In contrast, for the classical Klein – Gordon field at non-zero temperature, the Gibbs probability density that we would observe a configuration at a time is

For this reason, the pressure of a Fermi gas is non-zero even at zero temperature, in contrast to that of a classical ideal gas.

In languages that show the above distinctions, it is quite common to employ null affixation ( not ) to mark singular number, present tense and third persons ( English is unusual in its marking of the third person singular with a non-zero morpheme, by contrast with a null morpheme for others ).

During the Financial crisis of 2007 – 2010, Bulgaria marked a decline in its economy of 5. 5 % in 2009, but quickly restored its positive growth to 0. 2 % in 2010, in contrast to other Balkan countries.

Within 4 – 5 days the inflammation and the concomitant dead brain tissue are surrounded with a capsule, which gives the lesion the famous ring-enhancing lesion appearance on CT examination with contrast ( since intravenously applied contrast material can not pass through the capsule, it is collected around the lesion and looks as a ring surrounding the relatively dark lesion ).

* A prophecy of restoration ( 7: 11 – 13 ): Fallen Jerusalem is promised that she will be rebuilt and that her power will be greater than ever ( a contrast with the vision of peace in 4: 1-5 ).

Balinese caste structure has been described in early 20th century European literature to be based on three categories – triwangsa ( thrice born ) or the nobility, dwijati ( twice born ) in contrast to ekajati ( once born ) the low folks.

This is in deep contrast to the Lenin era ( 1917 – 1924 ), when six Congresses were held, five conferences and 69 meetings of the Central Committee.

By way of contrast, when introduced in 1985, the Amiga had compared favorably against 286-based systems with EGA graphics and rudimentary sound capabilities that frequently cost 2 – 3 times as much.

However, recent investigations of languages with very complex click systems such as Nǁng have revealed that the supposed velar – uvular contrast is actually a contrast of a simple clicks versus click – plosive airstream contours ( or consonant clusters, depending on analysis ).

In contrast to real numbers that have the property of varying " smoothly ", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

While he is a confirmed compatibilist on free will, in " On Giving Libertarians What They Say They Want " – Chapter 15 of his 1978 book Brainstorms, Dennett articulated the case for a two-stage model of decision making in contrast to libertarian views.

In contrast, their first six full-time coaches – Art Duncan, Adams, Ivan, Jimmy Skinner and Abel – covered a 42 – year period.

* Tarski's axioms: Alfred Tarski ( 1902 – 1983 ) and his students defined elementary Euclidean geometry as the geometry that can be expressed in first-order logic and does not depend on set theory for its logical basis, in contrast to Hilbert's axioms, which involve point sets.

* Staining – uses heavy metals such as lead, uranium or tungsten to scatter imaging electrons and thus give contrast between different structures, since many ( especially biological ) materials are nearly " transparent " to electrons ( weak phase objects ).

There is thus an ironic contrast between Paul's own temporal imprisonment and Philemon's temporal freedom ( and mastery over Onesimus ), balanced by the inversion of that relationship in what Paul sees as his own spiritual authority over Philemon and Philemon's spiritual subservience to Paul, who is claiming that Onesimus – temporally, a slave – is, spiritually speaking, not simply equal to his master but a brother of his.

Fermions contrast with bosons which obey Bose – Einstein statistics.

Until recently, fur seals were all grouped under a single subfamily of Pinnipedia, called Arctocephalinae, to contrast them with Otariinae – the sea lions – based on the most prominent common feature, namely the coat of dense underfur intermixed with guard hairs.

In contrast with this, zirconium is practically transparent to thermal neutrons, and it is commonly used for the metal components of nuclear reactors – especially the claddings of their nuclear fuel rods.

This is in contrast to macroeconomics, which involves the " sum total of economic activity, dealing with the issues of growth, inflation, and unemployment.

In word-final position these all contrast, as shown by the minimal triplet sum, sun, sung.

* By contrast, the event of getting a 6 the first time a die is rolled and the event that the sum of the numbers seen on the first and second trials is 8 are not independent.

In contrast, the sum of a number of i. i. d.

He also showed that the sum of the reciprocals of twin primes converges to a finite value, now called Brun's constant: by contrast, the sum of the reciprocals of all primes is divergent.

By contrast, an ordinary seamen in the Royal Navy received 19s per month to be paid in a lump sum at the end of a tour of duty which was around half the rate paid in the Merchant Navy.

In contrast, for prime q ≡ 1 ( mod 4 ), the sum of the quadratic residues minus the sum of the nonresidues in the range 1, 2, …, q − 1 is zero, implying that both sums equal.

Many in Hong Kong believe that Tung's responsiveness to this request, in contrast to what is commonly perceived to be his lack of desire, was due in part to the fact that Tung himself owes a personal debt to the PRC government: his family's shipping conglomerate Orient Overseas was bailed out for the sum of US $ 110 million by Chinese government-owned companies in the 1980s.

By contrast, more traditional partition functions involve random variables that are real-valued, and range over a simplex -- a simplex, being the geometric way of saying that the total of probabilities sum to one.

In contrast, the convolution ( equivalent to the cross-correlation of f ( t ) and g (− t ) ) gives the probability density function of the sum.

In contrast to ideal solutions, where volumes are strictly additive and mixing is always complete, the volume of a non-ideal solution is not, in general, the simple sum of the volumes of the component pure liquids and solubility is not guaranteed over the whole composition range.

This is in contrast to the sum command, which is not as interoperable.

In contrast, on the 7th of October 2008, Danske Bank wrote off a substantial sum largely due to property-related losses incurred by its Irish subsidiary-National Irish Bank.

Most distinctive is the idealist hermeneutic which stood ( and stands ) in contrast to the common sense realism of Hodge and subsequent American Reformed theology, i. e. Nevin starts with the whole before the parts, and the whole is indeed greater than the sum of the parts.

This is in marked contrast to the situation in Riemannian geometry where the curvature is a local invariant, an obstruction to the metric being locally a sum of squares of coordinate differentials.

In contrast to liberal individualism in theology, postliberal theology roots rationality not in the certainty of the individual thinking subject ( cogito ergo sum, " I think, therefore I am ") but in the language and culture of a living tradition of communal life.

However, in contrast to simple convergence, the SC integrates information to create an output that differs from the sum of its inputs.

The literature also describes a contrast between velar and uvular rear articulations for some languages.

A more practical definition of the term describes it as changes occurring on geological time scales, in contrast to microevolution, which occurs on the timescale of human lifetimes.

The term describes a general new attitude of Americans towards atomized individualism and away from communitarianism in clear contrast with the 1960s.

In contrast, the proposition, " Santa Claus is eating a cookie right now ," describes events that are happening at the time the proposition is uttered.

In contrast, the exponential distribution describes the time for a continuous process to change state.

In contrast to the Jewish tradition, which uses a term which can be translated as a " box " or " chest " to describe the Ark, surah 29: 14 of the Quran refers to it as a safina, an ordinary ship, and surah 54: 13 describes the ark as " a thing of boards and nails ".

In contrast to authors who identify language and cognition, he describes his own mathematical thinking as largely wordless, often accompanied by mental images that represent the entire solution to a problem.

The NIH describes computational / mathematical biology as the use of computational / mathematical approaches to address theoretical and experimental questions in biology and, by contrast, bioinformatics as the application of information science to understand complex life-sciences data.

By contrast, the Constitution of Ireland describes the President of Ireland throughout as " he ", yet two of the most recent presidents were women ; in 1997, four of the five candidates in the election were women.

In contrast, a Sprachraum ( from German, " language area "), also known as a dialect continuum, describes a group of genetically related dialects spoken across a geographical area, differing in their genetic relationship only slightly between areas that are geographically close, and gradually decreasing in mutual intelligibility as distances increase.

" The second type of the pastoral is literature that " describes the country with an implicit or explicit contrast to the urban.

By contrast, when a sentence is in spoken form and the verb involved is one of assertion, the use of that makes clear that the present speaker is making an indirect rather than a direct quotation, such that s / he is not imputing particular words to the person s / he describes as having made an assertion ; the demonstrative adjective that also does not fit such an example.

This equation basically describes the existence of the jet stream, a westerly current of air with maximum wind speeds close to the tropopause which is ( even though other factors are also important ) the result of the temperature contrast between equator and pole.

These are in contrast to kinematics, the branch of classical mechanics that describes the motion of objects without consideration of the causes leading to the motion.

On the Terminator 2 DVD, writer / director James Cameron describes his casting of Robert Patrick as a deliberate contrast to the original Terminator character portrayed by Arnold Schwarzenegger: " I wanted to find someone who would be a good contrast to Arnold.

This concept strikes a sharp contrast with the words " hedonism " and even " pleasure " in English today ; the former implies wanton pursuit of pleasure with disregard to all else, and the latter has no inherent connotations that extend the meaning beyond the immediate experiences it describes.

A heterodiegetic narrator, in contrast, describes the experiences of the characters that appear in the story.

By contrast, subtracting equation ( 2 ) from equation ( 1 ) results in an equation that describes how the vector r = x < sub > 1 </ sub > − x < sub > 2 </ sub > between the masses changes with time.

In contrast, in declarative programming languages the program describes the desired results, and doesn't specify changes to the state directly.

In contrast, gesellschaft ( often translated as society, civil society or association ) describes associations in which, for the individual, the larger association never takes precedence over the individual's self-interest, and these associations lack the same level of shared mores.

The democratization of knowledge is a concept that describes the spread of knowledge among common people, in contrast to knowledge being controlled by elite groups.

In a stark contrast to the addendum in subsequent editions of the book — which describes the dogs ' finding sanctuary from the hunters and being cleared of carrying the plague — the film concludes as the first edition of the book proper, with the dogs swimming out to sea.

When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences ( microscopy ) or theories ( microphysics, statistical physics ) considering objects of geometric lengths smaller than one millimeter.