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A function f(x) is said to be strictly increasing on an interval I if f(b)>f(a) for all b>a, where a,b in I. On the other hand, if f(b)>=f(a) for all b>a, the function is ...

Strong convergence is the type of convergence usually associated with convergence of a sequence. More formally, a sequence {x_n} of vectors in a normed space (and, in ...

phi(A)+phi(B)-phi(A union B)>=phi(A intersection B).

The structure factor S_Gamma of a discrete set Gamma is the Fourier transform of delta-scatterers of equal strengths on all points of Gamma, S_Gamma(k)=intsum_(x in ...

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

Let M be an oriented regular surface in R^3 with normal N. Then the support function of M is the function h:M->R defined by h(p)=p·N(p).

A surface in 3-space can be parameterized by two variables (or coordinates) u and v such that x = x(u,v) (1) y = y(u,v) (2) z = z(u,v). (3) If a surface is parameterized as ...

Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for ...

Surrogate data are artificially generated data which mimic statistical properties of real data. Isospectral surrogates have identical power spectra as real data but with ...

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...