Polynomial Ring Generated by Tableau Shapes

Ring With All Finitely Generated Modules Retractable

Rigid Divisibility Sequences Generated by Polynomial Iteration

The goal of this thesis is to explore the properties of a certain class of sequences, rigid divisibility sequences, generated by the iteration of certain polynomials whose coefficients are algebraic integers. The main goal is to provide, as far as is possible, a classification and description of those polynomials which generate rigid divisibility sequences.

Function Approximation by Polynomial Wavelets Generated

Wavelet functions have been successfully used in many problems as the activation function of feedforward neural networks ZB92],,STK92], PK93]. In this paper, a family of polynomial wavelets generated from powers of sigmoids is described which provides a robust way for designing neural network architectures. It is shown, through experimentation, that function members of this family can present a...

ring with all finitely generated modules retractable

Expansions in the Polynomial Ring

Astract We show here that some simple combinatorial facts concerning arrangements of pebbles on an n×n board have surprising consequences in the study of expansions in the polynomial ring Q[x 1 , x 2 ,. .. , x n ]. In particular in this manner we obtain a purely combinatorial proof of an identity of Lascoux-Schutzenberger given in Funkt. Anal 21 (1987) 77-78.