Orthonormal spin-flavor wave functions of Lorentz covariant quark models of the Bakamjian-Thomas type are constructed for nucleon resonances. Three different bases are presented. The manifestly Lorentz covariant Dirac-Melosh basis is related to the Pauli-Melosh basis and the symmetrized Bargmann-Wigner basis that are manifestly orthogonal.

The concept of a linear ordered orthogonal array is introduced, and its equivalent geometrical configuration is determined when its strength is 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.

Existing methods for solving Poisson's equation using basis functions can be made considerably more exible, yet simpler, by using non-orthogonal basis functions. The rst part of this paper describes how such basis sets can be constructed. The second part gives explicit formulas (up to quadratures and matrix inversions) for basis functions being spherical harmonics times radial functions; two ba...

For a class of orthogonal polynomials related to the q-Meixner polynomials corresponding to an indeterminate moment problem we give a one-parameter family of orthogonality measures. For these measures we complement the orthogonal polynomials to an orthogonal basis for the corresponding weighted L-space explicitly. The result is proved in two ways; by a spectral decomposition of a suitable opera...

An algebraic approach to the design of different binds of discrete wavelet transforma (orthogonal and biorthogonal single-/multiwavelet transforms, multiwavelet-like transforma) is taken. The different transfomrs are anaL ysed with respect to computational efforts, approzimation properties and symmetry. The design of the orthogonal and biorthogonal single-/multiwavelets requires the solution of...