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Let f(x) be a positive definite, measurable function on the interval (-infty,infty). Then there exists a monotone increasing, real-valued bounded function alpha(t) such that ...

An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.

Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form beta and the same Kirby-Siebenmann invariant kappa. Any beta can be realized by ...

A global minimum, also known as an absolute minimum, is the smallest overall value of a set, function, etc., over its entire range. It is impossible to construct an algorithm ...

A number of attractive 11-compounds of the regular icosahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The characteristic escape rate from a stable state of a potential in the absence of signal.

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

A two-dimensional map similar to the Hénon map but with the term -alphax_n^2 replaced by -alpha|x_n|. It is given by the equations x_(n+1) = 1-alpha|x_n|+y_n (1) y_(n+1) = ...

h_t+(|h|^nh_(xxx))_x=0, where h(x,t) is the height of a film at position x and time t and n is a parameter characteristic of the surface forces.

The Minkowski measure of a bounded, closed set is the same as its Lebesgue measure.