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The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...

If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a geometric realization of S, and is uniquely ...

If L is a subcollection of a simplicial complex K that contains all faces of its elements, then L is another simplicial complex called a simplicial subcomplex.

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

A power series sum^(infty)c_kx^k will converge only for certain values of x. For instance, sum_(k=0)^(infty)x^k converges for -1<x<1. In general, there is always an interval ...

The portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]<0, i.e., {x+iy:x in (-infty,infty),y in (-infty,0)}

The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc. The modulus ...

The word "place" has a special meaning in complex variables, where it roughly corresponds to a point in the complex plane (except that it reflects the Riemann sheet structure ...