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In order for a band-limited (i.e., one with a zero power spectrum for frequencies nu>B) baseband (nu>0) signal to be reconstructed fully, it must be sampled at a rate nu>=2B. ...

A scalar is a one-component quantity that is invariant under rotations of the coordinate system.

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

The Schwarzian derivative is defined by D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2. The Feigenbaum constant is universal for one-dimensional maps if its ...

The second Brocard Cevian triangle is the Cevian triangle of the second Brocard point. It has area Delta_2=(2a^2b^2c^2)/((a^2+b^2)(b^2+c^2)(c^2+a^2))Delta, where Delta is the ...

A 10-digit number satisfying the following property. Number the digits 0 to 9, and let digit n be the number of ns in the number. There is exactly one such number: 6210001000.

Given an ideal A, a semiprime ring is one for which A^n=0 implies A=0 for any positive n. Every prime ring is semiprime.

A graph G is said to be separable if it is either disconnected or can be disconnected by removing one vertex, called articulation. A graph that is not separable is said to be ...

Two distinct point pairs AC and BD separate each other if A, B, C, and D lie on a circle (or line) in such order that either of the arcs (or the line segment AC) contains one ...