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Suppose that in some neighborhood of x=0, F(x)=sum_(k=0)^infty(phi(k)(-x)^k)/(k!) (1) for some function (say analytic or integrable) phi(k). Then ...

A set S of integers is said to be recursive if there is a total recursive function f(x) such that f(x)=1 for x in S and f(x)=0 for x not in S. Any recursive set is also ...

A strict order > on the set of terms of a term rewriting system is called a reduction order if 1. The set of terms is well ordered with respect to >, that is, all its ...

A system in which words (expressions) of a formal language can be transformed according to a finite set of rewrite rules is called a reduction system. While reduction systems ...

Regular expressions define formal languages as sets of strings over a finite alphabet. Let sigma denote a selected alphabet. Then emptyset is a regular expression that ...

If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a ...

Let A be a relational system, and let L be a language which is appropriate for A. Let phi be a well-formed formula of L, and let s be a valuation in A. Then A|=_sphi is ...

The Shaw Prizes are $1 million cash awards offered annually by Run Run Shaw (b. 1907), a longtime movie and television producer. There are prizes for astronomy, life science ...

Consider a formula in prenex normal form, Q_1x_1...Q_nx_nN. If Q_i is the existential quantifier (1<=i<=n) and x_k, ..., x_m are all the universal quantifier variables such ...

Twenty golfers wish to play in foursomes for 5 days. Is it possible for each golfer to play no more than once with any other golfer? The answer is yes, and the following ...