Search Results for ""

A group automorphism is an isomorphism from a group to itself. If G is a finite multiplicative group, an automorphism of G can be described as a way of rewriting its ...

If a cyclic quadrilateral ABCD is inscribed in a circle c_1 of a coaxal system such that one pair AC of connectors touches another circle c_2 of the system at P, then each ...

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...

A generalization of the product rule for expressing arbitrary-order derivatives of products of functions, where (n; k) is a binomial coefficient. This can also be written ...

The Mangoldt function is the function defined by Lambda(n)={lnp if n=p^k for p a prime; 0 otherwise, (1) sometimes also called the lambda function. exp(Lambda(n)) has the ...

Given vectors u and v, the vector direct product, also known as a dyadic, is uv=u tensor v^(T), where tensor is the Kronecker product and v^(T) is the matrix transpose. For ...

The Johnson circumconic, a term used here for the first time, is the circumconic that passes through the vertices of both the reference triangle and the Johnson triangle. It ...