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A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

Specifying three sides uniquely determines a triangle whose area is given by Heron's formula, K=sqrt(s(s-a)(s-b)(s-c)), (1) where s=1/2(a+b+c) (2) is the semiperimeter of the ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for ...

A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function f. It therefore "blends" one function with another. ...

The Gelfand transform x|->x^^ is defined as follows. If phi:B->C is linear and multiplicative in the senses phi(ax+by)=aphi(x)+bphi(y) and phi(xy)=phi(x)phi(y), where B is a ...

In music, if a note has frequency f, integer multiples of that frequency, 2f,3f,4f and so on, are known as harmonics. As a result, the mathematical study of overlapping waves ...

Writing a Fourier series as f(theta)=1/2a_0+sum_(n=1)^(m-1)sinc((npi)/(2m))[a_ncos(ntheta)+b_nsin(ntheta)], where m is the last term, reduces the Gibbs phenomenon. The ...

A spiral that gives the solution to the central orbit problem under a radial force law r^..=-mu|r|^(-3)r^^, (1) where mu is a positive constant. There are three solution ...

A forgetful functor (also called underlying functor) is defined from a category of algebraic gadgets (groups, Abelian groups, modules, rings, vector spaces, etc.) to the ...