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Given a function of two variables df = (partialf)/(partialx)dx+(partialf)/(partialy)dy (1) = udx+vdy, (2) change the differentials from dx and dy to du and dy with the ...

F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for ...

Second and higher derivatives of the metric tensor g_(ab) need not be continuous across a surface of discontinuity, but g_(ab) and g_(ab,c) must be continuous across it.

A limb of a tree at a vertex v is the union of one or more branches at v in the tree. v is then called the base of the limb.

A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

Data resulting from the observation of a population on a number of variables over time. Whenever observations are made more than once, the data is considered to be ...

A function f is said to have a lower bound c if c<=f(x) for all x in its domain. The greatest lower bound is called the infimum.

If Omega subset= C is a domain and phi:Omega->C is a one-to-one analytic function, then phi(Omega) is a domain, and area(phi(Omega))=int_Omega|phi^'(z)|^2dxdy (Krantz 1999, ...

A type I move (conjugation) takes AB->BA for A, B in B_n where B_n is a braid group. A type II move (stabilization) takes A->Ab_n or A->Ab_n^(-1) for A in B_n, and b_n, Ab_n, ...

A random process whose future probabilities are determined by its most recent values. A stochastic process x(t) is called Markov if for every n and t_1<t_2...<t_n, we have ...