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Define psi(x)={1 0<=x<1/2; -1 1/2<x<=1; 0 otherwise (1) and psi_(jk)(x)=psi(2^jx-k) (2) for j a nonnegative integer and 0<=k<=2^j-1. So, for example, the first few values of ...

An elliptic function can be characterized by its real and imaginary half-periods omega_1 and omega_2 (Whittaker and Watson 1990, p. 428), sometimes also denoted ...

The two-dimensional Hammersley point set of order m is defined by taking all numbers in the range from 0 to 2^m-1 and interpreting them as binary fractions. Calling these ...

On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

The Jacobian of the derivatives partialf/partialx_1, partialf/partialx_2, ..., partialf/partialx_n of a function f(x_1,x_2,...,x_n) with respect to x_1, x_2, ..., x_n is ...

The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

"Implies" is the connective in propositional calculus which has the meaning "if A is true, then B is also true." In formal terminology, the term conditional is often used to ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only ...