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Any discrete finite wavelet transform can be represented as a matrix, and such a wavelet matrix can be computed in O(n) steps, compared to O(nlgn) for the Fourier matrix, ...

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

Let phi(x_1,...,x_m) be an L_(exp) formula, where L_(exp)=L union {e^x} and L is the language of ordered rings L={+,-,·,<,0,1}. Then there exist n>=m and f_1,...,f_s in ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

The zeta Fuchsians are class of functions discovered by Poincaré which are related to the automorphic functions.

The zonal polynomials are a class of orthogonal polynomials. They are a special case of the Jack polynomials corresponding to the case alpha=2.

The quintic equation x^5+ax^3+1/5a^2x+b=0 (1) is sometimes known as de Moivre's quintic (Spearman and Williams 1994). It has solutions x_j=omega^ju_1+omega^(4j)u_2 (2) for ...

Diagonalize a form over the rationals to diag[p^a·A,p^b·B,...], where all the entries are integers and A, B, ... are relatively prime to p. Then the p-signature of the form ...

Two integers are relatively prime if they share no common positive factors (divisors) except 1. Using the notation (m,n) to denote the greatest common divisor, two integers m ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...