Search results
Results from the WOW.Com Content Network
In theoretical computer science, a Markov algorithm is a string rewriting system that uses grammar-like rules to operate on strings of symbols. Markov algorithms have been shown to be Turing-complete , which means that they are suitable as a general model of computation and can represent any mathematical expression from its simple notation.
More precisely Markov's theorem can be stated as follows: [2] [3] given two braids represented by elements , ′ in the braid groups ,, their closures are equivalent links if and only if ′ can be obtained from applying to a sequence of the following operations:
The theorem was named after Carl Friedrich Gauss and Andrey Markov, although Gauss' work significantly predates Markov's. [3] But while Gauss derived the result under the assumption of independence and normality, Markov reduced the assumptions to the form stated above. [4] A further generalization to non-spherical errors was given by Alexander ...
Feller derives the equations under slightly different conditions, starting with the concept of purely discontinuous Markov process and then formulating them for more general state spaces. [5] Feller proves the existence of solutions of probabilistic character to the Kolmogorov forward equations and Kolmogorov backward equations under natural ...
Markov's principle is equivalent, in the language of real analysis, to the following principles: For each real number x, if it is contradictory that x is equal to 0, then there exists a rational number y such that 0 < y < |x|, often expressed by saying that x is apart from, or constructively unequal to, 0.
The first levels of the Markov number tree. There are two simple ways to obtain a new Markov triple from an old one (x, y, z).First, one may permute the 3 numbers x,y,z, so in particular one can normalize the triples so that x ≤ y ≤ z.
Choi's theorem on completely positive maps (operator theory) Chomsky–Schützenberger enumeration theorem (formal language theory) Chomsky–Schützenberger representation theorem (formal language theory) Choquet–Bishop–de Leeuw theorem (functional analysis) Chow's theorem (algebraic geometry) Chowla–Mordell theorem (number theory)
Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. [1] [2] A stationary Gauss–Markov process is unique [citation needed] up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process.