Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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The following are papers that have received final approval and are awaiting to be published. They are listed in the order of their initial submission date.
Papers are published in the order of their initial submission date and will be made available under “Current Issue” once scheduled to be included in a print issue.

Note: Please understand the below list is not in the exact publishing order of the papers as the list does not include papers under internal reviewing process nor those that have not been galley proofed by the authors.

Final published versions of all papers are available under “All Issues” and also under “Current Issue” for papers included in the current issue.

* Paper information have been automatically generated from the information submitted by authors in the online submission system.
  • Online first article April 15, 2024

    self-pair homotopy equivalences related to co-variant functors

    Ho Won Choi, Kee Young Lee, and Hye Seon Shin

    Abstract : The category of pairs is the category whose objects are maps between two based spaces and morphisms are pair-maps from one object to another object. We use covariant functors from the category of based topological spaces and based maps to the category of groups and homomorphisms to study the self-homotopy equivalences in the category of pairs. We introduce specific subgroups of groups of self-pair homotopy equivalences and put these groups together into certain sequences. We investigate properties of the sequence, in particular, the exactness. We apply the results to two special functors, homotopy and homology functors to determine the suggested several subgroups of groups of self-pair homotopy equivalences.

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  • Online first article April 15, 2024

    Smooth Singular Value Thresholding Algorithm for Low-Rank Matrix Completion Problem

    Geunseop Lee

    Abstract : The matrix completion problem is to predict missing entries of a data matrix using the low-rank approximation of the observed entries. Consequently, typical matrix completion problem approaches employ thresholding in the singular values of the data matrix. However, these approaches have some limitations. In particular, a discontinuity is present near the thresholding value, and the thresholding value must be manually selected. To overcome these difficulties, we propose a shrinkage and thresholding function that smoothly thresholds the singular values to obtain an accurate and robust estimation of the data matrix. Moreover, the proposed function is differentiable so that the thresholding values can be adaptively calculated during the iterations using Stein unbiased risk estimate. The experimental results show that the proposed algorithm yields a more accurate estimation with a faster execution than other matrix completion algorithms in image inpainting problems.

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  • Online first article April 15, 2024

    Properties of positive solutions for the fractional Laplacian systems with positive-negative mixed powers

    Zhongxue Lü, Mengjia Niu, Yuanyuan Shen, and Anjie Yuan

    Abstract : In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give four special cases.

  • Online first article February 26, 2024

    Continuity of the maximal commutators in Sobolev spaces

    Xixi Jiang and Feng Liu

    Abstract : We prove the Sobolev continuity of maximal commutator and its fractional variant with Lipschitz symbols, both in the global and local cases. The main result in global case answers a question originally posed by Liu and Wang in \cite{LW}.

  • Online first article April 9, 2024

    Singular hyperbolicity of C^1 generic three dimensional vector fields

    Manseob Lee

    Abstract : In the paper, we show that for a generic C^1 vector field X on a closed three dimensional manifold M, any isolated transitive set of X is singular hyperbolic. It is a partial answer of the conjecture in [13].

  • Online first article April 11, 2024

    Reduction of Abelian Varieties and Curves

    Moshe Jarden and Aharon Razon

    Abstract : Consider a noetherian domain R0 with quotient field K0. Let K be a finitely generated regular transcendental field extension of K0. We con- struct a noetherian domain R with Quot(R) = K that contains R0 and embed Spec(R0) into Spec(R). Then, we prove that key properties of abelian varieties and smooth geometrically integral projective curves over K are preserved under reduction modulo p for "almost all" p 2 Spec(R0).

  • Online first article April 16, 2024

    Totally real and complex subspaces of a right quaternionic vector space with a Hermitian form of signature (n,1)

    Sungwoon Kim

    Abstract : We study totally real and complex subsets of a right quaternionic vector space of dimension n + 1 with a Hermitian form of signature (n; 1) and extend these notions to right quaternionic projective space. Then we give a necessary and sufficient condition for a subset of a right quaternionic projective space to be totally real or complex in terms of the quaternionic Hermitian triple product. As an application, we show that the limit set of a non-elementary quaternionic Kleinian group is totally real (resp. commutative) with respect to the quaternionic Hermitian triple product if and only if it leaves a real (resp. complex) hyperbolic subspace invariant.

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  • Online first article April 11, 2024

    $(\mathcal{V},\mathcal{W},\mathcal{Y},\mathcal{X})$-Gorenstein complexes

    yanjie Li and Renyu Zhao

    Abstract : Let $\mathcal{V},\mathcal{W},\mathcal{Y},\mathcal{X}$ be four classes of left $R$-modules. The notion of $(\mathcal{V, W, Y, X})$-Gorenstein $R$-complexes is introduced, and it is shown that under certain mild technical assumptions on $\mathcal{V},\mathcal{W},\mathcal{Y},\mathcal{X}$, an $R$-complex $M$ is $(\mathcal{V, W, Y, X})$-Gorenstein if and only if the module in each degree of $M$ is $(\mathcal{V, W, Y, X})$-Gorenstein and the total Hom complexs Hom$_R(Y,M)$, Hom$_R(M,X)$ are exact for any $Y\in\widetilde{\mathcal{Y}}$ and any $X\in\widetilde{\mathcal{X}}$. Many known results are recovered, and some new cases are also naturally generated.

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  • Online first article April 11, 2024

    An invariant forth-order curve flow in centro-affine geometry


    Abstract : In this paper, we are devoted to focus on studying a forth order curve flow for a smooth closed curve in centro-affine geometry. Firstly, a new evolutionary equation about this curve flow is proposed. Then the related geometric quantities and some meaningful conclusions are obtained through the equation. Next, we obtain finite order differential inequalities for energy by applying interpolation inequalities, Cauchy Schwartz inequalities, etc. After using a completely new symbolic expression, the n-order differential inequality for energy is considered. Finally, by the means of energy estimation, we prove that the forth order curve flow has a smooth solution all the time for any smooth closed initial curve.

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  • Online first article April 11, 2024

    Asymptotic behavior for strongly damped wave equations on $\mathbb R^3$ with memory

    Xuan-Quang Bui, Duong Toan Nguyen, and Trong Luong Vu

    Abstract : We consider the following strongly damped wave equation on $\mathbb{R}^3$ with memory $$ u_{tt} - \alpha \Delta u_{t} - \beta \Delta u +\lambda u - \int_{0}^\infty \kappa'( s) \Delta u(t-s)ds+ f(x,u) +g(x,u_t)=h, $$ where a quite general memory kernel and the nonlinearity $f$ exhibit a critical growth. Existence, uniqueness and continuous dependence results are provided as well as the existence of regular global and exponential attractors of finite fractal dimension.

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March, 2024
Vol.61 No.2

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