Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2022-11-30
Blow up of solutions for a Petrovsky type equation with logarithmic nonlinearity
Jorge Ferreira, Nazl\i \, Irk\i l, Erhan Pi\c{s}kin, Carlos Raposo
, Mohammad ShahrouziAbstract : This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.
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2022-11-30
Some new classes of zero-difference balanced functions and related constant composition codes
Sankhadip RoyAbstract : 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.
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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.
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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 $\mathbb{F}_q$.
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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.
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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.
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2024-01-31
Topological sensitivity and its stronger forms on semiflows
Ruchi Das, Devender Kumar, Mohammad SalmanAbstract : In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space $X$, a syndetically transitive semiflow $(T,X,\pi)$ having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a $T_3$ space $X$, a transitive, nonminimal semiflow $(T,X,\pi)$ having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.
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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 $\leq 10$.
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2023-01-31
Multiplicative functions commutable with binary quadratic forms $x^2 \pm xy + y^2$
Poo-Sung ParkAbstract : If a multiplicative function $f$ is commutable with a quadratic form $x^2+xy+y^2$, i.e., \[ f(x^2+xy+y^2) = f(x)^2 + f(x)\,f(y) + f(y)^2, \] then $f$ is the identity function. In other hand, if $f$ is commutable with a quadratic form $x^2-xy+y^2$, then $f$ is one of three kinds of functions: the identity function, the constant function, and an indicator function for $\mathbb{N}\setminus p\mathbb{N}$ with a prime $p$.$\\ \\ \\$
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2022-11-30
On weakly $S$-prime submodules
Hani A. Khashan, Ece Yetkin~CelikelAbstract : Let $R$ be a commutative ring with a non-zero identity, $S$ be a multiplicatively closed subset of $R$ and $M$ be a unital $R$-module. In this paper, we define a submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ to be weakly $S$-prime if there exists $s\in S$ such that whenever $a\in R$ and $m\in M$ with $0\neq am\in N$, then either $sa\in(N:_{R}M)$ or $sm\in N$. Many properties, examples and characterizations of weakly $S$-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly $S$-prime.
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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 -
Products of composition, differentiation and multiplication from the cauchy spaces to the Zygmund space
Rita Hibschweiler
Bull. Korean Math. Soc. 2023; 60(4): 1061-1070
https://doi.org/10.4134/BKMS.b220471 -
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 -
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
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The $u$-$S$-global dimensions of commutative rings
Wei Qi, Xiaolei Zhang
Bull. Korean Math. Soc. 2023; 60(6): 1523-1537
https://doi.org/10.4134/BKMS.b220677 -
Vanishing theorems for weighted harmonic $1$-forms on smooth metric measure spaces
Xiaoli Chao, Weili Wang
Bull. Korean Math. Soc. 2023; 60(3): 623-636
https://doi.org/10.4134/BKMS.b210927 -
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 -
Boundedness and continuity for variation operators on the Triebel--Lizorkin spaces
Feng Liu, Yongming Wen, Xiao Zhang
Bull. Korean Math. Soc. 2022; 59(6): 1539-1555
https://doi.org/10.4134/BKMS.b210874
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