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The motivating force of topology, consisting of the study of smooth (differentiable) manifolds. Differential topology deals with nonmetrical notions of manifolds, while ...

A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because ...

The order-n dipole graph D_n is a multigraph consisting of two vertices and n multiple edges joining them. The dipole graph D_2 is a multigraph that can be considered to ...

For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ij):M_i->M_j i<=j be an R-module homomorphism. Call (M_i,sigma_(ij)) a direct system over I ...

The curve d(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u).

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...

A divergenceless vector field, also called a solenoidal field, is a vector field for which del ·F=0. Therefore, there exists a G such that F=del xG. Furthermore, F can be ...