Gibbs coined the term " statistical mechanics " and introduced key concepts in the corresponding mathematical description of physical systems, including the notions of chemical potential ( 1876 ), statistical ensemble ( 1878 ), and phase space ( 1901 ).

For contravariant functors the corresponding notions would be a functor that takes colimits to limits, or one that takes limits to colimits.

The use of both terms in the modern context of multilinear algebra is a specific example of corresponding notions in category theory.

As part of the predominating Grothendieck approach, there are three corresponding notions of fiber of a morphism: the first being the simple inverse image of a point.

Because each finitary relation on the natural numbers can be identified with a corresponding set of finite sequences of natural numbers, the notions of computable relation and computably enumerable relation can be defined from their analogues for sets.

In 2003, she won the most coveted award a TVB actress can receive, Favorite Lead Actress, beating other " fa dan ", a Cantonese term borrowed from Cantonese operas and roughly corresponding to modern notions of main actresses, such as Jessica Hsuan, Flora Chan, and Kenix Kwok.

Since broadcast frequencies are very limited in number, these objectives are to some extent inconsistent in that not all of them can be fully realized, and to the extent that each is realized, there is a corresponding reduction of the possibilities for fullest achievement of the others.

On the contrary, even in the heart of `` the Bible belt '' itself, as can be attested by any one who is called to work there, the industrial and technological revolutions have long been under way, together with the corresponding changes in man's picture of himself and his world.

Algebraically, these units can be thought of as the squares of the corresponding length units.

With Edward Frankland he found that nitriles can be hydrolyzed to the corresponding acids.

The frequency of alleles in a diploid population can be used to predict the frequencies of the corresponding genotypes ( see Hardy-Weinberg principle ).

It can send and receive messages to and from a corresponding device over any distance whatsoever with no delay.

When the price of a stock on the NYSE and its corresponding futures contract on OCX are out of sync, one can buy the less expensive one and sell it to the more expensive market.

The vector A can be written using any set of basis vectors and corresponding coordinate system.

Just as kets and bras can be transformed into each other ( making into ) the element from the dual space corresponding with is where A < sup >†</ sup > denotes the Hermitian conjugate ( or adjoint ) of the operator A.

which can be interpreted as the linear interpolant of corresponding points on the linear Bézier curves from P < sub > 0 </ sub > to P < sub > 1 </ sub > and from P < sub > 1 </ sub > to P < sub > 2 </ sub > respectively.

Schaefer's dichotomy theorem states that, for any restriction to Boolean operators that can be used to form these subformulae, the corresponding satisfiability problem is in P or NP-complete.

A registered citizen can only vote after his identity has been verified at the table corresponding to his registry.

* Chosen-plaintext ( chosen-ciphertext ): the attacker can obtain the ciphertexts ( plaintexts ) corresponding to an arbitrary set of plaintexts ( ciphertexts ) of his own choosing.

The player character automatically gains a spell with each experience level, and can permanently gain others using corresponding books, until all thirty spells available are learned.

Each key is mapped to a number and then can be mapped to a corresponding letter or command.

The time delay can be varied up to the maximum corresponding to the flow time over that known distance.

The wheels can be any regular polygon except a triangle, but the catenary must have parameters corresponding to the shape and dimensions of the wheels.

Rotating frames and fictitious forces can often reduce the description of motion in two dimensions to a simpler description in one dimension ( corresponding to a co-rotating frame ).

The Kerr Metric, corresponding to a black hole of mass and angular momentum, can be used to derive the effective potential for particle orbits restricted to the equator ( as defined by rotation ).

Using affine transformations multiple different euclidean transformations including translation can be combined by simply multiplying the corresponding matrices.

In mathematics, any vector space, V, has a corresponding dual vector space ( or just dual space for short ) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors.

Thus, one can consider data compression as data differencing with empty source data, the compressed file corresponding to a " difference from nothing ".

A diver who scores at least 310 points on the 3 meter springboard and 300 points on the 1 meter springboard in a 6 optional meet can participate in the particular zone championship corresponding to the geographic region in which his or her school lies.

The flame temperature can be approximated to the adiabatic flame temperature of the fuel with corresponding air-to-fuel ratio and compression pressure,.

It is worth noting that the vertices and edges of a convex polyhedron can be projected to form a graph ( sometimes called a Schlegel diagram ) on the sphere or on a flat plane, and the corresponding graph formed by the dual of this polyhedron is its dual graph.

By comparing reaction cells sealed from the same manifold temperature dependency corresponding to activation energies ranging from 11 to 18 Af was observed while dependence on the first power of the light intensity seemed to be indicated in most cases.

This terminology will also be applied to the corresponding points in the Aj.

On these generators let Af and Af be, respectively, the harmonic conjugates of Af and Af with respect to the two points in which the corresponding generator meets Aj.

As one would surmise, the procedure, however, could be repeated with the same object or with the same type of object often enough, so that the corresponding visual blots and the merest beginning of the tracing movement would provide clues as to the actual shape, which the patient then immediately could determine by a kind of inference.

by means of an origin statement which refers to an actual address, the corresponding index word will be reserved.

Once more the fallacious equation is advanced to argue that since business is restricted under the anti-monopoly laws, there must be a corresponding restriction against labor unions: the law must treat everybody equally.

Vowels not preceded by a consonant may be represented with a zero consonant letter, modified to indicate the vowel, or separate letters for each vowel, that are distinct from the corresponding dependent vowel signs.

The alpha component may be used to blend to red, green and blue components equally, as in 32-bit RGBA, or, alternatively, there may be three alpha values specified corresponding to each of the primary colors for spectral color filtering.

This however resulted in that year not corresponding with the lifetimes of historical figures reputed to be alive, or otherwise mentioned in connection with the Christian incarnation, e. g. Herod the Great or Quirinius.

But if the Frisian names Akkrum, Akkeringa and Dutch name Akkerghem, are derived from the personal name Akker there may be a corresponding Old English name from which Accrington may be derived.

In an " extended model " which includes hot dark matter in the form of neutrinos, then if the " physical baryon density " Ω < sub > b </ sub > h < sup > 2 </ sup > is estimated at about 0. 023 ( this is different from the ' baryon density ' Ω < sub > b </ sub > expressed as a fraction of the total matter / energy density, which as noted above is about 0. 046 ), and the corresponding cold dark matter density Ω < sub > c </ sub > h < sup > 2 </ sup > is about 0. 11, the corresponding neutrino density Ω < sub > v </ sub > h < sup > 2 </ sup > is estimated to be less than 0. 0062.

They are of two kinds: the " parallel texts ", which are parallel developments of the corresponding passages in the base text, and the speeches of Elihu ( Chapters 32-37 ), which consist of a polemic against the ideas expressed elsewhere in the poem, and so are claimed to be interpretive interpolations.

For example, there will only be one term x < sup > n </ sup >, corresponding to choosing x from each binomial.