Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2024-01-31
A function-field analogue of the Goldbach counting function and the associated Dirichlet series
Shigeki Egami, Kohji MatsumotoAbstract : We consider a function-field analogue of Dirichlet series associated with the Goldbach counting function, and prove that it can, or cannot, be continued meromorphically to the whole plane. When it cannot, we further prove the existence of the natural boundary of it.
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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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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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2024-01-31
Depth and Stanley depth of two special classes of monomial ideals
Xiaoqi WeiAbstract : In this paper, we define two new classes of monomial ideals $I_{l,d}$ and $J_{k,d}$. When $d\geq 2k+1$ and $l\leq d-k-1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/I_{l,d}^{t}$ for all $t\geq 1$. When $d=2k=2l$, we compute the depth and Stanley depth of quotient ring $S/I_{l,d}$. When $d\geq 2k$, we also compute the depth and Stanley depth of quotient ring $S/J_{k,d}$.
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2024-03-31
The boundedness of bilinear pseudodifferential operators in Triebel-Lizorkin and Besov spaces with variable exponents
Yin Liu, Lushun WangAbstract : In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear H\"{o}rmander class $BS_{1,1}^m$ in variable Triebel-Lizorkin spaces and variable Besov spaces.
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2023-03-31
Some estimates for generalized commutators of multilinear Calder\'on-Zygmund operators
Honghai Liu, Zengyan Si, Ling WangAbstract : Let $T$ be an $m$-linear Calder\'on-Zygmund operator. $T_{\vec{b},S}$ is the generalized commutator of $T$ with a class of measurable functions $\{b_{i}\}_{i=1}^\infty$. In this paper, we will give some new estimates for $T_{\vec{b},S}$ when $\{b_{i}\}_{i=1}^\infty$ belongs to Orlicz-type space and Lipschitz space, respectively.
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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 WongAbstract : 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.
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2022-11-30
Tamed exhaustion functions and Schwarz type lemmas for almost Hermitian manifolds
Weike YuAbstract : In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.
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2023-03-31
Hyperbolic and spherical power of a circle
Young Wook Kim, Sung-Eun Koh, Hyung Yong Lee, Heayong Shin, Seong-Deog YangAbstract : Suppose that a line passing through a given point $P$ intersects a given circle $\mathcal{C}$ at $Q$ and $R$ in the Euclidean plane. It is well known that $|PQ||PR|$ is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.
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2022-11-30
Some remarks on problems of subset sum
Min Tang, Hongwei XuAbstract : Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers and let $P(A)=\left\{\sum \varepsilon_ia_i: a_i\in A, \varepsilon_i=0\text{ or }1, \sum \varepsilon_i<\infty\right\}$. Burr posed the following question: Determine conditions on integers sequence $B$ that imply either the existence or the non-existence of $A$ for which $P(A)$ is the set of all non-negative integers not in $B$. In this paper, we focus on some problems of subset sum related to Burr's question.
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Homology and Serre class in $\mathrm{D}(R)$
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Representations over Green algebras of weak Hopf algebras based on Taft algebras
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