Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2024-01-31
On the generalized Ornstein-Uhlenbeck operators with regular and singular potentials in weighted $L^{p}$-spaces
Imen Metoui
Abstract : In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials \begin{align*} A_{\Phi,G,V,c} = \Delta-\nabla \Phi\cdot\nabla+G\cdot \nabla-V+c|x|^{-2} \end{align*} with a suitable domain generates a quasi-contractive, positive and analytic $C_{0}$-semigroup in $L^{p}(\mathbb{R}^{N},e^{-\Phi(x)}dx)$, $1
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2023-04-30
$C_{12}$-space forms
Gherici Beldjilali, Nour OubbicheAbstract : The aim of this paper is two-fold. First, we study the Chinea-Gonzalez class $C_{12}$ of almost contact metric manifolds and we discuss some fundamental properties. We show there is a one-to-one correspondence between $C_{12}$ and K\"ahlerian structures. Secondly, we give some basic results for Riemannian curvature tensor of $C_{12}$-manifolds and then establish equivalent relations among $\varphi$-sectional curvature. Concrete examples are given.
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2024-01-31
The class of $p$-demicompact operators on lattice normed spaces
Imen Ferjani, Bilel KrichenAbstract : In the present paper, we introduce a new class of operators called $p$-demicompact operators between two lattice normed spaces $X$ and $Y$. We study the basic properties of this class. Precisely, we give some conditions under which a $p$-bounded operator be $p$-demicompact. Also, a sufficient condition is given, under which each $p$-demicompact operator has a modulus which is $p$-demicompact. Further, we put in place some properties of this class of operators on lattice normed spaces.
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2023-07-31
The $p$-part of divisor class numbers for cyclotomic function fields
Daisuke ShiomiAbstract : In this paper, we construct explicitly an infinite family of primes $P$ with $h_P^{\pm} \equiv 0 \pmod {q^{\deg P}}$, where $h_P^{\pm}$ are the plus and minus parts of the divisor class number of the $P$-th cyclotomic function field over $\mathbb{F}_q(T)$. By using this result and Dirichlet's theorem, we give a condition of $A, M \in \mathbb{F}_q[T]$ such that there are infinitely many primes $P$ satisfying with $h_P^{\pm} \equiv 0 \pmod {p^e}$ and $P \equiv A \pmod M$.
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2024-01-31
The homological properties of regular injective modules
Wei Qi, Xiaolei ZhangAbstract : Let $R$ be a commutative ring. An $R$-module $E$ is said to be regular injective provided that $\Ext_R^1(R/I,E)=0$ for any regular ideal $I$ of $R$. We first show that the class of regular injective modules have the hereditary property, and then introduce and study the regular injective dimension of modules and regular global dimension of rings. Finally, we give some homological characterizations of total rings of quotients and Dedekind rings.
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2024-04-30
A survey of lengths of linear groups with respect to certain generating sets
Nguyen Thi Thai HaAbstract : In this paper, we summarise and present results on involution lengths and commutator lengths of certain linear groups such as special linear groups, projective linear groups, upper triangle matrix groups and Vershik-Kerov groups. Some open problems motivated by these results are also proposed.
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2024-01-31
Cyclic codes of length $p^s$ over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$
Roghayeh Mohammadi Hesari, Masoumeh Mohebbei, Rashid Rezaei, Karim SameiAbstract : Let $R_e=\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$, where $p$ is a prime number, $ e $ is a positive integer and $u^e=0$. In this paper, we first characterize the structure of cyclic codes of length $p^s$ over $R_e$. These codes will be classified into $2^e $ distinct types. Among other results, in the case that $e=4$, the torsion codes of cyclic codes of length $ p^s $ over $ R_4$ are obtained. Also, we present some examples of cyclic codes of length $p^s $ over $R_e$.
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2023-10-31
Approximately local derivations on $\ell^{1}$-Munn algebras with applications to semigroup algebras
Ahmad Alinejad, Morteza Essmaili, Hatam VahdatiAbstract : At the present paper, we investigate bounded approximately local derivations of $\ell^{1}$-Munn algebra ${\mathbb M}_{I}(\mathcal{A})$, where $I$ is an arbitrary non-empty set and $\mathcal A$ is an approximately locally unital Banach algebra. Indeed, we show that if ${_\mathcal A}B(\mathcal A ,{\mathcal A}^{\ast})$ and $B_{\mathcal A}(\mathcal A ,{\mathcal A}^{\ast})$ are reflexive, then every bounded approximately local derivation from ${\mathbb M}_{I}(\mathcal A)$ into any Banach ${\mathbb M}_{I}(\mathcal A)$-bimodule $ X$ is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra $\ell^{1}(S)$, where $S$ is a uniformly locally finite inverse semigroup.
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2023-10-31
Remarks on the gradient flow of $\alpha$ energy potential on the line
Hyojun An, Hyungjin HuhAbstract : We are interested in the gradient flow of $\alpha$ energy potential. We provide basic estimates and study asymptotic behaviors for the case $N=2, \ldots, 5$.
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2024-04-30
Riemannian submersions whose total manifold admits $h$-almost Ricci-Yamabe soliton
Mehraj Ahmad Lone, Towseef Ali WaniAbstract : In this paper, we study Riemannian submersions whose total manifold admits $h$-almost Ricci-Yamabe soliton. We characterize the fibers of the submersion and see under what conditions the fibers form $h$-almost Ricci-Yamabe soliton. Moreover, we find the necessary condition for the base manifold to be an $h$-almost Ricci-Yamabe soliton and Einstein manifold. Later, we compute scalar curvature of the total manifold and using this we find the necessary condition for $h$-almost Yamabe solition to be shrinking, expanding and steady. At the end, we give a non-trivial example.
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An improved global well-posedness result for the modified Zakharov equations in 1-D
Agus L. Soenjaya
Commun. Korean Math. Soc. 2022; 37(3): 735-748
https://doi.org/10.4134/CKMS.c210218 -
Mean values of derivatives of quadratic prime Dirichlet $L$-functions in function fields
Hwanyup Jung
Commun. Korean Math. Soc. 2022; 37(3): 635-648
https://doi.org/10.4134/CKMS.c210205 -
Golden para-contact metric manifolds
Gherici Beldjilali, Habib Bouzir
Commun. Korean Math. Soc. 2022; 37(4): 1209-1219
https://doi.org/10.4134/CKMS.c210383 -
On the semi-local convergence of contraharmonic-mean Newton's method (CHMN)
Ioannis K. Argyros, Manoj Kumar Singh
Commun. Korean Math. Soc. 2022; 37(4): 1009-1023
https://doi.org/10.4134/CKMS.c210306
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Some characterizations of conics and hypersurfaces with centrally symmetric hyperplane sections
Shin-Ok Bang, Dong Seo Kim, Dong-Soo Kim, Wonyong Kim
Commun. Korean Math. Soc. 2024; 39(1): 211-221
https://doi.org/10.4134/CKMS.c230119 -
Eigenvalue comparison for the discrete $(3,3)$~conjugate boundary value problem
Jun Ji, Bo Yang
Commun. Korean Math. Soc. 2023; 38(3): 925-935
https://doi.org/10.4134/CKMS.c210430 -
Maximal chain of ideals and $n$-maximal ideal
Hemin A. Ahmad, Parween A. Hummadi
Commun. Korean Math. Soc. 2023; 38(2): 331-340
https://doi.org/10.4134/CKMS.c220097 -
Circular spectrum and asymptotic periodic solutions to a class of non-densely defined evolution equations
Le Anh Minh, Nguyen Ngoc Vien
Commun. Korean Math. Soc. 2023; 38(4): 1153-1162
https://doi.org/10.4134/CKMS.c230015
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