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A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

Consider a probability space specified by the triple (S,S,P), where (S,S) is a measurable space, with S the domain and S is its measurable subsets, and P is a measure on S ...

A Bergman kernel is a function of a complex variable with the "reproducing kernel" property defined for any domain in which there exist nonzero analytic functions of class ...

A pseudoanalytic function is a function defined using generalized Cauchy-Riemann equations. Pseudoanalytic functions come as close as possible to having complex derivatives ...

A representation of a Lie algebra g is a linear transformation psi:g->M(V), where M(V) is the set of all linear transformations of a vector space V. In particular, if V=R^n, ...

A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

A topological space X fulfils the T1-separation axiom and is normal. A space fulfilling the T_4-separation axiom is said to be a T4-space.

Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain maps phi:C_*->D_* and ...