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A function f(x) is completely convex in an open interval (a,b) if it has derivatives of all orders there and if (-1)^kf^((2k))(x)>=0 for k=0, 1, 2, ... in that interval ...

A map f:X-->Y is called constant with constant value y if f(x)=y for all x in X, i.e., if all elements of X are sent to same element y of Y.

The cumulative count of property P for a sequence S_n={a_1,a_2,...,a_n} is a sequence of counts of the numbers of elements a_i with i<=k that satisfy P for k=1, 2, ..., n. ...

There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

Let f(x,y) be a homogeneous function of order n so that f(tx,ty)=t^nf(x,y). (1) Then define x^'=xt and y^'=yt. Then nt^(n-1)f(x,y) = ...

By analogy with the geometric centroid, the centroid of an arbitrary function f(x) is defined as <x>=(intxf(x)dx)/(intf(x)dx), (1) where the integrals are taken over the ...

The convex hull of two or more functions is the largest function that is concave from above and does not exceed the given functions.

The solution to a game in game theory. When a game saddle point is present max_(i<=m)min_(j<=n)a_(ij)=min_(j<=n)max_(i<=m)a_(ij)=v, and v is the value for pure strategies.

A global extremum, also known as an absolute extremum, is a global minimum or global maximum. It is impossible to construct an algorithm that will find a global extremum for ...