Related papers: Cosymmetries and Nijenhuis recursion operators for…
A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear PDE to a new symmetry. Therefore, the existence of a recursion operator guarantees that the PDE has infinitely many higher-order…
The paper is devoted to the study of Nijenhuis operators of arbitrary dimension $n$ in a neighborhood of a point at which the first $n-1$ coefficients of the characteristic polynomial are functionally independent, and the last coefficient…
We describe software for symbolic computations that we developed in order to find Hamiltonian operators for Witten--Dijkgraaf--Verlinde--Verlinde (WDVV) equations, and verify their compatibility. The computation involves nonlocal…
Commutative analogues of Clifford algebras are algebras defined in the same way as Clifford algebras except that their generators commute with each other, in contrast to Clifford algebras in which the generators anticommute. In this paper,…
In this paper, we develop a factorization method to reconstruct cavities in a heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this conductor. The factorization method is a very well known reconstruction method for…
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…
We introduce a notion of cobordism of Callias-type operators over complete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application we prove a gluing formula for Callias-type index. In particular, a…
We constructed the three nonequivalent gradings in the algebra $D_4 \simeq so(8)$. The first one is the standard one obtained with the Coxeter automorphism $C_1=S_{\alpha_2} S_{\alpha_1}S_{\alpha_3}S_{\alpha_4}$ using its dihedral…
We introduce a notion of noncommutative Poisson-Nijenhuis structure on the path algebra of a quiver. In particular, we focus on the case when the Poisson bracket arises from a noncommutative symplectic form. The formalism is then applied to…
This work is devoted to an intrinsic cohomology theory of Koszul-Vinberg algebras and their modules. Our results may be regarded as improvements of the attempt by Albert Nijenhuis in [NA]. The relationships between the cohomology theory…
Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ are investigated using the algorithm…
In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a Lie algebra with a representation. Then we introduce the…
In this paper, first we give the cohomologies of an $n$-Hom-Lie algebra and introduce the notion of a derivation of an $n$-Hom-Lie algebra. We show that a derivation of an $n$-Hom-Lie algebra is a $1$-cocycle with the coefficient in the…
Recently, some concepts such as Hom-algebras, Hom-Lie algebras, Hom-Lie admissible algebras, Hom-coalgebras are studied and some of classical properties of algebras and some geometric objects are extended on them. In this paper by recall…
We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…
In this paper, we introduce right-invariant Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called (Poisson bivector, Nijenhuis operator) structures. Also, we present a one-to-one correspondence between…
The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which…
We introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type $A$. These operators are related with Ruijsenaars' operators through a formula of Wronski type.
This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…
Firstly, we introduce a notion of anti-pre-Novikov algebras as a new framework for decomposing Novikov algebras. Anti-O-operators on Novikov algebras are developed to provide an algebraic framework for constructing anti-pre-Novikov…