Journal of the
Korean Mathematical Society
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ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2022-05-01
Construction of a solution of split equality variational inequality problem for pseudomonotone mappings in Banach spaces
Getahun Bekele WegaAbstract : The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.
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2023-07-01
Preresolving subcategories in extriangulated categories
Songsong Liu, Jiaqun WeiAbstract : In this paper, we introduce and study preresolving subcategories in an extriangulated category~$\mathscr{C}$. Let $\mathcal{Y}$ be a $\mathcal{Z}$-preresolving subcategory of $\mathscr{C}$ admitting a $\mathcal{Z}$-proper $\xi$-generator $\mathcal{X}$. We give the characterization of $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution dimension of an object in $\mathscr{C}$. Next, for an object $A$ in $\mathscr{C}$, if the $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution~dimension of $A$ is at most $n$, then all ``$n$-$\mathcal{X}$-syzygies" of $A$ are objects in $\mathcal{Y}$. Finally, we prove that $A$ has a $\mathcal{Z}$-proper $\mathcal{X}$-resolution if and only if $A$ has a $\mathcal{Z}$-proper $\mathcal{Y}$-resolution. As an application, we introduce $(\mathcal{X},\mathcal{Z})$-Gorenstein~subcategory $\mathcal{GX}_{\mathcal{Z}}(\xi)$ of $\mathscr{C}$ and prove that $\mathcal{GX}_{\mathcal{Z}}(\xi)$ is both $\mathcal{Z}$-resolving subcategory and $\mathcal{Z}$-coresolving subcategory of $\mathscr{C}$.
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2022-07-01
Uniqueness of quasi-roots in right-angled Artin groups
Eon-Kyung Lee, Sang-Jin LeeAbstract : We introduce the notion of quasi-roots and study their uniqueness in right-angled Artin groups.
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2022-05-01
On weighted compactness of commutators of bilinear fractional maximal operator
Qianjun He, Juan ZhangAbstract : Let $\mathcal{M}_{\alpha}$ be a bilinear fractional maximal operator and $BM_{\alpha}$ be a fractional maximal operator associated with the bilinear Hilbert transform. In this paper, the compactness on weighted Lebesgue spaces are considered for commutators of bilinear fractional maximal operators; these commutators include the fractional maximal linear commutators $\mathcal{M}_{\alpha,b}^{j}$ and $BM_{\alpha, b}^{j} $ $(j=1,2)$, the fractional maximal iterated commutator $\mathcal{M}_{\alpha,\vec{b}}$, and $BM_{\alpha, \vec{b}}$, where $b\in{\rm BMO}(\mathbb{R}^{d})$ and $\vec{b}=(b_{1},b_{2})\in{\rm BMO}(\mathbb{R}^{d})\times {\rm BMO}(\mathbb{R}^{d})$. In particular, we improve the well-known results to a larger scale for $1/2
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2024-03-01
Remarks on Ulrich bundles of small ranks over quartic fourfolds
Yeongrak KimAbstract : In this paper, we investigate a few strategies to construct Ulrich bundles of small ranks over smooth fourfolds in $\mathbb{P}^5$, with a focus on the case of special quartic fourfolds. First, we give a necessary condition for Ulrich bundles over a very general quartic fourfold in terms of the rank and the Chern classes. Second, we give an equivalent condition for Pfaffian fourfolds in every degree in terms of arithmetically Gorenstein surfaces therein. Finally, we design a computer-based experiment to look for Ulrich bundles of small rank over special quartic fourfolds via deformation theory. This experiment gives a construction of numerically Ulrich sheaf of rank $4$ over a random quartic fourfold containing a del Pezzo surface of degree $5$.
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2024-03-01
Asymptotic behavior of solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays
Cung The Anh, Vu Manh Toi, Phan Thi TuyetAbstract : This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space $BCL_{-\infty}(H)$. We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.
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2023-05-01
On relative Cohen-Macaulay modules
Zhongkui Liu, Pengju Ma, Xiaoyan YangAbstract : Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$. We give some descriptions of the $\mathfrak{a}$-depth of $\mathfrak{a}$-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaul-\\ayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.
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2022-07-01
Sharp Ore-type conditions for the existence of an even $[4,b]$-factor in a graph
Eun-Kyung Cho, Su-Ah Kwon, Suil OAbstract : Let $a$ and $b$ be positive even integers. An even $[a,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $d_H(v)$ is even and $a \le d_H(v) \le b$. Let $\kappa(G)$ be the minimum size of a vertex set $S$ such that $G-S$ is disconnected or one vertex, and let $\sigma_2(G)=\min_{uv \notin E(G)}(d(u)+d(v))$. In 2005, Matsuda proved an Ore-type condition for an $n$-vertex graph satisfying certain properties to guarantee the existence of an even $[2,b]$-factor. In this paper, we prove that for an even positive integer $b$ with $b \ge 6$, if $G$ is an $n$-vertex graph such that $n \ge b+5$, $\kappa(G) \ge 4$, and $\sigma_2(G) \ge \frac{8n}{b+4}$, then $G$ contains an even $[4,b]$-factor; each condition on $n$, $\kappa(G)$, and $\sigma_2(G)$ is sharp.
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2022-05-01
Stabilized-penalized collocated finite volume scheme for incompressible biofluid flows
Nasserdine Kechkar
, Mohammed LouaarAbstract : In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual $L^2$ and discrete $H^1$ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.
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2022-07-01
On $3^k$-regular cubic partitions
Nayandeep Deka Baruah, Hirakjyoti DasAbstract : Recently, Gireesh, Shivashankar, and Naika [11] found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the $3^k$-regular cubic partitions. We also find new families of congruences.
Most Read
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Dirichlet eigenvalue problems under Musielak-Orlicz growth
Allami Benyaiche, Ismail Khlifi
J. Korean Math. Soc. 2022; 59(6): 1139-1151
https://doi.org/10.4134/JKMS.j210669 -
Computations and conservativeness of traces of one-dimensional diffusions
Ali BENAMOR, Rafed MOUSSA
J. Korean Math. Soc. 2023; 60(4): 779-797
https://doi.org/10.4134/JKMS.j220258 -
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 -
On $S$-multiplication rings
Mohamed Chhiti, Soibri Moindze
J. Korean Math. Soc. 2023; 60(2): 327-339
https://doi.org/10.4134/JKMS.j220030
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On nonnil-exact sequences and nonnil-commutative diagrams
Wei Zhao, De chuan Zhou
J. Korean Math. Soc. 2023; 60(6): 1215-1231
https://doi.org/10.4134/JKMS.j220503 -
Cup product on relative bounded cohomology
HeeSook Park
J. Korean Math. Soc. 2023; 60(4): 823-833
https://doi.org/10.4134/JKMS.j220345 -
Computations and conservativeness of traces of one-dimensional diffusions
Ali BENAMOR, Rafed MOUSSA
J. Korean Math. Soc. 2023; 60(4): 779-797
https://doi.org/10.4134/JKMS.j220258 -
Weak Herz-type Hardy spaces with variable exponents and applications
Souad Ben Seghier
J. Korean Math. Soc. 2023; 60(1): 33-69
https://doi.org/10.4134/JKMS.j210764
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