Related papers: Modular local polynomials

In this paper, we further investigate the local criterion and present a class of permutation polynomials and their compositional inverses over $ \mathbb{F}_{q^2}$. Additionally, we demonstrate that linearized polynomial over…

We provide a formula and a generating function for the dimension of the vector space of relative symmetric polynomials of D_n for all its irreducible one-dimensional and two-dimensional representations which were defined originally by M.…

It is shown that the modulation spaces $M_{p}^{w}$ can be characterized by the approximation behavior of their elements using Local Fourier bases. In analogy to the Local Fourier bases, we show that the modulation spaces can also be…

Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…

We describe algorithms for computing various functors for algebraic D-modules, i.e. systems of linear partial differential equations with polynomial coefficients. We will give algorithms for restriction, tensor product, localization, and…

We notice that for $0<d\le 6$ the Poincar\'e polynomial of Simpson moduli space $M_{dm + 1}(\mathbb P_2)$ is divisible by the Poincar\'e polynomial of the projective space $\mathbb P_{3d-1}$. A somehow regular behaviour of the difference of…

We study the maximum modulus set, $\mathcal{M}(p)$, of a polynomial $p$. We are interested in constructing $p$ so that $\mathcal{M}(p)$ has certain exceptional features. Jassim and London gave a cubic polynomial $p$ such that…

We give a construction which produces irreducible complex rigid local systems on $\Bbb{P}_{\Bbb{C}}^1-\{p_1,\dots,p_s\}$ via quantum Schubert calculus and strange duality. These local systems are unitary and arise from a study of vertices…

The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…

Categories of locally ordered spaces are especially well-adapted to the realization of most precubical sets, though their colimits are not so easy to determine (in comparison with colimits in the category of d-spaces for example). We use…

The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…

For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…

When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d>1, one obtains a finite group G^d which is often the automorphism group of an abstract regular polytope. Building…

Let $(A,\mathfrak{m})$ be a hypersurface local ring of dimension $d \geq 1$ and let $I$ be an $\mathfrak{m}$-primary ideal. We show that there is a non-negative integer $r_I$ (depending only on $I$) such that if $M$ is any non-free maximal…

We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…

In this article we provide examples, methods and algorithms to determine conditions on the parameters of certain type of parametric optimization problems, such that among the resulting local minima and maxima there is at least one which…

In this paper we study the density of polynomials in some $L^2(M)$ spaces. Two choices of the measure $M$ and polynomials are considered: 1) a $(N\times N)$ matrix non-negative Borel measure on $\mathbb{R}$ and vector-valued polynomials…

Let K be a subfield of the complex numbers, and let D be the Weyl algebra of K-linear differential operators on K[x_1,...,x_n]. If M and N are holonomic left D-modules we present an algorithm that computes explicit generators for the finite…

We investigate how effectively finite metric spaces can be distinguished by distance-based invariants. As model spaces, we consider regular polygons, cycle graphs, and their generalization, circular metric spaces, and as invariants we…

Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…