Article
Mathematics
Sarah Peluse
Summary: The number of positive integers n ≤ N such that Z/(n(2)+n+1)Z contains a perfect difference set approaches N/log N asymptotically.
MATHEMATISCHE ANNALEN
(2021)
Article
Mathematics, Applied
Yanjiao Liu, Jianhua Yin
Summary: The generalized Turan number ex(n, Ks, H) is the maximum number of copies of a complete graph Ks in any H-free graph on n vertices. The paper presents the solution for ex(n, Ks, Se), while this paper determines the solution for ex(n, Ks, 2Se).
Article
Mathematics, Applied
Ari Shnidman, Ariel Weiss
Summary: In this study, we investigate the existence of a type of geometrically simple abelian varieties A, for which there exists a non-zero element of order p. By providing concrete examples and a general proof, we establish this conclusion.
FORUM OF MATHEMATICS SIGMA
(2022)
Article
Mathematics
Yu Jiang, Meilian Liang, Yanmei Teng, Xiaodong Xu
Summary: A novel approach to generating cyclic triangle-free graphs of prime order is proposed in this paper, resulting in many new lower bounds on R(3, t) being computed. Experimental results show an improvement of 5 or more in all related best known lower bounds, except the bound on R(3, 34).
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics
Richard H. Bamler, Bruce Kleiner
Summary: In this paper, we investigate the relationship between the diffeomorphism group and the isometry group of a compact orientable non-Haken 3-manifold X modeled on the Thurston geometry Nil. By combining previous work, we determine the homotopy type of Diff(X) for any compact orientable prime 3-manifold X.
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
(2023)
Article
Mathematics
Vito Barbarani
Summary: This work is divided into two parts. The first part solves combinatorics problems related to a new class of randomly generated objects, deriving the probability distribution of combinatorial counterparts of prime numbers and showing propositions equivalent to the Prime Number Theorem. The equivalent of the Riemann Hypothesis is proven false in this model. The second part generalizes the model to investigate conditions enabling both PNT and RH, finding a model where RH holds with probability 1, and predicting the number of consecutive prime pairs based on gap d.
Article
Mathematics
Wang Xiao, Aihua Li
Summary: This paper calculates the number of certain type of partitions of zero in Z/pZ when considering an odd prime number p ≡ 2 (mod 3). It focuses on the three-part partitions of 0 in Z/pZ with parts chosen from non-zero quadratic residues mod p. These partitions are divided into two types: type I with two identical parts and type II with distinct parts. The problem of counting such partitions is closely related to counting non-trivial solutions to the Diophantine equation x(2) + y(2) + z(2) = 0 in the ring Z/pZ, which are also classified as type I or type II.
Article
Energy & Fuels
Pengcheng Chen, Shadi Fatayer, Bruno Schuler, Jordan N. Metz, Leo Gross, Nan Yao, Yunlong Zhang
Summary: The study focused on the reactions of 2,7-dimethylpyrene (DMPY) to understand the role of methyl substituents in reducing the thermal severity required for chemical reactions. Various analytical techniques were used to characterize the complex mixture of thermal products, including monomers, dimers, and trimers. The research also identified a wide range of structural transformations, such as methyl transfer and polymerization reactions, and gained a detailed understanding of the role of H radicals during the polymerization of polycyclic aromatic hydrocarbons.
Article
Radiology, Nuclear Medicine & Medical Imaging
Xiuyuan Wei, Wenyin Zhang, Bo Yang, Jiuru Wang, Ziyun Xia
Summary: A new fragile medical watermarking scheme is proposed in this paper, utilizing prime number distribution theorem, chaotic mapping, and Hash. Experimental results show that the proposed scheme is imperceptible, efficient, and safe, offering good potential in medical image content authentication and tampering detection.
JOURNAL OF DIGITAL IMAGING
(2021)
Review
Mathematics, Applied
Olli Jarviniemi
Summary: The study introduces methods for determining the existence of infinitely many primes satisfying certain conditions. The results generalize the work of H.W. Lenstra and offer specific applications, including characterizing a set of integers and their conditional connection to the Riemann hypothesis.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Robert M. Guralnick, John Shareshian, Russ Woodroofe
Summary: We prove that every alternating group of degree at most one quadrillion can be generated by an element of prime order together with an element of prime power order.
MATHEMATICS OF COMPUTATION
(2023)
Article
Mathematics
Paulius Virbalas
Summary: The research focuses on two objectives: discovering new conditions for deg(alpha beta) = mp and determining the complete list of values deg(alpha beta) can take. For the first question, it is found that if the minimal polynomial of beta over Q is neither x(p) + c nor x(2) + cx + c(2), then deg(alpha beta) = mp and alpha beta is a primitive element of Q(alpha, beta). For the second question, it is determined that if p > 2 and p - 1 divides m, then for every divisor k of p - 1, there exist alpha and beta such that deg(alpha beta) = mp/k.
Article
Mathematics
Sebastian Baader, Ryan Blair, Alexandra Kjuchukova
Summary: The study proves the meridional rank conjecture for twisted links and arborescent links associated with bipartite trees with even weights. Lower bounds on meridional rank are determined through Coxeter quotients, while matching upper bounds on bridge number are found using the Wirtinger numbers of link diagrams.
MATHEMATISCHE ANNALEN
(2021)
Article
Mathematics, Applied
Shichun Yang, Qunying Liao
Summary: By basing on deep conclusions of prime number estimation, a refined form of the product of continuous prime numbers has been proposed, leading to an improvement of the corresponding inequality of Panaitopol and a more accurate conclusion.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2021)
Article
Mathematics, Applied
David Bartusel, Hartmut Fuehr, Vignon Oussa
Summary: This study investigates phase retrieval for group frames arising from permutation representations, with a focus on the action of the affine group of a finite field. Various versions of the phase retrieval problem, including conjugate phase retrieval, sign retrieval, and matrix recovery are examined. The main result shows that the canonical irreducible representation of the affine group has the strongest retrieval property, allowing for matrix reconstruction from scalar products with a group orbit consisting of rank-one projections. The study also provides explicit characterization, a linear matrix recovery algorithm, and examples for matrix recovery.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Mathematics
Matteo Varbaro, Hongmiao Yu
Summary: In this paper, a liaison theory via quasi-Gorenstein varieties is developed, and it is applied to derive the connectedness property of general quasi-Gorenstein subspace arrangements and the classical topological Lefschetz duality.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Eric J. Hanson, Xinrui You
Summary: In this paper, we demonstrate the use of arcs in computing bases for the Hom-spaces and first extension spaces between bricks over preprojective algebras of type A. We also classify the weak exceptional sequences over these algebras using this description. Furthermore, we explain the connection between our results and a similar combinatorial model for exceptional sequences over hereditary algebras of type A.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Valery Lunts, Spela Spenko, Michel Van den Bergh
Summary: This article provides a brief review of the cohomological Hall algebra and K-theoretical Hall algebra associated with quivers. It shows a homomorphism between them in the case of symmetric quivers. Additionally, the equivalence of categories of graded modules is established.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Luc Guyot, Ihsen Yengui
Summary: In this article, it is discussed that for any integral domain R, if R is a Bezout domain of Krull dimension <= 1, then its localization ring R(X) is also a Bezout domain of Krull dimension <= 1. The generalization of this result is explored in different cases such as valuation domains and lexicographic monomial orders, and an example is given to show that this result does not hold in the irrational case.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Pedro L. del Angel, E. Javier Elizondo, Cristhian Garay, Felipe Zaldivar
Summary: In this paper, we study the Grassmannian space of 2-dimensional isotropic subspaces with a specific form and symmetry, and characterize its irreducible subvarieties using symplectic Coxeter matroids. We also provide a complete characterization of symplectic matroids of rank 2 that can be represented over C.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Ioannis Emmanouil, Ilias Kaperonis
Summary: In this paper, we study the role of K-absolutely pure complexes in the homotopy category and the pure derived category. We prove that K-abspure is the isomorphic closure and investigate the relationship between strongly fp-injective modules and K-absolutely pure complexes. Furthermore, we demonstrate that, under certain conditions, a K-absolutely pure complex of strongly fp-injective modules can be a K(PInj)-preenvelope containing an injective module complex.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Miroslav Ploscica, Friedrich Wehrung
Summary: This study investigates the lattice of principal ideals in Abelian L-groups and presents relevant results. These results have important applications in the representation of distributive lattices and homomorphisms, as well as in solving the MV spectrum problem.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Christian Garcia, Thaisa Tamusiunas
Summary: We present a Galois correspondence for K-beta-rings, where beta is an action of a finite groupoid on a unital ring R. We recover the correspondence given in [11] for finite groupoids acting on commutative rings.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Andrea Lucchini, Dhara Thakkar
Summary: This paper studies the problem of minimum generating set for finite groups. By testing whether subsets of the group can generate the group, the minimum generating set can be determined. It is proved that the number of these tests can be significantly reduced if the chief series of the group is known, and at most |G|13/5 subsets need to be tested. This implies that the minimum generating set problem for finite groups can be solved in polynomial time.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Ulrich Meierfrankenfeld, Chris Parker, Gernot Stroth
Summary: This paper investigates the local and global structural properties of finite groups. By studying certain properties of finite groups, we obtain important conclusions about subgroups and extend previous research.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Shezad Mohamed
Summary: We prove the existence of a version of Weil descent, or Weil restriction, in the category of D-algebras. This result is obtained under a mild assumption on the associated endomorphisms. As a consequence, we establish the existence of the Weil descent functor in the category of difference algebras.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Annalisa Conversano, Nicolas Monod
Summary: This study solves the problem of whether all Lie groups can be represented faithfully on a countable set by reducing it to the case of simple Lie groups. It provides a solution for all solvable Lie groups and Lie groups with a linear Levi component, proving that every amenable locally compact second countable group acts faithfully on a countable set.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Wesley Fussner, George Metcalfe
Summary: This paper investigates the transfer of algebraic properties between quasivarieties and their relatively finitely subdirectly irreducible members, and establishes equivalences for certain properties under certain conditions. Additionally, the paper studies special cases of quasivarieties and proves decidability for possessing these properties under certain conditions.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Hao Li, Antun Milas
Summary: We analyze the structure of Feigin-Stoyanovsky's principal subspaces of affine Lie algebra and provide novel fermionic character formulas. We show that level one principal subspaces of type A are classically free as vertex algebras.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Raphael Ruimy
Summary: This article investigates the effect of the perverse t-structure in different dimensions and provides concrete examples. In the case of dimensions less than 2, the core of the t-structure is described. For schemes of finite type over a finite field, a best approximation of the perverse t-structure is constructed.
JOURNAL OF ALGEBRA
(2024)