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The triangular inequalities are the inequalities |x-y|<=z<=x+y for real numbers (x,y,z) (Messiah 1962, p. 1056). If these inequalities hold for any one permutation of ...

Trigonometric functions of pi/p for p prime have an especially complicated Galois-minimal representation. In particular, the case cos(pi/23) requires approximately 500 MB of ...

A generalization of spun knots due to Zeeman. This method produces four-dimensional knot types that cannot be produced by ordinary spinning.

Variables x_i and x_j are said to be uncorrelated if their covariance is zero: cov(x_i,x_j)=0. Independent statistics are always uncorrelated, but the converse is not ...

An expression in mathematics which does not have meaning and so which is not assigned an interpretation. For example, division by zero is undefined in the field of real ...

A graph in which individual nodes have no distinct identifications except through their interconnectivity. Graphs in which labels (which are most commonly numbers) are ...

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 ...

In general, there is no unique matrix solution A to the matrix equation y=Ax. Even in the case of y parallel to x, there are still multiple matrices that perform this ...

The W-transform of a function f(x) is defined by the integral where Gamma[(beta_m)+s, 1-(alpha_n)-s; (alpha_p^(n+1))+s, 1-(beta_q^(m+1))-s] =Gamma[beta_1+s, ..., beta_m+s, ...

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers ...