Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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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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2023-01-31
Stability and topology of translating solitons for the mean curvature flow with the small $L^m$ norm of the second fundamental form
Eungmo Nam, Juncheol PyoAbstract : In this paper, we show that a complete translating soliton $\Sigma^m$ in $\mathbb R^n$ for the mean curvature flow is stable with respect to weighted volume functional if $\Sigma$ satisfies that the $L^m$ norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of $\Sigma$ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial $f$-harmonic $1$-form of $L^2_f$ on $\Sigma$. With the additional assumption that $\Sigma$ is contained in an upper half-space with respect to the translating direction then it has only one end.
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2023-03-31
Double lines in the quintic del Pezzo fourfold
Kiryong ChungAbstract : Let $Y$ be the quintic del Pezzo $4$-fold defined by the linear section of $\textrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in $Y$. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree $2$ in $Y$. We also compute the intersection Poincar\'e polynomial of the stable map space.
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2023-05-31
Compact composition operators on Besov spaces on the unit ball
Chao ZhangAbstract : In this paper, we give new necessary and sufficient conditions for the compactness of composition operator on the Besov space and the Bloch space of the unit ball, which, to a certain extent, generalizes the results given by M. Tjani in [10].
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2023-09-30
Sharp inequalities involving the Chen-Ricci inequality for slant Riemannian submersions
Mehmet Akif Akyol, Nergiz (Önen) PoyrazAbstract : Main objective of the present paper is to establish Chen inequalities for slant Riemannian submersions in contact geometry. In this manner, we give some examples for slant Riemannian submersions and also investigate some curvature relations between the total space, the base space and fibers. Moreover, we establish Chen-Ricci inequalities on the vertical and the horizontal distributions for slant Riemannian submersions from Sasakian space forms.
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2023-01-31
Inductive limit in the category of $C^{\ast}$-ternary rings
Arpit Kansal, Ajay Kumar, Vandana RajpalAbstract : We show the existence of inductive limit in the category of $C^{\ast}$-ternary rings. It is proved that the inductive limit of $C^{\ast}$-ternary rings commutes with the functor $\mathcal{A}$ in the sense that if $(M_n, \phi_n)$ is an inductive system of $C^{\ast}$-ternary rings, then $\varinjlim \mathcal{A}(M_n)=\mathcal{A}(\varinjlim M_n)$. Some local properties (such as nuclearity, exactness and simplicity) of inductive limit of $C^{\ast}$-ternary rings have been investigated. Finally we obtain $\varinjlim M_n^{\ast\ast}=(\varinjlim M_n)^{\ast\ast}$.
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2023-11-30
Automorphisms of K3 surfaces with Picard number two
Kwangwoo LeeAbstract : It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.
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2022-11-30
Boundedness and continuity for variation operators on the Triebel--Lizorkin spaces
Feng Liu, Yongming Wen, Xiao ZhangAbstract : In this paper, we establish the boundedness and continuity for variation operators for $\theta$-type Calder\'{o}n--Zygmund singular integrals and their commutators on the Triebel--Lizorkin spaces. As applications, we obtain the corresponding results for the Hilbert transform, the Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators.
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2023-01-31
Stability of bifurcating stationary periodic solutions of the generalized Swift--Hohenberg equation
Soyeun JungAbstract : Applying the Lyapunov--Schmidt reduction, we consider \linebreak spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift--Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.
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2024-07-31
On the Singular locus of foliations over $\mathbb{P}^2$
Shi XuAbstract : For a foliation $\mathcal{F}$ of degree $r$ over $\mathbb{P}^2$, we can regard it as a maximal invertible sheaf $N_{\mathcal{F}}^{\vee}$ of $\Omega_{\mathbb{P}^2}$, which is represented by a section $s\in H^0(\Omega_{\mathbb{P}^2}(r+2))$. The singular locus ${\rm Sing}\mathcal{F}$ of $\mathcal{F}$ is the zero dimensional subscheme $Z(s)$ of $\mathbb{P}^2$ defined by $s$. Campillo and Olivares have given some characterizations of the singular locus by using some cohomology groups. In this paper, we will give some different characterizations. For example, the singular locus of a foliation over $\mathbb{P}^2$ can be characterized as the residual subscheme of $r$ collinear points in a complete intersection of two curves of degree $r+1$.
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Lens spaces admitting minimal symplectic fillings with the second Betti number one
Heesang Park, Dongsoo Shin
Bull. Korean Math. Soc. 2023; 60(1): 113-122
https://doi.org/10.4134/BKMS.b210923 -
On weakly $S$-prime submodules
Hani A. Khashan, Ece Yetkin~Celikel
Bull. Korean Math. Soc. 2022; 59(6): 1387-1408
https://doi.org/10.4134/BKMS.b210784 -
On the structure of certain subset of Farey sequence
Xing-Wang Jiang, Ya-Li Li
Bull. Korean Math. Soc. 2023; 60(4): 915-931
https://doi.org/10.4134/BKMS.b220396 -
Zero sums of dual Toeplitz products on the orthogonal complement of the Dirichlet space
Young Joo Lee
Bull. Korean Math. Soc. 2023; 60(1): 161-170
https://doi.org/10.4134/BKMS.b220042
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Estimate for bilinear Calder\'{o}n-Zygmund operator and its commutator on product of variable exponent spaces
Guanghui Lu, Shuangping Tao
Bull. Korean Math. Soc. 2022; 59(6): 1471-1493
https://doi.org/10.4134/BKMS.b210839 -
Prime-producing polynomials related to class number one problem of number fields
Jun Ho Lee
Bull. Korean Math. Soc. 2023; 60(2): 315-323
https://doi.org/10.4134/BKMS.b220094 -
$p$-Biharmonic hypersurfaces in Einstein space and conformally flat space
Ahmed Mohammed Cherif, Khadidja Mouffoki
Bull. Korean Math. Soc. 2023; 60(3): 705-715
https://doi.org/10.4134/BKMS.b220347 -
Uniqueness results on meromorphic functions and their difference operators sharing targets with weight
Thu Thuy Hoang, Hong Nhat Nguyen, Duc Thoan Pham
Bull. Korean Math. Soc. 2023; 60(2): 461-473
https://doi.org/10.4134/BKMS.b220190
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