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Also known as metric entropy. Divide phase space into D-dimensional hypercubes of content epsilon^D. Let P_(i_0,...,i_n) be the probability that a trajectory is in hypercube ...

Let Q_i denote anything subject to weighting by a normalized linear scheme of weights that sum to unity in a set W. The Kolmogorov axioms state that 1. For every Q_i in W, ...

The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and f and the functions h_j are convex, then a solution ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...

The commutator series of a Lie algebra g, sometimes called the derived series, is the sequence of subalgebras recursively defined by g^(k+1)=[g^k,g^k], (1) with g^0=g. The ...

In n-dimensional Lorentzian space R^n=R^(1,n-1), the light cone C^(n-1) is defined to be the subset consisting of all vectors x=(x_0,x_1,...,x_(n-1)) (1) whose squared ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

The limit test, also sometimes known as the nth term test, says that if lima_n!=0 or this limit does not exist as n tends to infinity, then the series suma_n does not ...