Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2024-03-01
Conics in quintic del Pezzo varieties
Kiryong Chung, Sanghyeon LeeAbstract : The smooth quintic del Pezzo variety $Y$ is well-known to be obtained as a linear sections of the Grassmannian variety $\mathrm{Gr}(2,5)$ under the Pl\"ucker embedding into $\mathbb{P}^{9}$. Through a local computation, we show the Hilbert scheme of conics in $Y$ for $\text{dim} Y \ge 3$ can be obtained from a certain Grassmannian bundle by a single blowing-up/down transformation.
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2024-05-01
Singular hyperbolicity of $C^1$ generic three dimensional vector fields
Manseob LeeAbstract : 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 \cite{MP}.
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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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2022-11-01
On limit behaviours for Feller's unfair-fair-game and its related model
Jun AnAbstract : Feller introduced an unfair-fair-game in his famous book \cite{Feller-1968}. In this game, at each trial, player will win $2^k$ yuan with probability $p_k=1/2^kk(k+1)$, $k\in \mathbb{N}$, and zero yuan with probability $p_0=1-\sum_{k=1}^{\infty}p_k$. Because the expected gain is 1, player must pay one yuan as the entrance fee for each trial. Although this game seemed ``fair", Feller \cite{Feller-1945} proved that when the total trial number $n$ is large enough, player will loss $n$ yuan with its probability approximate 1. So it's an ``unfair" game. In this paper, we study in depth its convergence in probability, almost sure convergence and convergence in distribution. Furthermore, we try to take $2^k=m$ to reduce the values of random variables and their corresponding probabilities at the same time, thus a new probability model is introduced, which is called as the related model of Feller's unfair-fair-game. We find out that this new model follows a long-tailed distribution. We obtain its weak law of large numbers, strong law of large numbers and central limit theorem. These results show that their probability limit behaviours of these two models are quite different.
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2024-03-01
A note on Sobolev type trace inequalities for $s$-harmonic extensions
Yongrui Tang, Shujuan ZhouAbstract : In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.
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2024-05-01
Collective behaviors of second-order nonlinear consensus models with a bonding force
Hyunjin Ahn
, Junhyeok Byeon, Seung-Yeal Ha, Jaeyoung Yoon Abstract : We study the collective behaviors of two second-order nonlinear consensus models with a bonding force, namely the Kuramoto model and the Cucker-Smale model with inter-particle bonding force. The proposed models contain feedback control terms which induce collision avoidance and emergent consensus dynamics in a suitable framework. Through the cooperative interplays between feedback controls, initial state configuration tends to an ordered configuration asymptotically under suitable frameworks which are formulated in terms of system parameters and initial configurations. For a two-particle system on the real line, we show that the relative state tends to the preassigned value asymptotically, and we also provide several numerical examples to analyze the possible nonlinear dynamics of the proposed models, and compare them with analytical results.
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2024-07-01
Asymptotic behavior for strongly damped wave equations on $\mathbb R^3$ with memory
Xuan-Quang Bui, Duong Toan Nguyen, Trong Luong VuAbstract : 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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2024-07-01
Multigrid methods for 3$D$ $H(\mathbf{curl})$ problems with nonoverlapping domain decomposition smoothers
Duk-Soon OhAbstract : We propose V--cycle multigrid methods for vector field problems arising from the lowest order hexahedral N\'{e}d\'{e}lec finite element. Since the conventional scalar smoothing techniques do not work well for the problems, a new type of smoothing method is necessary. We introduce new smoothers based on substructuring with nonoverlapping domain decomposition methods. We provide the convergence analysis and numerical experiments that support our theory.
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2023-03-01
The gradient flow equation of Rabinowitz action functional in a symplectization
Urs FrauenfelderAbstract : Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.
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2024-07-01
Analyzing the duration of success and failure in Markov-modulated Bernoulli processes
Yoora KimAbstract : A Markov-modulated Bernoulli process is a generalization of a Bernoulli process in which the success probability evolves over time according to a Markov chain. It has been widely applied in various disciplines for modeling and analysis of systems in random environments. This paper focuses on providing analytical characterizations of the Markov-modulated Bernoulli process by introducing key metrics, including success period, failure period, and cycle. We derive expressions for the distributions and the moments of these metrics in terms of the model parameters.
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Cup product on relative bounded cohomology
HeeSook Park
J. Korean Math. Soc. 2023; 60(4): 823-833
https://doi.org/10.4134/JKMS.j220345 -
The Harbourne-Hirschowitz condition and the anticanonical orthogonal property for surfaces
Abel Castorena, Juan Bosco Fr\'ias-Medina
J. Korean Math. Soc. 2023; 60(2): 359-374
https://doi.org/10.4134/JKMS.j220101 -
Preresolving subcategories in extriangulated categories
Songsong Liu, Jiaqun Wei
J. Korean Math. Soc. 2023; 60(4): 877-905
https://doi.org/10.4134/JKMS.j220485 -
Geometry of bilinear forms on a normed space $\mathbb{R}^n$
Sung Guen Kim
J. Korean Math. Soc. 2023; 60(1): 213-225
https://doi.org/10.4134/JKMS.j220277
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On the linear independence measures of logarithms of rational numbers. II
Abderraouf Bouchelaghem, Yuxin He, Yuanhang Li, Qiang Wu
J. Korean Math. Soc. 2024; 61(2): 293-307
https://doi.org/10.4134/JKMS.j230133 -
Remarks on Ulrich bundles of small ranks over quartic fourfolds
Yeongrak Kim
J. Korean Math. Soc. 2024; 61(2): 279-291
https://doi.org/10.4134/JKMS.j230104 -
Average entropy and asymptotics
Tatyana Barron, Manimugdha Saikia
J. Korean Math. Soc. 2024; 61(1): 91-107
https://doi.org/10.4134/JKMS.j230152 -
Shadowing property for ADMM flows
Yoon Mo Jung
, Bomi Shin , Sangwoon YunJ. Korean Math. Soc. 2024; 61(2): 395-408
https://doi.org/10.4134/JKMS.j230284
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