Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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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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2024-05-01
Reduction of abelian varieties and curves
Moshe Jarden, Aharon RazonAbstract : Consider a Noetherian domain $R_0$ with quotient field $K_0$. Let $K$ be a finitely generated regular transcendental field extension of $K_0$. We construct a Noetherian domain $R$ with $\Quot(R)=K$ that contains $R_0$ and embed $\Spec(R_0)$ 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 $\frp$ for ``almost all'' $\frp\in\Spec(R_0)$.
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2024-05-01
Continuity of the maximal commutators in Sobolev spaces
Xixi Jiang, Feng LiuAbstract : 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}.
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2024-05-01
\boldmath$(\mathcal{V},\mathcal{W},\mathcal{Y},\mathcal{X})$-Gorenstein complexes
yanjie Li, Renyu ZhaoAbstract : 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 $\bm{M}$ is $(\mathcal{V, W, Y, X})$-Gorenstein if and only if the module in each degree of $\bm{M}$ is $(\mathcal{V, W, Y, X})$-Gorenstein and the total Hom complexs Hom$_R(\bm{Y},\bm{M})$, Hom$_R(\bm{M},\bm{X})$ are exact for any $\bm{Y}\in\widetilde{\mathcal{Y}}$ and any $\bm{X}\in\widetilde{\mathcal{X}}$. Many known results are recovered, and some new cases are also naturally generated.
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2024-05-01
Properties of positive solutions for the fractional Laplacian systems with positive-negative mixed powers
Zhongxue Lü, Mengjia Niu, Yuanyuan Shen, Anjie YuanAbstract : 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 two special cases.
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Generalized hexagons embedded in metasymplectic spaces
Sebastian Petit, Hendrik Van Maldeghem
J. Korean Math. Soc. 2023; 60(4): 907-929
https://doi.org/10.4134/JKMS.j220528 -
Bailey pairs and strange identities
Jeremy Lovejoy
J. Korean Math. Soc. 2022; 59(5): 1015-1045
https://doi.org/10.4134/JKMS.j220167 -
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 -
Finite $p$-groups whose normal closures of non-normal subgroups have two orders
Lifang Wang
J. Korean Math. Soc. 2022; 59(4): 805-819
https://doi.org/10.4134/JKMS.j210711
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Combinatorial supersymmetry: Supergroups, superquasigroups, and their multiplication groups
Bokhee Im, Jonathan D.H. Smith
J. Korean Math. Soc. 2024; 61(1): 109-132
https://doi.org/10.4134/JKMS.j230164 -
Geometry of the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one
Sang-Bum Yoo
J. Korean Math. Soc. 2024; 61(1): 161-181
https://doi.org/10.4134/JKMS.j230278 -
Some abelian McCoy rings
Rasul Mohammadi, Ahmad Moussavi, masoome zahiri
J. Korean Math. Soc. 2023; 60(6): 1233-1254
https://doi.org/10.4134/JKMS.j220625 -
Prime factorization of ideals in commutative rings, with a focus on Krull rings
Gyu Whan Chang, Jun Seok Oh
J. Korean Math. Soc. 2023; 60(2): 407-464
https://doi.org/10.4134/JKMS.j220271
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