Article
Mathematics, Applied
Jinhua Wang, Tianming Gao, Chong Li, Xiaoqi Yang
Summary: The paper introduces the concept of relative regularity conditions and constants, exploring their equivalent characterizations in normed linear spaces and establishing sufficient conditions for bounded linear regularity property. The study extends classical results from Euclidean space to general normed linear spaces, developing a new technique to ensure the property for split feasibility problems. The presented conditions, based on the relative regularity constants, appear to be entirely novel and may lead to further advancements in the field.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rohit Nageshwar, Abdul Gaffar Khan, Tarun Das
Summary: In this paper, we investigate the properties of bi-asymptotically c-expansive maps on metric spaces and examine its relationship with other variants of expansivity. We also provide an example that illustrates the difference between expansive homeomorphisms and bi-asymptotically expansive maps. Additionally, we prove a spectral decomposition theorem for bi-asymptotically c-expansive continuous surjective maps with the shadowing property on compact metric spaces.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Nata Machado, Gilles G. de Castro
Summary: This article introduces the definitions of full and reduced non-self-adjoint operator algebras associated with etale categories and restriction semigroups, answering a question posed by Kudryavtseva and Lawson. Moreover, the semicrossed product algebra of an etale action of a restriction semigroup on a C*-algebra is defined, which plays a key role in connecting the operator algebra of a restriction semigroup with the operator algebra of its associated etale category. It is also proven that in the cases of etale groupoids and inverse semigroups, our operator algebras coincide with the C*-algebras of the referred objects.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Computer Science, Theory & Methods
S. G. Solodky, S. A. Stasyuk
Summary: The problem of numerical differentiation for periodic functions with finite smoothness is examined. Various truncation methods are developed for multivariate functions and their approximation properties are determined. Based on these findings, sharp bounds in terms of power scale are derived for the minimum radius of Galerkin information for the studied problem.
JOURNAL OF COMPLEXITY
(2024)
Article
Mathematics, Applied
Ville Puuska
Summary: We establish a duality between injective envelopes and flat covers over a commutative Noetherian ring. One case of this duality states that a morphism is an injective envelope, if and only if its Matlis dual is a flat cover. We also show that if we swap injective envelopes and flat covers in this duality, neither implication is true in general.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
R. Bell, P. Comparin, J. Li, A. Rincon-Hidalgo, A. Sarti, A. Zanardini
Summary: In this paper, a complete classification of non-symplectic automorphisms of K3 surfaces whose order is a multiple of seven is presented by describing the topological type of their fixed locus. New results for order 14 and alternative proofs for orders 21, 28 and 42 are provided for purely non-symplectic automorphisms, unifying the results on these automorphisms in the same paper. A complete characterization of the fixed loci of not purely non-symplectic automorphisms for each of these orders is also obtained. The methods used in this paper are completely different from those used in the recent paper by Brandhorst and Hofmann.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Fernando Montaner, Irene Paniello
Summary: In this study, we examine Jordan 3-graded Lie algebras satisfying 3-graded polynomial identities. By utilizing the Tits-Kantor-Koecher construction, we interpret the PI condition in terms of their associated Jordan pairs, thereby formulating an analogue of the Posner-Rowen Theorem for strongly prime PI Jordan 3-graded Lie algebras. Furthermore, we describe arbitrary PI Jordan 3-graded Lie algebras by introducing the Kostrikin radical of the Lie algebras.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Ippei Nagamachi, Teppei Takamatsu
Summary: In this paper, we study the invariants and related phenomena of regular varieties and rings over imperfect fields. We give a criterion for geometric normality of such rings, study the Picard schemes of curves, and define new invariants relating to δ-invariants, genus changes, conductors, and Jacobian numbers. As an application, we refine Tate's genus change theorem and show that the Jacobian number of a curve is 2p/(p - 1) times the genus change.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Vivek Mohan Mallick, Kartik Roy
Summary: This paper explores the relation between Perling's toric Proj of a multigraded ring A and Brenner and Schroer's homogeneous spectrum ProjMH A of the same ring. It shows that there is always a canonical open embedding and studies a criterion for them to be isomorphic.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Christoffer Soderberg
Summary: This article studies the properties of preprojective algebras of representation finite species. It focuses on understanding the structure of preprojective algebras through their Nakayama automorphism and the existence of almost Koszul complexes. It also introduces a higher dimensional analogue of representation finite algebras and provides a complete description of the almost Koszul complex for the preprojective algebra of a tensor product of two species.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Shiqi Xing
Summary: According to the theorem cited above, a finitely presented torsion-free module is SG-projective if and only if it is projective. In this paper, we prove that the w-conductor m[Y] of D is SG-projective but not projective, and all maximal w-ideals other than m[Y] are w-invertible. This implies that a finitely presented torsion-free SG-projective module does not necessarily need to be projective.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Andrew Buchanan, Ivan Dimitrov, Olivia Grace, Charles Paquette, David Wehlau, Tianyuan Xu
Summary: This paper applies quiver representation theory and stable representations to study the representations of free products, obtaining criteria for simple modules and proving their sufficiency in general position. It also establishes the semi-simplicity of modules in general position and derives a closed formula for parameters describing simple modules using quiver moduli spaces.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics
Kristof Berczi, Endre Boros, Kazuhisa Makino
Summary: This paper introduces the characteristics and representations of hypergraph Horn functions and matroid Horn functions, and studies the Boolean minimization problem of matroid Horn functions. We determine the size of an optimal representation for binary matroids and investigate the strong connection between our problem and Turán systems.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2024)
Article
Mathematics
Xiumin Ren, Qingqing Zhang, Rui Zhang
Summary: The article introduces a rational quadratic system and provides an upper bound on the number of solutions under specific conditions.
JOURNAL OF NUMBER THEORY
(2024)
Article
Mathematics, Applied
Yuval Ginosar
Summary: In this paper, an obstruction theory for discrete group graded algebras is proposed, which assigns a second cohomology class to each equivariance class of absolutely graded-simple modules. The set of equivariance classes forms an abelian monoid with a graded product, and the obstruction map is a homomorphism. Furthermore, graded products allow for twisting of graded algebras and their modules.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Diego Garcia-Lucas, Angel del Rio
Summary: This article proves that the Isomorphism Problem for group algebras can be reduced to group algebras over finite extensions of the prime field. In particular, the Modular Isomorphism Problem can be reduced to finite modular group algebras.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Jacques Alev, Francois Dumas, Cesar Lecoutre
Summary: This paper studies the enveloping algebras of Lie algebras of dimension 3, whose derived Lie subalgebra is of dimension 2, from the perspective of rational equivalence, over an algebraically closed base field in arbitrary characteristics.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Haibo Chen, Xiansheng Dai, Dong Liu, Yufeng Pei
Summary: In this paper, a new family of functors from the module category of the Weyl algebra to the module category of the super-Virasoro algebras is introduced. The properties of these functors, including irreducibility preservation and natural isomorphisms, are investigated. Using these functors, old irreducible super-Virasoro modules, including those from the irreducible intermediate series and irreducible U(h)-free modules, are recovered. Additionally, several families of new irreducible super-Virasoro modules are provided via the constructed functors.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Miodrag Cristian Iovanov, Emre Sen, Alexander Sistko, Shijie Zhu
Summary: This paper classifies pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. The algebra structure is explicitly determined for the link indecomposable component B containing the unit, and it is found that H is a crossed product of B and a certain group algebra.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Alexandra Pevzner
Summary: This study examines the action of a finite group G on a polynomial ring and analyzes the properties of the corresponding cofixed space. Under certain conditions, the cofixed space is related to ideals in the ring of symmetric polynomials, exhibiting distinct behavior as the characteristic of the base ring changes. Additionally, localizing the base ring at a prime integer p and varying the number of variables n reveals interesting patterns in the stability and complexity of these ideals.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
