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A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

The field of semidefinite programming (SDP) or semidefinite optimization (SDO) deals with optimization problems over symmetric positive semidefinite matrix variables with ...

Let A be a commutative ring and let C_r be an R-module for r=0,1,2,.... A chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0 is said to ...

The trilinear coordinates alpha:beta:gamma of a point P relative to a reference triangle are proportional to the directed distances a^':b^':c^' from P to the side lines of ...

For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesic curvature kappa_g. Curves with kappa_g=0 are called ...

Given a distance-regular graph G with integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G at distance i=d(x,y), there are exactly c_i neighbors of y in ...

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

If f(z) is continuous in a region D and satisfies ∮_gammafdz=0 for all closed contours gamma in D, then f(z) is analytic in D. Morera's theorem does not require simple ...

Multisection of a mathematical quantity or figure is division of it into a number of (usually) equal parts. Division of a quantity into two equal parts is known as bisection, ...

The Rabinovich-Fabrikant equation is the set of coupled linear ordinary differential equations given by x^. = y(z-1+x^2)+gammax (1) y^. = x(3z+1-x^2)+gammay (2) z^. = ...