Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Most Read

HOME VIEW ARTICLES Most Read
  • 2024-05-31

    On the growth of algebroid solutions of algebraic differential equations

    Manli Liu, Linlin Wu

    Abstract : Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].

  • 2023-05-31

    The classification of $\omega$-left-symmetric algebras in low dimensions

    Zhiqi Chen, Yang Wu

    Abstract : $\omega$-left-symmetric algebras contain left-symmetric algebras as a subclass and the commutator defines an $\omega$-Lie algebra. In this paper, we classify $\omega$-left-symmetric algebras in dimension 3 up to an isomorphism based on the classification of $\omega$-Lie algebras and the technique of Lie algebras.

  • 2024-05-31

    A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curves

    Muhittin Evren Aydın , Aykut Has , Beyhan Yılmaz

    Abstract : In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension $3$, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

  • 2023-09-30

    Weak potency and cyclic subgroup separability of certain free products and tree products

    Muhammad Sufi Mohd Asri, Wan Ainun Mior Othman, Kok Bin Wong, Peng Choon Wong

    Abstract : In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.

  • 2023-09-30

    Structure of idempotents in polynomial rings and matrix rings

    Juan Huang, Tai Keun Kwak, Yang Lee, Zhelin Piao

    Abstract : An idempotent $e$ of a ring $R$ is called {\it right} (resp., {\it left}) {\it semicentral} if $er=ere$ (resp., $re =ere$) for any $r\in R$, and an idempotent $e$ of $R\backslash \{0,1\}$ will be called {\it right} (resp., {\it left}) {\it quasicentral} provided that for any $r\in R$, there exists an idempotent $f=f(e,r)\in R\backslash \{0,1\}$ such that $er=erf$ (resp., $re=fre$). We show the whole shapes of idempotents and right (left) semicentral idempotents of upper triangular matrix rings and polynomial rings. We next prove that every nontrivial idempotent of the $n$ by $n$ full matrix ring over a principal ideal domain is right and left quasicentral and, applying this result, we can find many right (left) quasicentral idempotents but not right (left) semicentral.

    Show More  
  • 2024-03-31

    Wavelet characterizations of variable Hardy-Lorentz spaces

    Yao He

    Abstract : In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\mathbb R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\mathbb R^{n})$. Then, for any $q\in(0,1]$, via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\mathbb R^{n})$ in terms of wavelets.

  • 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 Udar

    Abstract : 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.

    Show More  
  • 2024-03-31

    On the generalized principally injective modules

    Fatemeh Gholami, Zohreh Habibi, Alireza Najafizadeh

    Abstract : Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.

  • 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 Wang

    Abstract : 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.

  • 2024-01-31

    Stability of total scalar curvature and the critical point equation

    Seungsu Hwang, Gabjin Yun

    Abstract : We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

Current Issue

January, 2025
Vol.62 No.1

Current Issue
Archives

Most Read

BKMS