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There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

The breaking up of self-intersecting polygons into simple polygons (illustrated above) is also called tessellation (Woo et al. 1999).

The l^infty-polynomial norm defined for a polynomial P=a_kx^k+...+a_1x+a_0 by ||P||_infty=max_(k)|a_k|. Note that some authors (especially in the area of Diophantine ...

The ith Pontryagin class of a vector bundle is (-1)^i times the ith Chern class of the complexification of the vector bundle. It is also in the 4ith cohomology group of the ...

The upper horizontal line segment in the above figure appears to be longer than the lower line segment despite the fact that both are the same length.

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

The study of harmonic functions (also called potential functions).

A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies: 1. Reflexivity: a<=a for all a in S. 2. Transitivity: a<=b and b<=c implies a<=c. A preorder ...

A knot obtained from a tangle which can be represented by a finite sequence of integers.

Find two numbers such that x^2=y^2 (mod n). If you know the greatest common divisor of n and x-y, there exists a high probability of determining a prime factor. Taking small ...