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An almost unit is a nonunit in the integral domain of formal power series with a nonzero first coefficient, P=a_1x+a_2x^2+..., where a_1!=0. Under the operation of ...

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

There are two completely different definitions of Cayley numbers. The first and most commonly encountered type of Cayley number is the eight elements in a Cayley algebra, ...

Also called a chain map. Given two chain complexes C_* and D_*, a chain homomorphism is given by homomorphisms alpha_i:C_i->D_i such that alpha degreespartial_C=partial_D ...

Suppose alpha:C_*->D_* and beta:C_*->D_* are two chain homomorphisms. Then a chain homotopy is given by a sequence of maps delta_p:C_p->D_(p-1) such that partial_D ...

In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

A common fraction is a fraction in which numerator and denominator are both integers, as opposed to fractions. For example, 2/5 is a common fraction, while (1/3)/(2/5) is ...

Let f*g denote the cross-correlation of functions f(t) and g(t). Then f*g = int_(-infty)^inftyf^_(tau)g(t+tau)dtau (1) = ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

erf(z) is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by ...