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The midpoint of the first and second Brocard points Omega and Omega^'. It has equivalent triangle center functions alpha = a(b^2+c^2) (1) alpha = sin(A+omega), (2) where ...

Any continuous function G:B^n->B^n has a fixed point, where B^n={x in R^n:x_1^2+...+x_n^2<=1} is the unit n-ball.

A real-valued stochastic process {B(t):t>=0} is a Brownian motion which starts at x in R if the following properties are satisfied: 1. B(0)=x. 2. For all times ...

The algorithm for the construction of a Gröbner basis from an arbitrary ideal basis. Buchberger's algorithm relies on the concepts of S-polynomial and polynomial reduction ...

A hypothetic building design problem in optimization with constraints proposed by Bhatti (2000, pp. 3-5). To save energy costs for heating and cooling, an architect wishes to ...

The Bump-Ng theorem (and also the title of the paper in which it was proved) states that the zeros of the Mellin transform of Hermite functions have real part equal to 1/2.

Given any open set U in R^n with compact closure K=U^_, there exist smooth functions which are identically one on U and vanish arbitrarily close to U. One way to express this ...

A real vector bundle pi:E->M has an orientation if there exists a covering by trivializations U_i×R^k such that the transition functions are vector space ...

The rank of a vector bundle is the dimension of its fiber. Equivalently, it is the maximum number of linearly independent local bundle sections in a trivialization. ...

The partial differential equation u_t+uu_x=nuu_(xx) (Benton and Platzman 1972; Zwillinger 1995, p. 417; Zwillinger 1997, p. 130). The so-called nonplanar Burgers equation is ...