ar X iv : m at h / 05 01 14 5 v 1 [ m at h . D S ] 1 0 Ja n 20 05 WAVELET CONSTRUCTIONS IN NON - LINEAR DYNAMICS

ar X iv : m at h / 05 01 25 7 v 1 [ m at h . C A ] 1 7 Ja n 20 05 FACTORIZATION OF SYMMETRIC POLYNOMIALS

We construct linear operators factorizing the three bases of symmetric polynomials: monomial symmetric functions mλ(x), elementary symmetric polynomials Eλ(x), and Schur functions sλ(x), into products of univariate polynomials.

ar X iv : m at h / 05 01 16 3 v 1 [ m at h . C A ] 1 1 Ja n 20 05 GENERALIZATIONS OF GONÇALVES ’ INEQUALITY

Let F (z) = N n=0 anz n be a polynomial with complex coefficients and roots α 1 ,. .. , α N , let F p denote its Lp norm over the unit circle, and let F 0 denote Mahler's measure of F. Gonçalves' inequality asserts that

ar X iv : m at h / 05 01 45 4 v 1 [ m at h . A G ] 2 5 Ja n 20 05 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES

We calculate the dimension of the locus of elliptic surfaces over P 1 with a section and a given Picard number, in the corresponding moduli space.

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric

ar X iv : m at h / 05 01 55 6 v 1 [ m at h . D G ] 3 1 Ja n 20 05 Geometric Algebras

This is the first paper in a series of three where we develope a systematic approach to the geometric algebras of multivectors and ex-tensors. The series is followed by another one where those algebraic concepts are used in a novel presentation of the differential geometry of (smooth) manifolds of arbitrary global topology. The key calcu-lational tool in our program is the euclidean geometrical...