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A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

The so-called rule of three is an educational tool utilized historically to verbalize the process of solving basic linear equations with four terms where three of the terms ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...

In a dynamical system, a bifurcation is a period doubling, quadrupling, etc., that accompanies the onset of chaos. It represents the sudden appearance of a qualitatively ...

The constant a_(-1) in the Laurent series f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n (1) of f(z) about a point z_0 is called the residue of f(z). If f is analytic at z_0, its ...

Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...

Consider the solid enclosed by the three hyperboloids specified by the inequalities x^2+y^2-z^2 <= 1 (1) y^2+z^2-x^2 <= 1 (2) z^2+x^2-y^2 <= 1. (3) This work dubs this solid ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

A genetic algorithm is a class of adaptive stochastic optimization algorithms involving search and optimization. Genetic algorithms were first used by Holland (1975). The ...