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Sergei Silvestrov

Publications and source records attributed to Sergei Silvestrov.

At least 19 recordsLinked to original sources
arXiv2026

Generalization of Strang-Fix remark for discrete maximum principles on tetrahedral meshes

Most of qualitative properties of finite element (FE) approximations for various PDE models, in particular the validity of the discrete maximum principles (DMPs), are usually guaranteed by certain geometric properties (e.g. acuteness/nonobtuseness) of FE meshes used. In this work, we revisit the linear FE discretization of the Poisson equation and discuss, in the context of DMPs, the representation of the stiffness matrix entries in terms of the edge lengths and cotangents of the dihedral angles of the tetrahedral meshes, thus avoiding the common use of face areas and element volumes. Using this type of entry representation, certain structural properties of meshes, and simple trigonometric relations, as proposed in the two-dimensional case by Strang and Fix, we show that DMPs still hold (as the stiffness matrices remain $M$-matrices) for many tetrahedral configurations with obtuse dihedral angles. Such a relaxation of the standard acuteness/nonobtuseness conditions can be vital in practical calculations, as these angle properties are difficult to preserve in global and local mesh refinements. Several representative examples are presented.

math.NA↗
arXiv2026

On Completeness of $n$-ary Hom-Nambu and Hom-Lie Superalgebras

We introduce and study completeness for multiplicative $n$-ary Hom-Nambu superalgebras. Because an $n$-ary Hom-Nambu bracket is not necessarily totally super-skew-symmetric, we define its center as the intersection of its positional centers. A multiplicative $n$-ary Hom-Nambu superalgebra is complete when its center is trivial, and every $α^{k+1}$-derivation is inner for all $k \geq 0$. We show that this notion reduces to the usual completeness for multiplicative $n$-Hom-Lie superalgebras. Furthermore, we establish a completeness criterion for surjective brackets with a zero twisting map and provide a complete $n$-ary Hom-Nambu superalgebra that is not an $n$-Hom-Lie superalgebra. We also study the direct sums of complete $n$-Hom-Lie superalgebras and the behavior of centers under twisting. Finally, starting from a multiplicative Hom-Lie superalgebra, we consider recursively induced multiplicative $n$-ary Hom-Nambu superalgebras. When the twisting map is surjective, we prove that triviality of the center is preserved and reflected in this construction. We also observe that every binary $α^k$-derivation satisfies the corresponding relative $α^k$-derivation identity for the induced bracket. Finally, we determine the complete members in the selected low-dimensional Hom-Lie and $3$-Hom-Lie superalgebra classifications.

math.RA↗
arXiv2026

Hom-unitality and hom-associative structures

We study hom-associative structures on general possibly non-associative algebras focusing on one-sided and two-sided unital algebras. New characterizations and aspects of these structures, along with some important subclasses, are explored for nonassociative algebras. By exploiting the observation that the twisting linear map in the hom-associativity axiom of one-sided unital hom-associative algebras is a left or right multiplication operator by an element of the algebra (obtained by the action of the twisting map on a corresponding one-sided unity), a new characterization of the multiplicative twisting operators (or, in other words, the multiplicative hom-associative algebras) is established for one-sided unital algebras. This demonstrates a strong connection between multiplicativity in hom-associative structures and the idempotents of the algebra, thereby further enhancing our understanding of the structure and special nature of multiplicative hom-associative algebra structures as a special subclass of arbitrary hom-associative structures with arbitrary linear twisting maps. Furthermore, new insights into subspaces and a subalgebra of hom-unities, that is, elements that induce hom-associativity by multiplication, are obtained. Moreover, because non-unital hom-associative algebras need not be twisted by a multiplication operator, a unitalization process is employed to describe a subalgebra of two-sided hom-unities that induce hom-associative structures on such algebras. This is formulated in terms of the eigenspaces of multiplication operators within the algebra. Additionally, the obtained insights and general results about the structure and characterization of hom-algebra structures are applied to some important known general classes of non-associative algebras, such as commutative, possibly non-associative algebras, Cayley-Dickson algebras, Leibniz algebras, and hom-Leibniz algebras.

math.RA↗
arXiv2026

Lower and upper bounds of joint $(f,δ)$-numerical radius functions

In this study, the classical results on the joint numerical radius for $n$-tuples of Hilbert space operators are extended to the setting of the joint $(f,δ)$-numerical radius. New and diverse contributions to this area are provided, including novel estimates for the lower and upper bounds of the $(f,δ)$-numerical radius in the context of sectorial operators.

math.FA↗
arXiv2025

Curved O-operator systems

In this paper, we introduce the notion of curved $\mathcal{O}$-operator systems as a generalization of T. Brzeziński's (curved) Rota-Baxter systems, and then investigate their relations with $\mathcal{O}$-operator systems, (tri)dendriform systems, pre-Lie algebras, associative Yang-Baxter pairs and quasitriangular covariant bialgebras.

math.RA↗
arXiv2025

Bialgebras, Manin triples of Malcev-Poisson algebras and post-Malcev-Poisson algebras

A Malcev-Poisson algebra is a Malcev algebra together with a commutative associative algebra structure related by a Leibniz rule. In this paper, we introduce the notion of Malcev-Poisson bialgebra as an analogue of a Malcev bialgebra and establish the equivalence between matched pairs, Manin triples and Malcev-Poisson bialgebras. Moreover, we introduce a new algebraic structure, called post-Malcev-Poisson algebras. Post-Malcev-Poisson algebras can be viewed as the underlying algebraic structures of weighted relative Rota-Baxter operators on Malcev-Poisson algebras.

math.RA↗
arXiv2025

Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations

In this paper, we first introduce the notion of twisted $\mathcal O$-operators on a Hom-Lie-Yamaguti algebra by a given $(2,3)$-cocycle with coefficients in a representation. We show that a twisted $\mathcal O$-operator induces a Hom-Lie-Yamaguti structure. We also introduce the notion of a weighted Reynolds operator on a Hom-Lie-Yamaguti algebra, which can serve as a special case of twisted $\mathcal O$-operators on Hom-Lie-Yamaguti algebras. Then, we define a cohomology of twisted $\mathcal O$-operator on Hom-Lie-Yamaguiti algebras with coefficients in a representation. Furthermore, we introduce and study the Hom-NS-Lie-Yamaguti algebras as the underlying structure of the twisted $\mathcal O$-operator on Hom-Lie-Yamaguti algebras. Finally, we investigate the twisted $\mathcal O$-operator on Hom-Lie-Yamaguti algebras induced by the twisted $\mathcal O$-operator on a Hom-Lie algebras.

math.RA↗
arXiv2024

Kupershmidt operators on $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras structures

The purpose of this paper is to introduce the class of noncommutative $3$-BiHom-Poisson color algebras, which is a combination of $3$-BiHom-Lie color algebras and BiHom-associative color algebras under a compatibility condition, called BiHom-Leibniz color identity, and then study their representations and associated Kupershmidt operators. In addition, we introduce the notion of noncommutative $3$-BiHom-pre-Poisson color algebras and investigate the relationship between noncommutative $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras via Kupershmidt operators.

math.RA↗
arXiv2023

Fixed point results for set-contractions on dislocated metric space with a directed graph

Generalized (rational) graph contractions in the framework of a dislocated metric space endowed with a directed graph are investigated. Fixed point results for set-contractions are obtained. We also provide some examples to illustrate our main results. Moreover, the well-posedness of obtained fixed point results are also shown. Our obtained results extend many results in the existing literature.

math.CO↗
arXiv2023

Unique common fixed points of four generalized contractive mappings in ordered partial metric spaces

The existence and uniqueness of the common fixed point for generalized contractive mappings in order partial metric spaces is investigated. The existence of nonnegative solution of implicit nonlinear integral equations is also studied. Some examples demonstrating the validity of our main results are constructed. The presented results extend and unify various comparable results in the existing literature.

math.GM↗
arXiv2023

Differential and linear integral operators representing polynomial covariance commutation relations in $C^\infty$

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance commutation relations by pairs consisting of a differential and linear integral operator are considered including conditions on kernels and coefficients of operators, and examples.

math.FA↗
arXiv2023

Volterra integral operators and general linear integral operators representing polynomial covariance type commutation relations on $L_p$ spaces

Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by integral operators are studied both for general polynomial covariance commutation relations and for important classes of polynomial covariance commutation relations associated to arbitrary monomials and to affine functions. Representations of the covariance type commutation relations by integral Volterra operators and integral convolution operators are investigated.

math.FA↗
arXiv2023

Convergence of commutator of linear integral operators with separable kernel representing monomial covariance type commutation relations in $L_p$

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations extending simultaneously the covariance and the reciprocal covariance type commutation relations. Necessary and sufficient conditions for the defining kernels of the integral operators are obtained for the operators to satisfy such commutation relations associated to pairs of polynomials. Representations by integral operators are studied both for general polynomial covariance type commutation relations and for important classes of polynomial covariance commutation relations associated with arbitrary monomials and affine functions. The convergence of commutators of operators in the sequences of non-commuting operators satisfying the corresponding monomial covariance commutation relation is investigated, and the sequences of such non-commuting operators converging to commuting operators, are presented.

math.FA↗