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Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...

A dihedron is a regular tiling or map on a sphere composed of two regular p-gons, each occupying a hemisphere and with edge lengths of 2pi/p on a unit sphere. Its Schläfli ...

An expansion based on the roots of x^(-n)[xJ_n^'(x)+HJ_n(x)]=0, where J_n(x) is a Bessel function of the first kind, is called a Dini expansion.

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 ...

A directed infinity in direction z is an infinite numerical quantity that is a positive real multiple of the complex number z. Directed infinity may be returned in the ...

A plane parallel to two (or more) skew lines, also called a director plane. The orientation of a director is fixed, but it is specified uniquely only if a point lying on it ...

A piecewise regular function that 1. Has a finite number of finite discontinuities and 2. Has a finite number of extrema can be expanded in a Fourier series which converges ...

Discrete group theory is a broad subject covering certain aspects of groups. Such topics as free groups, group presentations, fundamental groups, Kleinian groups, and ...

Two sets A_1 and A_2 are disjoint if their intersection A_1 intersection A_2=emptyset, where emptyset is the empty set. n sets A_1, A_2, ..., A_n are disjoint if A_i ...

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...