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A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...

A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance. Let chi_m^2 and chi_n^2 be independent variates ...

Given a sequence of independent random variates X_1, X_2, ..., if sigma_k^2=var(X_k) and rho_n^2=max_(k<=n)((sigma_k^2)/(s_n^2)), then lim_(n->infty)rho_n^2=0. This means ...

A fiber of a map f:X->Y is the preimage of an element y in Y. That is, f^(-1)(y)={x in X:f(x)=y}. For instance, let X and Y be the complex numbers C. When f(z)=z^2, every ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

Fischer's z-distribution is the general distribution defined by g(z)=(2n_1^(n_1/2)n_2^(n_2/2))/(B((n_1)/2,(n_2)/2))(e^(n_1z))/((n_1e^(2z)+n_2)^((n_1+n_2)/2)) (1) (Kenney and ...

An origami configuration that can be pressed to a plane figure without crumpling it or adding new creases.

Let Q(x) be a real or complex piecewise-continuous function defined for all values of the real variable x and that is periodic with minimum period pi so that Q(x+pi)=Q(x). ...

A technique in set theory invented by P. Cohen (1963, 1964, 1966) and used to prove that the axiom of choice and continuum hypothesis are independent of one another in ...