Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2023-11-01
Finite quotients of singular Artin monoids and categorification of the desingularization map
Helena Jonsson, Volodymyr Mazorchuk, Elin Persson Westin, Shraddha Srivastava, Mateusz Stroinski, Xiaoyu ZhuAbstract : We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category $\mathcal{O}$.
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2023-09-01
Summability in Musielak--Orlicz Hardy spaces
Jun Liu, Haonan XiaAbstract : Let $\varphi: \mathbb{R}^n\times[0,\infty)\to[0,\infty)$ be a growth function and $H^{\varphi}(\mathbb{R}^n)$ the Musielak--Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called $\theta$-summability is considered for multi-dimensional Fourier transforms in $H^{\varphi}(\mathbb{R}^n)$. Precisely, with some assumptions on $\theta$, the authors first prove that the maximal operator of the $\theta$-means is bounded from $H^{\varphi}(\mathbb{R}^n)$ to $L^{\varphi}(\mathbb{R}^n)$. As consequences, some norm and almost everywhere convergence results of the $\theta$-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner--Riesz, Weierstrass and Picard--Bessel summations, are also presented.
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2022-11-01
Maximal domains of solutions for analytic quasilinear differential equations of first order
Chong-Kyu Han, Taejung KimAbstract : We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.
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2024-01-01
Average entropy and asymptotics
Tatyana Barron, Manimugdha SaikiaAbstract : We determine the $N\to\infty$ asymptotics of the expected value of entanglement entropy for pure states in $H_{1,N}\otimes H_{2,N}$, where $H_{1,N}$ and $H_{2,N}$ are the spaces of holomorphic sections of the $N$-th tensor powers of hermitian ample line bundles on compact complex manifolds.
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2024-01-01
Rigidity and nonexistence of Riemannian immersions in semi-Riemannian warped products via parabolicity
Railane Antonia, Henrique de Lima, Márcio SantosAbstract : In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a pa\-ra\-bo\-li\-ci\-ty criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.
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2023-11-01
Some abelian McCoy rings
Rasul Mohammadi, Ahmad Moussavi, masoome zahiriAbstract : We introduce two subclasses of abelian McCoy rings, so-called $\pi$-\textit{CN}-rings and $\pi$-duo rings, and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as $2$-primal rings, bounded rings etc. It is shown that a ring $R$ is $\pi$-\textit{CN} whenever every nilpotent element of index $2$ in $R$ is central. These rings naturally generalize the long-known class of \textit{CN}-rings, introduced by Drazin \cite{drz}. It is proved that $\pi$-\textit{CN}-rings are abelian, McCoy and $2$-primal. We also show that, $\pi$-duo rings are strongly McCoy and abelian and also they are strongly right $AB$. If $R$ is $\pi$-duo, then $R[x]$ has property ($A$). If $R$ is $\pi$-duo and it is either right weakly continuous or every prime ideal of $R$ is maximal, then $R$ has property ($A$). A $\pi$-duo ring $R$ is left perfect if and only if $R$ contains no infinite set of orthogonal idempotents and every left $R$-module has a maximal submodule. Our achieved results substantially improve many existing results.
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2024-01-01
An intrinsic proof of Numata's theorem on Landsberg spaces
Salah Gomaa Elgendi, Amr SoleimanAbstract : In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension $n\geq 3$ of non-zero scalar curvature are Riemannian spaces of constant curvature.
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2024-01-01
Geometry of the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one
Sang-Bum YooAbstract : We describe the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one and its geometric structures in terms of the Hitchin map and a flat degeneration of the moduli space of Higgs bundles on an elliptic curve.
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2024-01-01
Combinatorial supersymmetry: Supergroups, superquasigroups, and their multiplication groups
Bokhee Im, Jonathan D.H. SmithAbstract : The Clifford algebra of a direct sum of real quadratic spaces appears as the superalgebra tensor product of the Clifford algebras of the summands. The purpose of the current paper is to present a purely set-theoretical version of the superalgebra tensor product which will be applicable equally to groups or to their non-associative analogues --- quasigroups and loops. Our work is part of a project to make supersymmetry an effective tool for the study of combinatorial structures. Starting from group and quasigroup structures on four-element supersets, our superproduct unifies the construction of the eight-element quaternion and dihedral groups, further leading to a loop structure which hybridizes the two groups. All three of these loops share the same character table.
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2023-03-01
Prime factorization of ideals in commutative rings, with a focus on Krull rings
Gyu Whan Chang, Jun Seok OhAbstract : Let $R$ be a commutative ring with identity. The structure theorem says that $R$ is a PIR (resp., UFR, general ZPI-ring, $\pi$-ring) if and only if $R$ is a finite direct product of PIDs (resp., UFDs, Dedekind domains, $\pi$-domains) and special primary rings. All of these four types of integral domains are Krull domains, so motivated by the structure theorem, we study the prime factorization of ideals in a ring that is a finite direct product of Krull domains and special primary rings. Such a ring will be called a general Krull ring. It is known that Krull domains can be characterized by the star operations $v$ or $t$ as follows: An integral domain $R$ is a Krull domain if and only if every nonzero proper principal ideal of $R$ can be written as a finite $v$- or $t$-product of prime ideals. However, this is not true for general Krull rings. In this paper, we introduce a new star operation $u$ on $R$, so that $R$ is a general Krull ring if and only if every proper principal ideal of $R$ can be written as a finite $u$-product of prime ideals. We also study several ring-theoretic properties of general Krull rings including Kaplansky-type theorem, Mori-Nagata theorem, Nagata rings, and Noetherian property.
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Regularity relative to a hereditary torsion theory for modules over a commutative ring
Lei Qiao, Kai Zuo
J. Korean Math. Soc. 2022; 59(4): 821-841
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On solvability of a class of degenerate Kirchhoff equations with logarithmic nonlinearity
U\u{g}ur Sert
J. Korean Math. Soc. 2023; 60(3): 565-586
https://doi.org/10.4134/JKMS.j220129 -
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yezhou Li, heqing sun
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Thomas algorithms for systems of fourth-order finite difference methods
Soyoon Bak, Philsu Kim, Sangbeom Park
J. Korean Math. Soc. 2022; 59(5): 891-909
https://doi.org/10.4134/JKMS.j210701
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Topologically stable points and uniform limits
Namjip Koo, Hyunhee Lee
J. Korean Math. Soc. 2023; 60(5): 1043-1055
https://doi.org/10.4134/JKMS.j220595 -
Continuum-wise expansiveness for $C^1$ generic vector fields
Manseob Lee
J. Korean Math. Soc. 2023; 60(5): 987-998
https://doi.org/10.4134/JKMS.j220359 -
Robust portfolio optimization under hybrid CEV and stochastic volatility
Jiling Cao, Beidi Peng, Wenjun Zhang
J. Korean Math. Soc. 2022; 59(6): 1153-1170
https://doi.org/10.4134/JKMS.j210728 -
On uniformly $S$-absolutely pure modules
Xiaolei Zhang
J. Korean Math. Soc. 2023; 60(3): 521-536
https://doi.org/10.4134/JKMS.j220055
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