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The problem of finding the number of different ways in which a product of n different ordered factors can be calculated by pairs (i.e., the number of binary bracketings of n ...

Clairaut's difference equation is a special case of Lagrange's equation (Sokolnikoff and Redheffer 1958) defined by u_k=kDeltau_k+F(Deltau_k), (1) or in "x notation," ...

y=x(dy)/(dx)+f((dy)/(dx)) (1) or y=px+f(p), (2) where f is a function of one variable and p=dy/dx. The general solution is y=cx+f(c). (3) The singular solution envelopes are ...

A function H that maps an arbitrary length message M to a fixed length message digest MD is a collision-free hash function if 1. It is a one-way hash function. 2. It is hard ...

Every finite group G of order greater than one possesses a finite series of subgroups, called a composition series, such that I<|H_s<|...<|H_2<|H_1<|G, where H_(i+1) is a ...

Let P be the principal (initial investment), r be the annual compounded rate, i^((n)) the "nominal rate," n be the number of times interest is compounded per year (i.e., the ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

A statement is in conjunctive normal form if it is a conjunction (sequence of ANDs) consisting of one or more conjuncts, each of which is a disjunction (OR) of one or more ...

The covariant derivative of a contravariant tensor A^a (also called the "semicolon derivative" since its symbol is a semicolon) is given by A^a_(;b) = ...

The coversine is a little-used entire trigonometric function defined by covers(z) = versin(1/2pi-z) (1) = 1-sinz, (2) where versin(z) is the versine and sinz is the sine. The ...