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The equation f(x_n|x_s)=int_(-infty)^inftyf(x_n|x_r)f(x_r|x_s)dx_r which gives the transitional densities of a Markov sequence. Here, n>r>s are any integers (Papoulis 1984, ...

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...

The cokernel of a group homomorphism f:A-->B of Abelian groups (modules, or abstract vector spaces) is the quotient group (quotient module or quotient space, respectively) ...

Given an arithmetic series {a_1,a_1+d,a_1+2d,...}, the number d is called the common difference associated to the sequence.

Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y=y*x. (1) Real numbers are commutative under addition x+y=y+x (2) and ...

A requirement necessary for a given statement or theorem to hold. Also called a criterion.

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are equipotential curve, isarithm, and isopleth. A plot of several ...

A formal structure for the organization of information. Examples of data structures include the list, queue, stack, and tree.

A continuum is a decomposable continuum if and only if it is the union of two of its proper subcontinua. A continuum that is not decomposable is an indecomposable continuum.

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...