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Multi-index notation is used to shorten expressions that contain many indices. Let x in R^n and write x=(x_1,...,x_n). A multi-index alpha is an n-tuple of integers alpha_j ...

Dynamical Systems

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

Multivariate zeta function, also called multiple zeta values, multivariate zeta constants (Bailey et al. 2006, p. 43), multi-zeta values (Bailey et al. 2006, p. 17), and ...

A Lindenmayer system, also known as an L-system, is a string rewriting system that can be used to generate fractals with dimension between 1 and 2. Several example fractals ...

A system of variables which can be written in the form of Hamilton's equations.

A system of circles obtained by multiplying each radius in a coaxal system by a constant. The Tucker circles are a coaxaloid system (Johnson 1929, p. 277).

A system of congruences a_i mod n_i with 1<=i<=k is called a complete residue system (or covering system) if every integer y satisfies y=a_i (mod n) for at least one value of ...

A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on ...

A lag system, introduced by Wang (1963), is a sort of opposite to a tag system. Lag systems allow dependence on more than just the first element, but remove only the first ...