Related papers: Algebraic solutions of linear differential equatio…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
In the framework of idempotent mathematics, analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck are studied. Idempotent versions of nuclear spaces (in the sense of A. Grothendieck) are discussed. The so-called…
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.
In this paper, we investigate the geometric, algebraic and analytic properties of the hyperelliptic $\mathrm{al}_{ab}$ functions of a hyperelliptic curve $X$ with genus $g$ as the $\mathrm{al}_{ab}$ functions together with the…
The main contribution of this paper is that every convex function with non-empty relative algebraic interior of its domain is Lipschitz and subdifferentiable in some algebraic sense without any additional topological constraints. The…
In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coefficients. We use monogenic functions that are defined on…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…
In this paper, we extend a classical approach to linear quadratic (LQ) optimal control via Popov operators to abstract linear differential-algebraic equations (ADAEs) in Hilbert spaces. To ensure existence of solutions, we assume that the…
Let X be a smooth projective curve of genus >1 over a field K which is finitely generated over the rationals. The section conjecture in Grothendieck's anabelian geometry says that the sections of the canonical projection from the arithmetic…
Two unanswered questions in the heart of the theory of Leavitt path algebras are whether Grothendieck group $K_0$ is a complete invariant for the class of unital purely infinite simple algebras and, a weaker question, whether $L_2$ (the…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed p-adic fields.…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…