Related papers: On differential equations invariant under two-vari…
In this paper, we show that when two systems of differential equations admitting a symmetry group are related by a point transformation it is always possible to generate invariant schemes, one for each system, that are also related by the…
Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. Applications to partial…
We introduce a new method for computing the heat invariants of a 2-dimensional Riemannian manifold based on a result by S.Agmon and Y.Kannai. Two explicit expressions for the heat invariants are presented. The first one depends on the…
In this paper we present two different problems within the framework of shift-invariant theory. First, we develop a triangular form for shift-preserving operators acting on finitely generated shift-invariant spaces. In case of the normal…
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar…
We solve the classification problem for integrable lattices of the form $u_{,t}=f(u_{-2},\dots,u_2)$ under the additional assumption of invariance with respect to the group of linear-fractional transformations. The obtained list contains 5…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
In this short paper we compute the values of Dijkgraaf-Witten invariants over $Z_2$ for all orientable Seifert manifolds with orientable bases.
This article is the first in the cycle from two parts. It develops the ideas of integral manifolds method of M. M. Bogolubov in the case of linear differential equations in $R^m$ with variable coefficients. We distinguish linear subspaces…
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution…
In this paper, we discuss foliations by real curves. We investigate differential equations which are modifications of du/dx = v along leaves. Our focus is on having a solution operator so that u is continuous if v is continuous.
We consider the algebra of invariants of binary forms of degree 10 with complex coefficients, construct a system of parameters with degrees 2, 4, 6, 6, 8, 9, 10, 14 and find the 106 basic invariants.
Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and…
We consider the question of computing invariant measures from an abstract point of view. We work in a general framework (computable metric spaces, computable measures and functions) where this problem can be posed precisely. We consider…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…