Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
Most Downloaded
HOME
VIEW ARTICLES
Most Downloaded
VIEW ARTICLES
Most Downloaded
-
2022-07-31
B\'ezout rings and weakly B\'ezout rings
Haitham El~AlaouiAbstract : In this paper, we study some properties of B\'ezout and weakly B\'ezout rings. Then, we investigate the transfer of these notions to trivial ring extensions and amalgamated algebras along an ideal. Also, in the context of domains we show that the amalgamated is a B{\'e}zout ring if and only if it is a weakly B\'ezout ring. All along the paper, we put the new results to enrich the current literature with new families of examples of non-B\'ezout weakly B\'ezout rings.
-
2022-07-31
$P$-extremal functions and Bernstein-Markov properties associated to compact sets in $\mathbb R^d$
Hoang Thieu Anh, Kieu Phuong Chi, Nguyen Quang Dieu, Tang Van LongAbstract : Given a compact subset $P \subset (\mathbb R^+)^d$ and a compact set $K$ in $\mathbb C^d$. We concern with the Bernstein-Markov properties of the triple $(P,K,\mu)$ where $\mu$ is a finite positive Borel measure with compact support $K$. Our approach uses (global) $P$-extremal functions which is inspired by the classical case (when $P=\Sigma$ the unit simplex) in [7].
-
2024-03-31
Six dimensional almost complex torus manifolds with Euler number six
Donghoon Jang, Jiyun ParkAbstract : An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let $M$ be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for $M$, and for each type of graph we construct such a manifold $M$, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch $\chi_y$-genus of $M$.
-
2023-03-31
Rings and modules which are stable under nilpotents of their injective hulls
Nguyen Thi Thu HaAbstract : It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right $R$-module is nilpotent-invariant. We prove that $R\cong R_1\times R_2$, where $R_1, R_2$ are rings which satisfy $R_1$ is a semi-simple Artinian ring and $R_2$ is square-free as a right $R_2$-module and all idempotents of $R_2$ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right $R$-modules. Such a module is shown to have isomorphic simple modules $eR$ and $fR$, where $e,f$ are orthogonal primitive idempotents such that $eRf\ne 0$.
-
2022-11-30
Some new classes of zero-difference balanced functions and related constant composition codes
Sankhadip Roy
Abstract : Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over $\mathbb F_p$, where $p$ is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-$p$-balanced functions over $\mathbb F_{p^n}$. Eventually, we use these results to construct some optimal constant composition codes.
-
2022-09-30
On transcendental meromorphic solutions of certain types of differential equations
Abhijit Banerjee, Tania Biswas, Sayantan MaityAbstract : In this paper, for a transcendental meromorphic function $f$ and $a\in \mathbb{C}$, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: \[f^n+af^{n-2}f'+ P_d(z,f) = \sum_{i=1}^{k}p_i(z)e^{\alpha_i(z)}, \] where $P_d(z,f)$ is a differential polynomial of $f$, $p_i$'s and $\alpha_{i}$'s are non-vanishing rational functions and non-constant polynomials, respectively. When $a=0$, we have pointed out a major lacuna in a recent result of Xue [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case $a\neq 0$ has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.
-
2022-07-31
The K\"{a}hler Different of a Set of Points in~$\mathbb{P}^{m}\!\times\mathbb{P}^{n}$
Nguyen T. Hoa, Tran N. K. Linh, Le N. Long, Phan T. T. Nhan, Nguyen T. P. NhiAbstract : Given an ACM set $\mathbb{X}$ of points in a multiprojective space $\mathbb{P}^{m}\!\times\mathbb{P}^{n}$ over a field of characteristic zero, we are interested in studying the K\"ahler different and the Cayley-Bacharach property for $\mathbb{X}$. In $\mathbb{P}^1\times \mathbb{P}^1$, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the K\"ahler different. However, this result fails to hold in $\mathbb{P}^{m}\!\times\mathbb{P}^{n}$ for $n>1$ or $m>1$. In this paper we start an investigation of the K\"ahler different and its Hilbert function and then prove that $\mathbb{X}$ is a complete intersection of type $(d_1,\ldots,d_m,d'_1,\ldots,d'_n)$ if and only if it has the Cayley-Bacharach property and the K\"ahler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of $\mathbb{X}$ under certain assumptions.
-
2022-05-31
Computation of Wedderburn decomposition of groups algebras from their subalgebra
Gaurav Mittal, Rajendra Kumar SharmaAbstract : In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra $\mathbb{F}_qG$ can be deduced from a subalgebra $\mathbb{F}_q(G/H)$ of factor group $G/H$ of $G$, where $H$ is a normal subgroup of $G$ of prime order $P$. Here, we assume that $q=p^r$ for some prime $p$ and the center of each Wedderburn component of $\mathbb{F}_qG$ is the coefficient field $\mathbb{F}_q$.
-
2023-03-31
On reversible $\mathbb{Z}_2$-double cyclic codes
Nupur PatankerAbstract : A binary linear code is said to be a $\mathbb{Z}_2$-double cyclic code if its coordinates can be partitioned into two subsets such that any simultaneous cyclic shift of the coordinates of the subsets leaves the code invariant. These codes were introduced in [6]. A $\mathbb{Z}_2$-double cyclic code is called reversible if reversing the order of the coordinates of the two subsets leaves the code invariant. In this note, we give necessary and sufficient conditions for a $\mathbb{Z}_2$-double cyclic code to be reversible. We also give a relation between reversible $\mathbb{Z}_2$-double cyclic code and LCD $\mathbb{Z}_2$-double cyclic code for the separable case and we present a few examples to show that such a relation doesn't hold in the non-separable case. Furthermore, we list examples of reversible $\mathbb{Z}_2$-double cyclic codes of length $\leq 10$.
-
2022-09-30
The Matrix representation of a composition operator on the Hardy space
Young-Bok ChungAbstract : We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.
Most Read
-
Constructions of regular sparse anti-magic squares
Guangzhou Chen
, Wen Li, Bangying Xin, Ming ZhongBull. Korean Math. Soc. 2022; 59(3): 617-642
https://doi.org/10.4134/BKMS.b210281 -
Biharmonic hypersurfaces with recurrent operators in the Euclidean space
Esmaiel Abedi, Najma Mosadegh
Bull. Korean Math. Soc. 2022; 59(6): 1595-1603
https://doi.org/10.4134/BKMS.b210910 -
On the Pocklington-Peralta square root algorithm in finite fields
Chang Heon Kim, Namhun Koo
, Soonhak KwonBull. Korean Math. Soc. 2022; 59(6): 1523-1537
https://doi.org/10.4134/BKMS.b210870 -
UN rings and group rings
Kanchan Jangra, Dinesh Udar
Bull. Korean Math. Soc. 2023; 60(1): 83-91
https://doi.org/10.4134/BKMS.b210917
Most Downloaded
-
MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon Hyun
Bull. Korean Math. Soc. 2023; 60(3): 561-574
https://doi.org/10.4134/BKMS.b210374 -
Bredon homology of wallpaper groups
Ramon Flores
Bull. Korean Math. Soc. 2023; 60(6): 1497-1522
https://doi.org/10.4134/BKMS.b220669 -
Weighted integral inequalities for modified integral Hardy operators
Duranta Chutia, Rajib Haloi
Bull. Korean Math. Soc. 2022; 59(3): 757-780
https://doi.org/10.4134/BKMS.b210469 -
On the construction of optimal linear codes of dimension four
ATSUYA KATO, TATSUYA MARUTA, KEITA NOMURA
Bull. Korean Math. Soc. 2023; 60(5): 1237-1252
https://doi.org/10.4134/BKMS.b220613
Editorial Office
✕
BKMS
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd