相关论文: Recursion operators for vacuum Einstein equations …

Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators…

BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and…

Factorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations…

The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any…

Lorentz's reciprocity lemma and Feld-Tai reciprocity theorem show the effect of interchanging the action and reaction in Maxwell's equations. We derive a free-space version of these reciprocity relations which generalizes the conservation…

For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Pleba\'nski based on the Darboux theorem. In the…

In this paper we review two concepts directly related to the Lax representations: Darboux transformations and Recursion operators for integrable systems. We then present an extensive list of integrable differential-difference equations…

In this paper, we provide a few properties of the weighted Moore--Penrose inverse for an arbitrary order tensor via the Einstein product. We again obtain some new sufficient conditions for the reverse-order law of the weighted…

An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The…

A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…

The inverse of the Vandermonde and confluent Vandermonde matrices are presented. In the case of the Vandermonde matrix, we present a decomposition in three factors, one of them a diagonal matrix. The evaluation of such inverse matrices is a…

In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive…

We study systematically the Lax description of the KdV hierarchy in terms of an operator which is the geometrical recursion operator. We formulate the Lax equation for the $n$-th flow, construct the Hamiltonians which lead to commuting…

A new class of exact solutions to the axisymmetric and stationary vacuum Einstein equations containing n arbitrary complex parameters and one arbitrary real solution of the axisymmetric three-dimensional Laplace equation is presented. The…

We derive a unique continuation theorem for the vacuum Einstein equations. Our method of proof utilizes Carleman estimates (most importantly one obtained recently by Ionescu and Klainerman), but also relies strongly on certain geometric…

We show that it is algebraically consistent to express some string field theory operators as inner derivations of the B-V algebra of string vertices. In this approach, the recursion relations for the string vertices are found to take the…

In this paper we consider a twofold Ellis-Gohberg type inverse problem in an abstract *-algebraic setting. Under natural assumptions, necessary and sufficient conditions for the existence of a solution are obtained, and it is shown that in…

Conformal Killing-Yano tensors are introduced as a generalization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of…

We study the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…

We present three reasons for rewriting the Einstein equation. The new version is physically equivalent but geometrically more clear. 1. We write $4 \pi$ instead of $8 \pi$ at the r.h.s, and we explain how this factor enters as surface area…