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The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" ...

The Heaviside step function is a mathematical function denoted H(x), or sometimes theta(x) or u(x) (Abramowitz and Stegun 1972, p. 1020), and also known as the "unit step ...

The order ideal in Lambda, the ring of integral laurent polynomials, associated with an Alexander matrix for a knot K. Any generator of a principal Alexander ideal is called ...

The determination of the number of alternating permutations having elements {1,2,...,n}.

A Sheffer sequence for (1,f(t)) is called the associated sequence for f(t), and a sequence s_n(x) of polynomials satisfying the orthogonality conditions ...

The evolute of the astroid is a hypocycloid evolute for n=4. Surprisingly, it is another astroid scaled by a factor n/(n-2)=4/2=2 and rotated 1/(2·4)=1/8 of a turn. For an ...

The average power of a complex signal f(t) as a function of time t is defined as <f^2(t)>=lim_(T->infty)1/(2T)int_(-T)^T|f(t)|^2dt, where |z| is the complex modulus (Papoulis ...

A pattern tau=(tau_1,...,tau_n) is said to avoid alpha=(alpha_1,...,alpha_k) if alpha is not contained in tau. In other words, tau avoids alpha iff no k-subset of tau is ...

For a measurable function mu, the Beltrami differential equation is given by f_(z^_)=muf_z, where f_z is a partial derivative and z^_ denotes the complex conjugate of z.

A relation between compact boundaryless manifolds (also called closed manifolds). Two closed manifolds are bordant iff their disjoint union is the boundary of a compact ...