Article
Mathematics, Applied
Carsten Dietzel
Summary: This paper classifies left braces of order p(2)q, where p and q are primes with q > p + 1, and provides proofs for three conjectures by Guarnieri and Vendramin regarding the number of isomorphism classes of left braces of order p2q for certain values of p and q.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics
T. Letourmy, L. Vendramin
Summary: In this paper, we define isoclinism of skew braces and explore its various applications. We examine some properties of skew braces that remain invariant under isoclinism, such as right nilpotency. This result has implications in the theory of set-theoretic solutions to the Yang-Baxter equation. Additionally, we introduce isoclinic solutions and study multipermutation solutions under isoclinism.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Premysl Jedlicka, Agata Pilitowska, Anna Zamojska-Dzienio
Summary: We study indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with cyclic permutation groups (cocyclic solutions). We provide a complete system of three invariants to classify finite non-isomorphic solutions of this type and use it to enumerate all of them.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Ali A. Alabdali, Nigel P. Byott
Summary: This study focused on determining the number of skew braces with two groups of order n on a squarefree integer, as well as enumerating skew braces with order being the product of three distinct primes. An application of the research includes proving a conjecture on the number of skew braces of a specific order for primes q > p >= 3.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics
Harvey Blau, Caroline Kettlestrings
Summary: This paper classifies the p-standard table algebras of order p(3) for any rational prime p, mainly in terms of wreath products and vectors (Legendre elements), obtaining real solutions to classical equations related to Legendre symbols. In the case of integer structure constants, criteria for isomorphism of table algebras and the determination of automorphism groups are established by characterizing real solutions to these equations.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Harvey I. Blau, Caroline Wroblewski
Summary: The classification of p-standard table algebras of order p3 for any rational prime p is completed, including the adjacency algebras of p-schemes of order p3. The remaining case, where the thin radical of the distinguished basis of the table algebra has order p2, is resolved. The algebras in this case are explicitly determined up to isomorphism as wreath products, partial wreath products, or as members of a more complex family called hexagonal standard table algebras. These algebras are parametrized by certain correspondences introduced in this article called hexagonal functions, which are defined in general from a subset of a group to an arbitrary set. (c) 2022 Elsevier Inc. All rights reserved.
JOURNAL OF ALGEBRA
(2023)
Review
Clinical Neurology
Stefano Negrini, Angelo Gabriele Aulisa, Pavel Cerny, Jean Claude de Mauroy, Jeb McAviney, Andrew Mills, Sabrina Donzelli, Theodoros B. Grivas, M. Timothy Hresko, Tomasz Kotwicki, Hubert Labelle, Louise Marcotte, Martin Matthews, Joe O'Brien, Eric C. Parent, Nigel Price, Rigo Manuel, Luke Stikeleather, Michael G. Vitale, Man Sang Wong, Grant Wood, James Wynne, Fabio Zaina, Marco Brayda Bruno, Suncica Bulat Wursching, Yilgor Caglar, Patrick Cahill, Eugenio Dema, Patrick Knott, Andrea Lebel, Grigorii Lein, Peter O. Newton, Brian G. Smith
Summary: This study aims to establish a classification of brace types for the effective treatment of patients with idiopathic scoliosis. The classification is based on the expertise of six level 1 experts and consensus from 26 other experts and societies' officials. The broad application of this classification could have significant value for brace research, education, clinical practice, and growth in this field.
EUROPEAN SPINE JOURNAL
(2022)
Article
Mathematics
Lorenzo Stefanello, Senne Trappeniers
Summary: We present a different perspective on the connection between Hopf-Galois structures and skew braces, based on a recent paper by A. Koch and P. J. Truman. We demonstrate that the known results regarding this connection easily extend to this new perspective, and new insights naturally emerge. As an application, we offer new insights into the surjectivity of the Hopf-Galois correspondence, providing a detailed explanation of the role of bi-skew braces in Hopf-Galois theory.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2023)
Article
Engineering, Civil
Canxing Qiu, Lizi Cheng, Xiuli Du
Summary: Combining self-centering braces and fluid viscous damping braces in parallel is a promising seismic-resistant strategy that can simultaneously control peak deformation, acceleration, base shear, and eliminate residual deformation. This paper extends the performance-based plastic design method to hybrid braced frames equipped with these braces. The design method selects target drift and yield mechanism, derives design base shear using energy equivalent concept, and incorporates regression functions of constant-ductility spectra obtained from nonlinear time history analysis. The designed hybrid braced frames can satisfy performance targets and the design method is robust. This method may also be applicable to other hybrid systems with displacement- and velocity-dependent damping braces.
ENGINEERING STRUCTURES
(2023)
Article
Physics, Applied
Taotao Zheng, Hao Ge, Ziwei Long, Chudong Xu, Ming-Hui Lu
Summary: In this study, the local density of states (LDOS) of topological states in a four-dimensional synthetic acoustic system was investigated. Fractional mode charges of one-half, one-quarter, and one-eighth were observed in the LDOS of the topological boundary and corner states. These findings provide insights into the topology in acoustic systems and offer a new method for characterizing topological states in topological acoustic systems.
APPLIED PHYSICS LETTERS
(2023)
Article
Materials Science, Multidisciplinary
Jian-Hao Zhang, Ke Ding, Shuo Yang, Zhen Bi
Summary: This work focuses on the generalization of decohered average symmetry-protected topological phases in open quantum systems, presenting examples of two types of intrinsic average higher-order topological phases with average subsystem symmetries. Additionally, a classification scheme based on generalized anomaly cancellation criteria of average symmetry is discussed.
Article
Mathematics
Yanhong Zhu, Shaofei Du
Summary: This paper characterizes the automorphism group G of nonorientable regular embeddings of simple graphs of order p(3), where p is a prime.
JOURNAL OF ALGEBRAIC COMBINATORICS
(2022)
Article
Engineering, Mechanical
A. Ankiewicz, A. Chowdury
Summary: This article describes the features of rogue waves in various nonlinear physical equations by using simplified forms of their intensities and finding 'volumes'. It presents analysis related to higher-order equations that can be applied to studies of optical fibers, ocean waves, and other aspects of physics. The research investigates the details of formations consisting of a central rogue wave with one or more solitons emerging from it.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Civil
Yi Xiao, Marc O. Eberhard, Ying Zhou, John F. Stanton
Summary: Self-centering energy dissipative (SCED) braces are designed to limit maximum story drifts during earthquakes and nearly eliminate residual drifts, with additional criteria needed to select hysteretic properties. Researchers conducted a parametric study on two typical SCED systems, comparing their seismic performances with a BRB system to develop recommendations for proportioning SCED braces, finding that property uncertainty increases residual drift.
EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS
(2021)
Article
Engineering, Civil
Onur Seker, Jay Shen, Mahmoud Faytarouni, Bulent Akbas
Summary: The study found discrepancies between the expected demand and capacity of traditional CHS bracings in seismic regions. To improve performance, a new method using channel encasement technology in bracing was proposed, and experimental and numerical investigations showed promising results in terms of cyclic stability and energy dissipation.
ENGINEERING STRUCTURES
(2021)
Article
Mathematics, Applied
Manoj K. Keshari, Sampat Sharma
Summary: Assuming R is an affine algebra of dimension d > 4 over a perfect field k of char = 2 and I is an ideal of R. (1) M Sd+1(R) is uniquely divisible prime to char k if R is reduced and k is infinite with c.d.(k) < 1. (2) Umd+1(R, I)/Ed+1(R, I) has a nice group structure if c.d.2(k) < 2. (3) Umd(R, I)/Ed(R, I) has a nice group structure if k is algebraically closed of char k = 2, 3 and either (i) k = Fp or (ii) R is normal.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Mathieu Anel, Georg Biedermann, Eric Finster, Andre Joyal
Summary: In this article, the work of Toen-Vezzosi and Lurie on Grothendieck topologies is revisited using the new tools of acyclic classes and congruences. An extended Grothendieck topology on any 8-topos is introduced and it is proven that the poset of extended Grothendieck topologies is isomorphic to that of topological localizations, hypercomplete localizations, Lawvere-Tierney topologies, and covering topologies. The notions of cotopological morphism, hypercompletion, hyperdescent, hypercoverings, hypersheaves, and forcing are also discussed.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Daniel Dugger, Christy Hazel, Clover May
Summary: This article provides a complete description of the derived category of perfect complexes of modules over the constant Mackey ring Z/$ for the cyclic group C2. While it is simple for $ odd, it relies on a new splitting theorem when $ = 2. The splitting theorem also allows for computing the associated Picard group and Balmer spectrum for compact objects in the derived category. Additionally, it gives a complete classification of finite modules over the C2-equivariant Eilenberg-MacLane spectrum HZ/2 and provides new proofs for some facts about RO(C2)-graded Bredon cohomology.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Mikhailo Dokuchaev, Itailma Rocha
Summary: In this study, we construct an abelian group C(Theta/R) formed by the isomorphism classes of partial generalized crossed products related to a unital partial representation Theta of a group G into the Picard semigroup PicS(R) of a non-necessarily commutative unital ring R. We identify an appropriate second partial cohomology group of G with a naturally defined subgroup C0(Theta/R) of C(Theta/R). Using these results, we generalize the works by Kanzaki and Miyashita by giving an analogue of the Chase-Harrison-Rosenberg exact sequence associated with an extension of rings and a unital partial representation of an arbitrary group into the monoid of R-subbimodules.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Markus Thuresson
Summary: Hereditary algebras are quasi-hereditary and exhibit certain regularity properties with respect to adapted partial orders. This article investigates the Ext-algebra of standard modules over path algebras of linear quivers and provides necessary and sufficient conditions for regular exact Borel subalgebras. The findings have implications for the understanding of linear quivers with arbitrary orientations.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Cordian Riener, Robin Schabert
Summary: This article focuses on the geometry of a class of hyperbolic polynomial families determined by linear conditions on the coefficients. These polynomials have all their roots on the real line. The set of hyperbolic polynomials is stratified according to the multiplicities of the real zeros, and this stratification also applies to the hyperbolic slices. The study shows that the local extreme points of hyperbolic slices correspond to hyperbolic polynomials with at most k distinct roots, and that the convex hull of such a family is generally a polyhedron. The article also explores the implications of these results for symmetric real varieties and symmetric semi-algebraic sets, particularly in terms of sparse representations and sampling.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Edward L. Green, Sibylle Schroll
Summary: This paper studies the ideal C in the path algebra KQ, proving that KQ/C is always finite dimensional with finite global dimension, and it is Morita equivalent to an incidence algebra.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Alexei Entin, Noam Pirani
Summary: This paper proves the existence of a Galois extension with ramification only at infinity for symmetric and alternating groups over finite fields of odd characteristic.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Yves Baudelaire Fomatati
Summary: This paper improves the algorithm for matrix factorization of polynomials, obtaining better results by refining the construction of one of the main ingredients of the algorithm.
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
Zongzhu Lin, Li Qiao
Summary: This article studies the Rota-Baxter algebra structure on the field A = k((t)), with P being the projection map. The representation theory and regular-singular decompositions of finite dimensional A-vector spaces are examined. The main result shows that the category of finite dimensional representations is semisimple, consisting of three isomorphism classes of one-dimensional irreducible representations. Additionally, the article uses the result to compute the generalized class number. (c) 2023 Elsevier B.V. All rights reserved.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Stephen Lack, Giacomo Tendas
Summary: In this paper, we characterize accessible V-categories with limits of a specified class by introducing the notion of companion C for a class of weights & psi;. We then characterize these categories as accessibly embedded and C-virtually reflective in a presheaf V-category, as well as the V-categories of C-models of sketches. Our theorem extends to the case of any weakly sound class & psi; and provides a new perspective on weakly locally presentable categories.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Pradeep K. Rai
Summary: In 1956, Green provided a bound on the order of the Schur multiplier of p-groups. This bound, which depends on the order of the group, is the best possible. Over time, the bound has been improved by incorporating additional factors such as the minimal number of generators and the order of the derived subgroup. We further enhance these bounds by considering the group's nilpotency class, with special emphasis on the cases of class 2 and maximal class.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Benjamin Dequene
Summary: Gentle algebras are a class of finite-dimensional algebras introduced by I. Assem and A. Skowronski in the 1980s. Modules over such algebras can be described using string and band combinatorics in the associated gentle quiver, as studied by M.C.R. Butler and C.M. Ringel. Nilpotent endomorphisms of quiver representations induce linear transformations over vector spaces at each vertex. Among all nilpotent endomorphisms, a well-defined Jordan form exists for these representations. This paper focuses on subcategories generated by the indecomposable representations of a gentle quiver, including a fixed vertex in their support, and characterizes the vertices such that the objects of this subcategory are determined up to isomorphism by their generic Jordan form.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Mark Lawson, Aidan Sims, Alina Vdovina
Summary: We construct a family of groups that are higher dimensional generalizations of the Thompson groups using suitable higher rank graphs. Inspired by the K-theory of C*-algebras, we introduce group invariants and demonstrate that many of our groups are non-isomorphic to the Brin-Thompson groups nV, where n ≥ 2.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
