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If one root of the equation f(x)=0, which is irreducible over a field K, is also a root of the equation F(x)=0 in K, then all the roots of the irreducible equation f(x)=0 are ...

A directed graph is called an arborescence if, from a given node x known as the root vertex, there is exactly one elementary path from x to every other node y.

The Fourier transform of e^(-k_0|x|) is given by F_x[e^(-k_0|x|)](k)=int_(-infty)^inftye^(-k_0|x|)e^(-2piikx)dx = ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

The Theodorus spiral, also known as the Einstein spiral, Pythagorean spiral, square root spiral, or--to contrast it with certain continuous analogs--the discrete spiral of ...

The natural norm induced by the L2-norm. Let A^(H) be the conjugate transpose of the square matrix A, so that (a_(ij))^(H)=(a^__(ji)), then the spectral norm is defined as ...

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.

The wave equation in prolate spheroidal coordinates is del ...

Q_n^((alpha,beta))(x)=2^(-n-1)(x-1)^(-alpha)(x+1)^(-beta) ×int_(-1)^1(1-t)^(n+alpha)(1+t)^(n+beta)(x-t)^(-n-1)dt. In the exceptional case n=0, alpha+beta+1=0, a nonconstant ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...