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  2. Infinitesimal generator (stochastic processes) - Wikipedia

    en.wikipedia.org/wiki/Infinitesimal_generator...

    The Kolmogorov forward equation in the notation is just =, where is the probability density function, and is the adjoint of the infinitesimal generator of the underlying stochastic process. The Klein–Kramers equation is a special case of that.

  3. Linear congruential generator - Wikipedia

    en.wikipedia.org/wiki/Linear_congruential_generator

    The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.

  4. Formula for primes - Wikipedia

    en.wikipedia.org/wiki/Formula_for_primes

    This has enough digits for equation to yield again the 25 primes less than 100. As with Mills' formula and Wright's formula above, in order to generate a longer list of primes, we need to start by knowing more digits of the initial constant, f 1 {\displaystyle f_{1}} , which in this case requires a longer list of primes in its calculation.

  5. Itô diffusion - Wikipedia

    en.wikipedia.org/wiki/Itô_diffusion

    The generator is used in the formulation of Kolmogorov's backward equation. Intuitively, this equation tells us how the expected value of any suitably smooth statistic of X evolves in time: it must solve a certain partial differential equation in which time t and the initial position x are the independent variables.

  6. Dirac equation - Wikipedia

    en.wikipedia.org/wiki/Dirac_equation

    In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, ... The generator generates ...

  7. Langevin equation - Wikipedia

    en.wikipedia.org/wiki/Langevin_equation

    In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing how a system evolves when subjected to a combination of deterministic and fluctuating ("random") forces. The dependent variables in a Langevin equation typically are collective (macroscopic) variables changing only slowly in comparison ...

  8. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    There are several methods for defining quadratic equations for calculating each leg of a Pythagorean triple. [15] A simple method is to modify the standard Euclid equation by adding a variable x to each m and n pair. The m,n pair is treated as a constant while the value of x is varied to produce a "family" of triples based on the selected triple.

  9. Unitary matrix - Wikipedia

    en.wikipedia.org/wiki/Unitary_matrix

    In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U −1 equals its conjugate transpose U *, that is, if = =, where I is the identity matrix.. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger (⁠ † ⁠), so the equation above is written

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