Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2024-03-31
Large time convergence for a chemotaxis model with degenerate local sensing and consumption
Philippe LAURENCOTAbstract : Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is $C^1$-smooth on $[0,\infty)$, vanishes at zero, and is positive on $(0,\infty)$. A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.
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2023-03-31
The catenary degree of the saturated numerical semigroups with prime multiplicity
Meral S\"{u}er
Abstract : In this paper, we formulate the set of all saturated numerical semigroups with prime multiplicity. We characterize the catenary degrees of elements of the semigroups we obtained which are important invariants in factorization theory. We also give the proper characterizations of the semigroups under consideration.
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2023-01-31
Lens spaces admitting minimal symplectic fillings with the second Betti number one
Heesang Park, Dongsoo ShinAbstract : We classify lens spaces with the Milnor fillable contact structure that admit minimal symplectic fillings whose second Betti numbers are one.
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2023-05-31
Characterization of weakly cofinite local cohomology modules
Moharram Aghapournahr, Marziye HatamkhaniAbstract : Let $R$ be a commutative Noetherian ring, $\mathfrak{a}$ an ideal of $R$,$M$ an arbitrary $R$-module and $X$ a finite $R$-module. We prove a characterization for ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{i}(M)$ and ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{i}(X,M)$ to be $\mathfrak{a}$-weakly cofinite for all $i$, whenever one of the following cases holds:(a) ${ara} (\mathfrak{a})\leq 1$, (b) $\dim R/\mathfrak{a} \leq 1$ or (c) $\dim R\leq 2$. We alsoprove that, if $M$ is a weakly Laskerian $R$-module, then ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{i}(X,M)$ is $\mathfrak{a}$-weakly cofinite for all $i$, whenever $\dim X\leq 2$ or $\dim M\leq 2$ (resp.$(R,\mathfrak{m})$ a local ring and $\dim X\leq 3$ or $\dim M\leq 3$). Let $d=\dim M<\infty$, we prove an equivalent condition for top local cohomology module ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{d}(M)$ to be weakly Artinian.
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2023-03-31
Model structures and recollements induced by duality pairs
Wenjing Chen, Ling Li, Yanping RaoAbstract : Let $(\mathcal{L}, \mathcal{A})$ be a complete duality pair. We give some equivalent characterizations of Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and construct some model structures and recollements associated to them.
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2023-05-31
System of generalized multi-valued resolvent equations: algorithmic and analytical approach
Javad Balooee, Shih-sen Chang, Jinfang TangAbstract : In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a $P$-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of $H(\cdot,\cdot)$-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every $H(\cdot,\cdot)$-co-accretive mapping is actually $P$-accretive and is not a new one. In the meanwhile, some important comments on $H(\cdot,\cdot)$-co-accretive mappings and the results related to them appeared in the literature are pointed out.
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2024-01-31
Rotationally symmetric solutions of the prescribed higher mean curvature spacelike equations in Minkowski spacetime
Man XuAbstract : In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to $+\infty$. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.
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2023-03-31
Primary decomposition of submodules of a free module of finite rank over a B\'ezout domain
Fatemeh Mirzaei, Reza NekooeiAbstract : Let $R$ be a commutative ring with identity. In this paper, we characterize the prime submodules of a free $R$-module $F$ of finite rank with at most $n$ generators, when $R$ is a $\text{GCD}$ domain. Also, we show that if $R$ is a B\'ezout domain, then every prime submodule with $n$ generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of $F$ over a B\'ezout domain and characterize the minimal primary decomposition of this submodule.
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2023-09-30
Spectral instability of rolls in the 2-dimensional generalized Swift-Hohenberg equation
Myeongju Chae, Soyeun JungAbstract : The aim of this paper is to investigate the spectral instability of roll waves bifurcating from an equilibrium in the $2$-dimensional generalized Swift-Hohenberg equation. We characterize unstable Bloch wave vectors to prove that the rolls are spectrally unstable in the whole parameter region where the rolls exist, while they are Eckhaus stable in $1$ dimension [13]. As compared to [18], showing that the stability of the rolls in the $2$-dimensional Swift-Hohenberg equation without a quadratic nonlinearity is determined by Eckhaus and zigzag curves, our result says that the quadratic nonlinearity of the equation is the cause of such instability of the rolls.
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2023-09-30
Conditional Fourier--Feynman transform and conditional convolution product associated with infinite dimensional conditioning function
Jae Gil Choi, Sang Kil ShimAbstract : In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier--Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.
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MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon Hyun
Bull. Korean Math. Soc. 2023; 60(3): 561-574
https://doi.org/10.4134/BKMS.b210374 -
Positive solution and ground state solution for a Kirchhoff type equation with critical growth
Caixia Chen, Aixia Qian
Bull. Korean Math. Soc. 2022; 59(4): 961-977
https://doi.org/10.4134/BKMS.b210567 -
Conjugacy classification of $n$-dimensional M\"obius group
Binlin Dai, Zekun Li
Bull. Korean Math. Soc. 2023; 60(2): 307-313
https://doi.org/10.4134/BKMS.b210928 -
Some polynomials with unimodular roots
Art\= uras Dubickas
Bull. Korean Math. Soc. 2022; 59(5): 1269-1277
https://doi.org/10.4134/BKMS.b210728
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A note on variation continuity for multilinear maximal operators
Xiao Zhang
Bull. Korean Math. Soc. 2024; 61(1): 207-216
https://doi.org/10.4134/BKMS.b230073 -
Some factorization properties of idealization in commutative rings with zero divisors
Sina Eftekhari, Sayyed Heidar Jafari, Mahdi Reza Khorsandi
Bull. Korean Math. Soc. 2024; 61(2): 291-299
https://doi.org/10.4134/BKMS.b220367 -
Periodic shadowable points
Namjip Koo, Hyunhee Lee, Nyamdavaa Tsegmid
Bull. Korean Math. Soc. 2024; 61(1): 195-205
https://doi.org/10.4134/BKMS.b230071 -
Regular $t$-balanced Cayley maps on split metacyclic $2$-groups
Haimiao Chen, Jingrui Zhang
Bull. Korean Math. Soc. 2024; 61(1): 13-27
https://doi.org/10.4134/BKMS.b220811
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