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The Gelfand transform x|->x^^ is defined as follows. If phi:B->C is linear and multiplicative in the senses phi(ax+by)=aphi(x)+bphi(y) and phi(xy)=phi(x)phi(y), where B is a ...

The function defined by y=ab^(q^x). It is used in actuarial science for specifying a simplified mortality law (Kenney and Keeping 1962, p. 241). Using s(x) as the probability ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

An apodization function, also called the Hann function, frequently used to reduce leakage in discrete Fourier transforms. The illustrations above show the Hanning function, ...

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point ...

A purple cow is a confirming instance of the hypothesis that all crows are black.

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

Let X be an infinite set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A,B in V(X) be finitary algebras with finitely many operations, and ...

An algorithm for partitioning (or clustering) N data points into K disjoint subsets S_j containing N_j data points so as to minimize the sum-of-squares criterion ...