474 Sentences With "suffices" | Random Sentence Generator

" Addressing Trump, Schumer went on: "For you, Twitter suffices.

But these days a simpler description suffices: it is dead.

No reassurance sustains him for too long; no validation suffices.

I'm not certain it suffices for the magnitude of the moment.

A bicycle inner tube suffices as resistance training for his legs.

A single election sweeping an unorthodox candidate into power hardly suffices.

There's not a lot of showiness here, but the material suffices.

Further, there's no special requirement of "corrupt" intent: Acting knowingly suffices.

In real life, zigzagging usually suffices to get through difficult terrain.

Second, a quick-and-dirty estimate often suffices to answer a question.

Germany is a very centrist country (see chart); Mrs Merkel suffices it.

For others, Google StreetView and talking to people in the area suffices.

That could send voting into the third round, where a plurality suffices.

A vague gesture towards the burning world we live in usually suffices.

Most people think one coat or jacket suffices during the colder months.

Citizenship is not a requirement to join the military; a green card suffices.

I also don't care that people think it's unnecessary when a long press suffices.

It suffices to say that Venezuela is the right's en vogue boogeyman for scary socialism.

It is a liberal mistake to think that bigotry suffices to explain the Trump phenomenon.

And merely "seeking" to receive the valuable item, or "agreeing" to receive the item, suffices.

It nurses grievances and indulges resentments; it doesn't call for courage; it finds that cowardice suffices.

Superficial thinking suffices for the gut thinker, whose quick decisions are impulses subject to quick change.

He tosses it in a bowl of fusilli—though any short pasta suffices, really—cooked al dente.

American car companies believe one type of female test dummy suffices to ensure women don't die in car crashes.

That alone suffices to show that plaintiffs are likely to succeed on the merits of their Establishment Clause claim.

Sometimes we'll just do one single alternate international version of a shot, that kind of suffices for a world audience.

James and his mates often play no less astutely but as if consumed, aware that no end suffices save victory.

One example suffices to explain why the Greens' conception of "adversarial" is directly at odds with an authentically scholarly museum.

"Nothing suffices to the disaster," wrote the dour French philosopher Maurice Blanchot in his seminal late work The Writing of Disaster.

Instead, a story about how someone's grandmother loved making lemon shortbread suffices for tantalizing backstory on The Great British Bake Off.

The audio of his narration suffices at first, but visual takes of the protagonist as raconteur lengthen as the film progresses.

"Only a stadium suffices to hold the ever-expanding Al Saud clan," an American diplomat wrote in a memorandum in 2009.

The firm found that, in 10 of the total 15 cities analyzed, median household income suffices to afford the median home.

"It suffices to say we have a lot more work to do to earn people's trust on how we work," he tweeted.

Give my students the time and attention they deserve, and let them be the judges of whether or not your work suffices.

Fellini, Zefferelli, Agnelli, Berlusconi — people for whom one name suffices — mingled with royalty, enjoying their hostess's insistence on French cuisine and wine.

When social change blows through, however, it rarely suffices to toss up an old windshield and argue it worked well last time.

For a grand cru, the pinnacle of the terroir hierarchy, the name of the vineyard alone suffices: La Tâche, say, or Musigny.

Some philosophers of art have said or suggested that placing any artifact in a museum suffices to make it a work of art.

It suffices, for now, to say this: Mr. Lehrer devotes many pages in "A Book About Love" to how we grow and evolve.

There's no need to exhibit Shakespearean poetic eloquence: simple empathy suffices, letting the bereaved know coworkers are willing to chat, listen, or help.

Her choice in 2010, Christian Wulff, was elected in a bruising third round of voting, when a plurality rather than an absolute majority suffices.

The event was planned by a lay organization called the Solo Dios Basta Foundation, or God Alone Suffices, but was supported by the clergy.

But it suffices to make a point: Periods of divided government can be an opportunity to develop initiatives for the next period of unified government.

Because of technological advances and the sheer amount of data now available about billions of other people, discretion no longer suffices to protect your privacy.

Typically, a seven-day lead time suffices in case the pharmacist needs to get in touch with your doctor or order more of the medication.

But it suffices to say this season's story "will focus on a much different aspect of intelligence gathering than we have in the past," Gansa said.

For those cord-cutting in an effort to save money, combining these two services, and then perhaps Hulu, along with a digital antenna for broadcast channels, typically suffices.

To find a lower bound for the chromatic number, it suffices to create a graph with a finite number of vertices that requires a particular number of colors.

Sigfox's bandwidth is extremely limited — 12 bytes per message; an example of 140 messages/day was cited — but that suffices for most sensors, and it's extremely low power.

Just as no single factor generally suffices to prove your home to the state, I realized that a complicated set of mutually reinforcing criteria determined what I called home.

Above the space set aside for a replacement library, the developers erected a 2000-story hotel and apartment tower called the Baccarat, for which the adjective "luxury" scarcely suffices.

I'm not very impressed with Salt Lake's local pizza places, so Dominos suffices, but it always makes me miss Mountain Mike's and Round Table — regional chains in my home state.

Close-ups are kept to a minimum — when Ford and Tench make a breakthrough, a medium shot of a criminal suffices to convey that they might be on the right track.

Sometimes, when words aren't cutting through as they should—a condition evident in the video when Cardi's yelling towards Minaj was greeted with Nicki pretending she didn't exist—the sandal suffices.

But since Parfit has argues that personal identity doesn't matter, it suffices to say that if some individual is brought into existence, it's better that said individual live a longer rather than shorter life.

So, too, with calling and e-mailing and writing and showing up in congressional offices: it would be good to know that these actions will succeed, but it suffices to know that they could.

In Israel, implied consent suffices—a deceased man need not have left a written document, but his widow just has to say that she believes he would give consent were he alive to do so.

First, the government shutdown has demonstrated that Trump's own incompetence suffices to cost him support in the polls and in the Senate — an indication that a larger crumbling of his political firewall might be possible.

"It suffices here to note that the prospect that the House will direct its Sergeant at Arms to arrest McGahn is vanishingly slim, so long as a more peaceable judicial alternative remains available," she wrote.

The awesome view through the semicircular tent openings of the Boscobel grounds, Constitution Marsh and the Hudson River beyond suffices for the eternalities; the production can afford to be more improvisatory, frolicsome and of our time.

Rick Doblin, the founder of Multidisciplinary Association for Psychedelic Studies (or MAPS), notes that for this older age group, a smaller dose of any psychedelic often suffices, as we can become more sensitive to drugs as we age.

But let us for the sake of argument suppose that China and Russia finally change course, fully cooperate with all those UN sanctions they've voted for, and that this suffices to bring North Korea to the bargaining table.

This isn't the time or place for a full evaluation of the scheduling system and the war on drugs, but it suffices to say that it is a complex and interesting business ecosystem that's teetering on the edge of widespread acceptance.

"These strikes were authorized by the president following a recommendation from Secretary [of Defense Ash] Carter and Chairman Dunford," said Pentagon Press Secretary Peter Cook in a brief media release that apparently suffices to announce a whole new war in 6900.

The startup's ambitions have certainly expanded since then, particularly through a partnership with Salesforce, though given the fact that this round was led by a toll road company it suffices to say that this use case is still firmly within their sights.

Were there any doubt as to the reverberative power of such digital organizing work, it suffices to note that over the past month, numerous FTP postings are being removed or hidden per day by corporate moderators and algorithms at Instagram and Facebook.

The gravity (pun intended) of the hanging — a single, towering line — suffices to curb the cheerfulness of the colors, and the unrelenting streaming forth of a sinister (fictional) substance also materializes on ARTER's walls in the ominous glow of the light boxes.

Starting off with a cut from British funk group Cymande and bringing in tracks by everyone from recent Hyperdub signee High Wolf to none other than Jimi Hendrix, it suffices to say that the trio's two hour selection was a masterful bout of delectable eclecticism.

With a low bar for membership—being born usually suffices—it has been there to hatch, match and dispatch anyone who wanted its services, a sort of religious public utility whose moderation has formed the English character and provided a glue for English society.

If those artworks, so radically different from each other, are related by "the essential grace that connects one with the universe in a strange, intense light," no outside referent is necessary for the strange, intense light emanating from Martin's painting; its grace suffices as a universe in itself.

Zeynep Tufekci argues that tech platforms' prediction algorithms have become so good that there is now no meaningful opt-out available when it comes to privacy features: Because of technological advances and the sheer amount of data now available about billions of other people, discretion no longer suffices to protect your privacy.

Typically, the President's annual meet-and-greet with the guests in the Oval Office suffices for pre-speech pomp and circumstance, however, according to Grisham, the first lady felt the need to host a different event, one that offered more personal exposure to the honorees and a chance to recount their stories.

A single word suffices to evoke the man who descended from the Sierra Maestra with his ragtag army to overthrow the dictatorship of Fulgencio Batista in 1959, purge Cuba of American domination, proclaim the empowerment of the poor, and embody Latin America's thirst for an end to government by the pampered coteries of imperialism.

But it suffices to say first that Indiana had a fairly active pro-Southern bloc during the war, and that Lincoln and other Union leaders may have legitimately feared that a state government sympathetic to the Confederacy—or at least to a negotiated peace with it—could undermine the war effort in a key state.

A simple magnet suffices to attract the liquid in a test tube.

It is clear that opinion research alone no longer suffices to fund larger institutions.

For programmers who need to store large amounts of data, the 64-bit address space usually suffices.

Naive set theory suffices for many purposes, while also serving as a stepping-stone towards more formal treatments.

The frailest shelter, covered with sea-lion's skins, suffices to keep them from the inclemencies of the weather.

Three days' exposure to the dusty air suffices to render them muddy, fetid, and swarming with infusorial life.

The weak neuters are so few, that a list suffices, to be found on the page for weak nouns.

Thus, it suffices to simply build one component out of each child subtree of the root (including the root).

46 inches of a constant width such as the loom in use suffices to weave. It was found in Uist.

Still, the average position can be approximated, as well as the distance between the touches, which suffices for some gesture applications.

Furthermore, in the special case when Y is (locally) noetherian, it suffices to check the case that A is a discrete valuation ring.

Whereas at one point in time fiches were required for foreign travelers at these types of checkpoints, now, a simple photocopy of the traveler's passport usually suffices.

The ticket office is manned only during part of the day; at other times a ticket machine, located outside the station building on the 'up' side, suffices.

The station buildings were demolished after the station became unstaffed. A PERTIS 'permit to travel' machine, located outside the station at road level on the 'up' side, suffices.

Similarly, the French find that "liberté" suffices, while English-speakers attribute different associations to "liberty" and "freedom": "freedom of speech" or "freedom of movement", but "the Statue of Liberty".

One of the most recent studies revealed that for women after menopause a low dose of 5 mg testosterone cream suffices to raise testosterone back to a premenopausal level.

Every saying 'Allah is the Greatest' is charity. Ordering the good is charity. Eradicating evil is charity. And what suffices for that (as a charity) are the two rak'as of Duha.

To achieve the optimal rate of communication, it suffices to choose an orthonormal basis to encode the message, and perform measurements that project onto to the same basis at the receiving end.

DM stacks are limited to quotients by finite group actions. While this suffices for many problems in moduli theory, it is too restrictive for others, and Artin stacks permit more general quotients.

The results of this section show that the computation of the pseudoinverse is reducible to its construction in the Hermitian case. It suffices to show that the putative constructions satisfy the defining criteria.

Then out comes my notebook. Sometimes they ask me why I am writing down what they have said, and I tell them it is because it has interested me. Usually that suffices.”Crawford, p.6.

Birkhäuser Verlag. 1988.Charles F. Dunkl and Donald E. Ramirez: To prove the existence of a Haar measure on a locally compact group G it suffices to exhibit a left-invariant Radon measure on G.

If no other house suffices, use the seventh house to represent 'any old person'. :The Eighth House ::Death, fears, anxiety. It is also commonly used to "the house of other people's money" . (see 'Turning the chart' below).

The signal box closed on 5 November 1972. The ticket office is manned only during the morning peak period; at other times a PERTIS 'permit to travel' machine, located at the entrance to the up platform, suffices.

A similar transformation suffices to reduce the equation to :u^5 - u + a = 0\, , which is the form required by the Hermite–Kronecker–Brioschi method, Glasser's method, and the Cockle–Harley method of differential resolvents described below.

The neck of the odontoid process is constricted where it is embraced posteriorly by the transverse ligament, so that this ligament suffices to retain the odontoid process in position after all the other ligaments have been divided.

Torres-Rojas, Francisco J. and Ahamad, Mustaque. Plausible clocks: constant size logical clocks for distributed systems. Distributed Computing, 12(4), 1999. In the limit, a single scalar (a Lamport clock) suffices, at the cost of removing any concurrency.

If not, it suffices to add a few other points and their tangents to get a good description of the curve. The methods for computing the remarkable points and their tangents are described below, after the section Projective curves.

The size of metadata can also be decreased by restricting the communication topology; for instance, in a star, tree or linear topology, a single scalar suffices. The search for efficient implementations of causal consistency is a very active research area.

In general, computations with the maximal atlas of a manifold are rather unwieldy. For most applications, it suffices to choose a smaller atlas. For example, if the manifold is compact, then one can find an atlas with only finitely many charts.

Poems written by Jiwchar Ganor have appeared in several literary journals. His first book of poetry, One Word Sometimes Suffices, was published with Pardes Publishing in 2017. Ganor's poem, "VEYADO SHLUCHA," was set to music by Israeli composer Amit Poznansky.

It is easy to check whether a value of is a solution: it suffices to compute the remainder of the Euclidean division of by each . Thus, to find the solution, it suffices to check successively the integers from to until finding the solution. Although very simple this method is very inefficient: for the simple example considered here, integers (including ) have to be checked for finding the solution, which is . This is an exponential time algorithm, as the size of the input is, up to a constant factor, the number of digits of , and the average number of operations is of the order of .

In graph theory, a branch of mathematics, the cop number or copnumber of an undirected graph is the minimum number of cops that suffices to ensure a win (i.e., a capture of the robber) in a certain pursuit-evasion game on the graph.

The station is now unmanned but was staffed when run by British Rail and was APTIS-equipped until December 1992. Nowadays, a PERTIS passenger-operated ticket machine suffices. This issues 'Permits to Travel' and is situated at the entrance to the westbound platform.

When solving a system over a finite field with elements, one is primarily interested in the solutions in . As the elements of are exactly the solutions of the equation , it suffices, for restricting the solutions to , to add the equation for each variable .

Logical NOR does not possess any of the five qualities (truth-preserving, false-preserving, linear, monotonic, self-dual) required to be absent from at least one member of a set of functionally complete operators. Thus, the set containing only NOR suffices as a complete set.

The output p-box will, however, always contain all distributions that are possible, so long as the input p-boxes were sure to enclose their respective underlying distributions. This property often suffices for use in risk analysis and other fields requiring calculations under uncertainty.

The increased charge increases the hydrophilicity of gliadins, causing them to stretch out in solution. Deamidation of 20% of glutamine side chains to glutamate suffices to generate a soluble product. This renders gluten soluble enough without alcohol to mix with other products like milk.

Eyke Hüllermeier. Case-Based Approximate Reasoning. Springer-Verlag, Berlin, 2007. One description of the difference between CBR and induction from instances is that statistical inference aims to find what tends to make cases similar while CBR aims to encode what suffices to claim similarly.

By Fermat's theorem, all local maxima and minima of a differentiable function occur at critical points. Therefore, to find the local maxima and minima, it suffices, theoretically, to compute the zeros of the gradient and the eigenvalues of the Hessian matrix at these zeros.

The binomial theorem is valid more generally for any elements and of a semiring satisfying . The theorem is true even more generally: alternativity suffices in place of associativity. The binomial theorem can be stated by saying that the polynomial sequence is of binomial type.

The venom is not very dangerous; symptomatic treatment suffices to treat an envenomation. The unthreatening nature of the snake, along with its relatively mild persecution by man, has made it one of the most common species throughout its range, even in areas occupied by humans.

Sanity cannot "capture such beauty or make sense of such feeling; only wit suffices to command the paradox and to yoke the extremes" (Dugaw 11). In this blinding light where good sense goes delirious, the reasoned esteem of friendship and the passion of love are indistinguishable.

Tricuspid valve stenosis itself usually doesn't require treatment. If stenosis is mild, monitoring the condition closely suffices. However, severe stenosis, or damage to other valves in the heart, may require surgical repair or replacement. The treatment is usually by surgery (tricuspid valve replacement) or percutaneous balloon valvuloplasty.

This level suffices for low to medium protection needs. This comprises about 80% of all IT systems according to BSI estimates. For systems with high to very high protection needs, risk analysis-based information security concepts, like for example ISO/IEC 27000-series standards, are usually used.

To exclude other differential diagnoses, a skin biopsy may be taken. Imaging studies can be used in order to detect any underlying bony abnormalities that cause abnormal pressure on the overlying skin. For this purpose, a plain radiograph usually suffices, but, occasionally, CT scanning is used.

In the life sciences the term adaptability is used variously. At one end of the spectrum, the ordinary meaning of the word suffices for understanding. At the other end, there is the term as introduced by Conrad,Conrad, M. 1972. Statistical and Hierarchical Aspects of Biological Organization. pp.

A liquor identification is also provided in some jurisdictions for residents to affirm their age of majority to sellers of liquor, although a state-issued ID that proves the individual is over the legal drinking age often suffices. This is another measure to prevent minors from purchasing alcohol.

Yuri Matiyasevich utilized a method involving Fibonacci numbers, which grow exponentially, in order to show that solutions to Diophantine equations may grow exponentially. Earlier work by Julia Robinson, Martin Davis and Hilary Putnam – hence, MRDP – had shown that this suffices to show that every computably enumerable set is Diophantine.

For the method of conditional probabilities to work, it suffices if the algorithm keeps the pessimistic estimator from decreasing (or increasing, as appropriate). The algorithm does not necessarily have to maximize (or minimize) the pessimistic estimator. This gives some flexibility in deriving the algorithm. The next two algorithms illustrate this. 1\.

It is a small, narrow body of water situated in the transition zone between the aspen parkland and boreal forest biomes. Sturgeon Lake is home to several species of fish including Lake Whitefish, Northern Pike, Yellow perch and Walleye. While not a deep lake, it still suffices for some watersports.

From June 2013 on until March 2019, Knoppix 7.2 was the most recent release with a CD edition. By 2018, its software had become very outdated, as the libc6 2.17 library no longer suffices for installation of several modern packages. The 7.x version range is known for instabilities with touchpads.

Judge Rader asked in his > Bilski dissent, "What form or amount of 'transformation' suffices?" The > court did not answer his question. It may be that a "substantial" physical > or chemical change of properties that is material to the objectives of the > invention is required, but this is still to be resolved.

When both aids are available, they are used in conjunction; if one aid is not available, the other suffices. The turtles swim at about during migration. Like all marine turtles, the loggerhead prepares for reproduction in its foraging area. This takes place several years before the loggerhead migrates to a mating area.

He proceeds on the assumption that if "man" is reduced, as according to Hume, to a collection of sensations, a single repeated perception, either in one man's life or in the experience of two different men, suffices to prove that time is a fallacy, since this repetition will destroy its linear sequence.

Both handles accomplish the same task, so pulling either one suffices. The F-22, WB-57, and F-16 have only one handle located between the pilot's legs, due to cockpit space limitations. The minimal ejection altitude for ACES II seat in inverted flight is about above ground level at 150 KIAS.

To Poros this assertion of his masculine adversary is more credible than the combined attestations of his loved one and suffices to convince him of her fidelity. Act 2 In the Royal Chambers of Poros. Poros consults with Gandartes on how to keep Alexander from crossing the Hydaspes. Eryxene announces the approach of Alexander.

The theorem does not hold when . To see this, it suffices to consider the function , which is clearly holomorphic in but cannot be continued as a holomorphic function on the whole . Therefore, the Hartogs's phenomenon is an elementary phenomenon that highlights the difference between the theory of functions of one and several complex variables.

Charing railway station serves Charing in Kent, England. It is down the line from . The station, and all trains serving it, is operated by Southeastern. The ticket office is manned only during part of the day; at other times a PERTIS 'permit to travel' machine, located outside the station building on the 'down' side, suffices.

The Bureau des sports organizes all the sports related activity at UNIGE. Free sports lessons are given everyday and it suffices to show one's student card to access. Other lessons organization with the university's partners demand a small fee. UNIGE is home to the Geneva university championships in basketball, indoor football, rowing, badminton, outdoor football.

It suffices to take for d the degree of the symmetric function, since the part in degree d of that ring is mapped isomorphically to rings with more indeterminates by φn for all n ≥ d. This implies that for studying relations between individual elements, there is no fundamental difference between symmetric polynomials and symmetric functions.

"[O]nly a procedure requiring a judicial determination suffices to impose a valid final restraint", he wrote in Freedman v. Maryland.Freedman v. Maryland, , 58, (1965) Brennan, J. In two later cases similar to Marcus, the Court reaffirmed it as applying to the seizure of allegedly obscene films as well. Lee Art Theatre, Inc. v.

Up to a full line must be buffered from each input file during line comparison, before the next output line is written. Some implementations read lines with the function which does not impose any line length limits if system memory suffices. Other implementations read lines with the function . This function requires a fixed buffer.

It suffices to check that each prime gap starting at p is smaller than 2 \sqrt p. A table of maximal prime gaps shows that the conjecture holds to 4×1018.Jens Kruse Andersen, Maximal Prime Gaps. A counterexample near 1018 would require a prime gap fifty million times the size of the average gap.

For polynomials with real coefficients, it is often useful to bound only the real roots. It suffices to bound the positive roots, as the negative roots of are the positive roots of . Clearly, every bound of all roots applies also for real roots. But in some contexts, tighter bounds of real roots are useful.

The chalice and paten would need to be consecrated with the chrism again if they were re-gilded. This ritual could only be performed by a Bishop or a priest with the faculties to do so. According to the new rubrics, a simple blessing suffices. However, it is still permitted that the bishop performs the consecration with chrism.

Myringotomy is usually performed as an outpatient procedure. General anesthesia is preferred in children, while local anesthesia suffices for adults. The ear is washed and a small incision made in the eardrum. Any fluid that is present is then aspirated, the tube of choice inserted, and the ear packed with cotton to control any slight bleeding that might occur.

Baer's criterion has been refined in many ways , including a result of and that for a commutative Noetherian ring, it suffices to consider only prime ideals I. The dual of Baer's criterion, which would give a test for projectivity, is false in general. For instance, the Z-module Q satisfies the dual of Baer's criterion but is not projective.

Preston, page 286. Jahanara is buried in a tomb in the Nizamuddin Dargah complex in New Delhi, which is considered "remarkable for its simplicity". The inscription on the tomb reads as follows: Allah is the Living, the Sustaining. Let no one cover my grave except with greenery, For this very grass suffices as a tomb cover for the poor.

For lower quality printing, uncoated copy paper suffices, but higher grades require coating. The traditional coatings are not widely used for inkjet papers. For matte inkjet papers, it is common to use silica as pigment together with polyvinyl alcohol (PVOH). Glossy inkjet papers can be made by multicoating, resin coating, or cast coating on a lamination paper.

In causal set theory, causality takes an even more prominent place. The basis for this approach to quantum gravity is in a theorem by David Malament. This theorem states that the causal structure of a spacetime suffices to reconstruct its conformal class. So knowing the conformal factor and the causal structure is enough to know the spacetime.

Page 3. In order to directly prove a conditional statement of the form "If p, then q", it suffices to consider the situations in which the statement p is true. Logical deduction is employed to reason from assumptions to conclusion. The type of logic employed is almost invariably first-order logic, employing the quantifiers for all and there exists.

Hydrochloric acid can be used to regulate the acidity (pH) of solutions. : OH^- + HCl -> H2O + Cl^- In industry demanding purity (food, pharmaceutical, drinking water), high-quality hydrochloric acid is used to control the pH of process water streams. In less- demanding industry, technical quality hydrochloric acid suffices for neutralizing waste streams and swimming pool pH control.

At the lower bound, as goes to 0 the function goes to , and the upper bound is itself , though the function goes to 0. Thus this is a doubly improper integral. Integrated, say, from 1 to 3, an ordinary Riemann sum suffices to produce a result of /6. To integrate from 1 to , a Riemann sum is not possible.

In mathematics, and particularly category theory, a coherence condition is a collection of conditions requiring that various compositions of elementary morphisms are equal. Typically the elementary morphisms are part of the data of the category. A coherence theorem states that, in order to be assured that all these equalities hold, it suffices to check a small number of identities.

Cauchy was the first to appreciate the importance of this view. Thereafter, the real question was no longer whether a solution is possible by means of known functions or their integrals, but whether a given differential equation suffices for the definition of a function of the independent variable or variables, and, if so, what are the characteristic properties.

It suffices for me to affirm, having studied the > opinions below and the expert briefs presented here, that the portion of DNA > isolated from its natural state sought to be patented is identical to that > portion of the DNA in its natural state; and that complementary DNA (cDNA) > is a synthetic creation not normally present in nature.

Intention is a prerequisite for salah, and what distinguishes real worship from 'going through the motions'. Some authorities hold that intention suffices in the heart, and some require that it be spoken, usually under the breath. But there is no evidence that the Islamic prophet Muhammad or any of his companions ever uttered a niyyah aloud before prayer.

In steam distillation, that positive flow is provided by steam from boiling water, rather than by the boiling of the substances of interest. The steam carries with it the vapors of the latter. The substance of interest does not need to be miscible water or soluble in it. It suffices that it has significant vapor pressure at the steam's temperature.

In fact, to turn an injective function into a bijective (hence invertible) function, it suffices to replace its codomain Y by its actual range . That is, let such that for all x in X; then g is bijective. Indeed, f can be factored as , where is the inclusion function from J into Y. More generally, injective partial functions are called partial bijections.

He moved the public against sects that he decided to be contrary to Shariah. He supported the tobacco ban of Murad IV (reigned 1623–1640). As he was reminded that coffee and tobacco is not banned by God, he has said that the prohibition of the ruler suffices. The Kadızades caused the decline in Ottoman education system, and science became conservative.

The male and female names refer to the same family.Wallace. Probably in deference to Italic, the nomen gentile could also be formed with -ie for males or -i and -a for females, perhaps from Italic -ios or its later form -ius, which can be made feminine: -ia.The Bonfantes, pages 88–89. Typically of Etruscan both suffices can be used together: -na-ie.Marchesini.

It is an offence to enter a building or it's vicinity with the intent to commit an offence or interfere with property. It suffices to be on the property as this offence is defined, but the prosecution must prove intent. Anyone convicted will, on summary conviction, be liable for a class C fine, a maximum prison term of 6 months or both.

If in the vending machine there is a packet of chips, a candy bar, and a can of soft drink, each costing one dollar, then for that price you can buy exactly one of these products. Thus we write . We do not write , which would imply that one dollar suffices for buying all three products together. However, from , we can correctly deduce , where .

A country facing these seven disasters will be destroyed easily by the enemy. The measure of a country's wealth in Mohism is a matter of sufficient provision and a large population. Thriftiness is believed to be key to this end. With contentment with that which suffices, men will be free from excessive labour, long-term war and poverty from income gap disparity.

Various forms of the implicit function theorem exist for the case when the function f is not differentiable. It is standard that local strict monotonicity suffices in one dimension. The following more general form was proven by Kumagai based on an observation by Jittorntrum. Consider a continuous function f : R^n \times R^m \to R^n such that f(x_0, y_0) = 0.

If is convex and the origin to belong to the algebraic interior of , then is a non-negative sublinear functional on , which implies in particular that it is subadditive and positive homogeneous. In order for to be a seminorm, it suffices for to be a disk (i.e. convex and balanced) and absorbing in , which are the most common assumption placed on .

In addition, it exhibits a finite input impedance and a non-zero output impedance. Although practical op-amps are not ideal, the model of an ideal op-amp often suffices to understand circuit operation at low enough frequencies. As discussed in the previous section, the feedback circuit stabilizes the closed-loop gain and desensitizes the output to fluctuations generated inside the amplifier itself.

Later, al-Muttaqi threw himself into the hands of Tuzun, who swore with the most sacred oaths that he would render true and faithful service. But he soon after deposed him from the Caliphate, and had his sight destroyed. The same day, Tuzun installed the blinded Caliph's cousin as his successor, with the title of al-Mustakfi, "For whom the Lord suffices".

One has to show that 1 is the smallest number that is no less than all . For this, it suffices to prove that, if a number is not larger than 1 and no less than all , then . So let such that for every positive integer . Therefore, This implies that the difference between and is less than the inverse of any positive integer.

The oral dose of 400 mg. thrice daily for 5 days suffices for the treatment of amoebic liver abscess. Adams29 in his analysis of 2,074 cases of liver abscess preferred metronidazole to other amoebicidal agents. A single oral dose of 2.5 G. metronidazole combined with closed aspiration has also produced dramatic response and cure in patients with amoebic liver abscess.

As in the above example, there is usually some cost associated with removing an edge. For this reason, we'd like to remove as few edges as possible. Removing one edge suffices in a simple cycle, but in general figuring out the minimum number of edges to remove is an NP-hard problem called the minimum feedback arc set or maximum acyclic subgraph problem.

It should not be crowded with too many symbols, only the essential. The ideal is only one charge. # It is forbidden to be repetitive in heraldry: one idea should not be symbolized with two or more charges. On the other hand, if one charge suffices to symbolize two or more ideas, it only strengthens the symbolism of the charge, and therefore the whole emblem.

The above statement is known to be equivalent to its order dual : x \vee (y \wedge z) = (x \vee y) \wedge (x \vee z) such that one of these properties suffices to define distributivity for lattices. Typical examples of distributive lattice are totally ordered sets, Boolean algebras, and Heyting algebras. Every finite distributive lattice is isomorphic to a lattice of sets, ordered by inclusion (Birkhoff's representation theorem).

In most cases, a rotation in the range of 7.5 degrees east to 23 degrees west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time, a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter.

To create a geometric object in JavaScript it suffices to click on an icon representing the object. The JavaScript instruction appears in the editor, with predefined parameters. The user has then only to edit these, and does not have to use mnemotechnics. But when a geometric object is created, the variable which called the routine is really a character string, containing the name of the object.

The axiom of countable choice (ACω) is strictly weaker than the axiom of dependent choice (DC), which in turn is weaker than the axiom of choice (AC). Paul Cohen showed that ACω, is not provable in Zermelo–Fraenkel set theory (ZF) without the axiom of choice . ACω holds in the Solovay model. ZF suffices to prove that the union of countably many countable sets is countable.

Common bleach including calcium hypochlorite (Ca[OCl]2) and sodium hypochlorite (NaOCl) are common, well-researched, low-cost oxidizers. The EPA recommends two drops of 8.25% sodium hypochlorite solution (regular, unscented chlorine bleach) mixed per one quart/liter of water and let stand 30 minutes. Two drops of 5% solution also suffices. Double the amount of bleach if the water is cloudy, colored, or very cold.

A point of a parametric surface which is not regular is irregular. There are several kinds of irregular points. It may occur that an irregular point becomes regular, if one changes the parametrization. This is the case of the poles in the parametrization of the unit sphere by Euler angles: it suffices to permute the role of the different coordinate axes for changing the poles.

Let F be a field (a division ring actually suffices) and let V be a \kappa-dimensional vector space over F. Then V is a pregeometry where closures of sets are defined to be their span. This pregeometry is homogeneous and modular. Vector spaces are considered to be the prototypical example of modularity. V is locally finite if and only if F is finite.

To prove the exchange relations, it suffices to check that it valid when applied to points the dense set of points in for which is quasi- invertible. It then reduces to the identity: In fact, if is quasi-invertible, then is quasi-invertible if and only if is quasi-invertible. This follows because is quasi-invertible if and only if is. Moreover, the above formula holds in this case.

Cybersell, Inc. v. Cybersell, Inc. was a trademark infringement case based on the use of an internet service mark. The United States District Court for the District of Arizona was asked to review whether the allegedly infringing use of a service mark in a home page on the World Wide Web suffices for personal jurisdiction in the state where the holder of the mark has its principal place of business.

Cultural family therapy (CFT) is a synthesis of family therapy and transcultural psychiatry. CFT is an interweaving of "stories" (family predicaments expressed in narratives of family life) and "tools" (clinical methods for working with and making sense of these stories in cultural context). By interweaving stories and tools, CFT is aimed at understanding and change. Neither one alone suffices, as each of them produces only part of the solution.

Auke, pron. [ˈaukə], is a quite common West Frisian masculine given name. It seems to have been a diminutive form originally (-ke is one of the most common diminutive suffices in West Frisian), which developed from the historic form Auwe or Auwen. According to onomatologist Rienk de Haan, Auwe was a very reduced form of certain Germanic names, possibly starting with Alf- (meaning "elf", "supernatural" or "nature spirit").

According to the Indologist Arvind Sharma, the Gita is generally accepted to be a 2nd-century-BCE text. A manuscript illustration of the battle of Kurukshetra, fought between the Kauravas and the Pandavas, recorded in the Mahabharata. Kashi Nath Upadhyaya, in contrast, dates it a bit earlier. He states that the Gita was always a part of the Mahabharata, and dating the latter suffices in dating the Gita.

Even though every equilibrium is efficient, neither of the above two theorems say anything about the equilibrium existing in the first place. To guarantee that an equilibrium exists, it suffices that consumer preferences be strictly convex. With enough consumers, the convexity assumption can be relaxed both for existence and the second welfare theorem. Similarly, but less plausibly, convex feasible production sets suffice for existence; convexity excludes economies of scale.

2 An object outside the critical distance is unlikely to be struck by the leader if there is a solidly grounded object within the critical distance. Locations that are considered safe from lightning can be determined by imagining a leader's potential paths as a sphere that travels from the cloud to the ground. For lightning protection, it suffices to consider all possible spheres as they touch potential strike points.

They also form the background for parameter estimation. In the case of extremum estimators for parametric models, a certain objective function is maximized or minimized over the parameter space. Theorems of existence and consistency of such estimators require some assumptions about the topology of the parameter space. For instance, compactness of the parameter space, together with continuity of the objective function, suffices for the existence of an extremum estimator.

Further east still, were the two Preston Hall Tunnels, of and length. These had been removed by 1995. The ticket office here closed by 1988; it was located in a wooden building on the up (London-bound) platform, where the part retained as a shelter continues in use. A PERTIS 'permit to travel' machine, located at road level at the foot of the steep staircase to the up platform, suffices.

Freight facilities were withdrawn on 6 January 1969. Although a new signal box was provided in 1961, it closed on 28 May 1984. The ticket office is staffed for only part of the day; at other times a PERTIS 'permit to travel' machine, located outside the station building on the 'down' side, suffices. A new footbridge replaced the life- expired concrete footbridge spanning the tracks here, completed in early 2010.

For forgings, AZ61 is most used, and here alloy M1 is employed where low strength is required and AZ80 for highest strength. For extrusions, a wide range of shapes, bars, and tubes are made from M1 alloy where low strength suffices or where welding to M1 castings is planned. Alloys AZ31, AZ61 and AZ80 are employed for extrusions in the order named, where increase in strength justifies their increased relative costs.

Clemens with A Hereford Beefstouw restaurant across the cathedral. A few nightlife spots are aimed at gays and lesbians specifically, including Gbar (nightclub) and Café Sappho. The Århus Set (Danish: Århus Sæt) is a set of drinks often ordered together, named for the city and consisting of two beverages, one Ceres Top beer and one shot Arnbitter, both originally from Aarhus. Ordering "a set" suffices in most bars and pubs.

This suffices to avoid unphysical divergences, e.g. in scattering amplitudes. The requirement of a UV fixed point restricts the form of the bare action and the values of the bare coupling constants, which become predictions of the asymptotic safety program rather than inputs. As for gravity, the standard procedure of perturbative renormalization fails since Newton's constant, the relevant expansion parameter, has negative mass dimension rendering general relativity perturbatively nonrenormalizable.

As each theorem is a corollary of the other, it suffices to prove Fourier's theorem. Thus, consider a polynomial , and an interval . When the value of increases from to , the number of sign variations in the sequence of the derivatives of may change only when the value of pass through a root of or one of its derivatives. Let us denote by either the polynomial or any of its derivatives.

The Court read asportation as merely a corroborative element of possession and control, and thus not necessary to establish possession and control of a car because transportation is the purpose of a car. Turning it on suffices to establish that the thief has taken possession and control.Id. at 379, 381. Additionally, the Model Penal Code eliminates the asportation requirement and instead requires that the defendant "exercise unlawful control".

Autopsies can be further classified into cases where external examination suffices, and those where the body is dissected and an internal examination is conducted. Permission from next of kin may be required for internal autopsy in some cases. Once an internal autopsy is complete the body is generally reconstituted by sewing it back together. Autopsy is important in a medical environment and may shed light on mistakes and help improve practices.

Fluctuations are damped in the neighborhood of the fixed point and a macroscopic description suffices. However, far from equilibrium stability is no longer a universal property and can be broken. In chemical systems, this occurs with the presence of autocatalytic reactions, such as in the example of the Brusselator. If the system is driven beyond a certain threshold, oscillations are no longer damped out, but may be amplified.

In the US, financial transactions begin with mutual identification between the customer and the financial institution. Although there are many Internet frauds involving fake financial institutions or criminals masquerading as a financial institution (i.e., phishing), the more difficult requirement is for the prospective customer to show acceptable identification to the bank. For basic relationships, a government-issued identification document, such as a passport or driver's license, usually suffices.

If player progress consists only of one variable, such as the stage number, then a short password such as a single word suffices. Algorithms can compress, encrypt, and otherwise manipulate save data containing many large variables. The less the algorithm encrypts, the more easily players may notice patterns, such as an increment by one every level. They can then exploit these patterns to cheat or even beat the game.

Ecclesiastical authority has the right to posit certain conditions for the return of the culprit, and every absolution from excommunication calls for the fulfillment of certain conditions which vary in severity, according to the case. The formula of absolution from excommunication is not strictly determined, and, since it is an act of jurisdiction, it suffices if the formula employed express clearly the effect which it is desired to attain.

A polynomial ring over a field is a unique factorization domain. The same is true for a polynomial ring over a unique factorization domain. To prove this, it suffices to consider the univariate case, as the general case may be deduced by a recurrence on the number of indeterminates. The unique factorization property is a direct consequence of Euclid's lemma: If an irreducible element divides a product, then it divides one of the factors.

Suppose that is a topological vector space and is a convex balanced and radial set. Then } is a neighborhood basis at the origin for some locally convex topology on . This TVS topology is given by the Minkowski functional formed by , , which is a seminorm on defined by . The topology is Hausdorff if and only if is a norm, or equivalently, if and only if } or equivalently, for which it suffices that be bounded in .

Visa requirements for Paraguayan citizens are administrative entry restrictions by the authorities of other states placed on citizens of Paraguay. Paraguayan citizens had visa-free or visa on arrival access to 143 countries and territories, ranking the Paraguayan passport 33rd with Grenada in terms of travel freedom according to the Henley Passport Index. In order to travel to another country, a Paraguayan citizen requires a passport, except within Mercosur when a Paraguayan Identity Card suffices.

For some systems (e.g., CentOS), the invocation through is not enabled by default, and the user obtains a error if invoked directly, or a login failure if the /etc/passwd file indicates as the user's shell. It suffices to create a link named pointing directly to . Though this invokes Bash directly, without the or options, Bash does recognize that it was invoked through and it does come up as a restricted shell.

Since every vector topology is translation invariant (i.e. for all , the map defined by is a homeomorphism), to define a vector topology it suffices to define a neighborhood basis (or subbasis) for it at the origin. Note that in general, the set of all balanced and absorbing subsets of a vector space does not satisfy the conditions of this theorem and does not form a neighborhood basis at the origin for any vector topology.

This reduces the offset to 0 in the Mersenne prime case, when d = 1.) Reducing a larger product ax to less than 2m = 2e+1 − 2d can be done by one or more reduction steps without an offset. If ad ≤ m, then one additional reduction step suffices. Since x < m, ax < am ≤ (a−1)2e, and one reduction step converts this to at most 2e − 1 + (a−1)d = m + ad − 1\.

Brainerd and Landweber, 1974 In fact, for showing that a computable function is primitive recursive, it suffices to show that its computational complexity is bounded above by a primitive recursive function of the input size. It follows that it is difficult to devise a computable function that is not primitive recursive, although some are known (see the section on Limitations below). The set of primitive recursive functions is known as PR in computational complexity theory.

The wf-policy is the rule to serve in each generation, as long as the accumulated resource space allows for it, with priority always the individuals with the smallest individual claims. The sf-policy is the rule to serve in each generation always with priority the largest individual resource claims, again as long as the accumulated resource space suffices. The societies adapting these policies strictly are called the wf-society, respectively the sf-society.

Heidelberg's student newspaper "ruprecht" is—with editions of more than 10,000 copies—one of Germany's largest student-run newspapers. It was recently distinguished by the MLP Pro Campus Press Award as Germany's best student newspaper. The jury of journalists from major newspapers commended its "well balanced, though critical attitude" and its "simply great" layout that "suffices highest professional demands." The ruprecht is financed entirely by advertising revenues, thus retaining independence from university management.

Between May to November 2014, he was also Minister of State for Information and Broadcasting. After taking charge of his ministry, Javadekar notably said that “the media itself suffices for self-regulation. Institutions are important for the functioning of democracy and priorities would be worked out after due consultation with the stakeholders”. Javadekar is now the Human Resource and Development Minister of India and also a veteran spokesperson of the Bharatiya Janata Party.

Lerín was occupied, and a severe defeat inflicted on Louis.The count's defeat inaugurated a (short) period of peace and stability for the kingdom; the Courts of Navarre unanimously put an end to the Brotherhood of Navarre in early 1510 on the grounds that "regular justice is well established, which suffices to keep the kingdom in peace"; the Brotherhood, founded in 1488, aimed at a more effective implementation of justice and persecution of crime within Navarre.

In a distributed data store, the same table would be implemented by creating columns families for "UID, first name, surname", "birthdate, gender", etc. If one needs only the males that were born between 1950 and 1960, for a query in the relational database, all the table has to be read. In a distributed data store, it suffices to access only the second standard column family, as the rest of information is irrelevant.

The basic practice of neo-Advaita is self-inquiry, via the question "Who am I?", or simply the direct recognition of the non-existence of the "I" or "ego." This recognition is taken to be equal to the Advaita Vedanta recognition of the identity of Atman and Brahman, or the recognition of the "Formless Self." According to neo-Advaitins, no preparatory practice is necessary, nor prolonged study of religious scriptures or tradition: insight alone suffices.

Should no single candidate achieve a majority of both houses then present, a third round is necessitated. In this final round, which can happen within 14 days of the first round, an absolute majority of deputies and senators present suffices. At this stage, the individual houses of parliament are not considered separately. Assuming that all members of parliament are present, all that is required to win is 141 votes, regardless of the house of origin.

In 2014 Schottel introduced a rudderpropeller with an additional electric motor (PTI - power take in) as a hybrid propulsion concept. Here, the electric motor suffices for partial-load duties, the diesel engine is employed for operation at greater load, and the electric motor can be switched on to provide additional power. The PTI and diesel engine are centrally-controlled as a single system. This thruster is installed in the tug Eddy, built by Holland Shipyard.

Such loads are two wire loads and a single element meter suffices. The non compliance of the meter occurs in measuring line to neutral loads. The meter design approximates a two element measurement by combining a half current value with the potential value of the line to line connection. The line to line potential is exactly twice the line to neutral connection if the two line to neutral connections are exactly balanced.

If a preference set is non-convex, then some prices determine a budget-line that supports two separate optimal-baskets. For example, we can imagine that, for zoos, a lion costs as much as an eagle, and further that a zoo's budget suffices for one eagle or one lion. We can suppose also that a zoo-keeper views either animal as equally valuable. In this case, the zoo would purchase either one lion or one eagle.

To begin with, some of the above laws are implied by some of the others. A sufficient subset of the above laws consists of the pairs of associativity, commutativity, and absorption laws, distributivity of ∧ over ∨ (or the other distributivity law—one suffices), and the two complement laws. In fact this is the traditional axiomatization of Boolean algebra as a complemented distributive lattice. By introducing additional laws not listed above it becomes possible to shorten the list yet further.

With the restriction to only this exponential, as shown by Galois theory, only compositions of Abelian extensions may be constructed, which suffices only for equations of the fourth degree and below. Something more general is required for equations of higher degree, so to solve the quintic, Hermite, et al. replaced the exponential by an elliptic modular function and the integral (logarithm) by an elliptic integral. Kronecker believed that this was a special case of a still more general method.

In order for a TVS to have the extension property, it must be complete (since it must be possible to extend the identity map from to the completion of ; i.e. to the map ). If is a continuous linear map from a vector subspace of into a complete space , then there always exists a unique continuous linear extension of from to the closure of in . Consequently, it suffices to only consider maps from closed vector subspaces into complete spaces.

The mere thought of her transcendent purity suffices to repel the alluring charms of sin and to inspire pleasure in the wonderful lustre of virtue. Self-denial is the second means which ascetics teaches us (cf. Matthew 16:24-25). Without it the combat between spirit and flesh, which are contrary to each other (Romans 7:23; 1 Corinthians 9:27; Galatians 5:17), will not lead to the victory of the spirit (Imitatio Christi, I, xxv).

If all are distinct then we're done, otherwise pick distinct indices such that and construct from by replacing with and deleting the element of (all other elements of are transferred to unchanged). Observe that and (since ) so by appealing to the inductive hypothesis we conclude that , as desired. It is clear that and that so to prove that is subadditive, it suffices to prove that when are such that , which implies that . This is an exercise.

Drawing on classical Chinese, Indian, Greek and Roman sources, Six Myths explores this and in the process gives its readership a general impression of what Kupperman believes a good life ought to be. The "broader theme", according to reviewer and Rhodes University philosopher Samantha Vice, "is an exploration of particular values and their role in making a life desirable."Vice 2006. Kupperman seeks also to debunk the apparently widely held notion that a simple account suffices.

Widely considered a request for one's own or a community's well being, a du'a serves as a direct spiritual connection with God. while a du'a may or may not be promptly or accurately answered, reason always lies behind God's spiritual deliverance of prayer requests. The outcome that God suffices, will always produce a greater benefit to all, rather than to that of the individual. The interpretation of one's personal interaction with God through du'a presents several differences.

In this final round, which can happen within 14 days of the first round, an absolute majority of deputies and senators present suffices. At this stage, the individual houses of parliament are not considered separately. Assuming that all members of parliament are present, all that is required to win is 141 votes, regardless of the house of origin. If no candidate wins in the third round, another ballot has to be considered in a subsequent joint session of parliament.

Further simple completeness conditions arise from the consideration of all non-empty finite sets. An order in which all non-empty finite sets have both a supremum and an infimum is called a lattice. It suffices to require that all suprema and infima of two elements exist to obtain all non-empty finite ones. A straightforward induction shows that every finite non-empty supremum/infimum can be decomposed into a finite number of binary suprema/infima.

Folkestone West railway station is on the South Eastern Main Line in England, serving the western area of Folkestone, Kent. It is down the line from London Charing Cross. All trains that call are operated by Southeastern. The ticket office, in a room on the extensive 'up' side buildings on the London-bound platform, is manned only during part of the day; at other times a PERTIS permit to travel machine, located outside the ticket office, suffices.

In favorable circumstances, every finite-dimensional representation is a direct sum of irreducible representations: such representations are said to be semisimple. In this case, it suffices to understand only the irreducible representations. Examples where this "complete reducibility" phenomenon occur include finite and compact groups, and semisimple Lie algebras. In cases where complete reducibility does not hold, one must understand how indecomposable representations can be built from irreducible representations as extensions of a quotient by a subrepresentation.

Tohorot 7:8 This may be legally accomplished by pouring on them one-fourth of a log of water. But that process suffices only where a person wishes to eat chullin, ma'aser, or terumah. If he desires to eat the sacrificial portions, he must dip his hands into forty seahs of water; and if about to handle the water of lustration, he must first subject his whole body to immersion.Chagigah 2:5; Gemara 18b et seq.

To calculate a circle's perimeter, knowledge of its radius or diameter and the number suffices. The problem is that is not rational (it cannot be expressed as the quotient of two integers), nor is it algebraic (it is not a root of a polynomial equation with rational coefficients). So, obtaining an accurate approximation of is important in the calculation. The computation of the digits of is relevant to many fields, such as mathematical analysis, algorithmics and computer science.

The given functions (f, g) may be discontinuous, provided that they are locally integrable (on the given interval). In this case, Lebesgue integration is meant, the conclusions hold almost everywhere (thus, in all continuity points), and differentiability of g is interpreted as local absolute continuity (rather than continuous differentiability). Sometimes the given functions are assumed to be piecewise continuous, in which case Riemann integration suffices, and the conclusions are stated everywhere except the finite set of discontinuity points.

Lord Millett, giving the leading judgment, held that this was a case concerning the vindication of property rights, not of unjust enrichment. The claimants could elect between (proportionate) beneficial ownership or an equitable lien, whichever was the most advantageous. One traces inherent value, and one set of tracing rules suffices. Just as if the trustee had taken money, bought a lottery ticket and won, it would be fair to take away the winnings without a change of position defence.

Many programming languages support passing and returning function values, which can be applied to arguments. Whether this suffices to call function values first-class is disputed. Some authors require it be possible to create new functions at runtime to call them 'first-class'. As a result, functions in C are not first- class objects; instead, they are sometimes called second-class objects, because they can still be manipulated in most of the above fashions (via function pointers).

Employees who traded before Dow Jones reported the news but claimed they honestly believed the news had become public raised a “good faith” defense. The court rejected this argument, holding that specific intent to defraud is not necessary to establish 10b-5 liability; a defendant's negligence suffices. In this case, because the TGS employees’ beliefs that the news was public were not reasonable, they had acted negligently and were liable.Texas Gulf Sulphur, 401 F.2d at 856.

Therefore, it suffices to show that if the whole weight of the interior of the triangle rests at I, and the whole weight of the section of the parabola at J, the lever is in equilibrium. Consider an infinitely small cross-section of the triangle given by the segment HE, where the point H lies on BC, the point E lies on AB, and HE is parallel to the axis of symmetry of the parabola. Call the intersection of HE and the parabola F and the intersection of HE and the lever G. If the whole weight of the triangle rests at I, it exerts the same torque on the lever JB as it does on HE. Thus, we wish to show that if the weight of the cross- section HE rests at G and the weight of the cross-section EF of the section of the parabola rests at J, then the lever is in equilibrium. In other words, it suffices to show that EF :GD = EH :JD.

Work of Grothendieck and David Mumford (see geometric invariant theory) opened up this area in the early 1960s. The more algebraic and abstract approach to moduli problems is to set them up as a representable functor question, then apply a criterion that singles out the representable functors for schemes. When this programmatic approach works, the result is a fine moduli scheme. Under the influence of more geometric ideas, it suffices to find a scheme that gives the correct geometric points.

When consumer preferences have concavities, then the linear budgets need not support equilibria: Consumers can jump between allocations. If a preference set is non‑convex, then some prices produce a budget supporting two different optimal consumption decisions. For example, we can imagine that, for zoos, a lion costs as much as an eagle, and further that a zoo's budget suffices for one eagle or one lion. We can suppose also that a zoo-keeper views either animal as equally valuable.

If S is not multiplicatively closed, it suffices to replace it by its multiplicative closure, consisting of the set of the products of elements of S (including the empty product 1). This does not change the result of the localization. The fact that we talk of "a localization with respect to the powers of an element" instead of "a localization with respect to an element" is an example of this. Therefore, we shall suppose S to be multiplicatively closed in what follows.

The general logarithm, to an arbitrary positive base, Euler presents as the inverse of an exponential function. Then the natural logarithm is obtained by taking as base "the number for which the hyperbolic logarithm is one", sometimes called Euler's number, and written e. This appropriation of the significant number from Gregoire de Saint-Vincent’s calculus suffices to establish the natural logarithm. This part of precalculus prepares the student for integration of the monomial xp in the instance of p = −1\.

Under clear weather conditions, civil twilight approximates the limit at which solar illumination suffices for the human eye to clearly distinguish terrestrial objects. Enough illumination renders artificial sources unnecessary for most outdoor activities. At civil dawn and at civil dusk sunlight clearly defines the horizon while the brightest stars and planets can appear. As observed from the Earth (see apparent magnitude), sky-gazers know Venus, the brightest planet, as the "morning star" or "evening star" because they can see it during civil twilight.

The question usually posed is how many pursuers are necessary to ensure the eventual capture of all the evaders. If one pursuer suffices, the graph is called a cop-win graph. In this case, a single evader can always be captured in time linear to the number of n nodes of the graph. Capturing r evaders with k pursuers can take in the order of rn time as well, but the exact bounds for more than one pursuer are still unknown.

If even less accuracy suffices, the following examples can be used: :How I wish I could recollect pi easily today! :May I have a large container of coffee, cream and sugar? This second one gives the value of π as 3.1415926535, while the first only brings it to the second five. Indeed, many published poems use truncation instead of one of the several roundings, thereby producing a less-accurate result when the first omitted digit is greater than or equal to five.

The symmetries of the Dynkin diagram, , correspond to the outer automorphisms of in triality. Let now be a connected reductive group over an algebraically closed field. Then any two Borel subgroups are conjugate by an inner automorphism, so to study outer automorphisms it suffices to consider automorphisms that fix a given Borel subgroup. Associated to the Borel subgroup is a set of simple roots, and the outer automorphism may permute them, while preserving the structure of the associated Dynkin diagram.

Fingal Head Light with keeper, circa 1906 A provisional light station was established on the head in 1872 and in 1878 a proper lighthouse, built as a sandstone construction in a round design, was inaugurated. It was part of a series of five such lighthouses established between 1878 and 1880. The tower stands only seven metres high, but that suffices since the headland itself adds additional height. Thus the focal plane of the lightsource is situated 24 m above sea level.

Dynamic logic has a higher toggle rate than static logic but the capacitive loads being toggled are smaller so the overall power consumption of dynamic logic may be higher or lower depending on various tradeoffs. When referring to a particular logic family, the dynamic adjective usually suffices to distinguish the design methodology, e.g. dynamic CMOS or dynamic SOI design. Dynamic logic is distinguished from so-called static logic in that dynamics logic uses a clock signal in its implementation of combinational logic circuits.

However, in functional analysis we almost always want to be real-valued (i.e. to never take on the value of ), which happens if and only if the set } is non-empty for every . In order for to be real-valued, it suffices for the origin of to belong to the algebraic interior (or core) of in . If is absorbing in , where recall that this implies that , then the origin belongs to the algebraic interior of in and thus is real-valued.

A general Apollonius problem can be transformed into the simpler problem of circle tangent to one circle and two parallel lines (itself a special case of the LLC special case). To accomplish this, it suffices to scale two of the three given circles until they just touch, i.e., are tangent. An inversion in their tangent point with respect to a circle of appropriate radius transforms the two touching given circles into two parallel lines, and the third given circle into another circle.

In this case, as it turned out, neither the wave—nor the particle—explanation alone suffices, as light behaves like waves and like particles. Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of natural laws, and the constancy of natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. Occam's razor and parsimony support, but do not prove, these axioms of science.

A causal schema refers to the way a person thinks about plausible causes in relation to a given effect. It provides him or her with the means of making causal attributions when the information provided is limited. The three causal schemata recognized by Kelley are Multiple Sufficient Causes, Multiple Necessary Causes, and Causal Schema for Compensatory Causes (Kelley, 1973). Multiple Sufficient Causes: He or she may believe that either cause A or cause B suffices to produce a given effect (Kelley et al.

In other words, is there an assignment of values to the variables such that when a nonzero polynomial is evaluated on these values, the result is nonzero? It suffices to choose each variable's value uniformly at random from a finite subset of at least d values to achieve bounded error probability, where d is the total degree of the polynomial.Madhu Sudan and Shien Jin Ong. Massachusetts Institute of Technology: 6.841/18.405J Advanced Complexity Theory: Lecture 6: Randomized Algorithms, Properties of BPP.

An open C tuning Open C tuning is an open tuning for guitar. The open-string notes form a C major chord, which is the triad (C,E,G) having the root note C, the major third (C,E), and the perfect fifth (C,G). When the guitar is strummed without fretting any strings, a C-major chord is sounded. By barring all of the strings for one fret (from one to eleven), one finger suffices to fret the other eleven major-chords.

A number of public service issues are discussed, including public interest considerations regarding license assignment, and what programming suffices to serve the public interest, defining the functions thereof. 4\. Statistics show increasing profitability on the part of radio broadcasters, but little improvement of programming. This contradicted the claim that broadcasters couldn't afford public interest programs. 5\. Four requirements for broadcast licensees are outlined: promote live, local shows; devote programming to discussing public issues; sustain "unsponsorable" programs; and eliminate "excess advertising".

The defendant cannot be reckless to the resisting of arrest, it must be an intention.Simester et al. (2010). pp. 443-444. Concerning the requirement to resist a lawful arrest, the defendant only lacks the required mens rea if he believes in facts which, if true, would make the arrest unlawful; not just that he believes the facts as they are make the arrest illegal - a mistake of fact suffices, a mistake of law does not.Simester et al. (2010). p. 444.

The WBGU emphasises that, in view of the seriousness of the soil problems outlined in this report, a new efficient institutional framework should now be established. For this reason the German Federal Government should decide in principle whether a differentiated "Soil Declaration" suffices or whether a global "Soil Convention" has to be striven for. This report provides the relevant arguments for both instruments. Global soil protection must obtain a similar attention on the international agenda as has been achieved for climate policy.

In the other rows i, only the entries in columns k and l change. Looping over these rows, if m_i is neither k nor l, it suffices to compare the old maximum at m_i to the new entries and update m_i if necessary. If m_i should be equal to k or l and the corresponding entry decreased during the update, the maximum over row i has to be found from scratch in O(n) complexity. However, this will happen on average only once per rotation.

After the development of the CIE system, color triangles were used as chromaticity diagrams, including briefly with the trilinear coordinates representing the chromaticity values. Since the sum of the three chromaticity values has a fixed value, it suffices to depict only two of the three values, using Cartesian co-ordinates. In the modern x,y diagram, the large triangle bounded by the imaginary primaries X, Y, and Z has corners (1,0), (0,1), and (0,0), respectively; colour triangles with real primaries are often shown within this space.

In fact, if is a divisor of such that , then is a divisor of such that . If one tests the values of in increasing order, the first divisor that is found is necessarily a prime number, and the cofactor cannot have any divisor smaller than . For getting the complete factorization, it suffices thus to continue the algorithm by searching a divisor of that is not smaller than and not greater than . There is no need to test all values of for applying the method.

This is clearly true for and so assume that , which implies that all are positive. If all are distinct then we're done, otherwise pick distinct indices such that and construct from by replacing with and deleting the element of (all other elements of are transferred to unchanged). Observe that and (since ) so by appealing to the inductive hypothesis we conclude that , as desired. It is clear that and that so to prove that is subadditive, it suffices to prove that when are such that , which implies that .

"one look at the sheer mass and volume of what we euphemistically call our popular culture suffices", from Winthrop Sargeant, 'In Defense of the High-Brow', an article from LIFE magazine, 11 April 1949, p. 102. The abbreviated form "pop" for popular, as in pop music, dates from the late 1950s.The New Grove Dictionary of Music and Musicians, volume 15, p. 85 entry Pop music Although terms "pop" and "popular" are in some cases used interchangeably, and their meaning partially overlap, the term "pop" is narrower.

Several are said to have made sudden fortunes through him, and hence when anyone has had a sudden increase of fortune they say "Forse avrà il Monaciello in casa" (perhaps he has had the little Monk in his house). This beneficent household demon may also be propitiated by food which they expect to see converted into gold; but he must not boast of such supernatural gifts, else they vanish as they come. It is believed that treasure suffices for the requirements of those who received it.

The translation team behind the New Jerusalem Bible (N.J.B.) however, maintains that the meaning is uncertain, and that translating "El Shaddai" as "Almighty God" is inaccurate. The N.J.B. leaves it untranslated as "Shaddai", and makes footnote suggestions that it should perhaps be understood as "God of the Mountain" from the Akkadian "shadu", or "God of the open wastes" from the Hebrew "sadeh" and the secondary meaning of the Akkadian word. The translation in the Concordant Old Testament is 'El Who-Suffices' (Genesis 17:1).

They will re-emerge as early as February if conditions are favourable, and migrate to bodies of water such as garden ponds to spawn. Where conditions are harsher, such as in the Alps, they emerge as late as early June. Common frogs hibernate in running waters, muddy burrows, or in layers of decaying leaves and mud at the bottom of ponds or lakes primarily with a current. The oxygen uptake through the skin suffices to sustain the needs of the cold and motionless frogs during hibernation.

Procedural models often exhibit database amplification, meaning that large scenes can be generated from a much smaller number of rules. If the employed algorithm produces the same output every time, the output need not be stored. Often, it suffices to start the algorithm with the same random seed to achieve this. Although all modeling techniques on a computer require algorithms to manage and store data at some point, procedural modeling focuses on creating a model from a rule set, rather than editing the model via user input.

In addition to unique graphical representations, Lapointe also devised a pronunciation for each of the sixteen digits. Using four consonants (HBKD) and four vowels (OAEI), one obtains sixteen combinations: HO, HA, HE, HI, BO, BA, BE, BI, KO, KA, KE, KI, DO, DA, DE, DI. To express any number, it suffices to enumerate the (hexadecimal) digits that make it up. For example: the number written as "2000" in base ten, which translates to "7D0" in conventionally-written hexadecimal, would in Bibi-binary be spoken aloud as "BIDAHO".

Any reversible gate can be implemented on a quantum computer, and hence the Toffoli gate is also a quantum operator. However, the Toffoli gate can not be used for universal quantum computation, though it does mean that a quantum computer can implement all possible classical computations. The Toffoli gate has to be implemented along with some inherently quantum gate(s) in order to be universal for quantum computation. In fact, any single-qubit gate with real coefficients that can create a nontrivial quantum state suffices.

For most situations, however, her strength suffices. To test a Slayer's natural ingenuity and practical capability, the Watcher's Council administers a test known as "the Cruciamentum" if/when they turn eighteen, which strips the Slayer of her powers and forces her to fight a powerful vampire without them ("Helpless"). The compound used to weaken the Slayer makes her typically weaker than most normal humans. This renders a Slayer who would still normally be physically fit without her powers remarkably feeble even for a human.

On the night of the Last Supper, reclining with His brethren, once the Law had been fully observed with the prescribed foods, as food to the crowd of Twelve He gives Himself with His hands. The Word as Flesh makes true bread into flesh by a word and the wine becomes the Blood of Christ. And if sense is deficient to strengthen a sincere heart Faith alone suffices. Therefore, the great Sacrament let us reverence, prostrate: and let the old Covenant give way to a new rite.

Propane is a popular choice for barbecues and portable stoves because the low boiling point of makes it vaporize as soon as it is released from its pressurized container. Therefore, no carburetor or other vaporizing device is required; a simple metering nozzle suffices. Propane powers buses, forklifts, taxis, outboard boat motors, and ice resurfacing machines and is used for heat and cooking in recreational vehicles and campers. Propane is also used in some locomotive diesel engines as a fuel added into the turbocharger yielding much better combustion.

A two-thirds vote is required to elect on any of the first three rounds of balloting and after that a majority suffices. The election is presided over by the Speaker of the Chamber of Deputies, who calls for the public counting of the votes. The vote is held in the Palazzo Montecitorio, home of the Chamber of Deputies, which is expanded and re-configured for the event. The president assumes office after having taken an oath before Parliament and delivering a presidential address.

Electric current is the flow of electric charge through an object, which produces no net loss or gain of electric charge. The most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the conventional current without regard to whether it is carried by positive charges moving in the direction of the conventional current or by negative charges moving in the opposite direction.

A set C of attributes is a concept intent if and only if C respects all valid implications. The system of all valid implications therefore suffices for constructing the closure system of all concept intents and thereby the concept hierarchy. The system of all valid implications of a formal context is closed under the natural inference. Formal contexts with finitely many attributes possess a canonical basis of valid implications,Guigues, J.L. and Duquenne, V. Familles minimales d'implications informatives résultant d'un tableau de données binaires.

Sketching is the method by which each -bit key at a node containing keys is compressed into only bits. Each key may be thought of as a path in the full binary tree of height starting at the root and ending at the leaf corresponding to . To distinguish two paths, it suffices to look at their branching point (the first bit where the two keys differ). All paths together have branching points, so at most bits are needed to distinguish any two of the keys.

The Raichur-Solapur Power Transmission line of 765 kV power capacity suffices the power grid accessing need of the southern states of Karanataka and Andhra Pradesh. The first waste-to-energy electricity plant in Maharashtra is situated in Solapur. The Gramadevata (Chief deity) of the city is Shri Shivyogi Siddheshwar. The "Nandidhwaj" procession on the Hindu festival of Makar Sankranti and on account of it an annual fair locally known as Gadda Yatra attracts large crowds and is associated with the marriage of Lord Siddheshwar.

Many astronomical and navigational computations use a sphere to model the Earth as a close approximation. However, a more accurate figure is needed for measuring distances and areas on the scale beyond the purely local. Better approximations can be had by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoid. For surveys of small areas, a planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature.

The formula's popularity grew considerably in the 19th century, mainly due to the efforts of Leo Dupont. According to H. C. Lea (1896), "As a rule ... it suffices to wear [the medal] devoutly, but, if some special favor is desired, it is advisable on a Tuesday to say five Glorias, three Aves and then three more Glorias to secure the protection of St. Benedict."Lea, Henry Charles (1896) A History of Auricular Confession and Indulgences in the Latin Church; Volume III: Indulgences. Philadelphia: Lea Brothers & Co. Reprinted 2002, Adamant Media Corp.

Certain data-center applications (such as large computer clusters) require the use of fiber-optic interconnects due to the distance limitations inherent in copper cabling. Typically, a network- oriented standard such as Ethernet or Fibre Channel suffices for these applications, but in some cases the overhead introduced by routable protocols is undesirable and a lower-level interconnect, such as InfiniBand, RapidIO, or NUMAlink is needed. Local-bus standards such as PCIe and HyperTransport can in principle be used for this purpose, but , solutions are only available from niche vendors such as Dolphin ICS.

For example, in Donkey Kong Country 2: Diddy's Kong Quest, Diddy Kong juggles a few balls if the player offers no controller input for a few seconds. Idle animations in modern 3D games are used to keep them realistic. In general, games meant for younger audiences are far more likely to have complex or humorous idle animations, while games for older people tend to have more basic idle animations. For example, in Super Mario 64, Mario will occasionally look around, and eventually fall asleep, while in other games, steady breathing suffices as an idle animation.

Sometimes, it is more convenient to deduce backwards, proving the statement for n-1, given its validity for n. However, proving the validity of the statement for no single number suffices to establish the base case; instead, one needs to prove the statement for an infinite subset of the natural numbers. For example, Augustin Louis Cauchy first used forward (regular) induction to prove the inequality of arithmetic and geometric means for all powers of 2, and then used backwards induction to show it for all natural numbers.Cauchy, Augustin-Louis (1821).

The language contains a complete set of grammar rules, including three unclear forms of verbs characterized by distinct suffixes which are added to root verbs like a form of conjugations. The suffix -tasa is intentionally added to a root word to form a verb, while the suffices -mu and -t indicate the verb is being nominalized or adjectified. The latter suffix, -t, is not commonly found in informal exchanges. The reason the verb forms have been deemed unclear by some scholars is because of inconsistency between root and suffix relationships.

A bite on the nape of the neck or the snout (and sometimes on the skull) suffices to kill smaller prey. Cheetahs have an average hunting success rate of 25–40%, higher for smaller and more vulnerable prey. Once the hunt is over, the prey is taken near a bush or under a tree; the cheetah, highly exhausted after the chase, rests beside the kill and pants heavily for five to 55 minutes. Meanwhile cheetahs nearby, who did not take part in the hunt, might feed on the kill immediately.

However, diagnosis may be confirmed with X-rays or CT scans, and these are required if other facial injuries are suspected. A fracture that runs horizontally across the septum is sometimes called a "Jarjavay fracture", and a vertical one, a "Chevallet fracture". Although treatment of an uncomplicated fracture of nasal bones is not urgent—a referral for specific treatment in five to seven days usually suffices—an associated injury, nasal septal hematoma, occurs in about 5% of cases and does require urgent treatment and should be looked for during the assessment of nasal injuries.

This was probably not a first name, as some scholars have thought, but rather an indicator that he came from Pisan territory, which suggests his birthplace was in peninsular Italy (near Pisa), yet his home to be in Sardinia, where he undoubtedly composed his main work. This work, however, was badly handled by copyists, with the result that the surviving manuscripts of the Doctrina are riddled with errors, unclear, and inaccessible. What can be gleaned, however, suffices to demonstrate that Terramagnino's work lacked originality. His Occitan, too, is not he best and there are Italianisms.

To pick a development object it suffices to right-click on it. The cursor then changes into a special symbol or pebble corresponding to the type of the object: "bubble" (ellipse) for a class, dot for a breakpoint, cross for a feature etc. As you move the cursor a line is displayed from the original object to the current position. You can then drop the pebble into any matching place: either an icon representing a hole with the same overall shape (class hole, breakpoint hole, feature hole etc.) or a window with a compatible type.

An irregular paradigm is one in which the derived forms of a word cannot be deduced by simple rules from the base form. For example, someone who knows only a little English can deduce that the plural of girl is girls but cannot deduce that the plural of man is men. Language learners are often most aware of irregular verbs, but any part of speech with inflections can be irregular. For most synchronic purposes—first-language acquisition studies, psycholinguistics, language-teaching theory—it suffices to note that these forms are irregular.

All members of either the Evangelical Lutheran Church of Finland and the Finnish Orthodox Church (the two state churches of Finland) pay an income-based church tax of between 1% and 2%, depending on the municipality. On average the tax is about 1.4%. Formerly, to stop paying church tax, one had to formally leave the church by personally going to local register office and waiting during an allowance of time for reflection. This requirement was removed in 2003 and currently a written (but not signed) statement to the church suffices.

The first reading is where the minister or his deputy submits it to Parliament. At the second reading, the bill is discussed and debated by MPs. Until the mid-1970s, both English and Malay (the national language) were used for debates, but henceforth, only Malay was permitted, unless permission was obtained from the Speaker of the House. At the third reading, the minister or his deputy formally submit it to a vote for approval. A 2/3 majority is usually required to pass the bill, but in certain cases, a simple majority suffices.

Furthermore, many members of parliament in the governing AKP have internally also objected by arguing that the current presidential system suffices. Erdoğan himself is currently barred from running for a fourth term as prime minister in the 2015 general elections due to current AKP by-laws, largely sparking accusations from the public that Erdoğan's proposals were stated in light of him only intending to prolong his rule as the most dominant figure in politics. The constitutional proposals have mostly so far been delayed in deliberations or lacked any broad agreement for reforms.

On the other hand, if the debtor offers a lesser sum in settlement and expressly or by implication admits that he owes the full debt, he commits an act of insolvency, because he tacitly acknowledges that he cannot pay the debt (Laeveldse Kooperasie Bpk v Joubert). The debtor does not have to make the arrangement or offer personally. One made by a third person with his knowledge and permission suffices. The object of the arrangement or offer must be to release the debtor from liability, wholly or in part.

The individual segments of a fourteen-segment display. A fourteen-segment display (FSD) (sometimes referred to as a starburst display or Union Jack display) is a type of display based on 14 segments that can be turned on or off to produce letters and numerals. It is an expansion of the more common seven-segment display, having an additional four diagonal and two vertical segments with the middle horizontal segment broken in half. A seven-segment display suffices for numerals and certain letters, but unambiguously rendering the ISO basic Latin alphabet requires more detail.

Both handles accomplish the same task, so pulling either one suffices. The F-16 has only one handle located between the pilot's knees, since the cockpit is too narrow for side-mounted handles. Non-standard egress systems include Downward Track (used for some crew positions in bomber aircraft, including the B-52 Stratofortress), Canopy Destruct (CD) and Through-Canopy Penetration (TCP), Drag Extraction, Encapsulated Seat, and even Crew Capsule. Early models of the F-104 Starfighter were equipped with a Downward Track ejection seat due to the hazard of the T-tail.

A smaller range of voltage control then suffices to stabilize the oscillator frequency in applications where temperature varies, such as heat buildup inside a transmitter. Placing the oscillator in a crystal oven at a constant but higher-than-ambient temperature is another way to stabilize oscillator frequency. High stability crystal oscillator references often place the crystal in an oven and use a voltage input for fine control.For example, an HP/Agilent 10811 reference oscillator The temperature is selected to be the turnover temperature: the temperature where small changes do not affect the resonance.

In social decision making, to rank all alternatives is not usually a goal. It often suffices to find some alternative. The approach focusing on choosing an alternative investigates either social choice functions (functions that map each preference profile into an alternative) or social choice rules (functions that map each preference profile into a subset of alternatives). As for social choice functions, the Gibbard–Satterthwaite theorem is well-known, which states that if a social choice function whose range contains at least three alternatives is strategy-proof, then it is dictatorial.

With hop-by-hop routing, each routing table lists, for all reachable destinations, the address of the next device along the path to that destination: the next hop. Assuming that the routing tables are consistent, the simple algorithm of relaying packets to their destination's next hop thus suffices to deliver data anywhere in a network. Hop-by-hop is the fundamental characteristic of the IP Internet layer and the OSI Network Layer. When a router interface is configured with an IP address and subnet mask, the interface becomes a host on that attached network.

Ultimately it is this fact, combined with the Goddard–Thorn theorem, which leads to bosonic string theory failing to be consistent in dimensions other than 26. The regularization of is also involved in computing the Casimir force for a scalar field in one dimension.See v:Quantum mechanics/Casimir effect in one dimension An exponential cutoff function suffices to smooth the series, representing the fact that arbitrarily high-energy modes are not blocked by the conducting plates. The spatial symmetry of the problem is responsible for canceling the quadratic term of the expansion.

Theorem: If K1 and K2 are the complexity functions relative to Turing complete description languages L1 and L2, then there is a constant c – which depends only on the languages L1 and L2 chosen – such that :∀s. −c ≤ K1(s) − K2(s) ≤ c. Proof: By symmetry, it suffices to prove that there is some constant c such that for all strings s :K1(s) ≤ K2(s) + c. Now, suppose there is a program in the language L1 which acts as an interpreter for L2: function InterpretLanguage(string p) where p is a program in L2.

Thus, testing with 2, 3, and 5 suffices up to n = 48 not just 25 because the square of the next prime is 49, and below n = 25 just 2 and 3 are sufficient. Should the square root of n be integral, then it is a factor and n is a perfect square. An example of the trial division algorithm, using successive integers as trial factors, is as follows (in Python): def trial_division(n: int) -> List[int]: """Return a list of the prime factors for a natural number.""" a = [] # Prepare an empty list.

Since the Banach–Alaoglu theorem is usually proven via Tychonoff's theorem, it relies on the ZFC axiomatic framework, and in particular the axiom of choice. Most mainstream functional analysis also relies on ZFC. However, the theorem does not rely upon the axiom of choice in the separable case (see below): in this case one actually has a constructive proof. In the non-separable case, the Ultrafilter Lemma, which is strictly weaker than the axiom of choice, suffices for the proof of the Banach-Alaoglu theorem, and is in fact equivalent to it.

Neon test lamp for line voltages A test light, test lamp, voltage tester, or mains tester is a piece of electronic test equipment used to determine the presence of electricity in a piece of equipment under test. A test light is simpler and less costly than a measuring instrument such as a multimeter, and often suffices for checking for the presence of voltage on a conductor. Properly designed test lights include features to protect the user from accidental electric shock. Non-contact test lights can detect voltage on insulated conductors.

Ning describes a method for interrelating Reynolds number with Mach number. In order to maneuver in the atmosphere at faster speeds than supersonic, the forms of propulsion can still be airbreathing systems, but a ramjet no longer suffices for a system to attain Mach 5, as a ramjet slows down the airflow to subsonic. Some systems (waveriders) use a first stage rocket to boost a body into the hypersonic regime. Other systems (boost-glide vehicles) use scramjets after their initial boost, in which the speed of the air passing through the scramjet remains supersonic.

This proof, published by Gabriel Lamé in 1844, represents the beginning of computational complexity theory, and also the first practical application of the Fibonacci numbers. This result suffices to show that the number of steps in Euclid's algorithm can never be more than five times the number of its digits (base 10). For if the algorithm requires N steps, then b is greater than or equal to FN+1 which in turn is greater than or equal to φN−1, where φ is the golden ratio. Since b ≥ φN−1, then N − 1 ≤ logφb.

If the first names of family members are unique only within each family, then each person can be uniquely identified by the combination of first name and family name; there is only one Jane Doe, though there may be many Janes. Within the namespace of the Doe family, just "Jane" suffices to unambiguously designate this person, while within the "global" namespace of all people, the full name must be used. Prominent examples for namespaces include file systems, which assign names to files. Some programming languages organize their variables and subroutines in namespaces.

Kőnig's lemma may be considered to be a choice principle; the first proof above illustrates the relationship between the lemma and the axiom of dependent choice. At each step of the induction, a vertex with a particular property must be selected. Although it is proved that at least one appropriate vertex exists, if there is more than one suitable vertex there may be no canonical choice. In fact, the full strength of the axiom of dependent choice is not needed; as described below, the axiom of countable choice suffices.

The mathematical procedure for determining the correlated color temperature involves finding the closest point to the light source's white point on the Planckian locus. Since the CIE's 1959 meeting in Brussels, the Planckian locus has been computed using the CIE 1960 color space, also known as MacAdam's (u,v) diagram. Today, the CIE 1960 color space is deprecated for other purposes: Owing to the perceptual inaccuracy inherent to the concept, it suffices to calculate to within 2K at lower CCTs and 10K at higher CCTs to reach the threshold of imperceptibility. CIE 1960 UCS.

Faults where a replica sends different values in different directions (for instance, the correct Output to some of its fellow replicas and incorrect Outputs to others) are called Byzantine Failures. Byzantine failures may be random, spurious faults, or malicious, intelligent attacks. 2F+1 replicas, with non-cryptographic hashes suffices to survive all non-malicious Byzantine failures (with high probability). Malicious attacks require cryptographic primitives to achieve 2F+1 (using message signatures), or non-cryptographic techniques can be applied but the number of replicas must be increased to 3F+1.

He expounded the Academic, Peripatetic, and Stoic systems in such a way as to show that these three schools deviated from one another only in minor points. Antiochus was chiefly interested in ethics, in which he tried to find a middle way between Zeno of Citium, Aristotle, and Plato. For instance, he said that virtue suffices for eudaimonia, but for the highest grade of happiness, bodily and external goods are necessary as well. This eclectic tendency was enabled by the fact that most of Plato's works were non-dogmatic.

The Wiesbaden group made the building of five eye clinics in Burkina Faso, Mali and Niger possible and enabled young people to study ophthalmology or train to be opticians. The fifth clinic in Mopti, Mali, was named after Bardenhewer in 2011, "Centre ophtalmologique Père Joseph Werner Bardenhewer". He published a book by the cardinal of Burkina Faso, Philippe Ouédraogo, translated into German as Gott allein genügt (God alone suffices) by Stefanie Götzmann in 2018. Bardenhewer traveled to West Africa, seeking direct contact with the institutions there, such as in 2018 to Burkina Faso.

The bride's diamond ring is worn on top of the engagement band at the wedding and thereafter, especially at formal occasions or parties; otherwise the engagement band suffices for daily wear for both parties. At the wedding, the rings are swapped from the right to the left hand. In Brazil, they are always made of gold, and there is no tradition for the engagement ring. Both men and women wear the wedding band on their right hand while engaged, and, after they marry, they shift the rings to their left hands.

Both sides of the Crofton formula are additive over concatenation of curves, so it suffices to prove the formula for a single line segment. Since the right-hand side does not depend on the positioning of the line segment, it must equal some function of the segment's length. Because, again, the formula is additive over concatenation of line segments, the integral must be a constant times the length of the line segment. It remains only to determine the factor of 1/4; this is easily done by computing both sides when γ is the unit circle.

To factorize the initial polynomial, it suffices to factorize each square-free factor. Square-free factorization is therefore the first step in most polynomial factorization algorithms. Yun's algorithm extends this to the multivariate case by considering a multivariate polynomial as a univariate polynomial over a polynomial ring. In the case of a polynomial over a finite field, Yun's algorithm applies only if the degree is smaller than the characteristic, because, otherwise, the derivative of a non-zero polynomial may be zero (over the field with p elements, the derivative of a polynomial in xp is always zero).

First, if planar regions separated by the graph are not triangulated, i.e. do not have exactly three edges in their boundaries, we can add edges without introducing new vertices in order to make every region triangular, including the unbounded outer region. If this triangulated graph is colorable using four colors or fewer, so is the original graph since the same coloring is valid if edges are removed. So it suffices to prove the four color theorem for triangulated graphs to prove it for all planar graphs, and without loss of generality we assume the graph is triangulated.

Kc (and hence K) is a fine-structural countably iterable extender model below long extenders. (It is not currently known how to deal with long extenders, which establish that a cardinal is superstrong.) Here countable iterability means ω1+1 iterability for all countable elementary substructures of initial segments, and it suffices to develop basic theory, including certain condensation properties. The theory of such models is canonical and well understood. They satisfy GCH, the diamond principle for all stationary subsets of regular cardinals, the square principle (except at subcompact cardinals), and other principles holding in L. Kc is maximal in several senses.

Elave on his return after seven years away must first bear accusations that his master, William of Lythwood, spoke heresy and took the pilgrimage as penance, which were not true. The accusations came out in the presence of an Augustinian canon with strong views on heresy and anything but blind faith on the part of the laity. The Canon said: "Faith is to be received, not taken apart by the wit of a mere man".Peters, Ellis The Heretic's Apprentice, 1989, Chapter Two Elave successfully defends his master by telling he died shriven, which suffices for Abbot Radulfus.

To see that the problem is insolvable (when starting with just one cup upside down), it suffices to concentrate on the number of cups the wrong way up. Denoting this number by W, the goal of the problem is to change W from 1 to 0, i.e. by -1. The problem is insoluble because any move changes W by an even number. Since a move inverts two cups and each inversion changes W by +1 (if the cup was the right way up) or -1 (otherwise), a move changes W by the sum of two odd numbers, which is even, completing the proof.

By the fundamental theorem of arithmetic, every integer greater than 1 has a unique (up to the order of the factors) factorization into prime numbers, which are those integers which cannot be further factorized into the product of integers greater than one. For computing the factorization of an integer , one needs an algorithm for finding a divisor of or deciding that is prime. When such a divisor is found, the repeated application of this algorithm to the factors and gives eventually the complete factorization of . For finding a divisor of , if any, it suffices to test all values of such that and .

In principle, it suffices to test only prime divisors. This needs to have a table of prime numbers that may be generated for example with the sieve of Eratosthenes. As the method of factorization does essentially the same work as the sieve of Eratosthenes, it is generally more efficient to test for a divisor only those numbers for which it is not immediately clear whether they are prime or not. Typically, one may proceed by testing 2, 3, 5, and the numbers > 5, whose last digit is 1, 3, 7, 9 and the sum of digits is not a multiple of 3.

A major reason for the notion of a good cover is that the Leray spectral sequence of a fiber bundle degenerates for a good cover, and so the Čech cohomology associated with a good cover is the same as the Čech cohomology of the space. (Such a cover is known as a Leray cover.) However, for the purposes of computing the Čech cohomology it suffices to have a more relaxed definition of a good cover in which all intersections of finitely many open sets have contractible connected components. This follows from the fact that higher derived functors can be computed using acyclic resolutions.

Gasparri holds it as received practice that it suffices if the reasons alleged be actually true at the moment when the petition is presented. It is certain, however, that the executor required by Penitentiaria rescripts may safely fulfil his mission even if the pope should die before he had begun to execute it. The executor named for public impediments is usually the ordinary who forwards the supplica and for secret impediments an approved confessor chosen by the petitioner. Except when specially authorized, the person delegated cannot validly execute a dispensation before he has seen the original of the rescript.

One explanation put forth by Gregory N. Carlson is the treatment of bare plurals as names of a semantic type called "kinds" that is distinct from typical individuals. With individuals being the topic of traditional semantic discourse, kinds represent the "sort" of individual. "A dog" is an indefinite instantiation of the kind "dogs", "the man" is a definite instantiation of the kind "men". This suffices to explain all of the above sentences except (3), as each are true in a possible world if and only if the ascribed attribute is a property of the kind inputted into the predicate.

The tube both conducts the fluid and stores it until it is required. The distance that the animal can propel the slime varies; usually it squirts it about a centimetre, but the maximal range has variously been reported to be ten centimetres, or even nearly a foot, although accuracy drops with range. It is not clear to what extent the range varies with the species and other factors. One squirt usually suffices to snare a prey item, although larger prey may be further immobilised by smaller squirts targeted at the limbs; additionally, the fangs of spiders are sometimes targeted.

To explain this resonance and strengthened sound, the example of the overtones on C has been used; and C's overtones is a standard example for explaining the sequence of overtones. The open-string notes form a C major chord, which is the triad (C,E,G) having the root note C, the major third (C,E), and the perfect fifth (C,G). When the guitar is strummed without fretting even one string, a C-major chord is sounded. By barring all of the strings for one fret (from one to eleven), one finger suffices to fret the other eleven major-chords.

A set of points in a -dimensional affine space (-dimensional Euclidean space is a common example) is in general linear position (or just general position) if no of them lie in a -dimensional flat for . These conditions contain considerable redundancy since, if the condition holds for some value then it also must hold for all with . Thus, for a set containing at least points in -dimensional affine space to be in general position, it suffices to know that no hyperplane contains more than points -- i.e. the points do not satisfy any more linear relations than they must.

The SOC are followed by most medical professionals who specialize in the care of transgender individuals, and are the most widely followed clinical guidelines for the treatment of transgender persons in use. Hence, the SOC criteria for HRT and GRS, including completion of an RLE when applicable, must usually be met for one who seeks such treatments to receive them. As of the seventh version of the SOC, a three-month minimum requirement of RLE is no longer part of WPATH's recommended criteria for HRT. A referral letter alone from a qualified mental health professional now suffices.

Consequently, to define an étale cover of a scheme X, it suffices to first cover X by open affine subschemes, that is, to take a Zariski cover, and then to define an étale cover of an affine scheme. An étale cover of an affine scheme X can be defined as a surjective family {uα : Xα → X} such that the set of all α is finite, each Xα is affine, and each uα is étale. Then an étale cover of X is a family {uα : Xα → X} which becomes an étale cover after base changing to any open affine subscheme of X.

The rank of subdeacon suffices for election; the Abbé Legendre relates in his memoirs as a contemporary incident that one of these young legislators, after an escapade, was soundly flogged by his perceptor who had accompanied him to Paris. The assemblies at all times reserved to themselves the right of deciding upon the validity of procurators and the authority of deputies. They wished also to reserve the right of electing their own president, whom they always chose from among the bishops. However, to conciliate rivalries, several were usually nominated for the presidency, only one of whom exercised that function.

The HFE gene responsible for haemochromatosis is distal on chromosome 6 from HLA-A and more so from HLA-B, the distance suffices (3 million nucleotides) to allow equilibration of the loci. Nonetheless, a linkage has been found between A3-B7 haplotype and haemochromatosis. The region is almost 1.4 million nucleotides in length and contains many other genes that could be involved. A more recent study looked at a number of linked gene-alleles and found I82-2:D6S265-1:HLA-A3:D6S128-2:HLA-F1:D6S105-8 was constantly associated while B7 appeared beyond the haplotype linked to disease.

Exactly the same argument suffices to prove the column case, and so we conclude that each row and column contains no element more than once. Because the group is finite, the pigeonhole principle guarantees that each element of the group will be represented in each row and in each column exactly once. Thus, the Cayley table of a group is an example of a latin square. Another, maybe simpler proof: the cancellation property implies that for each x in the group, the one variable function of y f(x,y)= xy must be a one to one map.

Rajbali Pandey (1969), Hindu Saṁskāras: Socio-religious Study of the Hindu Sacraments, , pages 56–58 To answer this question, the medieval era texts of various schools discussed and offered diverse views on whether the ritual is a rite of passage for the baby's anticipation in the womb (garbha), or for the wife (kshetra). A rite of passage of the baby would imply that Garbhadhana sanskara is necessary for each baby and therefore every time the couple intend to have a new baby, while a rite of passage of the wife would imply a one time ritual suffices.

The axioms of associativity and unique solutions in the definition of an n-ary group are stronger than they need to be. Under the assumption of n-ary associativity it suffices to postulate the existence of the solution of equations with the unknown at the start or end of the string, or at one place other than the ends; e.g., in the 6-ary case, xabcde=f and abcdex=f, or an expression like abxcde=f. Then it can be proved that the equation has a unique solution for x in any place in the string.

During summer, on the sunny side the curtains should be closed and the hatches opened (note, though, that the south side is the one without glass). The result is a 'double wall' of glass on the outer side and curtains on the inner side, with an upward draft caused by the Sun's heat. This suffices for ventilation and the two surface ducts (as shown on the drawings) were partly intended for mechanical ventilation (with an exhauster fan), but this has turned out to be unnecessary. During winter, heating is done with a hot water installation (of course fuelled with coal) with natural circulation.

The platforms are of 6-car length only, despite the majority of services throughout the day being formed of 8 cars. The original station building remains on the down (Country-bound) platform 2, with a substantial wooden shelter on the up (London-bound) platform. The ticket office is manned for limited hours during the morning peak period on Mondays to Fridays; at other times a PERTIS 'permit to travel' machine, also located on the down platform, suffices. A passenger information screen is located on the down platform 2 and provides information relating to train running times for both platforms.

Waddington used the term along with canalisation and homeorhesis, which describes a system that returns to a steady trajectory, in contrast to homeostasis, which describes a system which returns to a steady state. Waddington explains development with the metaphor of a ball rolling down a hillside, where the hill's contours channel the ball in a particular direction. In the case of a pathway or creode which is deeply carved in the hillside, external disturbance is unlikely to prevent normal development. He notes that creodes tend to have steeper sides earlier in development, when external disturbance rarely suffices to alter the developmental trajectory.

If U\subseteq A \subseteq X are as above, we say that U can be excised if the inclusion map of the pair (X \setminus U,A \setminus U ) into (X, A) induces an isomorphism on the relative homologies: H_n(X \setminus U,A \setminus U) \cong H_n(X,A) The theorem states that if the closure of U is contained in the interior of A, then U can be excised. Often, subspaces which do not satisfy this containment criterion still can be excised --it suffices to be able to find a deformation retract of the subspaces onto subspaces that do satisfy it.

In the case of English, this is usually restricted to degendered pronouns such as "he/she" or "s/he". Most other Indo- European languages include more far-reaching use of grammatical gender. In these, the separate gendered desinences (grammatical suffices) of the words may be given divided by slashes or set off with parentheses. For example, in Spanish, is a son and a is a daughter; some proponents of gender-neutral language advocate the use of or when writing for a general audience or addressing a listener of unknown gender.. Less commonly, the æ ligature or at sign is used instead: .

Due to limited use of international typewriters and unicode computer encoding, the suffix may be simplified to -ic, historically transcribed with a phonetic ending, -ich or -itch in foreign languages. Other common surname suffixes found among Serbian surnames are - _ov_ , - _ev_ , - _in_ and - _ski_ (without -ić) which is the Slavic possessive case suffix, thus Nikola's son becomes Nikolin, Petar's son Petrov, and Jovan's son Jovanov. Other, less common suffices are -alj/olj/elj, -ija, -ica, -ar/ac/an. The ten most common surnames in Serbia, in order, are Jovanović, Petrović, Nikolić, Marković, Đorđević, Stojanović, Ilić, Stanković, Pavlović and Milošević.

The reduction of a polynomial f by the Gröbner basis G of an ideal I yields 0 if and only if f is in I. This allows to test the membership of an element in an ideal. Another method consists in verifying that the Gröbner basis of G∪{f} is equal to G. To test if the ideal I generated by f1, ...,fk is contained in the ideal J, it suffices to test that every fi is in J. One may also test the equality of the reduced Gröbner bases of J and J∪{f1, ...,fk}.

Wi-Fi access points are not required by law to identify (they are unlicensed transmitters) but the Wi-Fi standards include provision for an identifier called an SSID, which is transmitted as a routine part of Wi-Fi network traffic. However, since a number of standard Wi-Fi channels are shared with the amateur radio spectrum, amateur radio-operated High Speed Multimedia (HSMM), or "hinternet", access points usually use the call sign of the control operator as the SSID, this suffices as proper station identification for the access point being operated as an amateur radio transceiver.

In a given region it is sometimes arranged that all television transmitters are located in roughly the same direction and use frequencies spaced closely enough that a single antenna suffices for all. A single transmitter location may transmit signals for several channels. CABD (communal antenna broadcast distribution) is a system installed inside a building to receive free-to-air TV/FM signals transmitted via radio frequencies and distribute them to the audience. Analog television signals are susceptible to ghosting in the image, multiple closely spaced images giving the impression of blurred and repeated images of edges in the picture.

Galiani not only has theoretical brilliance with his idea of “natural” laws in economics, but also was a practical man, skeptical about the reach of abstract theory, particularly when action was necessary and urgent. He was repelled by the wide-eyed policies called for by the physiocrats, which he believed were, unrealistic, impractical and, in times of crisis, downright dangerous. Galiani disagreed the physiocratic argument which is said that in order to provide a sufficient supply of grain, it suffices to establish a completely free trade. In fact, the foreign trade agreed with the physiocrats that internal free trade can benefit the economy.

For example, consider the problem of finding all circles in the Euclidean plane up to congruence. Any circle can be described uniquely by giving three points, but many different sets of three points give the same circle: the correspondence is many-to-one. However, circles are uniquely parameterized by giving their center and radius: this is two real parameters and one positive real parameter. Since we are only interested in circles "up to congruence", we identify circles having different centers but the same radius, and so the radius alone suffices to parameterize the set of interest.

The next target application was transferring video streams through an external cable connection between a desktop computer and display, or a DVD player and a TV. NSC introduced higher performance follow-ons to FPD-Link called the LVDS Display Interface (LDI) and OpenLDI standards. These standards allow a maximum pixel clock of 112 MHz, which suffices for a display resolution of 1400 × 1050 (SXGA+) at 60 Hz refresh. A dual link can boost the maximum display resolution to 2048 × 1536 (QXGA) at 60 Hz. FPD-Link works with cable lengths up to about 5m, and LDI extends this to about 10m.

In the field of topology, a Fréchet–Urysohn space is a topological space with the property that for every subset the closure of in is identical to the sequential closure of in . Fréchet–Urysohn spaces are a special type of sequential space. Fréchet–Urysohn spaces are the most general class of spaces for which sequences suffice to determine all topological properties of subsets of the space. That is, Fréchet–Urysohn spaces are exactly those spaces for which knowledge of which sequences converge to which limits (and which sequences don't) suffices to completely determine the space's topology.

For instance, if one wants a cyclical, weekly schedule, such that each student gets their workshop courses on non-consecutive days, then H would be the complement graph of C7. A graph homomorphism from G to H is then a schedule assigning courses to time slots, as specified. To add a requirement saying that, e.g., no single student has courses on both Friday and Monday, it suffices to remove the corresponding edge from H. A simple frequency allocation problem can be specified as follows: a number of transmitters in a wireless network must choose a frequency channel on which they will transmit data.

Prior to the 20th century, it was a commonly held belief that nature itself was simple and that simpler hypotheses about nature were thus more likely to be true. This notion was deeply rooted in the aesthetic value that simplicity holds for human thought and the justifications presented for it often drew from theology. Thomas Aquinas made this argument in the 13th century, writing, "If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments [if] one suffices."Pegis 1945.

In the second context, it is used after it has been shown that a defendant had copied to determine if what had been copied is legally actionable or amounts to misappropriation. Some courts use "striking" or "probative" instead of "substantial" to describe the level of similarity needed in the first context to avoid confusion. The second meaning, which Justice Jon O. Newman referred to in 1997 as the more proper use, defines "the threshold for determining that the degree of similarity suffices to demonstrate actionable infringement" exists, "after the fact of copying has been established." Ringgold v.

Limans are structures with small dams which catch runoff from a wadi to hold about 400-600mm of water, which suffices for the growth of drought-hardy tree species. Limans can be built wherever tributary wadis [...] widen or come onto a large plain with potential arable land [...]. A check-dam [...] is built to retain runoff waters [...]. A spillway regulates the level of the water [...] to prevent the destruction of the check-dam.. The embankment height should be 3-4 times the designed water depth, and the outlet should be to the side of the main flow to prevent direct through flow.

The first problem is reducible to the second one, by taking the intersection of the output gate and n. Indeed, the new output get will be empty if and only if n was not an element of the former output gate. The first problem is reducible to the third one, by asking if the node n is a subset of the output node. The second problem is reducible to the first one, it suffices to multiply the output gate by 0, then 0 will be in the output gate if and only if the former output gate were not empty.

Rajbali Pandey (1969), Hindu Saṁskāras: Socio-religious Study of the Hindu Sacraments, , pages 56–58 To answer this question, the medieval era texts of various schools discussed and offered diverse views on whether the ritual is a rite of passage for the baby's anticipation in the womb (garbha), or for the wife (kshetra). A rite of passage of the baby would imply that Garbhadhana sanskara is necessary for each baby and therefore every time the couple intend to have a new baby, while a rite of passage of the wife would imply a one time ritual suffices.

Wiring diagram of a single transformer hybridFor use in 2-wire repeaters, the single transformer version suffices, since amplifiers in the repeaters have grounded inputs and outputs. X, Y, and Z share a common ground. As shown at left, signal into W, the 2-wire port, will appear at X and Z. But since Y is bridged from center of coil to center of X and Z, no signal appears. Signal into X will appear at W and Y. But signal at Z is the difference of what appears at Y and, through the transformer coil, at W, which is zero.

Because populist tradition ascertains the paramountcy of the "people" (instead of class) as a political subject,Carlos De La Torre, Populist Seduction in Latin America, 2nd. Edition. Ohio University, 2010, , p. xii it suffices to say that, in the 21st century, the large numbers of voters living in extreme poverty in Latin America has remained a bastion of support for new populist candidates. By early 2008 governments with varying forms of populism and with some form of left leaning (albeit vague) social democratic or democratic socialist platform had come to dominate virtually all Latin American nations with the exceptions of Colombia, El Salvador and Mexico.

Shelton was the site of one of the largest arson fires in the United States history. It happened in 1975 when the Sponge Rubber Products plant (formerly owned by B.F. Goodrich) was set on fire. Charles Moeller, president of parent company Grand Sheet Metal Products, was acquitted of criminal charges, but in a suit under civil law (where preponderance of evidence suffices to establish a factual claim), a jury found in 1988 the insurer was entitled to disallow claims on the fire losses, based on the finding that the company's top officials arranged the fire to claim insurance money. Eight others were convicted or pleaded guilty.

That the theory of simple types suffices for avoiding also the epistemological paradoxes is shown by a closer analysis of these. (Cf. Ramsey 1926 and Tarski 1935, p. 399).".Gödel 1944:126 footnote 17: "Russell's mathematical logic" appearing in Kurt Gödel: Collected Works: Volume II Publications 1938–1974, Oxford University Press, New York NY, (v.2.pbk). He concluded the (1) theory of simple types and (2) axiomatic set theory, "permit the derivation of modern mathematics and at the same time avoid all known paradoxes" (Gödel 1944:126); furthermore, the theory of simple types "is the system of the first Principia [Principia Mathematica] in an appropriate interpretation. . . .

"Transactions of the Greenwich Antiquarian Society Vols 1-2 p. 153 (1907) Charles North, London "In cases of death by violence, and in Somersetshire amongst other counties, also in cases of death by misadventure, it was further the duty of the coroner, as the King's officer, not to lose an opportunity of recovering the murdrum, or murder fine which the district could only escape by a proper presentment of Englishry. This was a fruitful source of revenue. How common these fines were in the rough days of the 13th century a glance through the pleas of the crown in the assize rolls suffices to show.

Using a fountain code, it suffices for a receiver to retrieve any subset of encoding symbols of size slightly larger than the set of source symbols. (In practice, the broadcast is typically scheduled for a fixed period of time by an operator based on characteristics of the network and receivers and desired delivery reliability, and thus the fountain code is used at a code rate that is determined dynamically at the time when the file is scheduled to be broadcast.) Another application is that of hybrid ARQ in reliable multicast scenarios: parity information that is requested by a receiver can potentially be useful for all receivers in the multicast group.

Politically, the neolatin Dalmatian city-states were often isolated and compelled to either fall back on the Venetian Republic for support, or tried to make it on their own. The geographical position of the Dalmatian city states suffices to explain the relatively small influence exercised by Byzantine culture throughout the six centuries (535-1102) during which Dalmatia was part of the Eastern empire. Towards the close of this period Byzantine rule tended more and more to become merely nominal, while the influence of the Republic of Venice increased. The medieval Dalmatia had still included much of the hinterland covered by the old Roman province of Dalmatia.

The omission stems from a past failure to relate the work of two groups of artists working on opposite sides of Atlantic without contact or influence upon each other yet both equally free of formulated systems or of constitutes "Schools" And the evidence postulated is to bring together "fourteen painters" each offering different yet complementary spatial concepts. Though limited the range exhibited suffices to evoke a contemporary break both with the geometric language of Minimal Art and with optical art. Space is no longer coherence but coexistence of heterogeneities. A coexistence expressed as clearly in the entire range or canvasses presented, as in individual works.

Suppose we are given a PostBQP family of circuits to decide a language L. We assume without loss of generality (e.g. see the inessential properties of quantum computers) that all gates have transition matrices that are represented with real numbers, at the expense of adding one more qubit. Let denote the final quantum state of the circuit before the postselecting measurement is made. The overall goal of the proof is to construct a PP algorithm to decide L. More specifically it suffices to have L correctly compare the squared amplitude of in the states with to the squared amplitude of in the states with to determine which is bigger.

Sepu (Sociedad Española de Precios Únicos), Spain's first department store, was founded in Barcelona on 9 January 1934 by Swiss citizens of Jewish origin, Henry Reisembach and Edouard Wormsde, who also opened a second store in Madrid. In the 1930s they were the subject of a vigorous campaign on the part of the Falange. Arriba directly accused the company of exploiting its employees while taking advantage of links to political power: > These Jews of SEPU provide grounds to deal with them daily, by their > relations with the employees they exploit. If their mere presence suffices > to produce indignation, if the outrages committed by their staff suffice to > rouse the most tranquil.

In algebraic geometry, a morphism of schemes :f: X -> Y is called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective. (EGA I, (3.5.4)) This is a generalization of the notion of a purely inseparable extension of fields (sometimes called a radicial extension, which should not be confused with a radical extension.) It suffices to check this for K algebraically closed. This is equivalent to the following condition: f is injective on the topological spaces and for every point x in X, the extension of the residue fields :k(f(x)) ⊂ k(x) is radicial, i.e.

The rightmost operand in a valid prefix expression thus empties the stack, except for the result of evaluating the whole expression. When starting at the right, the pushing of tokens is performed similarly, just the evaluation is triggered by an operator, finding the appropriate number of operands that fits its arity already at the stacktop. Now the leftmost token of a valid prefix expression must be an operator, fitting to the number of operands in the stack, which again yields the result. As can be seen from the description, a push-down store with no capability of arbitrary stack inspection suffices to implement this parsing.

For a nondeterministic finite automaton A with n states and an m letter alphabet, it is decidable in time O(n2m) whether A is unambiguous. It suffices to use a fixpoint algorithm to compute the set of pairs of states q and q' such that there exists a word w which leads both to q and to q' . The automaton is unambiguous if and only if there is no such a pair such that both states are accepting. There are at most O(n2) state pairs, and for each pair there are m letters to consider to resume the fixpoint algorithm, hence the computation time.

In other words, a backjump indicates that the visit of a region of the search tree had been a mistake. This part of the search tree can therefore be ignored when considering a possible backjump from x_l or from one of its ancestors. Variables whose values are sufficient to prove unsatisfiability in the subtree rooted at a node are collected in the node and sent (after removing the variable of the node) to the node above when retracting. This fact can be exploited by collecting, in each node, a set of previously assigned variables whose evaluation suffices to prove that no solution exists in the subtree rooted at the node.

She mentions also Greek manuscripts with the tetragrammaton in square Aramaic script, the paleo-Hebrew abbreviation 𐤉𐤉‬‬, κύριος, θεός, and concludes that "it suffices to say that in old Hebrew and Greek witnesses, God has many names [...] Finally, before Kurios became a standard rendering Adonai, the Name of God was rendered with Theos." In view of the conflicting opinions of scholars, the question of how the Septuagint originally represented the Tetragrammaton (יהוה? ιαω? or κύριος?) is of doubtful relevance in relation to what was in the copies in use in the second half of the first century CE, when the New Testament texts were first composed.

The statement in terms of remainders given in cannot be generalized to any principal ideal domain, but its generalization to Euclidean domains is straightforward. The univariate polynomials over a field is the typical example of a Euclidean domain, which is not the integers. Therefore, we state the theorem for the case of a ring of univariate domain R=K[X] over a field K. For getting the theorem for a general Euclidean domain, it suffices to replace the degree by the Euclidean function of the Euclidean domain. The Chinese remainder theorem for polynomials is thus: Let P_i(X) (the moduli) be, for , pairwise coprime polynomials in R=K[X].

Some properties of the GCD are in fact easier to see with this description, for instance the fact that any common divisor of a and b also divides the GCD (it divides both terms of ua + vb). The equivalence of this GCD definition with the other definitions is described below. The GCD of three or more numbers equals the product of the prime factors common to all the numbers, but it can also be calculated by repeatedly taking the GCDs of pairs of numbers. For example, : Thus, Euclid's algorithm, which computes the GCD of two integers, suffices to calculate the GCD of arbitrarily many integers.

An indirect presidential election was held in French Polynesia on 24 February 2008 following the legislative election held on 27 January and 10 February 2008. It had originally been planned to be held in late February or early March, but was brought forward after an agreement by the three party groups in the Assembly. In the first two rounds, an absolute majority is required to be elected, and in the third round, a relative majority suffices; should two candidates be tied in the third round, the older one is declared elected. Gaston Flosse was reelected with the support of the pro-independence Union for Democracy with 29 to 27 votes.

Even the most powerful flares are barely detectable in the total solar irradiance (the "solar constant"). Solar flares occur in a power-law spectrum of magnitudes; an energy release of typically 1020 joules of energy suffices to produce a clearly observable event, while a major event can emit up to 1025 joules. Flares are closely associated with the ejection of plasmas and particles through the Sun's corona into outer space; flares also copiously emit radio waves. If the ejection is in the direction of the Earth, particles associated with this disturbance can penetrate into the upper atmosphere (the ionosphere) and cause bright auroras, and may even disrupt long range radio communication.

The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interaction and spacetime geometry. It is based upon a nontrivial fixed point of the corresponding renormalization group (RG) flow such that the running coupling constants approach this fixed point in the ultraviolet (UV) limit. This suffices to avoid divergences in physical observables. Moreover, it has predictive power: Generically an arbitrary starting configuration of coupling constants given at some RG scale does not run into the fixed point for increasing scale, but a subset of configurations might have the desired UV properties.

162 U. Pa. L. Rev. 1093 (2014). However, Justice Kennedy declines to define when a board is dominated or what State involvement is needed, writing “It suffices to note that the inquiry regarding active supervision is flexible and context- dependent.” The Dentists Board further argued that denying it antitrust immunity would remove the main incentive for dentists to serve on the board. Justice Kennedy responds by citing the Hippocratic Oath, writing “those who pursue a calling must embrace ethical standards that derive from a duty separate from the dictates of the state.”135 S. Ct. 1101 citing Steven H. Miles, The Hippocratic Oath and the Ethics of Medicine (2004).

RA can express any (and up to logical equivalence, exactly the) first-order logic (FOL) formulas containing no more than three variables. (A given variable can be quantified multiple times and hence quantifiers can be nested arbitrarily deeply by "reusing" variables.) Surprisingly, this fragment of FOL suffices to express Peano arithmetic and almost all axiomatic set theories ever proposed. Hence RA is, in effect, a way of algebraizing nearly all mathematics, while dispensing with FOL and its connectives, quantifiers, turnstiles, and modus ponens. Because RA can express Peano arithmetic and set theory, Gödel's incompleteness theorems apply to it; RA is incomplete, incompletable, and undecidable. (N.

Some shops have cages or rooms dedicated to keeping certain tools or supplies; for instance, a room may be dedicated to only welding supplies, gas tanks, etcetera; or where janitorial supplies or other consumables such as grinding disks are stored. Depending on the size of the operation, management, and controls, these areas may be restricted and locked, or these could be manned by an employee, as by a tool crib attendant; in other instances, the storage rooms or cages are accessible to all personnel. Not all shops have a tool crib or storage room(s) though, and in many cases, a large cabinet suffices.

Higher degree curves are more computationally expensive to evaluate. When more complex shapes are needed, low order Bézier curves are patched together, producing a composite Bézier curve. A composite Bézier curve is commonly referred to as a "path" in vector graphics languages (like PostScript), vector graphics standards (like SVG) and vector graphics programs (like Artline, Timeworks Publisher, Adobe Illustrator, CorelDraw, Inkscape, and Allegro). In order to join Bézier curves into a composite Bézier curve without kinks, a property called G1 continuous, it suffices to force the control point at which two constituent Bézier curves meet to lie on the line defined by the two control points on either side.

In geodetic applications, where is small, the integrals are typically evaluated as a series . For arbitrary , the integrals (3) and (4) can be found by numerical quadrature or by expressing them in terms of elliptic integrals . provides solutions for the direct and inverse problems; these are based on a series expansion carried out to third order in the flattening and provide an accuracy of about for the WGS84 ellipsoid; however the inverse method fails to converge for nearly antipodal points. continues the expansions to sixth order which suffices to provide full double precision accuracy for and improves the solution of the inverse problem so that it converges in all cases.

To take them into account, while still ignoring quantum effects, one should use the Kerr–Newman metric. If we do, we find the angular momentum and charge of the electron are too large for a black hole of the electron's mass: a Kerr- Newman object with such a large angular momentum and charge would instead be 'super-extremal', displaying a naked singularity, meaning a singularity not shielded by an event horizon. To see that this is so, it suffices to consider the electron's charge and neglect its angular momentum. In the Reissner–Nordström metric, which describes electrically charged but non- rotating black holes, there is a quantity , defined by } }} where is the electron's charge and is the vacuum permittivity.

Lord Oliver wrote: Lord Oliver held that to afford copyright protection on a copy of a work, "[t]here must in addition be some element of material alteration or embellishment which suffices to make the totality of the work an original work". He stated that such an alteration or embellishment must be "visually significant", and that it is insufficient simply for the alteration to convey "information". Thus the court held that the modifications that Interlego had made to its designs did not constitute an original work, and thus were not afforded copyright protection. Although they may have involved skill, labour, and judgement, that skill, labour, and judgement lay solely in the process of copying.

In males, the lone X chromosome has only one dystrophin gene. If there's a mutation in that gene, a male's muscles will lack dystrophin and slowly degenerate; mutations in the gene for dystrophin were identified as the cause of DMD by MDA researchers in 1986. A female almost always has two dystrophin genes, one on each X chromosome, and, even if one of these isn't working, the other gene suffices to keep dystrophin levels high enough to preserve muscle function in both the heart and skeletal muscles. Nevertheless, research has shown that a small minority of females having both a working and a non-working dystrophin gene can exhibit symptoms of DMD.

Francisco de Salinas. Francisco de Salinas (1513, Burgos – 1590, Salamanca) was a Spanish music theorist and organist, noted as among the first to describe meantone temperament in mathematically precise terms, and one of the first (along with Guillaume Costeley) to describe, in effect, 19 equal temperament. In his De musica libri septem of 1577 he discusses 1/3-, 1/4- and 2/7-comma meantone tunings. Of 1/3-comma meantone, which is essentially identical to the meantone of 19-et, he remarks that it is "languid" but not "offensive to the ear", and he notes that a keyboard of 19 tones to the octave suffices to give a circulating version of meantone.

More generally, if the action of G on X is ergodic (meaning that X cannot be reduced by invariant proper Borel sets of X) then any system of imprimitivity on X is homogeneous. We now discuss how the structure of homogeneous systems of imprimitivity can be expressed in a form which generalizes the Koopman representation given in the example above. In the following, we assume that μ is a σ-finite measure on a standard Borel G-space X such that the action of G respects the measure class of μ. This condition is weaker than invariance, but it suffices to construct a unitary translation operator similar to the Koopman operator in the example above.

A solution (a, b, c) for a given n leads to a solution for all the factors of n: if h is a factor of n then there is an integer g such that n = gh. Then (ag, bg, cg) is a solution for the exponent h: : (ag)h \+ (bg)h = (cg)h. Therefore, to prove that Fermat's equation has no solutions for n > 2, it suffices to prove that it has no solutions for n = 4 and for all odd primes p. For any such odd exponent p, every positive-integer solution of the equation ap + bp = cp corresponds to a general integer solution to the equation ap + bp + cp = 0\.

Colorado's highest court adopted the Rowland unified duty of care analysis in 1971. The resulting explosion of lawsuits against Colorado landowners caused the state legislature to enact the Colorado Premises Liability Act in 1986, which enacted a cleaned-up statutory version of the common law classifications and simultaneously expressly displaced all common law remedies against landowners in order to prevent state courts from again expanding their liability. In the Republic of Ireland, under the Occupiers' Liability Act, 1995, the duty of care to trespassers, visitors and "recreational users" can be restricted by the occupier; provided reasonable notice is given, for which a prominent notice at the usual entrance to the premises usually suffices.

More generally, game semantics may be applied to predicate logic; the new rules allow a dominant quantifier to be removed by its "owner" (the Verifier for existential quantifiers and the Falsifier for universal quantifiers) and its bound variable replaced at all occurrences by an object of the owner's choosing, drawn from the domain of quantification. Note that a single counterexample falsifies a universally quantified statement, and a single example suffices to verify an existentially quantified one. Assuming the axiom of choice, the game-theoretical semantics for classical first-order logic agree with the usual model-based (Tarskian) semantics. For classical first- order logic the winning strategy for the Verifier essentially consists of finding adequate Skolem functions and witnesses.

For decades, Lowe-Porter's translations of Mann were the only versions that existed in the English-speaking world, aside from Herman George Scheffauer's. Mann expressed his appreciation to Lowe-Porter for her work, nicknaming her "die Lowe", but also added the caveat, "insofar as my linguistic knowledge suffices". Critic Theodore Ziolkowski said of Lowe- Porter's translation of Mann's Buddenbrooks: > Lowe-Porter provided a valuable service by making Mann's novel initially > accessible to the English and American publics. Other commentaries on her translations have included the following: > The Lowe-Porter translations of Thomas Mann, despite occasional inaccuracies > almost inevitable in works of such length and complexity, convey the ironic > and pyrotechnical style of the original with great effectiveness.

This is slow for several reasons: it is inherently O(n) in the length of the strings; it typically requires reads from several regions of memory, which take time; and the reads fill up the processor cache, meaning there is less cache available for other needs. With interned strings, a simple object identity test suffices after the original intern operation; this is typically implemented as a pointer equality test, normally just a single machine instruction with no memory reference at all. String interning also reduces memory usage if there are many instances of the same string value; for instance, it is read from a network or from storage. Such strings may include magic numbers or network protocol information.

4th 714 (1998). Colorado's highest court adopted the Rowland unified duty of care analysis in 1971. The resulting explosion of lawsuits against Colorado landowners caused the state legislature to enact the Colorado Premises Liability Act in 1986, which enacted a cleaned-up statutory version of the common law classifications and simultaneously expressly displaced all common law remedies against landowners in order to prevent state courts from again expanding their liability. In the Republic of Ireland, under the Occupiers' Liability Act, 1995, the duty of care to trespassers, visitors and "recreational users" can be restricted by the occupier; provided reasonable notice is given, for which a prominent notice at the usual entrance to the premises usually suffices.

Turning finally to Bilski's method, the court held it patent-ineligible. First, the court said, Bilski did not argue that the rejected claims recited any specific or "particular" machine, so that the court found it unnecessary to decide any issues relating to the machine-implementation branch of the test. "We leave to future cases the elaboration of the precise contours of machine implementation, as well as the answers to particular questions, such as whether or when recitation of a computer suffices to tie a process claim to a particular machine."However, one of Benson's rejected claims had a computer part (shift register) as a recited element, and the Court dismissed this machine limitation as meaningless from a practical standpoint.

Kazakhstan announces 2012 oil and gas production figures) Kazakhstan's gas production suffices to meet domestic demand of 10.5 billion cubic meters (2012). However, due to limited internal gas pipeline network that does not connect all the production centers (west) with demand centers (south, east, north), the country needs to import gas from Uzbekistan to satisfy the demand in the south of the country and from Russia to satisfy demand in the north and east. In 2012, the country exported 8.8 billion cubic meters of gas to China through the Central Asia – China pipeline. Kazakhstan serves as a major transit country for gas exports from Turkmenistan and Uzbekistan that are destined to Russia and China.

Distinguishing between gamma- rays of slightly different energy is an important consideration in the analysis of complex spectra, and the ability of a GRS to do so is characterized by the instrument's spectral resolution, or the accuracy with which the energy of each photon is measured. Semi-conductor detectors, based on cooled germanium or silicon detecting elements, have been invaluable for such applications. Because the energy level spectrum of nuclei typically dies out above about 10 MeV, gamma-ray instruments looking to still higher energies generally observe only continuum spectra, so that the moderate spectral resolution of scintillation (often sodium iodide (NaI) or caesium iodide, (CsI) spectrometers), often suffices for such applications.

This result is known as Euclid's lemma. Specifically, if a prime number divides L, then it must divide at least one factor of L. Conversely, if a number w is coprime to each of a series of numbers a1, a2, ..., an, then w is also coprime to their product, a1 × a2 × ... × an. Euclid's lemma suffices to prove that every number has a unique factorization into prime numbers. To see this, assume the contrary, that there are two independent factorizations of L into m and n prime factors, respectively : Since each prime p divides L by assumption, it must also divide one of the q factors; since each q is prime as well, it must be that p = q.

The Petitioner sarcastically notes that "The Respondent now takes the position that the State of Hawaii has a compelling interest in engaging in blatant discrimination today – and indefinitely into the future – in order to make up for even-handed treatment of all Hawaiian citizens, regardless of race, in the past" (32). Nor may a compelling interest be inferred from the necessity for the State to uphold its "trust" relationship with the natives, for the Supreme Court "has never held that a legislatively declared 'trust' relationship suffices to justify racial discrimination in voting" (31). Furthermore, the use of Morton v. Mancari to illustrate the nature of that implied "special relationship" has no bearing on Hawaii.

For instance, he said that virtue suffices for happiness, but for the highest grade of happiness bodily and external goods are necessary as well. This eclectic tendency was favoured by the lack of dogmatic works by Plato. Middle Platonism was promoted by the necessity of considering the main theories of the post-Platonic schools of philosophy, such as the Aristotelian logic and the Stoic psychology and ethics (theory of goods and emotions). On the one hand the Middle Platonists were engaged like the later Peripatetics in scholarly activities such as the exposition of Plato's doctrines and the explanation of his dialogues; on the other hand they attempted to develop the Platonic theories systematically.

Under the statutes of various common law jurisdictions, assault is both a crime and a tort. Generally, a person commits criminal assault if he purposely, knowingly, or recklessly inflicts bodily injury upon another; if he negligently inflicts bodily injury upon another by means of dangerous weapon; or if through physical menace, he places another in fear of imminent serious bodily injury.Summary of Model Penal Code § 211.1 (simple assault) A person commits tortious assault when he engages in "any act of such a nature as to excite an apprehension of battery [bodily injury]". In some jurisdictions, there is no requirement that actual physical violence result—simply the "threat of unwanted touching of the victim" suffices to sustain an assault claim.

If the sign choice was consistent then, having returned to the original configuration, one will have the original sign. This is what needs to be checked. The original spacetime is 3-dimensional, call the space M. Now we are considering a circle in configuration space, which is the same thing as a single configuration on the space M\times S^1. To find out the number of times that the sign of the square root vanishes as one goes around the circle, it suffices to count the number of zeroes of the determinant on M\times S^1, because each time that a pair of eigenvalues changes sign there will be a zero.

For this innovation the Vipassana Movement has been criticised, especially in Sri Lanka.Robert H. Sharf, Division of Social and Transcultural Psychiatry, Department of Psychiatry, Faculty of Medicine, McGill University Though both terms appear in the Sutta Pitaka, Gombrich and Brooks argue that the distinction as two separate paths originates in the earliest interpretations of the Sutta Pitaka, not in the suttas themselves. The suttas contain traces of ancient debates between Mahayana and Theravada schools in the interpretation of the teachings and the development of insight. Out of these debates developed the idea that bare insight suffices to reach liberation, by discerning the Three marks (qualities) of (human) existence (tilakkhana), namely dukkha (suffering), anatta (non-self) and anicca (impermanence).

Another application of widest paths arises in the Ford–Fulkerson algorithm for the maximum flow problem. Repeatedly augmenting a flow along a maximum capacity path in the residual network of the flow leads to a small bound, , on the number of augmentations needed to find a maximum flow; here, the edge capacities are assumed to be integers that are at most . However, this analysis does not depend on finding a path that has the exact maximum of capacity; any path whose capacity is within a constant factor of the maximum suffices. Combining this approximation idea with the shortest path augmentation method of the Edmonds–Karp algorithm leads to a maximum flow algorithm with running time .

Hacking, Ian. (1983) "19th-century Cracks in the Concept of Determinism", Journal of the History of Ideas, 44 (3), 455-475 Thereafter, it was known under both names, but the "law of large numbers" is most frequently used. After Bernoulli and Poisson published their efforts, other mathematicians also contributed to refinement of the law, including Chebyshev, Markov, Borel, Cantelli and Kolmogorov and Khinchin. Markov showed that the law can apply to a random variable that does not have a finite variance under some other weaker assumption, and Khinchin showed in 1929 that if the series consists of independent identically distributed random variables, it suffices that the expected value exists for the weak law of large numbers to be true.

It should be stressed that this ontological interpretation was never previously published, although several fluid models have been presented as early as 1890, for the same purpose. The last article by the same author, namely, "Turbulence, electromagnetism, and quantum mechanics: A common perspective" was published in the book Photon: Old problems in light of new ideas (Dvoeglazov 2000). The metafluid dynamics was not created by trial-and- error of mechanical models of aether and is not an analogy that was revived; a juxtaposition of the fields that are involved in earlier models and those that are involved in the metafluid dynamics suffices as a proof. For historical references, see, the comprehensive book by Whittaker (1951).

Presl had invented Czech neologisms for most of the then known chemical elements; ten of these, including vodík - hydrogen, kyslík - oxygen, uhlík - carbon, dusík - nitrogen and křemík - silicon, have entered the language. Presl also created naming conventions for oxides where the electronegative component of the compound became the noun, and the electropositive component became an adjective. The adjectives were associated with a suffix, according to the valence number of the component they represented (originally there were five suffices: -ný, -natý, -itý, -ový, -elý, later expanded to eight by Vojtěch Šafařík: -ný, -natý, -itý, -ičitý, -ičný and -ečný, -ový, -istý, -ičelý, representing oxidation numbers from 1 to 8). For example železnatý corresponds to "ferrous" and železitý to "ferric".

An indirect presidential election was held in Suriname on 19 July 2010 following the legislative election. If the National Assembly of Suriname twice fails to elect a new president with a two-thirds majority, the election will go to the People's Assembly of Suriname, composed of members of parliament, district and provincial councils, where a simple majority suffices. A first vote was expected on 8 July 2010, but only procedural issues were discussed at the meeting; the election was set for 19 July 2010 on the following day. Shortly before the election, former dictator Dési Bouterse succeeded in establishing a coalition with the A Combinatie and the People's Alliance, giving him the votes required for the presidential election.

The lemma ensures that (for a large enough k), it is possible to do the construction while leaving enough strings for the relativized ENP answers. Also, we can ensure that for the relativized ENP, linear time suffices, even for function problems (if given a function oracle and linear output size) and with exponentially small (with linear exponent) error probability. Also, this construction is effective in that given an arbitrary oracle A we can arrange the oracle B to have PA≤PB and EXPNPA=EXPNPB=BPPB. Also, for a ZPP=EXP oracle (and hence ZPP=BPP=EXP

SWAG is used to describe an estimate derived from a combination of factors including past experience, general impressions, and heuristic or approximate calculations rather than an exhaustive search, proof, or rigorous calculation. The SWAG is an educated guess but is not regarded as the best or most accurate estimate. The SWAG is not computed or proven rigorously, but the proponent asserts his or her own judgement suffices to rationalize the estimate; and it may, in time, be viable to produce a rigorous forecast of increased precision. Various other backronyms of SWAG have been published, including "sophisticated wild-ass guess", "Silly Wild-Ass Guess", "Semi-Wild-Ass Guess", "Stupid Wild- Ass Guess", and "Scientific Wildly Aimed Guess".

But then, under π the element originally at position k is moved to the final position rather than to position l, and the element originally at the final position is moved to position l. From there on, the sequence of positions for π again follows the sequence for σ, and all positions will have been visited before getting back to the initial position, as required. As for the equal probability of the permutations, it suffices to observe that the modified algorithm involves (n−1)! distinct possible sequences of random numbers produced, each of which clearly produces a different permutation, and each of which occurs—assuming the random number source is unbiased—with equal probability.

In a metrizable space (or more generally first-countable spaces, or Fréchet–Urysohn space), sequences usually suffices to characterize, or "describe," most topological properties (such as the closures of sets or continuity of functions). But there are many spaces where sequences can _not_ be used to describe even basic topological properties like closure or continuity. This failure of sequences was the motivation for defining notions such as nets and filters, which never fail to characterize topological properties. ;Generalizing sequence convergence Nets directly generalize the notion of a sequence since nets are, by definition, maps from an arbitrary directed set into the space , so that a sequence is just a net whose domain is .

The previously described algorithm can be significantly improved in both speed and correctness by making the observation that it suffices to only shoot rays to every obstacle's vertices. This is because any bends or corners along the boundary of a visibility polygon must be due to some corner (i.e. a vertex) in an obstacle. algorithm naive_better_algorithm(p, S) is V := \emptyset for each obstacle b in S: for each vertex v of b: // shoot a ray from p to v r := distance from p to v \theta := angle of v with respect to p for each obstacle b' in S: r := min(r, distance from p to b') add vertex (\theta, r) to V return V The above algorithm may not be correct.

In this example, we actually need ten distinct clocks because we need to track ten independent events. Another clock s may be used to check how much time an elevator spent at a particular floor. A model of this elevator can then use those clocks to assert whether the elevator's program satisfies properties such as "assuming the elevator is not kept on a floor for more than fifteen seconds, then no one has to wait for the elevator for more than three minutes". In order to check whether this statement holds, it suffices to check that, in every run of the model in which the clock s is always smaller than fifteen seconds, each clock c_i is turned off before it reaches three minutes.

John Steinbeck's short story "The Chrysanthemums" centers around the yellow florets, which are often associated with optimism and lost love. When the protagonist, Elisa, finds her beloved chrysanthemums tossed on the ground, her hobby and womanhood have been ruined; this suffices the themes of lost appreciation and femininity in Steinbeck's work. In 2009, Vanessa Diffenbaugh published a New York Times-bestselling novel centered on floriography, The Language of Flowers, as well as her own flower dictionary. In the poetic anthology Vivere e non vivere (2018) by the Italian writer Sabrina Gatti, Julie, the protagonist, is identified in the Lilium or in the Hydrangea, using the language of flowers, a topic to which the same writer in 2019 dedicates an essay entitled Florigrafia.

Theorem. If γ is a continuous Jordan curve on a Riemann surface X, there is a smooth closed 1-form α of compact support such that for any closed smooth 1-form ω on X. ::It suffices to prove this when γ is a regular closed curve. By the inverse function theorem, there is a tubular neighbourhood of the image of γ, i.e. a smooth diffeomorphism of the annulus into X such that . Using a bump function on the second factor, a non-negative function g with compact support can be constructed such that g is smooth off γ, has support in a small neighbourhood of γ, and in a sufficiently small neighbourhood of γ is equal to 0 for and 1 for .

At high temperatures, equilibrium thermodynamic models appear to be satisfactory for the description of kaolinite dissolution and nucleation, because the thermal energy suffices to overcome the energy barriers involved in the nucleation process. The importance of syntheses at ambient temperature and atmospheric pressure towards the understanding of the mechanism involved in the nucleation of clay minerals lies in overcoming these energy barriers. As indicated by Caillère and Hénin (1960) the processes involved will have to be studied in well- defined experiments, because it is virtually impossible to isolate the factors involved by mere deduction from complex natural physico-chemical systems such as the soil environment. Fripiat and Herbillon (1971), in a review on the formation of kaolinite, raised the fundamental question how a disordered material (i.e.

Naive Set Theory. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday use of set theory concepts in contemporary mathematics.. "The working mathematicians usually thought in terms of a naive set theory (probably one more or less equivalent to ZF) ... a practical requirement [of any new foundational system] could be that this system could be used "naively" by mathematicians not sophisticated in foundational research" (p. 236). Sets are of great importance in mathematics; in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets.

But in Taiwan, 影響 is usually transliterated Yinxiang and the issues of the magazine that appeared in the 1970s featured both and the English words Influence magazine (rather than Impact magazine)on the front cover.Many readers of the journal will remember this. It also suffices to look at old copies held by libraries or the Taipei Film Archive to confirm it. The name Influence magazine is additionally confirmed by the film director Lee Daw- ming, a former editor of Yinxiang. (Check his article entitled “Influence Magazine 《影響》雜誌,” mentioned in: External links. - The English words “Influence Magazine” are highlighted by him, as they form part of the heading of this article written in Mandarin.) - The issue discussed here is of course of minor importance.

The lines PM and KQ are arcs of parallel circles of length (a\cos\varphi)\delta\lambda with\lambda in radian measure. In deriving a point property of the projection at P it suffices to take an infinitesimal element PMQK of the surface: in the limit of Q approaching P such an element tends to an infinitesimally small planar rectangle. Infinitesimal elements on the sphere and a normal cylindrical projection Normal cylindrical projections of the sphere have x=a\lambda and y equal to a function of latitude only. Therefore, the infinitesimal element PMQK on the sphere projects to an infinitesimal element P'M'Q'K' which is an exact rectangle with a base \delta x=a\,\delta\lambda and height \delta y.

In that regard, the Sherman Act does not create a regime of strict liability. #A good faith belief, rather than an absolute certainty, that a price concession is being offered to meet an equally low price offered by a competitor suffices to invoke the defense available under § 2(b) of the Clayton Act. #The ex parte meeting between the trial judge and the jury foreman was improper, and the Court of Appeals would have been justified in reversing the convictions solely because of the risk that the foreman believed the judge was insisting on a dispositive verdict. #The trial judge's charge concerning participation in the conspiracy, although perhaps not completely clear, was sufficient, but his charge on withdrawal from the conspiracy was erroneous.

Structure of alpha-bungarotoxin (blue) in complex with the alpha-9 nAChR subunit (orange), showing interactions with loops I and II. α-neurotoxins antagonistically bind irreversibly to nAChRs of skeletal muscles, thereby blocking the action of ACh at the postsynaptic membrane, inhibiting ion flow and leading to paralysis. nAChRs contain two binding sites for snake venom neurotoxins. The observation that a single molecule of the toxin suffices to inhibit channel opening is in agreement with experimental data on the amount of toxin per receptor. Some computational studies of the mechanism of inhibition using normal mode dynamics suggest that a twist-like motion caused by ACh binding may be responsible for pore opening, and that this motion is inhibited by toxin binding.

Vander Heeren 1912, "Cases in which the sin of scandal occurs (1)" To do a good act or an indifferent act, even knowing that it will inspire others to sin — as when a student studies diligently to do well, knowing it will cause envy — is not scandalous. Again, to ask someone to commit perjury is scandalous, but for a judge to require witnesses to give an oath even when he knows the witness is likely to commit perjury is not scandalous. It does not require that the other person actually commit sin; to be scandalous, it suffices that the act is of a nature to lead someone to sin. Scandal is performed with the intention of inducing someone to sin.

No canonical statute has positively defined what this length of time is, and so its determination is left to the wisdom of canonists. Authors generally hold that for the legalizing of a custom in accordance with or beside the law (juxta or prœter legem) a space of ten years is sufficient; while for a custom contrary (contra) to law many demand a lapse of forty years. The reason given for the necessity of so long a space as forty years is that the community will only slowly persuade itself of the opportuneness of abrogating the old and embracing the new law. The opinion, however, which holds that ten years suffices to establish a custom even contrary to the law may be safely followed.

It has been suggested that a solution of this kind may be out of reach because it is algorithmically impossible in the general case to analyze any arbitrary code to determine if it is malicious, as such an analysis reduces to the halting problem over a linear bounded automaton, which is unsolvable. It is, however, unnecessary to address the general case (that is, to sort all programs into the categories of malicious or non-malicious) under most circumstances in order to eliminate a wide range of malicious behaviors. It suffices to recognize the safety of a limited set of programs (e.g., those that can access or modify only a given subset of machine resources) while rejecting both some safe and all unsafe programs.

To show that Kawasaki's condition necessarily holds for any flat-folded figure, it suffices to observe that, at each fold, the orientation of the paper is reversed. Thus, if the first crease in the flat-folded figure is placed in the plane parallel to the -axis, the next crease must be rotated from it by an angle of , the crease after that by an angle of (because the second angle has the reverse orientation from the first), etc. In order for the paper to meet back up with itself at the final angle, Kawasaki's condition must be met. Showing that the condition is also a sufficient condition is a matter of describing how to fold a given crease pattern so that it folds flat.

A minor of a biased graph Ω = (G, B) is the result of any sequence of taking subgraphs and contracting edge sets. For biased graphs, as for graphs, it suffices to take a subgraph (which may be the whole graph) and then contract an edge set (which may be the empty set). A subgraph of Ω consists of a subgraph H of the underlying graph G, with balanced circle class consisting of those balanced circles that are in H. The deletion of an edge set S, written Ω − S, is the subgraph with all vertices and all edges except those of S. Contraction of Ω is relatively complicated. To contract one edge e, the procedure depends on the kind of edge e is.

Whether the item consumed provides much in terms of nourishment is utterly beside the point. That it tastes yummy going down more than suffices to keep customers coming back.Andrew J. Bacevich, "Tom Clancy, Military Man" The Baffler No. 24 (2014), pp. 157-160 online, quoting p 157. By 1988, Clancy had earned $1.3 million for The Hunt for Red October and had signed a $3 million contract for his next three books. In 1992, he sold North American rights to Without Remorse for $14 million, a record for a single book. By 1997, Penguin Putnam Inc. (part of Pearson Education) reportedly paid Clancy $50 million for world rights to two new books and another $25 million to Red Storm Entertainment for a four-year book/multimedia deal.

Scola was named Bishop of Grosseto on 18 July 1991, and was consecrated by Cardinal Bernardin Gantin (with Bishops Abele Conigli and Adelmo Tacconi serving as co-consecrators) on the following 21 September. As Bishop of Grosseto he promoted a renewal of catechesis in the diocese. Scola chose as his episcopal motto Sufficit gratia tua ("Your grace suffices", 2 Corinthians 12:9). Among Scola's chief pastoral concerns in Grosseto were the education of children and youths, vocations and clergy formation (he reopened the diocesan seminary), new approaches to parish life, the pastoral care of labourers (particularly during the difficult period of the dismantling of mines in Grosseto), culture and the family, and the opening of a diocesan mission in Santa Cruz, Bolivia.

Given a triangle ABC, let TA, TB, and TC be the extouch points in which the A-excircle meets line BC, the B-excircle meets line CA, and C-excircle meets line AB, respectively. The lines ATA, BTB, CTC concur in the Nagel point N of triangle ABC. Another construction of the point TA is to start at A and trace around triangle ABC half its perimeter, and similarly for TB and TC. Because of this construction, the Nagel point is sometimes also called the bisected perimeter point, and the segments ATA, BTB, CTC are called the triangle's splitters There exists an easy construction of the Nagel point. Starting from each vertice of a triangle, it suffices to carry twice the length of the opposite edge.

One layout has a high-level circuit supported by 87mm high pillars which have been created from three of the middle-rise piers firmly stacked together. This height suffices to clear an HO Railroad on a roadbed-type track, as well as any US-1 road circuit running a loaded car transporter. There were also three Plastic Construction Kits: a Mobil Truck Station, a Howard Johnson's Truck Stop, and a P.I.E. Freight Terminal, each molded in several colors to be glued together. These were supplied by Pola, in what was then West Germany and were also sold for a time as part of the Tyco model railroad range, but in plain Tyco 'Brown Box' packaging, sometimes with slightly different colorings or markings or with lights.

The unique solution λ represents the rate of growth of the economy, which equals the interest rate. Proving the existence of a positive growth rate and proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann.For this problem to have a unique solution, it suffices that the nonnegative matrices A and B satisfy an irreducibility condition, generalizing that of the Perron–Frobenius theorem of nonnegative matrices, which considers the (simplified) eigenvalue problem : A - λ I q = 0, where the nonnegative matrix A must be square and where the diagonal matrix I is the identity matrix. Von Neumann's irreducibility condition was called the "whales and wranglers" hypothesis by David Champernowne, who provided a verbal and economic commentary on the English translation of von Neumann's article.

If there is an additional magnitude of value or a loss of value after transformation, then the relation between values (proportional to labor) and prices (proportional to total capital advanced) is incomplete. Various solutions and impossibility theorems have been offered for the transformation, but the debate has not reached any clear resolution. LTV does not deny the role of supply and demand influencing price, since the price of a commodity is something other than its value. In Value, Price and Profit (1865), Karl Marx quotes Adam Smith and sums up: > It suffices to say that if supply and demand equilibrate each other, the > market prices of commodities will correspond with their natural prices, that > is to say, with their values as determined by the respective quantities of > labor required for their production.

The unique solution λ represents the growth factor which is 1 plus the rate of growth of the economy; the rate of growth equals the interest rate.For this problem to have a unique solution, it suffices that the nonnegative matrices A and B satisfy an irreducibility condition, generalizing that of the Perron–Frobenius theorem of nonnegative matrices, which considers the (simplified) eigenvalue problem : A − λ I q = 0, where the nonnegative matrix A must be square and where the diagonal matrix I is the identity matrix. Von Neumann's irreducibility condition was called the "whales and wranglers" hypothesis by D. G. Champernowne, who provided a verbal and economic commentary on the English translation of von Neumann's article. Von Neumann's hypothesis implied that every economic process used a positive amount of every economic good.

In 1972, Christian B. Anfinsen was awarded the Nobel Prize for seminal experiments performed mostly by his postdoctoral fellow, Michael Sela. They showed with artificially unfolded proteins that the primary amino acid sequence suffices to dictate the proper spontaneous refolding of proteins into their functional three-dimensional native structures. Yet, they also observed that proteins can often misfolded and precipitate into large insoluble aggregates. They suggested that in cells, unknown factors could possibly assist protein folding. In 1988, Goloubinoff helped follow up Anfinsen’s finding: a class of highly conserved proteins, many of which belonging to the heat shock proteins and were dubbed “molecular chaperones” by R. John Ellis, could mediate the assembly of protein complexes such as phages and RubisCO, preventing the formation of non-functional, protein aggregates.

Chicago Transit Authority control tower 18 guides elevated Chicago 'L' north and southbound Purple and Brown lines intersecting with east and westbound Pink and Green lines and the looping Orange line above the Wells and Lake street intersection in the loop. In a simple case where two routes with one or two tracks each meet at a junction, a fairly simple layout of tracks suffices to allow trains to transfer from one route to the other. More complicated junctions are needed to permit trains to travel in either direction after joining the new route, for example by providing a triangular track layout. In this latter case, the three points of the triangle may be given different names, for example using points of the compass as well as the name of the overall place.

One of the first was Fujifilm's FinePix S3 Pro digital SLR, which has their proprietary "Super CCD SR sensor" specifically developed to overcome the issue of limited dynamic range, using interstitial low-sensitivity photosites (pixels) to capture highlight details. The CCD is thus able to expose at both low and high sensitivities within one shot by assigning a honeycomb of pixels to different intensities of light. Greater scene contrast can be accommodated by making one or more exposures of the same scene using different exposure settings and then combining those images. It often suffices to make two exposures, one for the shadows, and one for the highlights; the images are then overlapped and blended appropriately, so that the resulting composite represents a wider range of colors and tones.

Clearly mα = mβ when β is a permutation of α, so one usually considers only those mα for which α1 ≥ α2 ≥ … ≥ αn, in other words for which α is a partition of an integer. These monomial symmetric polynomials form a vector space basis: every symmetric polynomial P can be written as a linear combination of the monomial symmetric polynomials. To do this it suffices to separate the different types of monomial occurring in P. In particular if P has integer coefficients, then so will the linear combination. The elementary symmetric polynomials are particular cases of monomial symmetric polynomials: for 0 ≤ k ≤ n one has :e_k(X_1,\ldots,X_n)=m_\alpha(X_1,\ldots,X_n) where α is the partition of k into k parts 1 (followed by n − k zeros).

For example, `length/2` can be used to determine the length of a list (`length(List, L)`, given a list `List`) as well as to generate a list skeleton of a given length (`length(X, 5)`), and also to generate both list skeletons and their lengths together (`length(X, L)`). Similarly, `append/3` can be used both to append two lists (`append(ListA, ListB, X)` given lists `ListA` and `ListB`) as well as to split a given list into parts (`append(X, Y, List)`, given a list `List`). For this reason, a comparatively small set of library predicates suffices for many Prolog programs. As a general purpose language, Prolog also provides various built-in predicates to perform routine activities like input/output, using graphics and otherwise communicating with the operating system.

Rothenberg defined propriety in a very general context; however for nearly all purposes it suffices to consider what in musical contexts is often called a periodic scale, though in fact these correspond to what mathematicians call a quasiperiodic function. These are scales which repeat at a certain fixed interval higher each note in a certain finite set of notes. The fixed interval is typically an octave, and so the scale consists of all notes belonging to a finite number of pitch classes. If βi denotes a scale element for each integer i, then βi+℘ = βi + Ω, where Ω is typically an octave of 1200 cents, though it could be any fixed amount of cents; and ℘ is the number of scale elements in the Ω period, which is sometimes termed the size of the scale.

In the courts, the United States Court of Appeals for the First Circuit, in Doe v. Bush, said: "[T]he text of the October Resolution itself spells out justifications for a war and frames itself as an 'authorization' of such a war." in effect saying an authorization suffices for declaration and what some may view as a formal Congressional "Declaration of War" was not required by the Constitution. The last time the United States formally declared war, using specific terminology, on any nation was in 1942, when war was declared against Axis-allied Hungary, Bulgaria, and Romania, because President Franklin Roosevelt thought it was improper to engage in hostilities against a country without a formal declaration of war. Since then, every American president has used military force without a declaration of war.

This is described in the Journal of Asian Studies by Ichito Ishida and Delmer M. Brown, "The southeast corner of the first floor has openings in the walls, since a pond is located on that corner of the building, beyond which the moon rises between the peaks of Higashiyama. And since a lake extending northeastward reflected light that suffices even for reading, the room on the northeast corner has been planned as a library. Therefore the natural objects do not merely surround the building, twisting it out of shape but supply intrinsic motivation for the structural design." The sand garden of Ginkaku-ji has become particularly well known; and the carefully formed pile of sand which is said to symbolize Mount Fuji is an essential element in the garden.

Newton was concerned to address the problem of how it is that we can experimentally determine the true motions of bodies in light of the fact that absolute space is not something that can be perceived. Such determination, he says, can be accomplished by observing the causes of motion (that is, forces) and not simply the apparent motions of bodies relative to one another (as in the bucket argument). As an example where causes can be observed, if two globes, floating in space, are connected by a cord, measuring the amount of tension in the cord, with no other clues to assess the situation, alone suffices to indicate how fast the two objects are revolving around the common center of mass. (This experiment involves observation of a force, the tension).

The worshipper bows at four points in the Amidah: at the beginning and end of two blessings, Avot and Hoda'ah. It is the custom of the Ashkenazim that one bends the knees when saying "Blessed," then bows at "are You," and straightens while saying "O Lord." (At the beginning of Hoda'ah, one instead bows while saying the opening words "We are grateful to You" without bending the knees.) The reason for this procedure is that the Hebrew word for "blessed" (baruch) is related to "knee" (berech); while the verse in Psalms states, "The Lord straightens the bent."Psalms 146, Mishnah Berurah 113 At each of these bows, one must bend over until the vertebrae protrude from one's back; one physically unable to do so suffices by nodding the head.

Their isolation lemma chooses a random number of random hyperplanes, and has the property that, with non-negligible probability, the intersection of any fixed non-empty solution space with the chosen hyperplanes contains exactly one element. This suffices to show the Valiant–Vazirani theorem: there exists a randomized polynomial-time reduction from the satisfiability problem for Boolean formulas to the problem of detecting whether a Boolean formula has a unique solution. introduced an isolation lemma of a slightly different kind: Here every coordinate of the solution space gets assigned a random weight in a certain range of integers, and the property is that, with non-negligible probability, there is exactly one element in the solution space that has minimum weight. This can be used to obtain a randomized parallel algorithm for the maximum matching problem.

That is, if a graph is formed as the union of -cliques that intersect pairwise in at most one vertex, then can be -colored.. In the framework of edge coloring simple hypergraphs, defines a number from a simple hypergraph as the number of hypergraph vertices that belong to a hyperedge of three or more vertices. He shows that, for any fixed value of , a finite calculation suffices to verify that the conjecture is true for all simple hypergraphs with that value of . Based on this idea, he shows that the conjecture is indeed true for all simple hypergraphs with . In the formulation of coloring graphs formed by unions of cliques, Hindman's result shows that the conjecture is true whenever at most ten of the cliques contain a vertex that belongs to three or more cliques.

The contents of the Mishnah's twelve chapters may be summarized as follows: # When, and by whom, an animal must be killed to be ritually fit for food; the instrument with which the killing must be done; the space within which the incision must be made, and the exceeding of which renders the animal "terefah." Incidentally, it discusses the differences between shechitah and melikah (pinching off the heads of birds brought as sacrifices; see , ), and the various degrees in which different vessels are susceptible to impurity. # The organs that must be severed: in quadrupeds, the trachea and the gullet, or the greater part of each, must be cut through; in fowls, cutting through one of these organs, or the greater part of one, suffices. In both cases the jugular vein must be severed.

These problems already trivially lie in co-NP. This was the first strong evidence that these problems are not NP-complete, since if they were, it would imply that NP is subset of co-NP, a result widely believed to be false; in fact, this was the first demonstration of a problem in NP intersect co-NP not known, at the time, to be in P. Producing certificates for the complement problem, to establish that a number is composite, is straightforward: it suffices to give a nontrivial divisor. Standard probabilistic primality tests such as the Baillie–PSW primality test, the Fermat primality test, and the Miller–Rabin primality test also produce compositeness certificates in the event where the input is composite, but do not produce certificates for prime inputs.

The problem was famously voiced in 1936 by Louis de La Vallee Poussin, in his text Musila et Narada: Le Chemin de Nirvana. Schmithausen notes that the mention of the four noble truths as constituting the core of "liberating insight", which is attained after mastering the Rupa Jhanas, is a later addition to texts such as Majjhima Nikaya 36. Schmithausen discerns three possible roads to liberation as described in the suttas, to which Vetter adds the sole practice of dhyana itself, which he sees as the original "liberating practice": # The four Rupa Jhanas themselves constituted the core liberating practice of early buddhism, c.q. the Buddha; # Mastering the four Rupa Jhanas, whereafter "liberating insight" is attained; # Mastering the four Rupa Jhanas and the four Arupa Jhanas, where-after "liberating insight" is attained; # Liberating insight itself suffices.

Both dry instant mixes and liquid concentrates can be replicated at home. A liquid concentrate can be made by brewing an unusually concentrated pot of highly spiced tea, so that the dilution of a small amount into a cup of hot water or a glass of cold milk results in roughly the same concentration of tea as in a normally proportioned brew; e.g., to make a syrup from which one ounce suffices to make one eight- ounce cup of normal chai when diluted, brew tea (and the proportional quantity of spices) at eight times normal concentration. Similarly, unsweetened iced- tea powder can be tailored to individual taste with powdered spices, sugar, and (if desired for convenience and texture) dry nonfat milk and dry non-dairy creamer; the result can be mixed with hot water to produce a form of instant chai masala.

An elliptic curve may be defined as any curve of genus one with a rational point: a common model is a nonsingular cubic curve, which suffices to model any genus one curve. In this model the distinguished point is commonly taken to be an inflection point at infinity; this amounts to requiring that the curve can be written in Tate- Weierstrass form, which in its projective version is :y^2z + a_1 xyz + a_3 yz^2 = x^3 + a_2 x^2z + a_4 xz^2 + a_6 z^3. If the characteristic of the field is different from 2 and 3, then a linear change of coordinates allows putting a_1=a_2=a_3=0, which gives the classical Weierstrass form :y^2 = x^3 + p x + q. Elliptic curves carry the structure of an abelian group with the distinguished point as the identity of the group law.

However, if the resulting integer value is too large to fit in a single byte, the actual numerical value assigned is implementation-defined. Most platforms have 8-bit types, which limits a useful hex escape sequence to two hex digits. However, hex escape sequences longer than two hex digits might be useful inside a wide character or wide string literal(prefixed with L): char s1[] = "\x12"; // single char with value 0x12 (18 in decimal) char s1[] = "\x1234"; // single char with implementation-defined value, unless char is long enough wchar_t s2[] = L"\x1234"; // single wchar_t with value 0x1234, provided wchar_t is long enough (16 bits suffices) An octal escape sequence consists of followed by one, two, or three octal digits. The octal escape sequence ends when it either contains three octal digits already, or the next character is not an octal digit.

Moreover, any reasonable choice for the adjacent transpositions will work: it suffices to choose at each step a transposition of i and where i is a descent of the permutation as modified so far (so that the transposition will remove this particular descent, although it might create other descents). This is so because applying such a transposition reduces the number of inversions by 1; as long as this number is not zero, the permutation is not the identity, so it has at least one descent. Bubble sort and insertion sort can be interpreted as particular instances of this procedure to put a sequence into order. Incidentally this procedure proves that any permutation σ can be written as a product of adjacent transpositions; for this one may simply reverse any sequence of such transpositions that transforms σ into the identity.

After examining the continuing historical regression of the geographical environment where Basque was spoken, the linguist Wilhem von Humboldt predicted in 1809 that this language might disappear in less than a century from the list of living languages. The social, economic, political and cultural processes set in motion by industrialisation and liberalism during the 19th century led to an even greater decline in Basque. As a fact, it suffices to say that Basque remained on the margin of the school, where even its use became forbidden. Among the initiatives that emerged in the 20th century to deal with the risk of the disappearance of Basque are the creation of the Society of Basque Studies and the Royal Academy of the Basque Language (Euskaltzaindia) in 1919 and the creation of Ikastolas (schools in Basque), initially in the 1930s and later in the 1960s.

The invasion exponent S_r(m) is defined as the expected growth rate of an initially rare mutant in the environment set by the resident (r), which means the frequency of each phenotype (trait value) whenever this suffices to infer all other aspects of the equilibrium environment, such as the demographic composition and the availability of resources. For each r, the invasion exponent can be thought of as the fitness landscape experienced by an initially rare mutant. The landscape changes with each successful invasion, as is the case in evolutionary game theory, but in contrast with the classical view of evolution as an optimisation process towards ever higher fitness. We will always assume that the resident is at its demographic attractor, and as a consequence S_r(r) = 0 for all r, as otherwise the population would grow indefinitely.

Nor was there a sufficient awareness of the concept of gauge symmetry to understand that Riemannian geometries do not possess the requisite structure to embody a locally gauged Lorentz symmetry, such as would be required to be able to express continuity equations and conservation laws for rotational and boost symmetries, or to describe spinors in curved spacetime geometries. The result of adding this infrastructure is a Riemann–Cartan geometry. In particular, to be able to describe spinors requires the inclusion of a spin structure, which suffices to produce such a geometry. The chief difference between a Riemann–Cartan geometry and Riemannian geometry is that in the former, the affine connection is independent of the metric, while in the latter it is derived from the metric as the Levi-Civita connection, the difference between the two being referred to as the contorsion.

Let the coefficient of this term be , then is either zero or a symmetric polynomial with a strictly smaller leading monomial. Writing this difference inductively as a polynomial in the elementary symmetric polynomials, and adding back to it, one obtains the sought for polynomial expression for . The fact that this expression is unique, or equivalently that all the products (monomials) of elementary symmetric polynomials are linearly independent, is also easily proved. The lemma shows that all these products have different leading monomials, and this suffices: if a nontrivial linear combination of the were zero, one focuses on the contribution in the linear combination with nonzero coefficient and with (as polynomial in the variables ) the largest leading monomial; the leading term of this contribution cannot be cancelled by any other contribution of the linear combination, which gives a contradiction.

To summarize this Federal Court finding it suffices to say that because of the serious interests at stake to the accused, full unfettered access to the Military Police report was essential in order to assist him point out inconsistencies or credibility issues in his accusers. Personnel subject to either administrative (release or C&P;) or disciplinary action are therefore entitled to an unedited version of any evidence used against them. Since Testing for Cause mandates that an accused be provided with a summary of the reasonable grounds, it may well be the case that they are entitled to a copy of an MP report into their alleged drug use prior to the seizure of urine. DND and the CF have made no policy changes to reflect this new requirement; it is entirely possible that the old practice of filtering such information persists.

In contrast to earlier, largely failed attempts to establish mini computers as a new class of mainstream personal computing devices built around comparatively expensive platforms requiring proprietary software applications or imposing severe usability limitations, the recent success of netbooks can also be attributed to the fact that PC technology has now matured enough to allow truly cost optimized implementations with enough performance to suit the needs of a majority of PC users. This is illustrated by the fact that typical system performance of a netbook is on the level of a mainstream PC in 2001, at around one quarter of the cost. While this performance level suffices for most of the user needs, it caused an increased interest in resource-efficient applications such as Google's Chrome, and forced Microsoft to extend availability of Windows XP to secure market share.

Algebraic-group factorisation algorithms are algorithms for factoring an integer N by working in an algebraic group defined modulo N whose group structure is the direct sum of the 'reduced groups' obtained by performing the equations defining the group arithmetic modulo the unknown prime factors p1, p2, ... By the Chinese remainder theorem, arithmetic modulo N corresponds to arithmetic in all the reduced groups simultaneously. The aim is to find an element which is not the identity of the group modulo N, but is the identity modulo one of the factors, so a method for recognising such one-sided identities is required. In general, one finds them by performing operations that move elements around and leave the identities in the reduced groups unchanged. Once the algorithm finds a one-sided identity all future terms will also be one-sided identities, so checking periodically suffices.

267-268 To put this improvement in perspective, it suffices to look at the situation of the machine guns. A Romanian battalion of 1917 had 8 machine guns. In 1916, Romania had 10 divisions with 30 machine guns each, and 13 divisions with 15 machine guns each.Michael B. Barrett, Indiana University Press, 2013, Prelude to Blitzkrieg: The 1916 Austro-German Campaign in Romania, p. 17 In other words, a Romanian battalion of 1917 had over half the number of machine guns of a Romanian division of 1916. The Romanian Army Chief of Staff since the end of 1916 had been General Constantin Prezan.Spencer C. Tucker, ABC-CLIO, Oct 28, 2014, World War I: The Definitive Encyclopedia and Document Collection [5 volumes]: The Definitive Encyclopedia and Document Collection, p. 1270 Prezan was widely regarded as more of a courtier than a serious army officer.

To show that the tree contains every primitive Pythagorean triple, but no more than once, it suffices to show that for any such triple there is exactly one path back through the tree to the starting node (3, 4, 5). This can be seen by applying in turn each of the unimodular inverse matrices A−1, B−1, and C−1 to an arbitrary primitive Pythagorean triple (d, e, f), noting that by the above reasoning primitivity and the Pythagorean property are retained, and noting that for any triple larger than (3, 4, 5) exactly one of the inverse transition matrices yields a new triple with all positive entries (and a smaller hypotenuse). By induction, this new valid triple itself leads to exactly one smaller valid triple, and so forth. By the finiteness of the number of smaller and smaller potential hypotenuses, eventually (3, 4, 5) is reached.

In Agip (Africa) Ltd v Jackson[1992] 4 All ER 385 and Twinsectra v Yardley, Lord Millett remarked that it is not necessary that the dishonest assistant should be aware of the identity of the victim or nature of the breach and knowledge that the money is not at the free disposal of the assisted person suffices to impose liability. Similarly, in Barlow Clowes, Lord Hoffmann said it is unnecessary for the dishonest assistant to know of the existence of breach or the facts; it is enough if he /she knows or suspects he is assisting in misappropriation of money without knowing money is held on trust. What level of suspicion suffice to trigger the liability continues to trouble the courts. In Abou-Rahmah, Arden LJ opined that the dishonest assistant is not dishonest if he only has general suspicions about impropriety as opposed to particular suspicions regarding specific transactions.

Gödel's incompleteness theorems show that Hilbert's program cannot be realized: if a consistent recursively enumerable theory is strong enough to formalize its own metamathematics (whether something is a proof or not), i.e. strong enough to model a weak fragment of arithmetic (Robinson arithmetic suffices), then the theory cannot prove its own consistency. There are some technical caveats as to what requirements the formal statement representing the metamathematical statement "The theory is consistent" needs to satisfy, but the outcome is that if a (sufficiently strong) theory can prove its own consistency then either there is no computable way of identifying whether a statement is even an axiom of the theory or not, or else the theory itself is inconsistent (in which case it can prove anything, including false statements such as its own consistency). Given this, instead of outright consistency, one usually considers relative consistency: Let S and T be formal theories.

On Corsica, some sites of that culture were continuously occupied until the Iron Age. Jubainville's list of those toponyms in Corsica include, north of the Tavignano River: Venzolasca, Grillasca village in Olmeto, Feciasco and Prucinasca in Barbaggio, Martinasche in Nonza, Cipronasco in Sisco, Palasca, the Ruisseau de Bartasca in Calvi, Popolasca, the hamlet of Caposciasca in Pianello, Baraniasche in Castello-di-Rostino, Velflasca in Zalana. South of the Tavignano: Mount Ecilasca near Pietroso, Mount Filasca near Corrano, hamlet of Solasca in Peri, Fiummasca in Rosazia, Acellasca in Pietrosella, Moraschi in Bocognano, Bodiciasche in Cauro. The -asco suffices are not present in Sartène but Jubainville points to another set in use there: -inco, -inca, as in the Golfe de Valinco, Stavolinca peak, and in Bastia: the Bevinco river, as well as Mount Revinco; Corte: le Ruisseau de Saninco; Ajaccio: the hamlet of Capinca in Carbuccia.

In computational complexity theory, Yao's principle (also called Yao's minimax principle or Yao's lemma) states that the expected cost of a randomized algorithm on the worst-case input is no better than the expected cost for a worst-case probability distribution on the inputs of the deterministic algorithm that performs best against that distribution. Thus, to establish a lower bound on the performance of randomized algorithms, it suffices to find an appropriate distribution of difficult inputs, and to prove that no deterministic algorithm can perform well against that distribution. This principle is named after Andrew Yao, who first proposed it. Yao's principle may be interpreted in game theoretic terms, via a two-player zero-sum game in which one player, Alice, selects a deterministic algorithm, the other player, Bob, selects an input, and the payoff is the cost of the selected algorithm on the selected input.

The task of whoever wants to draw a true, deeply sincere portrait of a disappeared man is made difficult. In doubt, it suffices to allow one's heart to speak and to simply say what one knows; age and experience having taught us to judge the expression of our feelings. Those who have not heard him can not imagine the male sonority combined with a nobility of style of a rare dignity he had. His charm without concession to facility, his astounding technique, always ready and always at ease, his sovereign authority in the playing style as well in the attitude, as far from the morgue as the false modesty; in short, these qualities so diverse, united in such right proportions, made him an inevitable choice among all the virtuosos of all countries for the ensembles of Enesco, Kreisler, Cortot, Thibaud, Casals, Francescatti, or Saint-Saens, Debussy, d'Indy and so many others.

To see that the theorem is true, it suffices to notice that if there were no such number n_0, one could algorithmically test membership of a number n in this non-computable set by simultaneously running the algorithm A to see whether n is output while also checking all possible k-tuples of natural numbers seeking a solution of the equation :p(n,x_1,\ldots,x_k)=0. We may associate an algorithm A with any of the usual formal systems such as Peano arithmetic or ZFC by letting it systematically generate consequences of the axioms and then output a number n whenever a sentence of the form : eg \exists x_1,\ldots , x_k [p(n,x_1,\ldots,x_k)=0] is generated. Then the theorem tells us that either a false statement of this form is proved or a true one remains unproved in the system in question.

In order for this to create problems for the defender of transitivity, it need not be the case that, as Kant thought, the intrinsic moral worth of actions is more important than their consequences—it suffices that, when agents act rightly rather than wrongly, this fact has some intrinsic value, however small. Temkin shows that if we grant even this much, then it is very difficult to maintain the transitivity of the value of outcomes, since the intransitivity among our obligations to choose will infect the outcomes we are choosing among. What these arguments show is that many of our deepest beliefs regarding how to assess the goodness of outcomes are fundamentally incompatible. In light of these arguments, it appears that, if we are to achieve consistency in our normative beliefs, then very serious revisions are required in our understanding of the good and of practical reasoning.

There is doubt in the strict sense when the intellect neither assents nor dissents, because either there are no positive arguments for and against the law, or the arguments for and against the law are equal in strength. The opinion which favours the law, and which is technically called the safe opinion, can be more probable (in the specialized sense being discussed) than the opinion which favours liberty and which still retains solid (objective) probability. In estimating the degree which is required and which suffices for solid probability, moralists lay down the general principle that an opinion is solidly probable which by reason of intrinsic or extrinsic arguments is able to gain the assent of many prudent men. Adherents to Catholic probabilism hold that extrinsic authority can have sufficient weight to make an opinion solidly probable; but there is divergence of view in estimating what number of experts is able to give an opinion this solid probability.

For example, the case described in degree 4 vertex situation is the configuration consisting of a single vertex labelled as having degree 4 in G. As above, it suffices to demonstrate that if the configuration is removed and the remaining graph four-colored, then the coloring can be modified in such a way that when the configuration is re- added, the four-coloring can be extended to it as well. A configuration for which this is possible is called a reducible configuration. If at least one of a set of configurations must occur somewhere in G, that set is called unavoidable. The argument above began by giving an unavoidable set of five configurations (a single vertex with degree 1, a single vertex with degree 2, ..., a single vertex with degree 5) and then proceeded to show that the first 4 are reducible; to exhibit an unavoidable set of configurations where every configuration in the set is reducible would prove the theorem.

Echtra Condla, ["The adventure of Conle"] is an Old Irish echtra tale known in two variants from eight manuscripts, the earliest of which has been dated to the 12th C.. - the tale may have been written down first as early as the 8th C. The two variants do not diverge sharply from one another, so that a single summary suffices for both. The tale tells of the 'seduction' of Conle (Connla), son of Conn of the Hundred Battles by a woman of the Aos Si. In addition to what seems to be a story from pre-Christian tradition the story also incorporates what has interpreted to be a post-Christian anti-druidic message from the woman herself, foretelling the coming of Christianity. The echtra contains most of what is known of Conle son of Conn of the Hundred Battles, aka Conle the Ruddy, or Conle the Fair.Condla Ruad - the red, or ruddy; Condla Cain - the fair.

The House of Lords held that for banks to have a valid security they must ensure that their customers have independent legal advice if they are in a couple where the loan will, based on constructive or actual knowledge (either suffices), be used solely for the benefit of one person. A bank (or its solicitor) is "put on inquiry" (fixed with constructive knowledge) that there may be the risk of undue influence or misrepresentation, if they transact for security over a domestic home, but the loan will only benefit one person and not the other. The solicitor who would give independent advice, however, could also be acting as a solicitor for the bank, or both a husband and wife (or either partner). The solicitor would certify that he or she was satisfied that both borrowers had given their fully informed and true consent, although if this ultimately turned out to be wrong, the bank's security would not be affected.

It was known almost from the time of the first synthesis of GTN by Ascanio Sobrero in 1846 that handling and tasting of nitroglycerin could cause sudden intense headaches, From p. 248: "Il faut toutefois être sur ses gardes en faissant cet essai, car il suffit d'en tenir une très-petite quantité (ce qu'on peut en prendre en y mouillant légèrement le bout du petit doigt) sur la langue pour en éprouver une migraine assez forte pendant pleusieurs heures. Cette action sur le corps humain a été constatée par plusieurs personnes dans mon laboratoire, et je l'ai éprouvée plusieurs fois sur moi-même avant que je fusse certain qu'elle a des propriétés toxiques." (It is always necessary to be on one's guard when making this test, for it suffices to take a very small quantity of it (which one can take by lightly wetting, in it, the tip of the little finger) on [one's] tongue in order to feel a quite strong headache for several hours.

Defining all the various types among these two denominations involves a highly specialized area of study that encompasses a sizable amount of additional information whose many details need accompanying illustrations and as such is beyond the scope of this section. It suffices to say that most of the types are common to less common with only two types that are rare and valuable, one a 2-cent, 1916 issue, type II, the other a 2-cent 1919 issue, type II.2-cent, issue of Nov.17, 1916, type II (Scott 491) 2-cent, issue of Jun.14, 1919, type II (Scott 539); Scotts Specialized Catalogue of US Stamps Because it requires knowledge of and magnification to see the subtle variations in the lines of the image the valuable stamps can and have gone unnoticed for years before they are ever discovered, and sometimes turn up in common stamp collections, but this is very uncommon as these types are indeed rare.

To be admitted as a chaber, one must declare his determination never to give terumah or ma'aser to a priest or a Levite who is classified as an am ha'aretz; nor to allow his ordinary food to be prepared by an am ha'aretz; nor to eat his ordinary food (chullin, grain and fruit from which terumah and ma'aser have been separated) except in a certain state of Levitical cleanness.Tosefta, Demai 2:2 This declaration must be made before three members of the order. If they are satisfied that the candidate has lived up to the rules in his private life, he is accepted at once; otherwise he is admitted as a "ben ha-k'neset" (son of the union, neophyte)Compare Bekhorot 5:5; Zavim 3:2 for thirty days. According to Beit Shammai, this period suffices only when membership is sought for the lesser degrees of purity, while for the higher degrees the probation period lasts for a year.

Kęszyca Leśna covers some 10 km of military tunnels Paradyż Abbey in Gościkowo Once the bridge across the River Oder (and the now open border between Germany and Poland) has been passed, E11 (here unmarked) goes straight through the town center of Słubice, until 1945 a suburban part of Frankfurt (Oder) under the name of Dammvorstadt, but a separate township in a different country since then. Two kilometers out of town, E11 curbs left toward the little village of Drzecin, where the first white-yellow-white markings are found. These lead in a few days to Lubniewice, where the markings change to white-blue-white.Up to here, map N-33-125/126 suffices, although it does not mention E11. The detailed routing is: Oder bridge between Frankfurt (Oder) and Słubice - town centerof Słubice (no marking) - Drzecin (yellow) - Stare Biskupice - Sułów - Drzeńsko - Lubiechnia Wielka - Lubiechnia Mała - Ośno Lubuskie (34 km) - Trzebów - Jarnatów - Lubniewice (67 km).

To convert an arbitrary complex number to quater- imaginary, it is sufficient to split the number into its real and imaginary components, convert each of those separately, and then add the results by interleaving the digits. For example, since –1+4i is equal to –1 plus 4i, the quater-imaginary representation of –1+4i is the quater-imaginary representation of –1 (namely, 103) plus the quater-imaginary representation of 4i (namely, 20), which gives a final result of –1+4i = 1232i. To find the quater-imaginary representation of the imaginary component, it suffices to multiply that component by 2i, which gives a real number; then find the quater-imaginary representation of that real number, and finally shift the representation by one place to the right (thus dividing by 2i). For example, the quater-imaginary representation of 6i is calculated by multiplying 6i × 2i = –12, which is expressed as 3002i, and then shifting by one place to the right, yielding: 6i = 302i.

The Roman soldiers defending Gallia had adopted the Gallic god Mogons (Mogounus, Moguns, Mogonino), for the meaning of which etymology offers two basic options: "the great one", similar to Latin magnus, which was used in aggrandizing names such as Alexander magnus, "Alexander the Great" and Pompeius magnus, "Pompey the great", or the god of "might" personified as it appears in young servitors of any type whether of noble or ignoble birth.A second hypothesis suggests that Moguns was a wealthy Celt whose estate was taken for the fort and that a tax district was formed on the area parallel to other tax districts with a -iacum suffix (Arenacum, Mannaricium). There is no evidence for this supposedly wealthy man or his estate, but there is plenty for the god. According to Carl Darling Buck in Comparative Grammar of Greek and Latin, -yo- and -k- are general Indo- European formative suffices and are not related to taxes.

A Δ-Y transform can be performed by removing a triangular face from a polyhedron and extending its neighboring faces until the point where they meet, but only when that triple intersection point of the three neighboring faces is on the correct side of the polyhedron; when the triple intersection point is not on the correct side, a projective transformation of the polyhedron suffices to move it to the correct side. Therefore, by induction on the number of Δ-Y and Y-Δ transforms needed to reduce a given graph to K4, every polyhedral graph can be realized as a polyhedron. A later work by Epifanov strengthened Steinitz's proof that every polyhedral graph can be reduced to K4 by Δ-Y and Y-Δ transforms. Epifanov proved that if two vertices are specified in a planar graph, then the graph can be reduced to a single edge between those terminals by combining Δ-Y and Y-Δ transforms with series-parallel reductions.. Epifanov's proof was complicated and non-constructive, but it was simplified by Truemper using methods based on graph minors.

Some Religious Dimensions of Genocide Michael Sells, 1995 According to Tim Judah "there was another side to The Mountain Wreath far more sinister than its praise of tyrannicide. With its call for the extermination of those Montenegrins who had converted to Islam, the poem was also a paean to ethnic cleansing ... it helps explain how the Serbian national consciousness has been moulded and how ideas of national liberation are inextricably linked with killing your neighbour and burning his village." Regarding the claims about the poem's influence in ethnic cleansing, Pavlović argues that it suffices to say that, at present, some 20% of the Montenegrin population is of Islamic faith, and that Montenegrins of the Islamic faith and their socio-cultural heritage have been in the past and are at present an integral part of the general matrix of Montenegrin society, as seen in Montenegro demographics. Pavlović argues that Njegoš the politician was trying to accomplish the restructuring of a tribal society into a nation in accordance with the concept of national awakening in the 19th century.

Certainly all three have their devotees and detractors, but their presence has been inescapable." in Stephen Holden from The New York Times, in his review of Houston's Radio City Music Hall concert on July 20, 1993, praised her attitude as a singer, writing, "Whitney Houston is one of the few contemporary pop stars of whom it might be said: the voice suffices. While almost every performer whose albums sell in the millions calls upon an entertainer's bag of tricks, from telling jokes to dancing to circus pyrotechnics, Ms. Houston would rather just stand there and sing." With regard to her singing style, he added: "Her [Houston's] stylistic trademarks – shivery melismas that ripple up in the middle of a song, twirling embellishments at the ends of phrases that suggest an almost breathless exhilaration – infuse her interpretations with flashes of musical and emotional lightning." Elysa Gardner of the Los Angeles Times in her review for The Preacher's Wife Soundtrack highly praised Houston's vocal ability, commenting, "She is first and foremost a pop diva – at that, the best one we have.

If P also has a greatest element Î (so that it is a bounded poset), then the previous condition can be simplified to the requirement that all maximal chains in P have the same (finite) length. This suffices, since any pair of maximal chains in [Ô,x] can be extended by a maximal chain in [x,Î] to give a pair of maximal chains in P. :Note Stanley defines a poset to be graded of length n if all its maximal chains have length n (Stanley 1997, p.99). This definition is given in a context where interest is mostly in finite posets, and although the book subsequently often drops the part "of length n", it does not seem appropriate to use this as definition of "graded" for general posets, because (1) it says nothing about posets whose maximal chains are infinite, in particular (2) it excludes important posets like Young's lattice. Also it is not clear why in a graded poset all minimal elements, as well as all maximal elements, should be required to have the same length, even if Stanley gives examples making clear that he does mean to require that (ibid, pp.

Thus, having concluded that the tribe itself was terminated, the Court held that the statute of limitations should apply: > Without special federal protection for the Tribe, the state statute of > limitations should apply to its claim in this case. For it is well > established that federal claims are subject to state statutes of limitations > unless there is a federal statute of limitations or a conflict with federal > policy. Although federal policy may preclude the ordinary applicability of a > state statute of limitations for this type of action in the absence of a > specific congressional enactment to the contrary, the Catawba Act clearly > suffices to reestablish the usual principle regarding the applicability of > the state statute of limitations. In striking contrast to the situation in > [Oneida II], the Catawba Act represents an explicit redefinition of the > relationship between the Federal Government and the Catawbas; an intentional > termination of the special federal protection for the Tribe and its members; > and a plain statement that state law applies to the Catawbas as to all > “other persons or citizens.”476 U.S. at 507-08 (footnote and citation > omitted).

To multiply two fixed-point numbers, it suffices to multiply the two underlying integers, and assume that the scaling factor of the result is the product of their scaling factors. This operation involves no rounding. For example, multiplying the numbers 123 scaled by 1/1000 (0.123) and 25 scaled by 1/10 (2.5) yields the integer 123×25 = 3075 scaled by (1/1000)×(1/10) = 1/10000, that is 3075/10000 = 0.3075. If the two operands belong to the same fixed- point type, and the result is also to be represented in that type, then the product of the two integers must be explicitly multiplied by the common scaling factor; in this case the result may have to be rounded, and overflow may occur. For example, if the common scaling factor is 1/100, multiplying 1.23 by 0.25 entails multiplying 123 by 25 to yield 3075 with an intermediate scaling factor of 1/10000. This then must be multiplied by 1/100 to yield either 31 (0.31) or 30 (0.30), depending on the rounding method used, to result in a final scale factor of 1/100.

13-4 > The superiority of reward is not here the consequence of competition, but of > its absence: not a compensation for disadvantages inherent in the > employment, but an extra advantage; a kind of monopoly price, the effect not > of a legal, but of what has been termed a natural monopoly... independently > of... artificial monopolies [i.e. grants by government], there is a natural > monopoly in favour of skilled labourers against the unskilled, which makes > the difference of reward exceed, sometimes in a manifold proportion, what is > sufficient merely to equalize their advantages. If unskilled labourers had > it in their power to compete with skilled, by merely taking the trouble of > learning the trade, the difference of wages might not exceed what would > compensate them for that trouble, at the ordinary rate at which labour is > remunerated. But the fact that a course of instruction is required, of even > a low degree of costliness, or that the labourer must be maintained for a > considerable time from other sources, suffices everywhere to exclude the > great body of the labouring people from the possibility of any such > competition.

The proof shows that any problem in NP can be reduced in polynomial time (in fact, logarithmic space suffices) to an instance of the Boolean satisfiability problem. This means that if the Boolean satisfiability problem could be solved in polynomial time by a deterministic Turing machine, then all problems in NP could be solved in polynomial time, and so the complexity class NP would be equal to the complexity class P. The significance of NP-completeness was made clear by the publication in 1972 of Richard Karp's landmark paper, "Reducibility among combinatorial problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for its intractability, are NP-complete. Karp showed each of his problems to be NP-complete by reducing another problem (already shown to be NP-complete) to that problem. For example, he showed the problem 3SAT (the Boolean satisfiability problem for expressions in conjunctive normal form with exactly three variables or negations of variables per clause) to be NP- complete by showing how to reduce (in polynomial time) any instance of SAT to an equivalent instance of 3SAT.

A double couple model suffices to explain an earthquake's far-field pattern of seismic radiation, but tells us very little about the nature of an earthquake's source mechanism or its physical features.. While slippage along a fault was theorized as the cause of earthquakes (other theories included movement of magma, or sudden changes of volume due to phase changes; .), observing this at depth was not possible, and understanding what could be learned about the source mechanism from the seismic waves requires an understanding of the source mechanism.. Modeling the physical process by which an earthquake generates seismic waves required much theoretical development of dislocation theory, first formulated by the Italian Vito Volterra in 1907, with further developments by E. H. Love in 1927.. More generally applied to problems of stress in materials,. an extension by F. Nabarro in 1951 was recognized by the Russian geophysicist A. V. Vvedenskaya as applicable to earthquake faulting.; . In a series of papers starting in 1956 she and other colleagues used dislocation theory to determine part of an earthquake's focal mechanism, and to show that a dislocation – a rupture accompanied by slipping — was indeed equivalent to a double couple,, and see bibliography; ; ; .

According to various existing civil codes, a suretyship, when the underlying obligation is "non-valuable", is null and void unless the invalidity is the result of personal incapacity of the principal debtorCodes Civil, France and Belgium, 2012; Spain, 1824; Portugal, 822; Italy, 1899; Netherlands, 1858; Lower Canada, 1932 In some countries, however, the mere personal incapacity of a minor to borrow suffices to eliminate the guarantee of a loan made to himSpain, 1824; Portugal, 822, §2, 1535, 1536 The Egyptian codes sanction guarantees expressly entered into "in view of debtor's want of legal capacity" to contract a valid principal obligation Egyptian Codes, Mixed Suits, 605; Native Tribunals, 496 The Portuguese code retains the surety's liability, in respect of an invalid principal obligation, until the latter has been legally rescindedart. 822, §I According to several codes civil sureties are divided into conventional, legal and judicial,Codes Civil, France and Belgium, 2015, 2040 et seq.; Spain, 1823; Lower Canada, 1930 while the Spanish code further divides them into gratuitous and for valuable consideration.art. 1, 823 The German code civil requires the surety's promise to be verified by writing where he has not executed the principal obligation.art.

As a background fact, we use the identity E[x^2] = \mu^2 + \sigma^2 which follows from the definition of the standard deviation and linearity of expectation. A very helpful observation is that for any distribution, the variance equals half the expected value of (x_1 - x_2)^2 when x_1, x_2 are an independent sample from that distribution. To prove this observation we will use that E[x_1x_2] = E[x_1]E[x_2] (which follows from the fact that they are independent) as well as linearity of expectation: :E[(x_1 - x_2)^2] = E[x_1^2] - E[2x_1x_2] + E[x_2^2] = (\sigma^2 + \mu^2) - 2\mu^2 + (\sigma^2 + \mu^2) = 2\sigma^2 Now that the observation is proven, it suffices to show that the expected squared difference of two observations from the sample population x_1, \ldots, x_n equals (n-1)/n times the expected squared difference of two observations from the original distribution. To see this, note that when we pick x_u and x_v via u, v being integers selected independently and uniformly from 1 to n, a fraction n/n^2 = 1/n of the time we will have u = v and therefore the sampled squared difference is zero independent of the original distribution.