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A quantity used to test nested hypotheses. Let H^' be a nested hypothesis with n^' degrees of freedom within H (which has n degrees of freedom), then calculate the maximum ...

There are three types of boundary conditions commonly encountered in the solution of partial differential equations: 1. Dirichlet boundary conditions specify the value of the ...

For discrete problems in which no efficient solution method is known, it might be necessary to test each possibility sequentially in order to determine if it is the solution. ...

Let n-1=FR where F is the factored part of a number F=p_1^(a_1)...p_r^(a_r), (1) where (R,F)=1, and R<sqrt(n). Pocklington's theorem, also known as the Pocklington-Lehmer ...

Define a Bouniakowsky polynomial as an irreducible polynomial f(x) with integer coefficients, degree >1, and GCD(f(1),f(2),...)=1. The Bouniakowsky conjecture states that ...

There are a number of functions in mathematics commonly denoted with a Greek letter lambda. Examples of one-variable functions denoted lambda(n) with a lower case lambda ...

MANOVA ("multiple analysis of variance") is a procedure for testing the equality of mean vectors of more than two populations. The technique is analogous to ANOVA for ...

The cubefree part is that part of a positive integer left after all cubic factors are divided out. For example, the cubefree part of 24=2^3·3 is 3. For n=1, 2, ..., the first ...

Let phi(n) be any function, say analytic or integrable. Then int_0^inftyx^(s-1)sum_(k=0)^infty(-1)^kx^kphi(k)dx=(piphi(-s))/(sin(spi)) (1) and ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...