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Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p) and numbers are assigned to the edges of a grid. A b-cluster is an ...

If a function analytic at the origin has no singularities other than poles for finite x, and if we can choose a sequence of contours C_m about z=0 tending to infinity such ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

A projective module generalizes the concept of the free module. A module M over a nonzero unit ring R is projective iff it is a direct summand of a free module, i.e., of some ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

Consider the general system of two first-order ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y). (2) Let x_0 and y_0 denote fixed points with x^.=y^.=0, so ...

A singular integral is an integral whose integrand reaches an infinite value at one or more points in the domain of integration. Even so, such integrals can converge, in ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

The Hilbert transform (and its inverse) are the integral transform g(y) = H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y) (1) f(x) = ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...