classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to decrease in...

According to the theorem, every such algebra is isomorphic to one of the following: R (the real numbers) C (the complex numbers) H (the quaternions)...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

N\hookrightarrow W} are homotopy equivalences. The h-cobordism theorem gives sufficient conditions for an h-cobordism to be trivial, i.e., to be C-isomorphic...

field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a divisor of | G | {\displaystyle...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, return...

In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after...

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...

Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h :...

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct...

The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate...

In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented...

1982 by William Wootters and Wojciech H. Zurek as well as Dennis Dieks the same year). The aforementioned theorems do not preclude the state of one system...

that emerged in the first half of the 20th century. The theorem was first proved by Marshall H. Stone. Stone was led to it by his study of the spectral...

In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does...

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients...

: 158  His Theorem I, on the Goldbach conjecture, was stated above. His Theorem II is a result on the twin prime conjecture. It states that if h is a positive...

In calculus, the squeeze theorem (also known as the sandwich theorem, among other names) is a theorem regarding the limit of a function that is bounded...

\left({\frac {P(X(t)=i)}{\pi _{i}}}\right),} is monotonically increasing (H-theorem). This is a consequence of the convergence to the equilibrium distribution...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus...

Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region K {\displaystyle...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

In mathematics, the inverse function theorem is a theorem that asserts that, if a real function f has a continuous derivative near a point where its derivative...

The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence...

original papers on the statistical interpretation of thermodynamics, the H-theorem, transport theory, thermal equilibrium, the equation of state of gases...

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...