Related papers: Hyperdeterminant and an integrable partial differe…
This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the…
We consider a linear partial integro-differential equation that arises in the modeling of various physical and biological processes. We study the problem in a spatial periodic domain. We analyze numerical stability and numerical convergence…
In this paper we describe the derivations of orthosymplectic Lie superalgebras over a superring. In particular, we derive sufficient conditions under which the derivations can be expressed as a semidirect product of inner and outer…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
The hyperdeteminants considered here are the simplest analogues of determinants for higher rank tensors which have been defined by Cayley, and apply only to tensors with an even number of indices. We have shown in a previous article that…
This is a complement to our paper arXiv:0802.1461. We study irreducibility of spectral determinants of some one-parametric eigenvalue problems in dimension one with polynomial potentials.
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
For a purely imaginary sign-definite perturbation of a self-adjoint operator, we obtain exponential representations for the perturbation determinant in both upper and lower half-planes and derive respective trace formulas.
We derive here some mathematical properties of the Weertman equation and show it is the limit of an evolution equation. The Weertman equation is a semilinear integrodifferential equation involving a fractional Laplacian. In addition to this…
The phenomenon of removable singularity is studied for overedetermined systems of differential equations. We show that the dimension of the characteristic variety plays a key role in the problem.
The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…
A recurring task in particle physics and statistics is to compute the complex critical points of a product of powers of affine-linear functions. The logarithmic discriminant characterizes exponents for which such a function has a degenerate…
We use ideas from our previous work to obtain some theorems that will allow us to obtain the integer solution of a quadratic polynomial in two variables that represents a natural number
In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that…
In this work, for an equation of high even order with a fractional derivative in the sense of Caputo, a problem is studied in a rectangular domain with conjugation conditions. A criterion for the uniqueness of a solution is given. The…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
We study the factorization of the PT symmetric Hamiltonian. The general expression for the superpotential corresponding to the PT symmetric potential is obtained and explicit examples are presented.
A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.
Motivated by applications to probability and mathematical finance, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable…