Nonsquare spectral factors via factorizations of a unitary function

On uniformly nonsquare points and nonsquare points of Orlicz spaces*

For Orlicz spaces endowed with the Orlicz norm and the Luxemburg norm, the criteria for uniformly nonsquare points and nonsquare points are given.

Factors and Factorizations of Graphs

Unitary Matrix Integrals, Primitive Factorizations, and Jucys-Murphy Elements

A factorization of a permutation into transpositions is called “primitive” if its factors are weakly ordered. We discuss the problem of enumerating primitive factorizations of permutations, and its place in the hierarchy of previously studied factorization problems. Several formulas enumerating minimal primitive and possibly non-minimal primitive factorizations are presented, and interesting co...

Spectral Factorizations and Sums Ofsquares Representations

In this paper we nd a characterization for when a multivariable trigonometric polynomial can be written as a sum of squares. In addition, the truncated moment problem is addressed. A numerical algorithm for nding a sum of squares representation is presented as well. In the one-variable case, the algorithm nds a spectral factorization. The latter may also be used to nd inner-outer factor-izations.

Factors affecting pitch judgments as a function of spectral composition.

Stimulated by a recent paper by Platt and Racine (1985), we discuss the factors that probably are involved in certain inconsistencies observed in pitch judgments of tones with different spectral composition. Typically, discrepancies reported in the literature are of the order of 10 cents in magnitude. We point out that measurement of such small pitch effects is heavily dependent on systematic i...