See quantum circuit for a more precise formulation.

A precise formulation of local realism in terms of a local hidden variable theory was proposed by John Bell.

Both notions, as described here, are somewhat vague, and indeed the precise formulation of these principles is controversial.

Since the precise notion of " manifold " was not available to Hilbert, there is room for some debate about the formulation of the problem in contemporary mathematical language.

This example illustrates that the conclusion reached from a statistical test may depend on the precise formulation of the null and alternative hypotheses.

This can be made precise in various contexts with slightly different ways of formulation.

The modal-logical treatment of provability helped demonstrate the " intensionality " of Gödel's Second Incompleteness Theorem, meaning that the theorem's correctness depends on the precise formulation of the provability predicate.

The intuition mentioned above ( that constructions that can be carried out in D can be " lifted " to D < sup > C </ sup >) can be made precise in several ways ; the most succinct formulation uses the language of adjoint functors.

A more precise formulation is that if a function is in both L < sup > 1 </ sup >( R ) and L < sup > 2 </ sup >( R ), then its Fourier transform is in L < sup > 2 </ sup >( R ), and the Fourier transform map is an isometry with respect to the L < sup > 2 </ sup > norm.

The precise formulation of the idea is made difficult by the fact that physicists do not yet know how many independent physical constants there are.

A precise mathematical definition of this matrix is given in the article on the formulation of the standard model.

In the idelic formulation of class field theory, one obtains a precise one-to-one correspondence between abelian extensions and appropriate groups of ideles, where equivalent generalized ideal class groups in the ideal-theoretic language correspond to the same group of ideles.

An early table, featuring reinvestment from one period to the next and a geometric series, is found in the tableau économique of the Physiocrats, which is credited as the " first precise formulation " of such interdependent systems and the origin of multiplier theory.

They provide a precise formulation of the relationship between spacetime geometry and the properties of matter, using the language of mathematics.

However, while a number of arguments have been devised which show that some form of the bound must exist in order for the laws of thermodynamics and general relativity to be mutually consistent, the precise formulation of the bound has been a matter of debate.

In the decade and a half prior to the Spanish Civil War ( 1919-1936 ), the Academy managed to consolidate itself as an institution and set about its project of promoting the birth of a standard literary language, although it was unable to provide a precise, solid academic formulation for that aim.

The formulation of more precise versions of the meaning of compactification in this context has been promoted by discoveries such as the mysterious duality.

This is a more precise formulation of the intuition that asset volatility tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time.

Although for technical reasons the precise equations formulated in the original ADM paper are rarely used in numerical simulations, most or all practical approaches to numerical relativity use a " 3 + 1 decomposition " of spacetime into three-dimensional space and one-dimensional time that is closely related to the ADM formulation, because the ADM procedure reformulates the Einstein field equations into a constrained initial value problem that can be addressed encoded on a computer for solution.

The fact that concepts change does not mean that they are arbitrary ; experience can be formulated in many diverse and incompatible ways, but to the extent that they are rooted in experience, each formulation has its own precise relationship to experience.

As such, the term Ringer's lactate should not be equated with one precise formulation.

According to Victor Brochard “ the five tropes can be regarded as the most radical and most precise formulation of skepticism that has ever been given.

Market trade supplies no universal morality of its own, except the law of contract and basic practical requirements to settle transactions, while at the same time legal rules, however precise in their formulation, cannot control every last detail of transactions and the interpretation ( or implications ) thereof.

Without a precise formulation of

They arise in situations in which one believes that what happens depends not only on the external world, but also on the precise pattern of behavior of the individual or group.

The arrangement of the spines is very precise, and is described by what is called the Müllerian law.

To find out what the precise law is that applies to a particular set of facts, one has to locate precedential decisions on the topic, and reason from those decisions by analogy.

Here, the focus is not on finding precise solutions to the equations defining the dynamical system ( which is often hopeless ), but rather to answer questions like " Will the system settle down to a steady state in the long term, and if so, what are the possible attractors?

Although much circumstantial evidence has been found to suggest that fewer different amino acids were used in the past than today, precise and detailed hypotheses about which amino acids entered the code in what order have proved far more controversial.

A just man is a man in just the right place, doing his best and giving the precise equivalent of what he has received.

The lack of a consistent, rigorous, and precise understanding of what typically makes up one unit of cultural transmission remains a problem in debates about memetics.

The precise detailed religious requirements for matzah are not universally agreed upon ; for example there is disagreement over what grains may be used, whether matzah which is wetted after being baked then becomes chametz or not, and so on.

This number is in the neighborhood of what a triangular perimeter ought to be but it cannot be verified against anything Pytheas may have said, nor is Diodorus Siculus very precise about the locations of the legs.

" Egyptian strongholds in Canaan are also mentioned, including a temple dedicated to Amun, which some scholars place in Gaza ; however, the lack of detail indicating the precise location of these strongholds means that it is unknown what impact these had, if any, on Philistine settlement along the coast.

Note that " secure " here has a precise mathematical meaning, and there are multiple different ( meaningful ) definitions of what it means for an encryption scheme to be " secure ".

The definition can be made more precise by specifying what is meant by image or pattern, e. g., a function of position with values in a set of colors.

As Holland has it: " What precise heights of oratory he attained, what stirring and memorable phrases he pronounced, we have no way of knowing ... only by the effect it had on the assembly can we gauge what surely must have been its electric and vivifying quality-for Themistocles ' audacious proposals, when put to the vote, were ratified.

By 1972, the clean and press was discontinued because athletes started to push with legs and bend backwards instead of strictly pressing the weight overhead, and this left the sole elements of what is today's modern Olympic weightlifting programme – the snatch and the clean and jerk. The snatch entails pulling with a wide grip the barbell overhead without pressing out with the arms. It is a very precise lift that can be nullified by a lack of balance of the athlete. The clean and jerk is more forgiving using a narrower grip pull the bar to the shoulders and then using the strength of the legs push until arms reach full extension without a press out.

Anyone who knows him can describe his piercing nature and precise ways of expression through his own simple words of what Lev Davidovich Landau once meant:

As weapons have grown more precise, the need for mass formations dropping masses of bombs has decreased, and it is now possible for a single bomb to accomplish what in the past took many bombers.

" A more precise description of just what Pope Nicholas ordered constructed is found in the writings of the Viterbese chronicler Nicola della Tuccia, who, in the 1470s, described the new Bagno del Papa as a battlemented building about 30 x 20 m in size with high towers at the corners of its southern facade.

To be more precise, it is necessary to specify what kind of objects may appear in the entries of the matrix.

In the following years, during which he continued in an influential situation in Canterbury, but at what precise date is unknown, he wrote a Life of Becket.

However, it is never made explicitly clear how many screens are monitored at once, or what the precise criteria ( if any ) for monitoring a given screen are ( although we do see that during an exercise program that Winston takes part in every morning, the instructor can see him, meaning telescreens are possibly a variant of videophones ); Telescreens do not have night vision technology, thus, they cannot surveil in the dark ; this is compensated by the fact that telescreens are incredibly sensitive, and can pick up a heartbeat.

The precise semantics of subtyping crucially depends on the particulars of what " safely used in a context where " means in a given programming language.

( This is approximately correct, although uncertainty as to what should count as a turn makes precise verification impossible ).

He admired Eastern theatre because of the codified, highly ritualized and precise physicality of Balinese dance performance, and advocated what he called a " Theatre of Cruelty ".