Related papers: A decomposition theorem on differential polynomial…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
We give a characterization of decomposition theory in linear algebra.
We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.
In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…
In this paper we partially settle our conjecture from [1] (math.SP/0701143) on roots of eigenpolynomials for degenerate exactly-solvable operators. Namely, for any such operator, we establish a lower bound (which supports our conjecture)…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
In this article, we prove an asymptotic formula for mean values of long Dirichlet polynomials with higher order shifted divisor functions, assuming a smoothed additive divisor conjecture for higher order shifted divisor functions. As a…
We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.
An algebraic deformation theory of dialgebra morphisms is obtained.
A peeling theorem for the Weyl tensor in higher dimensional Lorentzian manifolds is presented. We obtain it by generalizing a proof from the four dimensional case. We derive a generic behavior, discuss interesting subcases and retrieve the…
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
In this note we provide proofs of various expressions for expectation values of symmetric polynomials in $\beta$-deformed eigenvalue models with quadratic, linear, and logarithmic potentials. The relations we derive are also referred to as…
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
Recently, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with…
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
We consider random polynomials with independent identically distributed coefficients with a fixed law. Assuming the Riemann hypothesis for Dedekind zeta functions, we prove that such polynomials are irreducible and their Galois groups…
An algebraic deformation theory of coalgebra morphisms is constructed.
We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric polynomials.
The main aim of this paper is to define and investigate a new class of the degenerate poly-Frobenius-Genocchi polynomials with the help of the polyexponential functions. In this paper, we define the degenerate poly-Frobenius-Genocchi…