Related papers: Independence of hyperlogarithms over function fiel…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial…
This paper is concerned with the characterizations of the Friedrichs extension for a class of singular discrete linear Hamiltonian systems. The existence of recessive solutions and the existence of the Friedrichs extension are proved under…
The field equations for both generic bosonic and generic locally supersymmetric 2D dilatonic gravity theories in the absence of matter are written as free differential algebras. This constitutes a generalization of the gauge theoretic…
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate…
For a joint probability density function f(x) of a random vector X the mixed partial derivatives of log f(x) can be interpreted as limiting cumulants in an infinitesimally small open neighborhood around x. Moreover, setting them to zero…
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
The paper generalizes Lazarus Fuchs' theorem on the solutions of complex ordinary linear differential equations with regular singularities to the case of ground fields of arbitrary characteristic, giving a precise description of the shape…
We construct the field A generated by n algebraically independent elements, and show that the linear space of derivations over this field is faithfully represented by the linear space of the n-th fold Cartesian product of this field acting…
Given $k \ge 2$ polynomials in $d \ge 1$ variables with coefficients in a field of characteristic $0$, such that no two are linearly dependent, we show that for any integer $r$ greater than $\max\left\{k {k-1 \choose 2}, 2\right\}$, the…
This article studies separating invariants for the ring of multisymmetric polynomials in $m$ sets of $n$ variables over an arbitrary field $\mathbb{K}$. We prove that in order to obtain separating sets it is enough to consider polynomials…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions, along with their derivatives, then there is already…
We show that for every second order Fuchsian linear differential equation $E$ with $n$ singularities of which $n-3$ are apparent there exists a hypergeometric equation $H$ and a linear differential operator with polynomial coefficients…
Given some vector fields on a smooth manifold satisfying H\"ormander's condition, we define a bi-graded pseudo-differential calculus which contains the classical pseudo-differential calculus and a pseudo-differential calculus adapted to the…
This research concerns coefficient conditions for linear differential equations in the unit disc of the complex plane. In the higher order case the separation of zeros (of maximal multiplicity) of solutions is considered, while in the…
After H\"older proved his classical theorem about the Gamma function, there has been a whole bunch of results showing that solutions to linear difference equations tend to be hypertranscendental i.e. they cannot be solution to an algebraic…
We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator $D$ of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras…
Mathematical programs with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality-, and switching-constrained optimization problems.…
In the book, I considered differential equations of order $1$ over Banach $D$\Hyph algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. I considered examples of…