# Journal of theKorean Mathematical SocietyJKMS

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

## Current Issue

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July, 2022 | Volume 59, No. 4
• ### 2022-07-01

#### The moduli spaces of Lorentzian left-invariant metrics on three-dimensional unimodular simply connected Lie groups

Mohamed Boucetta, Abdelmounaim Chakkar

Abstract : Let $\mathrm{G}$ be an arbitrary, connected, simply connected and unimodular Lie group of dimension $3$. On the space $\mathfrak{M}(\mathrm{G})$ of left-invariant Lorentzian metrics on $\mathrm{G}$, there exists a natural action of the group ${\rm Aut}(\mathrm{G})$ of automorphisms of $\mathrm{G}$, so it yields an equivalence relation $\backsimeq$ on $\mathfrak{M}(\mathrm{G})$, in the following way: $h_1\backsimeq h_2 \Leftrightarrow h_2=\phi^{*}(h_1) \;\textrm{for some}\; \phi \in {\rm Aut}(\mathrm{G}).$ In this paper a procedure to compute the orbit space ${\rm Aut}(\mathrm{G})/\mathfrak{M}(\mathrm{G})$ (so called moduli space of $\mathfrak{M}(\mathrm{G})$) is given.

• ### 2022-07-01

#### On $3^k$-regular cubic partitions

Nayandeep Deka Baruah, Hirakjyoti Das

Abstract : Recently, Gireesh, Shivashankar, and Naika \cite{GSN20} found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the $3^k$-regular cubic partitions. We also find new families of congruences.

• ### 2022-07-01

#### Foliations from left orders

Hyungryul Baik, Sebastian Hensel, Chenxi Wu

Abstract : We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension $2$, and exhibit connections to various problems in dimension $3$.

• ### 2022-07-01

#### Uniqueness of quasi-roots in right-angled Artin groups

Eon-Kyung Lee, Sang-Jin Lee

Abstract : We introduce the notion of quasi-roots and study their \linebreak uniqueness in right-angled Artin groups.

• ### 2022-07-01

#### Gorenstein quasi-resolving subcategories

Weiqing Cao, Jiaqun Wei

Abstract : In this paper, we introduce the notion of Gorenstein quasi-resolving subcategories (denoted by $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$) in term of quasi-resolving subcategory $\mathcal{X}$. We define a resolution dimension relative to the Gorenstein quasi-resolving categories $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$. In addition, we study the stability of $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$ and apply the obtained properties to special subcategories and in particular to modules categories. Finally, we use the restricted flat dimension of right $B$-module $M$ to characterize the finitistic dimension of the endomorphism algebra $B$ of a $\mathcal{GQ}_{\mathcal{X}}$-projective $A$-module $M$.

• ### 2022-07-01

#### Sharp Ore-type conditions for the existence of an even $[4,b]$-factor in a graph

Eun-Kyung Cho, Su-Ah Kwon, Suil O

Abstract : Let $a$ and $b$ be positive even integers. An even $[a,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $d_H(v)$ is even and $a \le d_H(v) \le b$. Let $\kappa(G)$ be the minimum size of a vertex set $S$ such that $G-S$ is disconnected or one vertex, and let $\sigma_2(G)=\min_{uv \notin E(G)}(d(u)+d(v))$. In 2005, Matsuda proved an Ore-type condition for an $n$-vertex graph satisfying certain properties to guarantee the existence of an even $[2,b]$-factor. In this paper, we prove that for an even positive integer $b$ with $b \ge 6$, if $G$ is an $n$-vertex graph such that $n \ge b+5$, $\kappa(G) \ge 4$, and $\sigma_2(G) \ge \frac{8n}{b+4}$, then $G$ contains an even $[4,b]$-factor; each condition on $n$, $\kappa(G)$, and $\sigma_2(G)$ is sharp.

• ### 2022-07-01

#### A note on the zeros of Jensen polynomials

Young-One Kim, Jungseob Lee

Abstract : Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some recent results on Jensen polynomials, relevant to the Riemann hypothesis, are extended and improved.

• ### 2022-07-01

#### C*-algebraic Schur product theorem, P\'{O}lya-Szeg\H{O}-Rudin question and Novak's conjecture

Krishnanagara Mahesh~Krishna

Abstract : Striking result of Vyb\'{\i}ral \cite{VYBIRAL} says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vyb\'{\i}ral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C*-algebras and derive the results of Schur and Vyb\'{\i}ral. As an application, we state C*-algebraic version of Novak's conjecture and solve it for commutative unital C*-algebras. We formulate P\'{o}lya-Szeg\H{o}-Rudin question for the C*-algebraic Schur product of positive matrices.

• ### 2022-07-01

#### Finite $p$-groups whose normal closures of non-normal subgroups have two orders

Lifang Wang

Abstract : We describe the structure of finite $p$-groups in which all normal closures of non-normal subgroups have two orders for $p>2$.

• ### 2022-07-01

#### Regularity relative to a hereditary torsion theory for modules over a commutative ring

Lei Qiao, Kai Zuo

Abstract : In this paper, we introduce and study regular rings relative to the hereditary torsion theory $w$ (a special case of a well-centered torsion theory over a commutative ring), called $w$-regular rings. We focus mainly on the $w$-regularity for $w$-coherent rings and $w$-Noetherian rings. In particular, it is shown that the $w$-coherent $w$-regular domains are exactly the Pr\"ufer $v$-multiplication domains and that an integral domain is $w$-Noetherian and $w$-regular if and only if it is a Krull domain. We also prove the $w$-analogue of the global version of the Serre--Auslander-Buchsbaum Theorem. Among other things, we show that every $w$-Noetherian $w$-regular ring is the direct sum of a finite number of Krull domains. Finally, we obtain that the global weak $w$-projective dimension of a $w$-Noetherian ring is 0, 1, or $\infty$.

## 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