Related papers: Cartan equivalence problem for third order differe…
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
Ordinary differential equations have an arithmetic analogue in which functions are replaced by numbers and the derivation operator is replaced by a Fermat quotient operator. In this survey we explain the main motivations, constructions,…
The aim of this article is further development of the theory of linear difference equations with constant coefficients. We present a new algorithm for calculating the solution to the Cauchy problem for a three-dimensional difference…
In the inverse problem of the calculus of variations one is asked to find a Lagrangian and a multiplier so that a given differential equation, after multiplying with the multiplier, becomes the Euler--Lagrange equation for the Lagrangian.…
In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…
In previous works, questioning the mathematical nature of the connection in the translations gauge theory formulation of Teleparallel Equivalent to General Relativity (TEGR) Theory led us to propose a new formulation using a Cartan…
We find shift operators for the Dotsenko-Fateev equation, which is a differential equation of order 3, and for the three Fuchsian differential equations of order 4, 5 and 6, respectively, which are connected with the Dotsenko-Fateev…
In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…
In a recent paper we presented a truncation-type method of deriving Backlund transformations for ordinary differential equations. This method is based on a consideration of truncation as a mapping that preserves the locations of a natural…
We solve the local equivalence problem for second order (smooth or analytic) ordinary differential equations. We do so by presenting a {\em complete convergent normal form} for this class of ODEs. The normal form is optimal in the sense…
A progress report on experiences with a gauge fixing method proposed in LATTICE 94 is presented. In this algorithm, an SU(N) operator is diagonalized at each site, followed by gauge fixing the diagonal (Cartan) part of the links to Coulomb…
For the equations $y''=P(x,y) + 3Q(x,y)y' + 3R(x,y){y'}^2 + S(x,y){y'}^3$ the problem of equivalence is considered. Some classical results are resumed in order to prepare the background for the study of special subclass of such equations,…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
We consider partial liftings of maps at fibrations and compare the primary obstruction to extend the lifting with the obstruction to extend the lifting as a simple map into the total space. A relation between these two obstructions is…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
In this paper, we study the linear complementarity problems on the monotone extended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed…
In general, high order splitting methods suffer from an order reduction phenomena when applied to the time integration of partial differential equations with non-periodic boundary conditions. In the last decade, there were introduced…