For an image pixel information can be converted to the moments of some basis Qk, e.g. Fourier–Mellin, Zernike, monomials, etc. Given sufficient number of moments pixel information can be completely recovered, for insufficient number of moments only partial information can be recovered and the image reconstruction is, at best, of interpolatory type. Standard approach is to present interpolated v...

This work was carried out while the authors were at Washington University, St. Louis, in the Mathematics and Electrical Engineering Departments, respectively. Di Biase thanks the C.N.R. (Italy) for support, through grants 203.01.55 and 203.01.63. We propose an improvement upon the standard algorithm for computing the kernel of a polynomial map, assuming that the map sends monomials into monomia...

let  $r$ be a commutative noetherian ring and $i$ be an ideal of $r$. we say that $i$ satisfies the persistence property if  $mathrm{ass}_r(r/i^k)subseteq mathrm{ass}_r(r/i^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{ass}_r(r/i)$ denotes the set of associated prime ideals of $i$. in this paper, we introduce a class of square-free monomial ideals in the polynomial ring  $r=k[x_1,ld...

The multigraded Poincaré-Betti series P k R(x̄; t) of a monomial ring k[x̄]/〈M〉 on a finite number of monomial generators has the form ∏ xi∈x̄ (1+xit)/bR,k(x̄; t), where bR,k(x̄; t) is a polynomial depending only on the monomial set M and the characteristic of the field k. I present a computer program designed to calculate the polynomial bR,k for a given field characteristic and a given set of monom...

Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing recurrence relations of a sequence with the Berlekamp–Massey algorithm. Likewise, multivariate interpolation and multidimensional cyclic code decoding require guessing sequence. Several algorithms solve this problem. The so-ca...

Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the standard monomial basis for a larger degree d. The standard way of solving polynomial eigenvalue problems proceeds by linearization, which in...

This presentation will introduce noncommutative analogs of monomial symmetric functions (and their dual, forgotten symmetric functions). In analogy to the classical theory, expansion of ribbon Schur functions in this basis in nonnegative. Moreover, one can define fundamental noncommutative symmetric functions by analogy with quasi-symmetric theory. The expansion of ribbon Schur functions in thi...

This paper simplifies and generalizes an earlier result of the author's on Gauss interpolation formulas for the one-dimensional heat equation. Such formulas approximate a function at a point (x*, t*) in terms of a linear combination of its values on an initial-boundary curve in the (x, t) plane. The formulas are characterized by the requirement that they be exact for as many basis functions as ...

For n ≥ 3, let Ωn be the set of line segments between the vertices of a convex n-gon. For j ≥ 2, a j-crossing is a set of j line segments pairwise intersecting in the relative interior of the n-gon. For k ≥ 1, let ∆n,k be the simplicial complex of (type-A) generalized triangulations, i.e. the simplicial complex of subsets of Ωn not containing any (k + 1)-crossing. The complex ∆n,k has been the ...

Let A be a commutative Noetherian ring, and let R = A[X] be the polynomial ring in an infinite collection X of indeterminates over A. Let SX be the group of permutations of X. The group SX acts on R in a natural way, and this in turn gives R the structure of a left module over the left group ring R[SX ]. We prove that all ideals of R invariant under the action of SX are finitely generated as R[...