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The system of partial differential equations (partial_t+partial_z^3+partial_(z^_)^3)v+partial_z(uv)+partial_(z^_)(vw) (1) partial_(z^_)u=3partial_zv (2) ...

Let H=l^2, (alpha_n) be a bounded sequence of complex numbers, and (xi_n) be the (usual) standard orthonormal basis of H, that is, (xi_n)(m)=delta_(nm), n,m in N, where ...

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

A k-partite graph is a graph whose graph vertices can be partitioned into k disjoint sets so that no two vertices within the same set are adjacent.

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

An algorithm that can be used to factor a polynomial f over the integers. The algorithm proceeds by first factoring f modulo a suitable prime p via Berlekamp's method and ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...