Related papers: On a differential inclusion related to the Born-In…
In this note, we explore the connections between the confluent Vandermonde matrix over an arbitrary field and several mathematical topics, including interpolation polynomials, Hasse derivatives, LU factorization, companion matrices and…
We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those…
Extensions to the trapezoidal rule using derivative information are studied for periodic integrands and integrals along the entire real line. Integrands which are analytic within a half plane or within a strip containing the path of…
In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
We have developed a Green's function formalism to compute the local field distribution near an interface separating two media of different dielectric constants. The Maxwell's equations are converted into a surface integral equation; thus it…
In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial differential equation describing the time evolution of the…
This research introduces a new method for the transition from partial to ordinary differential equations that is based on the Kolmogorov superposition theorem. In this paper, we discuss the numerical implementation of the Kolmogorov theorem…
We study Bohr type inequalities within the framework of fractional calculus. Using Riemann Liouville fractional differential and integral operators, we establish generalized Bohr radii for analytic functions in the unit disk, including the…
In a gravitational field, we analyze the Maxwell equations, the correponding electromagnetic wave and continuity equations. A particular solution for parellel electric and magnetic fields in a gravitational background is presented. These…
An integral for a scalar function with respect to a multimeasure $N$ taking its values in a locally convex space is introduced. The definition is independent of the selections of $N$ and is related to a functional version of the…
We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…
In this paper we study the relationship of the Brouwer degree of a vector field with the dynamics of the induced flow. Analogous relations are studied for the index of a vector field. We obtain new forms of the Poincar% \'{e}-Hopf theorem…
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the…
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter Ref.19 is extended to the case of the multisymplectic…
We study a few approaches to identify inclusion (up to a shift) between two convex bodies in ${\mathbb R}^n$. To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or…
In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation…