Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2023-01-31

    The $u$-$S$-weak global dimensions of commutative rings

    Xiaolei Zhang

    Abstract : In this paper, we introduce and study the $u$-$S$-weak global dimension $u$-$S$$(R)$ of a commutative ring $R$ for some multiplicative subset $S$ of $R$. Moreover, the $u$-$S$-weak global dimensions of factor rings and polynomial rings are investigated.

  • 2022-10-31

    Liouville theorems for the multidimensional fractional Bessel operators

    Vanesa Galli, Sandra Molina, Alejandro Quintero

    Abstract : In this paper, we establish Liouville type theorems for the fractional powers of multidimensional Bessel operators extending the results given in \cite{GMQ18}. In order to do this, we consider the distributional point of view of fractional Bessel operators studied in \cite{Mo18}.

  • 2022-07-31

    New volume comparison with almost Ricci soliton

    Shahroud azami, Sakineh Hajiaghasi

    Abstract : In this paper we consider a condition on the Ricci curvature involving vector fields which enabled us to achieve new results for volume comparison and Laplacian comparison. These results in special case obtained with considering volume non-collapsing condition. Also, by applying this condition we get new results of volume comparison for almost Ricci solitons.

  • 2022-07-31

    An improved global well-posedness result for the modified Zakharov equations in 1-D

    Agus L. Soenjaya

    Abstract : The global well-posedness for the fourth-order modified Zakharov equations in 1-D, which is a system of PDE in two variables describing interactions between quantum Langmuir and quantum ion-acoustic waves is studied. In this paper, it is proven that the system is globally well-posed in $(u,n)in L^2 imes L^2$ by making use of Bourgain restriction norm method and $L^2$ conservation law in $u$, and controlling the growth of $n$ via appropriate estimates in the local theory. In particular, this improves on the well-posedness results for this system in cite{GZG} to lower regularity.

  • 2022-07-31

    Mean values of derivatives of quadratic prime Dirichlet $L$-functions in function fields

    Hwanyup Jung

    Abstract : In this paper, we establish an asymptotic formula for mean value of $L^{(k)}(frac{1}{2},chi_{P})$ averaging over $mb P_{2g+1}$ and over $mb P_{2g+2}$ as $g oinfty$ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}(frac{1}{2},chi_{u})$ averaging over $mc I_{g+1}$ and over $mc F_{g+1}$ as $g oinfty$ in even characteristic.

  • 2024-01-31

    Generalized derivations in ring with involution involving symmetric and skew symmetric elements

    Souad DAKIR, Hajar EL MIR, Abdellah MAMOUNI

    Abstract : In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

  • 2022-07-31

    Quantization for a probability distribution generated by an infinite iterated function system

    Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury

    Abstract : Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on $mathbb R$. For such a probability measure $P$, an induction formula to determine the optimal sets of $n$-means and the $n$th quantization error for every natural number $n$ is given. In addition, using the induction formula we give some results and observations about the optimal sets of $n$-means for all $ngeq 2$.

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  • 2023-07-31

    A study of differential identities on $\sigma$-prime rings

    Adnan Abbasi, Md Arshad Madni, Muzibur Rahman Mozumder

    Abstract : Let $\mathcal{R}$ be a $\sigma$-prime ring with involution $\sigma$. The main \linebreak objective of this paper is to describe the structure of the $\sigma$-prime ring $\mathcal{R}$ with involution $\sigma$ satisfying certain differential identities involving three derivations $\psi_1, \psi_2$ and $\psi_3$ such that $\psi_1[t_1,\sigma(t_1)]+[\psi_2(t_1),\psi_2(\sigma(t_1))] + [\psi_3(t_1),\sigma(t_1)]\in \mathcal{J}_Z$ for all $t_1\in \mathcal{R}$. Further, some other related results have also been discussed.

  • 2023-04-30

    H-quasi-hemi-slant submersions

    Sumeet Kumar, Sushil Kumar, Rajendra Prasad, Aysel Turgut Vanli

    Abstract : In this paper, h-quasi-hemi-slant submersions and almost h-quasi-hemi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds are introduced. Fundamental results on h-quasi-hemi-slant submersions: the integrability of distributions, geometry of foliations and the conditions for such submersions to be totally geodesic are investigated. Moreover, some non-trivial examples of the h-quasi-hemi-slant submersion are constructed.

  • 2023-01-31

    On covering and quotient maps for $\mathcal{I}^{\mathcal{K}}$-convergence in topological spaces

    Debajit Hazarika, Ankur Sharmah

    Abstract : In this article, we show that the family of all $\mathcal{I}^\mathcal{K}$-open subsets in a topological space forms a topology if $\mathcal{K}$ is a maximal ideal. We introduce the notion of $\mathcal{I}^\mathcal{K}$-covering map and investigate some basic properties. The notion of quotient map is studied in the context of $\mathcal{I}^\mathcal{K}$-convergence and the relationship between $\mathcal{I}^\mathcal{K}$-continuity and $\mathcal{I}^\mathcal{K}$-quotient map is established. We show that for a maximal ideal $\mathcal{K}$, the properties of continuity and preserving $\mathcal{I}^\mathcal{K}$-convergence of a function defined on $X$ coincide if and only if $X$ is an $\mathcal{I}^\mathcal{K}$-sequential space.

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April, 2024
Vol.39 No.2

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