Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-09-30
Spin structures on complex projective spaces and circle actions
Donghoon JangAbstract : It is known that the complex projective space $\mathbb{CP}^n$ admits a spin structure if and only if $n$ is odd. In this paper, we provide another proof that $\mathbb{CP}^{2m}$ does not admit a spin structure, by using a circle action.
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2023-11-30
Partial sums and inclusion relations for starlike functions associated with an evolute of a nephroid curve
Gurpreet Kaur, Sumit NagpalAbstract : A class of normalized univalent functions $f$ defined in an open unit disk of the complex plane is introduced and studied such that the values of the quantity $zf'(z)/f(z)$ lies inside the evolute of a nephroid curve. The inclusion relations of the newly defined class with other subclasses of starlike functions and radius problems concerning the second partial sums are investigated. All the obtained results are sharp.
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2023-09-30
Canal hypersurfaces generated by non-null curves in Lorentz-Minkowski 4-space
Mustafa Altın, Ahmet Kazan, Dae Won YoonAbstract : In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hypercones whose centers lie on a non-null curve with non-null Frenet vector fields in $E_{1} ^{4}$ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in $E_{1}^{4}$ by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.
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2023-05-31
MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon HyunAbstract : In this paper, we focus on establishing the MacWilliams-type identities on vectorial Boolean functions with bent component functions. As their applications, we provide a bound for the non-existence of vectorial dual-bent functions with prescribed minimum degree, and several Gleason-type theorems are presented as well.
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2023-11-30
The $u$-$S$-global dimensions of commutative rings
Wei Qi, Xiaolei ZhangAbstract : Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $u$-$S$-projective dimension and $u$-$S$-injective dimension of an $R$-module, and then explore the $u$-$S$-global dimension $u$-$S$-\gld$(R)$ of a commutative ring $R$, i.e., the supremum of $u$-$S$-projective dimensions of all $R$-modules. Finally, we investigate $u$-$S$-global dimensions of factor rings and polynomial rings.
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2023-05-31
Vanishing theorems for weighted harmonic $1$-forms on smooth metric measure spaces
Xiaoli Chao, Weili WangAbstract : In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or $m$-Bakry-\'{E}mery-Ricci curvature bounded from below.
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2022-05-31
Weighted integral inequalities for modified integral Hardy operators
Duranta Chutia, Rajib HaloiAbstract : In this article, we study the weak and extra-weak type integral inequalities for the modified integral Hardy operators. We provide suitable conditions on the weights $\omega, \rho, \phi$ and $\psi$ to hold the following weak type modular inequality \begin{align*} \mathcal{U}^{-1} \bigg ( \int_{ \{ | \mathcal{I}f | > \gamma\}} \mathcal{U} \Big(\gamma \omega \Big ) \rho \bigg ) & \leq \mathcal{V}^{-1} \bigg ( \int_{0}^{\infty} \mathcal{V} \Big ( C |f| \phi\Big) \psi \bigg ), \end{align*} where $\mathcal{I}$ is the modified integral Hardy operators. We also obtain a necesary and sufficient condition for the following extra-weak type integral inequality \begin{align*} \omega \bigg ( \Big\{ |\mathcal{I}f| > \gamma \Big \} \bigg) &\leq \mathcal{U}\circ \mathcal{V}^{-1} \bigg ( \int_{0}^{\infty} \mathcal{V} \bigg ( \dfrac{C |f| \phi}{\gamma} \bigg) \psi \bigg ). \end{align*} Further, we discuss the above two inequalities for the conjugate of the modified integral Hardy operators. It will extend the existing results for the Hardy operator and its integral version.
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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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2023-11-30
Bredon homology of wallpaper groups
Ramon FloresAbstract : In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the stabilizers.
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2023-09-30
On the construction of optimal linear codes of dimension four
ATSUYA KATO, TATSUYA MARUTA, KEITA NOMURAAbstract : A fundamental problem in coding theory is to find $n_q(k,d)$, the minimum length $n$ for which an $[n,k,d]_q$ code exists. We show that some $q$-divisible optimal linear codes of dimension $4$ over $\mbox{$\mathbb{F}$}_q$, which are not of Belov type, can be constructed geometrically using hyperbolic quadrics in PG$(3,q)$. We also construct some new linear codes over $\mbox{$\mathbb{F}$}_q$ with $q=7,8$, which determine $n_7(4,d)$ for $31$ values of $d$ and $n_8(4,d)$ for $40$ values of $d$.
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Computation of Wedderburn decomposition of groups algebras from their subalgebra
Gaurav Mittal, Rajendra Kumar Sharma
Bull. Korean Math. Soc. 2022; 59(3): 781-787
https://doi.org/10.4134/BKMS.b210478 -
Pricing American lookback options under a stochastic volatility model
Donghyun Kim, Junhui Woo, Ji-Hun Yoon
Bull. Korean Math. Soc. 2023; 60(2): 361-388
https://doi.org/10.4134/BKMS.b220134 -
Some remarks on problems of subset sum
Min Tang, Hongwei Xu
Bull. Korean Math. Soc. 2022; 59(6): 1339-1348
https://doi.org/10.4134/BKMS.b210262 -
On complete convergence for weighted sums of coordinatewise negatively associated random vectors in Hilbert spaces
Vu Thi Ngoc Anh, Nguyen Thi Thanh Hien
Bull. Korean Math. Soc. 2022; 59(4): 879-895
https://doi.org/10.4134/BKMS.b210509
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On semi-regular injective modules and strong dedekind rings
Renchun Qu
Bull. Korean Math. Soc. 2023; 60(4): 1071-1083
https://doi.org/10.4134/BKMS.b220516 -
On the $p$-adic valuation of generalized harmonic numbers
Çağatay Altuntaş
Bull. Korean Math. Soc. 2023; 60(4): 933-955
https://doi.org/10.4134/BKMS.b220399 -
Automorphisms of K3 surfaces with Picard number two
Kwangwoo Lee
Bull. Korean Math. Soc. 2023; 60(6): 1427-1437
https://doi.org/10.4134/BKMS.b220371 -
$A_{\alpha}$-spectral extrema of graphs with given size and matching number
Xingyu Lei, Shuchao Li, Jianfeng Wang
Bull. Korean Math. Soc. 2023; 60(4): 873-893
https://doi.org/10.4134/BKMS.b220340
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