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Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

If one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in mn ways.

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

The security of a cryptosystem must not depend on keeping the cryptographic algorithm secret.

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

If f(z) is meromorphic in a region R enclosed by a contour gamma, let N be the number of complex roots of f(z) in gamma, and P be the number of poles in gamma, with each zero ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

P_n(cosalpha)=(sqrt(2))/piint_0^alpha(cos[(n+1/2)phi])/(sqrt(cosphi-cosalpha))dphi, where P_n(x) is a Legendre polynomial.