that exceeds the current highest bid by the smallest possible increment. Conversely, under proxy bidding, the price paid is determined only by competitors' bids and not by the amount of the new bid; this eliminates the economically rational incentive to place a bid below the amount one is willing to pay or to place multiple increasing bids. An "economically rational" bidder will therefore bid the maximum amount they are willing to pay on their first bid, and never raise their bid. eBay's approach, however, reveals the bidder's limit to rival bidders early in the auction, which can sometimes artificially inflate the price of the item higher than its actual intrinsic value, and ultimately encourages the practice of auction sniping.
Taihōs planned air complement varied considerably throughout her design and construction. Initially, it was envisioned she would carry 126 aircraft (with 30 of these in reserve). Later, this was pared down to 64, raised again to 78 and finally reduced to 53. One reason for the discrepancy in numbers was (in sharp contrast to the United States) the Imperial Japanese Navy's lack of insistence that its carrier planes have the smallest possible folded wingspan (many designs' folded only near the tips, while the wings of the Yokosuka D4Y Suisei dive-bomber did not fold at all). Her aircraft capacity was also changed based on previous wartime experience and the fact that Taihō was expected to carry larger newer-model carrier planes still under development at the time of her construction: 24 Mitsubishi A7M2 Reppu "Sam" fighters, 25 Aichi B7A2 Ryusei "Grace" torpedo- dive bombers and four Nakajima C6N1 Saiun "Myrt" reconnaissance planes.
This ion is isoelectronic with the hydrogen molecule. He22+ is the smallest possible molecule with a double positive charge. It is detectable using mass spectroscopy. The negative helium dimer He2− is metastable and was discovered by Bae, Coggiola and Peterson in 1984 by passing He2+ through cesium vapor. Subsequently, H. H. Michels theoretically confirmed its existence and concluded that the 4Πg state of He2− is bound relative to the a2Σ+u state of He2. The calculated electron affinity is 0.233 eV compared to 0.077 eV for the He−[4P∘] ion. The He2− decays through the long-lived 5/2g component with τ∼350 μsec and the much shorter-lived 3/2g, 1/2g components with τ∼10 μsec. The 4Πg state has a 1σ2g1σu2σg2πu electronic configuration, its electron affinity E is 0.18±0.03 eV, and its lifetime is 135±15 μsec; only the v=0 vibrational state is responsible for this long-lived state.
In the mathematical field of graph theory, the Chvátal graph is an undirected graph with 12 vertices and 24 edges, discovered by . It is triangle-free: its girth (the length of its shortest cycle) is four. It is 4-regular: each vertex has exactly four neighbors. And its chromatic number is 4: it can be colored using four colors, but not using only three. It is, as Chvátal observes, the smallest possible 4-chromatic 4-regular triangle-free graph; the only smaller 4-chromatic triangle-free graph is the Grötzsch graph, which has 11 vertices but has maximum degree 5 and is not regular. This graph is not vertex- transitive: the automorphisms group has one orbit on vertices of size 8, and one of size 4. By Brooks’ theorem, every k-regular graph (except for odd cycles and cliques) has chromatic number at most k. It was also known since that, for every k and l there exist k-chromatic graphs with girth l.
In it he showed that a system of bodies at rest tends to reach a position in which any change would create the smallest possible change in a quantity that he argued could be assimilated to action. In 1744, in another paper to the Paris Academy, he gave his Accord de plusieurs lois naturelles qui avaient paru jusqu'ici incompatibles (Agreement of several natural laws that had hitherto seemed to be incompatible) to show that the behaviour of light during refraction – when it bends on entering a new medium – was such that the total path it followed, from a point in the first medium to a point in the second, minimised a quantity which he again assimilated to action. Finally, in 1746 he gave a further paper, the Loix du mouvement et du repos (Laws of movement and rest), this time to the Berlin Academy of Sciences, which showed that point masses also minimise action. Point masses are bodies that can be treated for the purposes of analysis as being a certain amount of matter (a mass) concentrated at a single point.
A connected dominating set of a graph G is a set D of vertices with two properties: #Any node in D can reach any other node in D by a path that stays entirely within D. That is, D induces a connected subgraph of G. #Every vertex in G either belongs to D or is adjacent to a vertex in D. That is, D is a dominating set of G. A minimum connected dominating set of a graph G is a connected dominating set with the smallest possible cardinality among all connected dominating sets of G. The connected domination number of G is the number of vertices in the minimum connected dominating set.. Any spanning tree T of a graph G has at least two leaves, vertices that have only one edge of T incident to them. A maximum leaf spanning tree is a spanning tree that has the largest possible number of leaves among all spanning trees of G. The max leaf number of G is the number of leaves in the maximum leaf spanning tree..
Marketing scholars have suggested that strategic marketing arose in the late 1970s and its origins can be understood in terms of a distinct evolutionary path:Brown, L., Competitive Marketing Strategy: Dynamic Manoeuvring for Competitive Position, Melbourne, Nelson, 1997; West, D., Ford, J. and Ibrahim, E., Strategic Marketing: Creating Competitive Advantage, Oxford, Oxford University Press, 2010, p. 50-56; Schaars, S.p., Marketing Strategy, The Free Press, 1998, [Chapter 4 - 'A Brief History of Marketing Strategy'], pp 18-29 : Budgeting Control (also known as scientific management) : Date: From late 19th century : Key Thinkers: Frederick Winslow Taylor, Frank and Lillian Gilbreth, Henry L. Gantt, Harrington Emerson : Key Ideas: Emphasis on quantification and scientific modelling, reduce work to smallest possible units and assign work to specialists, exercise control through rigid managerial hierarchies, standardise inputs to reduce variation, defects and control costs, use quantitative forecasting methods to predict any changes. :Long Range Planning : Date: From 1950s : Key Thinkers: Herbert A. Simon : Key Ideas: Managerial focus was to anticipate growth and manage operations in an increasingly complex business world.
Seacraft technologies, especially navigational aids, have been transformed since these books were written, yet they contain timeless wisdom about taking a small ship to sea and bringing her home - without fuss. In Safety in Small Craft Rayner writes: "In any reasonable weather it is the diminutive size of the yacht which makes long passages under sail such thrilling affairs, and one of the reasons why I, for one, find the smallest possible craft the most rewarding" as well, he added, as costing less. Ben Rayner's greatest peacetime contribution lay in his approach to designing, building and selling such small craft. A fascination with making model destroyers at school evolved into the making of Robinetta in which for a few years he voyaged for pleasure - a pleasure which, after his long war service, he made available to thousands. Starting with Robinetta - based in 2006 on the River Orwell near Harwich and still sailing, and then the rebuilt Orchid to share with his youngest son, Rayner graduated via the one-off Corvette to the Westerly 22, to the Westerly 25, the Westerly 30, the Windrush (a re-worked W25), and the Nomad (a re- worked W22).
Increasingly, the British came to favor the idea of "limited liability", under which if the "continental commitment" were to be made, Britain should only send the smallest-possible expeditionary force to Europe and to reserve its main efforts towards the war in the air and on the sea.Bond, pp. 200–201. Britain's refusal to make the "continental commitment" on the same scale as World War I caused tensions with the French, who believed that it would be impossible to defeat Germany without another large-scale "continental commitment" and deeply disliked the idea that they should do the bulk of the fighting on their land. In 1934, French Foreign Minister Louis Barthou decided to end to any potential German aggression by building a network of alliances intended to encircle Germany, and he made overtures to the Soviet Union and Italy. Until 1933, the Soviet Union had supported German efforts to challenge the Versailles system, but the strident anticcommunism of the German regime and its claim for Lebensraum led the Soviets change positions on the question of maintaining the Versailles system. In September 1933, the Soviet Union ended its secret support for German rearmament, which had started in 1921.
Shannon's source coding theorem states a lossless compression scheme cannot compress messages, on average, to have more than one bit of information per bit of message, but that any value less than one bit of information per bit of message can be attained by employing a suitable coding scheme. The entropy of a message per bit multiplied by the length of that message is a measure of how much total information the message contains. If one were to transmit sequences comprising the 4 characters 'A', 'B', 'C', and 'D', a transmitted message might be 'ABADDCAB'. Information theory gives a way of calculating the smallest possible amount of information that will convey this. If all 4 letters are equally likely (25%), one can't do better (over a binary channel) than to have 2 bits encode (in binary) each letter: 'A' might code as '00', 'B' as '01', 'C' as '10', and 'D' as '11'. If 'A' occurs with 70% probability, 'B' with 26%, and 'C' and 'D' with 2% each, one could assign variable length codes, so that receiving a '1' says to look at another bit unless 2 bits of sequential 1s have already been received.
Optimal (span-5) radio coloring of a 6-cycle In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphs such that the labels of adjacent vertices differ by at least two, and the labels of vertices at distance two from each other differ by at least one. Radio coloring was first studied by , under a different name, -labeling.. It was called radio coloring by Frank Harary because it models the problem of channel assignment in radio broadcasting, while avoiding electromagnetic interference between radio stations that are near each other both in the graph and in their assigned channel frequencies. The span of a radio coloring is its maximum label, and the radio coloring number of a graph is the smallest possible span of a radio coloring.. See in particular Section 3, "Radio coloring". For instance, the graph consisting of two vertices with a single edge has radio coloring number 3: it has a radio coloring with one vertex labeled 1 and the other labeled 3, but it is not possible for a radio coloring of this graph to use only the labels 1 and 2.

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