Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2023-03-01
On $S$-multiplication rings
Mohamed Chhiti, Soibri MoindzeAbstract : Let $R$ be a commutative ring with identity and $S$ be a multiplicatively closed subset of $R$. In this article we introduce a new class of ring, called $S$-multiplication rings which are $S$-versions of multiplication rings. An $R$-module $M$ is said to be $S$-multiplication if for each submodule $N$ of $M$, $sN\subseteq JM\subseteq N$ for some $s\in S$ and ideal $J$ of $R$ (see for instance [4, Definition 1]). An ideal $I$ of $R$ is called $S$-multiplication if $I$ is an $S$-multiplication $R$-module. A commutative ring $R$ is called an $S$-multiplication ring if each ideal of $R$ is $S$-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and $S$-$PIR$. Moreover, we generalize some properties of multiplication rings to $S$-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.
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2022-11-01
The Difference of Hyperharmonic Numbers via Geometric and Analytic Methods
\c{C}a\u{g}atay Altunta\c{s}
, Haydar G\"{o}ral, Do\u{g}a Can Sertba\c{s}Abstract : Our motivation in this note is to find equal hyperharmonic numbers of different orders. In particular, we deal with the integerness property of the difference of hyperharmonic numbers. Inspired by finiteness results from arithmetic geometry, we see that, under some extra assumption, there are only finitely many pairs of orders for two hyperharmonic numbers of fixed indices to have a certain rational difference. Moreover, using analytic techniques, we get that almost all differences are not integers. On the contrary, we also obtain that there are infinitely many order values where the corresponding differences are integers.
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2023-01-01
Cross-intercalates and geometry of short extreme points in the Latin polytope of degree 3
Bokhee Im, Jonathan D. H. SmithAbstract : The polytope of tristochastic tensors of degree three, the Latin polytope, has two kinds of extreme points. Those that are at a maximum distance from the barycenter of the polytope correspond to Latin squares. The remaining extreme points are said to be short. The aim of the paper is to determine the geometry of these short extreme points, as they relate to the Latin squares. The paper adapts the Latin square notion of an intercalate to yield the new concept of a cross-intercalate between two Latin squares. Cross-intercalates of pairs of orthogonal Latin squares of degree three are used to produce the short extreme points of the degree three Latin polytope. The pairs of orthogonal Latin squares fall into two classes, described as parallel and reversed, each forming an orbit under the isotopy group. In the inverse direction, we show that each short extreme point of the Latin polytope determines four pairs of orthogonal Latin squares, two parallel and two reversed.
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2023-01-01
Pseudo-Riemannian Sasaki solvmanifolds
Diego Conti, Federico A. Rossi, Romeo Segnan DalmassoAbstract : We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-K\"ahler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension $5$ and those of dimension $7$ whose K\"ahler reduction in the above sense is abelian.
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2023-03-01
Unconditional stability and convergence of fully discrete FEM for the viscoelastic Oldroyd flow with an introduced auxiliary variable
Huifang Zhang, Tong ZhangAbstract : In this paper, a fully discrete numerical scheme for the viscoelastic Oldroyd flow is considered with an introduced auxiliary variable. Our scheme is based on the finite element approximation for the spatial discretization and the backward Euler scheme for the time discretization. The integral term is discretized by the right trapezoidal rule. Firstly, we present the corresponding equivalent form of the considered model, and show the relationship between the origin problem and its equivalent system in finite element discretization. Secondly, unconditional stability and optimal error estimates of fully discrete numerical solutions in various norms are established. Finally, some numerical results are provided to confirm the established theoretical analysis and show the performances of the considered numerical scheme.
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2022-09-01
Bailey pairs and strange identities
Jeremy LovejoyAbstract : Zagier introduced the term ``strange identity" to describe an asymptotic relation between a certain $q$-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.
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2023-01-01
Rational homology disk smoothings and Lefschetz fibrations
Hakho ChoiAbstract : In this article, we generalize the results discussed in \cite{MR2783383} by introducing a genus to generic fibers of Lefschetz fibrations. That is, we give families of relations in the mapping class groups of genus-1 surfaces with boundaries that represent rational homology disk smoothings of weighted homogeneous surface singularities whose resolution graphs are $3$-legged with a bad central vertex.
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2023-03-01
Relative Rota-Baxter systems on Leibniz algebras
Apurba Das, Shuangjian GuoAbstract : In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.
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2022-09-01
Fourier transform of anisotropic mixed-norm Hardy spaces with applications to Hardy--Littlewood inequalities
Jun Liu, Yaqian Lu, Mingdong ZhangAbstract : Let $\vec{p}\in(0,1]^n$ be an $n$-dimensional vector and $A$ a dilation. Let $H_A^{\vec{p}}(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H_{A}^{\vec{p}}(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f\in H_A^{\vec{p}}(\mathbb{R}^n)$ coincides with a continuous function $F$ on $\mathbb{R}^n$ in the sense of tempered distributions. Moreover, the function $F$ can be controlled pointwisely by the product of the Hardy space norm of $f$ and a step function with respect to the transpose matrix of $A$. As applications, the authors obtain a higher order of convergence for the function $F$ at the origin, and an analogue of Hardy--Littlewood inequalities in the present setting of $H_A^{\vec{p}}(\mathbb{R}^n)$.
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2023-05-01
Two-sided estimates for transition probabilities of symmetric Markov chains on ${ \mathbb{Z} }^d$
Zhi-He ChenAbstract : In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ${ \mathbb{Z} }^d$, whose one-step transition probability is comparable to $|x-y|^{-d}\phi_j(|x-y|)^{-1}$ with $\phi_j$ being a positive regularly varying function on $[1,\infty)$ with index $\alpha\in [2,\infty)$. For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).
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On $3^k$-regular cubic partitions
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Construction of a Mattila--Sj\"{o}lin type function over a finite field
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Prime factorization of ideals in commutative rings, with a focus on Krull rings
Gyu Whan Chang, Jun Seok Oh
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Minimal surface system in Euclidean four-space
Hojoo Lee
J. Korean Math. Soc. 2023; 60(1): 71-90
https://doi.org/10.4134/JKMS.j220095
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$(\mathcal{F}, \mathcal{A})$-Gorenstein flat homological dimensions
V\'ictor Becerril
J. Korean Math. Soc. 2022; 59(6): 1203-1227
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Complete noncompact submanifolds of manifolds with negative curvature
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, Yanling Gao, Jing Mao , Zhiqi XieJ. Korean Math. Soc. 2024; 61(1): 183-205
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Multiple weighted estimates for multilinear commutators of multilinear singular integrals with generalized kernels
Liwen Gao, Yan Lin, Shuhui Yang
J. Korean Math. Soc. 2024; 61(2): 207-226
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Periodic surface homeomorphisms and contact structures
Dheeraj Kulkarni, Kashyap Rajeevsarathy, Kuldeep Saha
J. Korean Math. Soc. 2024; 61(1): 1-28
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