Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-09-30
Betchov-Da Rios equation by null Cartan, pseudo null and partially null curve in Minkowski spacetime
Melek Erdoğdu, Yanlin Li, Ayşe YavuzAbstract : The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of $s$ parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of $s$ parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan $s$ parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null $s$ parameter curve.
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2023-11-30
Singularity formation for a nonlinear variational sine-Gordon equation in a multidimensional space
Fengmei Qin, Kyungwoo Song, Qin WangAbstract : We study a multidimensional nonlinear variational sine-Gor\-don equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.
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2024-01-31
Depth and Stanley depth of two special classes of monomial ideals
Xiaoqi WeiAbstract : In this paper, we define two new classes of monomial ideals $I_{l,d}$ and $J_{k,d}$. When $d\geq 2k+1$ and $l\leq d-k-1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/I_{l,d}^{t}$ for all $t\geq 1$. When $d=2k=2l$, we compute the depth and Stanley depth of quotient ring $S/I_{l,d}$. When $d\geq 2k$, we also compute the depth and Stanley depth of quotient ring $S/J_{k,d}$.
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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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2024-03-31
On the generalized principally injective modules
Fatemeh Gholami, Zohreh Habibi, Alireza NajafizadehAbstract : Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.
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2024-01-31
$C^*$-algebra of local conjugacy equivalence relation on strongly irreducible subshift of finite type
Chengjun Hou, Xiangqi QiangAbstract : Let $G$ be an infinite countable group and $A$ be a finite set. If $ \Sigma \subseteq A^{G}$ is a strongly irreducible subshift of finite type and $\mathcal{G}$ is the local conjugacy equivalence relation on $ \Sigma$. We construct a decreasing sequence $\mathcal{R}$ of unital $C^*$-subalgebras of $C(\Sigma)$ and a sequence of faithful conditional expectations $\mathcal{E}$ defined on $C(\Sigma)$, and obtain a Toeplitz algebra $\mathcal{T}(\mathcal{R},\mathcal{E})$ and a $C^*$-algebra $C^*(\mathcal{R},\mathcal{E})$ for the pair $(\mathcal{R},\mathcal{E})$. We show that $C^*(\mathcal{R},\mathcal{E})$ is $\ast$-isomorphic to the reduced groupoid $C^*$-algebra $C_r^*(\mathcal{G})$.
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2024-01-31
List injective coloring of planar graphs with girth at least five
Hongyu ChenAbstract : A vertex coloring of a graph $G$ is called injective if any two vertices with a common neighbor receive distinct colors. A graph $G$ is injectively $k$-choosable if any list $L$ of admissible colors on $V(G)$ of size $k$ allows an injective coloring $\varphi$ such that $\varphi(v)\in L(v)$ whenever $v\in V(G)$. The least $k$ for which $G$ is injectively $k$-choosable is denoted by $\chi_{i}^{l}(G)$. For a planar graph $G$, Bu et al.~proved that $\chi_{i}^{l}(G)\leq\Delta+6$ if girth $g\geq5$ and maximum degree $\Delta(G)\geq8$. In this paper, we improve this result by showing that $\chi_{i}^{l}(G)\leq\Delta+6$ for $g\geq5$ and arbitrary $\Delta(G)$.
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2024-01-31
Unconditionally stable Gauge-Uzawa finite element methods for the Darcy-Brinkman equations driven by temperature and salt concentration
Yangwei Liao, Demin LiuAbstract : In this paper, the Gauge-Uzawa methods for the Darcy-Brinkman equations driven by temperature and salt concentration \linebreak (DBTC) are proposed. The first order backward difference formula is adopted to approximate the time derivative term, and the linear term is treated implicitly, the nonlinear terms are treated semi-implicit. In each time step, the coupling elliptic problems of velocity, temperature and salt concentration are solved, and then the pressure is solved. The unconditional stability and error estimations of the first order semi-discrete scheme are derived, at the same time, the unconditional stability of the first order fully discrete scheme is obtained. Some numerical experiments verify the theoretical prediction and show the effectiveness of the proposed methods.
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2024-01-31
A note on variation continuity for multilinear maximal operators
Xiao ZhangAbstract : This note is devoted to establishing the variation continuity of the one-dimensional discrete uncentered multilinear maximal operator. The above result is based on some refine variation estimates of the above maximal functions on monotone intervals. The main result essentially improves some known ones.
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2024-01-31
A function-field analogue of the Goldbach counting function and the associated Dirichlet series
Shigeki Egami, Kohji MatsumotoAbstract : We consider a function-field analogue of Dirichlet series associated with the Goldbach counting function, and prove that it can, or cannot, be continued meromorphically to the whole plane. When it cannot, we further prove the existence of the natural boundary of it.
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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 -
On certain estimates for rough generalized parametric Marcinkiewicz integrals
Daiqing Zhang
Bull. Korean Math. Soc. 2023; 60(1): 47-73
https://doi.org/10.4134/BKMS.b210850 -
Brouwer degree for mean field equation on graph
Yang Liu
Bull. Korean Math. Soc. 2022; 59(5): 1305-1315
https://doi.org/10.4134/BKMS.b210756
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$S$-versions and $S$-generalizations of idempotents, pure ideals and Stone type theorems
Bayram Ali Ersoy, Ünsal Tekir, Eda Yıldız
Bull. Korean Math. Soc. 2024; 61(1): 83-92
https://doi.org/10.4134/BKMS.b230023 -
A note on Artinian local rings
Kui Hu, Hwankoo Kim, Dechuan Zhou
Bull. Korean Math. Soc. 2022; 59(5): 1317-1325
https://doi.org/10.4134/BKMS.b210759 -
Application of Rothe's method to a nonlinear wave equation on graphs
Yong Lin, Yuanyuan Xie
Bull. Korean Math. Soc. 2022; 59(3): 745-756
https://doi.org/10.4134/BKMS.b210445 -
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
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