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A set fixed within the framework of a theory and consisting of all objects considered in this theory. The complement of the universal set is the empty set.

Let the greatest term H of a sequence be a term which is greater than all but a finite number of the terms which are equal to H. Then H is called the upper limit of the ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

Any discrete finite wavelet transform can be represented as a matrix, and such a wavelet matrix can be computed in O(n) steps, compared to O(nlgn) for the Fourier matrix, ...

A sequence of numbers V={nu_n} is said to be weakly complete if every positive integer n beyond a certain point N is the sum of some subsequence of V (Honsberger 1985). ...

The operator e^(nut^2/2) which satisfies e^(nut^2/2)p(x)=1/(sqrt(2pinu))int_(-infty)^inftye^(-u^2/(2nu))p(x+u)du for nu>0.

A function, continuous in a finite closed interval, can be approximated with a preassigned accuracy by polynomials. A function of a real variable which is continuous and has ...

A finite sequence of n letters from some alphabet is said to be an n-ary word.

A zero-sum game is a game in which players make payments only to each other. In such a game, one player's loss is the other player's gain, so the total amount of "money" ...

Theory of Computation