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In mathematics, a continuous-time random walk (CTRW) is a generalization of a random walk where the wandering particle waits for a random time between jumps. It is a stochastic jump process with arbitrary distributions of jump lengths and waiting times. [1] [2] [3] More generally it can be seen to be a special case of a Markov renewal process.
In number theory, Vieta jumping, also known as root flipping, is a proof technique. It is most often used for problems in which a relation between two integers is given, along with a statement to prove about its solutions. In particular, it can be used to produce new solutions of a quadratic Diophantine equation from known ones.
An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion ), the search path of a foraging animal, or the price of a fluctuating ...
Poisson process, an example of a jump process; Continuous-time Markov chain (CTMC), an example of a jump process and a generalization of the Poisson process; Counting process, an example of a jump process and a generalization of the Poisson process in a different direction than that of CTMCs; Interacting particle system, an example of a jump ...
The jump can be iterated into transfinite ordinals: there are jump operators for sets of natural numbers when is an ordinal that has a code in Kleene's (regardless of code, the resulting jumps are the same by a theorem of Spector), [2] in particular the sets 0 (α) for α < ω 1 CK, where ω 1 CK is the Church–Kleene ordinal, are closely ...
Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection , coronal mass ejections , condensed matter physics , and pattern theory and computational vision .
This Diophantine equation has a solution which follows directly from the Euclidean algorithm; in fact, it has infinitely many periodic solutions positive and negative. If (x 0, y 0) is a solution of 1024x–15625y=1, then N 0 =x 0 · 8404, F 0 =y 0 · 8404 is a solution of (2), which means any solution must have the form
In mathematics, a jumping line or exceptional line of a vector bundle over projective space is a projective line in projective space where the vector bundle has exceptional behavior, in other words the structure of its restriction to the line "jumps". Jumping lines were introduced by R. L. E. Schwarzenberger in 1961. [1] [2] The jumping lines ...