# Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

HOME VIEW ARTICLES Ahead of Print Articles
The following are papers that have received final approval and are awaiting to be published. They are listed in the order of their initial submission date.
Papers are published in the order of their initial submission date and will be made available under “Current Issue” once scheduled to be included in a print issue.

Note: Please understand the below list is not in the exact publishing order of the papers as the list does not include papers under internal reviewing process nor those that have not been galley proofed by the authors.

Final published versions of all papers are available under “All Issues” and also under “Current Issue” for papers included in the current issue.

* Paper information have been automatically generated from the information submitted by authors in the online submission system.
• ### Published online July 26, 2022

#### A generalization of Maynard's results on the Brun-Titchmarsh Theorem to number fields

Jeoung-Hwan Ahn and Soun-Hi Kwon

Abstract : Maynard proved that there exists an effectively computable constant $q_1$ such that if $q \geq q_1$, then $\pi(x;q,a) < \frac{2 { {Li}}(x)}{\phi(q)}$ for $x \geq q^8$. In this paper, we will show the following. Let $\delta_1$ and $\delta_2$ be positive constants with $0< \delta_1, \delta_2 < 1$ and $\delta_1+\delta_2 > 1$. Assume that $L \neq {\mathbb Q}$ is a number field. Then there exists an effectively computable constant $d_1$ such that for $d_L \geq d_1$ and $x \geq \exp \left( 326 n_L^{\delta_1} \left(\log d_L\right)^{1+\delta_2}\right)$, we have $\pi_C(x) < 2 \frac{|C|}{|G|} {\ {Li}}(x)$.

• ### Published online July 26, 2022

#### Dynamic behavior of cracked beams and shallow arches

Semion Gutman, Junhong Ha, and Sudeok Shon

Abstract : We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles using the Extended Hamilton's Principle, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of the beams and arches is studied under the assumptions of the weak and strong damping. The presence of the cracks forces a weaker regularity results for the arch motion, as compared to the beam case.

• ### Published online August 1, 2022

#### Thomas algorithms for systems of fourth-order finite difference methods

Soyoon Bak, Philsu Kim, and Sangbeom Park

Abstract : The main objective of this paper is to develop a concrete inverse formula of the system induced by the fourth-order finite difference method for two-point boundary value problems with Robin boundary conditions. This inverse formula facilitates to make a fast algorithm for solving the problems. Our numerical results show the efficiency and accuracy of the proposed method, which is implemented by the Thomas algorithm.

• ### Published online July 28, 2022

#### Multiple solutions of a perturbed Yamabe-type equation on graph

Yang Liu

Abstract : Let $u$ be a function on locally finite graph $G=(V, E)$ and $\Omega$ be a bounded subset of $V$. Let $\varepsilon>0$, $p>2$ and $0\leq\lambda0$ such that for all $\varepsilon\in(0,\varepsilon_0)$, the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation \begin{equation*}\label{b3}\left\{\begin{array}{lll} -\Delta u=f(u)+\varepsilon h &{\rm in}& \Omega\\[1.5ex] u=0 &{\rm on}&\p\Omega,\end{array}\ri. \end{equation*}\\ and prove similar result for certain nonlinear term $f(u)$.

• ### Published online August 1, 2022

#### Fourier Transform of Anisotropic Mixed-norm Hardy Spaces with Applications to Hardy-Littlewood Inequalities

Jun Liu, Yaqian Lu, and Mingdong Zhang

Abstract : Let $\vec{p}\in(0,1]^n$ be a $n$-dimensional vector and $A$ a dilation. Let $H_A^{\vec{p}}(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H_{A}^{\vec{p}}(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f\in H_A^{\vec{p}}(\mathbb{R}^n)$ coincides with a continuous function $F$ on $\mathbb{R}^n$ in the sense of tempered distributions. Moreover, the function $F$ can be controlled pointwisely by the product of the Hardy space norm of $f$ and a step function with respect to the transpose matrix of $A$. As applications, the authors obtain a higher order of convergence for the function $F$ at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of $H_A^{\vec{p}}(\mathbb{R}^n)$.

• ### Published online June 9, 2022

#### New Congruences For $\ell$-Regular Overpartitions

Ankita Jindal and Nabin K. Meher

Abstract : For a positive integer $\ell,$ $\overline{A}_{\ell}(n)$ denotes the number of overpartitions of $n$ into parts not divisible by $\ell.$ In this article, we find certain Ramanujan-type congruences for $\overline{A}_{ r \ell}(n),$ when $r\in\{8, 9\}$ and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for $\overline{A}_{ 13}(n)$ by using an algorithm developed by Radu and Sellers \cite{Radu2011}.

• ### Published online July 28, 2022

#### weakly equivariant classification of small covers over a product of simplicies

Aslı Güçlükan İlhan and Sabri Kaan Gürbüzer

Abstract : Given a dimension function ω, we introduce the notion of an ω-vector weighted digraph and an ω-equivalence between them. Then we establish a bijection between the weakly (Z/2)^n-equivariant homeomorphism classes of small covers over a product of simplices Δ^ω(1) × · · · × Δ^ω(k) and the set of ω-equivalence classes of ω-vector weighted digraphs with k-labeled vertices where n = ω(1)+· · ·+ω(k). Using this bijection, we obtain a formula for the number of weakly (Z/2)^n-equivariant homeomorphism classes of small covers over a product of three simplices.

• ### Published online June 3, 2022

#### Spectral decomposition for homeomorphisms on non-metrizable totally disconnected spaces

Jumi Oh

Abstract : We introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces.

• ### Published online July 29, 2022

#### Matrices similar to centrosymmetric matrices

Benjamín A Itzá-Ortiz and Rubén Alejandro Martínez-Avendaño

Abstract : In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal submatrix, and conditions under which a matrix can be dilated to a matrix similar to a centrosymmetric matrix.

• ### Published online July 25, 2022

#### Bailey pairs and strange identities

Jeremy Lovejoy

Abstract : Zagier introduced the term strange identity" to describe an asymptotic relation between a certain $q$-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.

## Current Issue

• ### Synchronized components of a subshift

Manouchehr Shahamat

J. Korean Math. Soc. 2022; 59(1): 1-12
https://doi.org/10.4134/JKMS.j200112

• ### Regularity of the generalized Poisson operator

Pengtao Li, Zhiyong Wang, Kai Zhao

J. Korean Math. Soc. 2022; 59(1): 129-150
https://doi.org/10.4134/JKMS.j210224

• ### Construction for self-orthogonal codes over a certain non-chain Frobenius ring

Boran Kim

J. Korean Math. Soc. 2022; 59(1): 193-204
https://doi.org/10.4134/JKMS.j210357

• ### Parabolic quaternionic Monge-Amp\{e}re equation on compact manifolds with a flat hyperK\"ahler metric

Jiaogen Zhang

J. Korean Math. Soc. 2022; 59(1): 13-33
https://doi.org/10.4134/JKMS.j200626

• ### Synchronized components of a subshift

Manouchehr Shahamat

J. Korean Math. Soc. 2022; 59(1): 1-12
https://doi.org/10.4134/JKMS.j200112

• ### Practical FHE parameters against lattice attacks

Jung Hee Cheon, Yongha Son, Donggeon Yhee

J. Korean Math. Soc. 2022; 59(1): 35-51
https://doi.org/10.4134/JKMS.j200650

• ### Parabolic quaternionic Monge-Amp\{e}re equation on compact manifolds with a flat hyperK\"ahler metric

Jiaogen Zhang

J. Korean Math. Soc. 2022; 59(1): 13-33
https://doi.org/10.4134/JKMS.j200626

• ### Regularity of the generalized Poisson operator

Pengtao Li, Zhiyong Wang, Kai Zhao

J. Korean Math. Soc. 2022; 59(1): 129-150
https://doi.org/10.4134/JKMS.j210224