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A function f(x) is said to be square integrable if int_(-infty)^infty|f(x)|^2dx is finite.

The definition of an Anosov map is the same as for an Anosov diffeomorphism except that instead of being a diffeomorphism, it is a map. In particular, an Anosov map is a C^1 ...

In mathematics, a formal language is normally defined by an alphabet and formation rules. The alphabet of a formal language is a set of symbols on which this language is ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

If replacing each number by its square in a magic square produces another magic square, the square is said to be a bimagic square. Bimagic squares are also called doubly ...

There are two common definitions of the trapezium. The American definition is a quadrilateral with no parallel sides; the British definition is a quadrilateral with two sides ...

If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...

Assume that f is a nonnegative real function on [0,infty) and that the two integrals int_0^inftyx^(p-1-lambda)[f(x)]^pdx (1) int_0^inftyx^(q-1+mu)[f(x)]^qdx (2) exist and are ...

The Gibbs phenomenon is an overshoot (or "ringing") of Fourier series and other eigenfunction series occurring at simple discontinuities. It can be reduced with the Lanczos ...

Sequences of integers generated in the Collatz problem. For example, for a starting number of 7, the sequence is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...