Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
Most Read
HOME
VIEW ARTICLES
Most Read
VIEW ARTICLES
Most Read
-
2023-05-31
On a Spitzer-type law of large numbers for partial sums of independent and identically distributed random variables under sub-linear expectations
Miaomiao Wang, Min Wang, Xuejun WangAbstract : In this paper, under some suitable conditions, we study the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables in upper expectation space. Some general results on necessary and sufficient conditions of the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables under sub-linear expectations are established, which extend the corresponding ones in classic probability space to the case of sub-linear expectation space.
-
2023-05-31
An altered group ring construction of the $[24,12,8]$ and $[48,24,12]$ Type II linear block code
Shefali Gupta, Dinesh UdarAbstract : In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders $2,3,4,$ and $5$, and by applying the construction over the binary field and the ring $F_{2}+uF_{2}$, we obtain extremal binary self-dual codes of various lengths: $12, 16, 20, 24, 32, 40,$ and $48$. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code $[24,12,8]$ and the unique Extended Quadratic Residue $[48,24,12]$ Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.
-
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.
-
2022-09-30
Estimates for the Riesz transforms associated with Schr\"odinger type operators on the Heisenberg group
Yanhui WangAbstract : We consider the Schr\"odinger type operator \(\mathcal{L}=(-\Delta_{\mathbb{H}^n})^2+V^2 \) on the Heisenberg group $\mathbb{H}^n,$ where $\Delta_{\mathbb{H}^n}$ is the sub-Laplacian and the non-negative potential \(V\) belongs to the reverse H\"older class \(RH_s$ for $ s\geq Q/2$ and $Q\geq 6.\) We shall establish the $(L^p,L^q)$ estimates for the Riesz transforms $ T_{\alpha,\beta,j} =V^{2\alpha}\nabla_{\mathbb{H}^n}^j \mathcal{L}^{-\beta},~j=0,1,2,3,$ where $\nabla_{\mathbb{H}^n}$ is the gradient operator on $\mathbb{H}^n,~ 0
-
2024-01-31
On the Semigroup of partition-preserving transformations whose characters are bijective
Mosarof Sarkar, Shubh Narayan SinghAbstract : Let $\mathcal{P}=\{X_i\colon i\in I\}$ be a partition of a set $X$. We say that a transformation $f\colon X \to X$ preserves $\mathcal{P}$ if for every $X_i \in \mathcal{P}$, there exists $X_j \in \mathcal{P}$ such that $X_if \subseteq X_j$. Consider the semigroup $\mathcal{B}(X,\mathcal{P})$ of all transformations $f$ of $X$ such that $f$ preserves $\mathcal{P}$ and the character (map) $\chi^{(f)}\colon I \to I$ defined by $i\chi^{(f)}=j$ whenever $X_if\subseteq X_j$ is bijective. We describe Green's relations on $\mathcal{B}(X,\mathcal{P})$, and prove that $\mathcal{D} = \mathcal{J}$ on $\mathcal{B}(X,\mathcal{P})$ if $\mathcal{P}$ is finite. We give a necessary and sufficient condition for $\mathcal{D} = \mathcal{J}$ on $\mathcal{B}(X,\mathcal{P})$. We characterize unit-regular elements in $\mathcal{B}(X,\mathcal{P})$, and determine when $\mathcal{B}(X,\mathcal{P})$ is a unit-regular semigroup. We alternatively prove that $\mathcal{B}(X,\mathcal{P})$ is a regular semigroup. We end the paper with a conjecture.
-
2022-09-30
Evaluation formula for Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces
Seung Jun Chang, Jae Gil ChoiAbstract : In this paper, we establish an evaluation formula to calculate the Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces $(H,B,\nu)$. To do this we first derive a translation theorem for the Wiener integral of functionals associated with operators in $\mathcal L(B)$, the Banach space of bounded linear operators from $B$ to itself. We then apply the translation theorem to establish an integration by parts formula for the Wiener integral of functionals combined with operators in $\mathcal L(B)$. We finally apply this parts formula to evaluate the Wiener integral of certain polynomials in terms of natural dual pairings.
-
2023-07-31
Toeplitz-type operators on the Fock space $F_{\alpha}^{2}$
Chunxu Xu, Tao YuAbstract : Let $j$ be a nonnegative integer. We define the Toeplitz-type operators $T_{a}^{(j)}$ with symbol $a\in L^{\infty}(C)$, which are variants of the traditional Toeplitz operators obtained for $j=0$. In this paper, we study the boundedness of these operators and characterize their compactness in terms of its Berezin transform.
-
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.
-
2024-01-31
$S$-versions and $S$-generalizations of idempotents, pure ideals and Stone type theorems
Bayram Ali Ersoy, Ünsal Tekir, Eda YıldızAbstract : Let $R$ be a commutative ring with nonzero identity and $M$ be an $R$-module. In this paper, we first introduce the concept of $S$-idempotent element of $R$. Then we give a relation between $S$-idempotents of $R$ and clopen sets of $S$-Zariski topology. After that we define $S$-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is $S$-pure but the converse may not be true. Afterwards, we show that there is a relation between $S$-pure ideals of $R$ and closed sets of $S$-Zariski topology that are stable under generalization.
-
2023-09-30
Conditional Fourier--Feynman transform and conditional convolution product associated with infinite dimensional conditioning function
Jae Gil Choi, Sang Kil ShimAbstract : In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier--Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.
Most Read
-
The $H^1$-uniform attractor for the 2D non-autonomous tropical climate model on some unbounded domains
Pigong Han, Keke Lei, Chenggang Liu, Xuewen Wang
Bull. Korean Math. Soc. 2022; 59(6): 1439-1470
https://doi.org/10.4134/BKMS.b210800 -
Hopf hypersurfaces of the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$ satisfying certain commuting conditions
Xiaomin Chen, Yifan Yang
Bull. Korean Math. Soc. 2022; 59(6): 1567-1594
https://doi.org/10.4134/BKMS.b210904 -
Homology and Serre class in $\mathrm{D}(R)$
Zhicheng Wang
Bull. Korean Math. Soc. 2023; 60(1): 23-32
https://doi.org/10.4134/BKMS.b210703 -
Szeg\"{o} projections for Hardy spaces in quaternionic Clifford analysis
Fuli He
, Song Huang, Min KuBull. Korean Math. Soc. 2022; 59(5): 1215-1235
https://doi.org/10.4134/BKMS.b210688
Most Downloaded
-
On the determinant of a dual periodic singular fiber
Cheng Gong, Jun Lu, Sheng-Li Tan
Bull. Korean Math. Soc. 2023; 60(5): 1365-1374
https://doi.org/10.4134/BKMS.b220710 -
Results on the algebraic differential independence of the Riemann zeta function and the Euler gamma function
Xiao-Min Li, Yi-Xuan Li
Bull. Korean Math. Soc. 2023; 60(6): 1651-1672
https://doi.org/10.4134/BKMS.b220813 -
Operators $A$, $B$ for which the Aluthge transform $\widetilde{AB}$ is a generalised $n$-projection
Bhagwati Duggal, In Hyoun Kim
Bull. Korean Math. Soc. 2023; 60(6): 1555-1566
https://doi.org/10.4134/BKMS.b220747 -
Rings with a right duo factor ring by an ideal contained in the center
Jeoung Soo Cheon, Tai Keun Kwak, Yang Lee, Zhelin Piao, Sang Jo Yun
Bull. Korean Math. Soc. 2022; 59(3): 529-545
https://doi.org/10.4134/BKMS.b201014
Editorial Office
✕
BKMS
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd