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A theorem stating the existence of an object, such as the solution to a problem or equation. Strictly speaking, it need not tell how many such objects there are, nor give ...

The validity of a logical argument refers to whether or not the conclusion follows logically from the premises, i.e., whether it is possible to deduce the conclusion from the ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

The Laplace-Carson transform F of a real-valued function f is an integral transform defined by the formula F(p)=pint_0^inftye^(-pt)f(t)dt. (1) In most cases, the function F ...

The term "pathological" is used in mathematics to refer to an example specifically cooked up to violate certain almost universally valid properties. Pathological problems ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

A contingency table, sometimes called a two-way frequency table, is a tabular mechanism with at least two rows and two columns used in statistics to present categorical data ...

The biconjugate gradient method often displays rather irregular convergence behavior. Moreover, the implicit LU decomposition of the reduced tridiagonal system may not exist, ...