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The mathematical study of how to manipulate the parameters affecting the behavior of a system to produce the desired or optimal outcome.

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 ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

The radical circle of the excircles has center at the Spieker center X_(10) and radius R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)). Its circle function is ...

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

A global minimum, also known as an absolute minimum, is the smallest overall value of a set, function, etc., over its entire range. It is impossible to construct an algorithm ...

The Goldberg graphs are a family of graphs discovered by Goldberg (1981) which are snarks for n=5, 7, 9, .... Precomputed properties of Goldberg graphs are implemented in the ...

A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...

Let Gamma be a representation for a group of group order h, then sum_(R)Gamma_i(R)_(mn)Gamma_j(R)_(m^'n^')^*=h/(sqrt(l_il_j))delta_(ij)delta_(mm^')delta_(nn^'). The proof is ...

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...