Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2022-07-01
Foliations from left orders
Hyungryul Baik, Sebastian Hensel, Chenxi WuAbstract : 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 $3$.
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2023-03-01
Ricci-Bourguignon solitons and Fischer-Marsden conjecture on generalized Sasakian-space-forms with $\beta$-Kenmotsu structure
Sudhakar Kumar Chaubey, Young Jin SuhAbstract : Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with $\beta$-Kenmotsu structure. It is proven that a $(2n+1)$-dimensional generalized Sasakian-space-form with $\beta$-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with $\beta$-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either $\Psi \backslash T^{k} \times M^{2n+1-k}$ or gradient $\eta$-Yamabe soliton.
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2022-07-01
Finite $p$-groups whose normal closures of non-normal subgroups have two orders
Lifang WangAbstract : We describe the structure of finite $p$-groups in which all normal closures of non-normal subgroups have two orders for $p>2$.
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2023-03-01
Ramanujan continued fractions of order eighteen
Yoon Kyung ParkAbstract : As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction $C(\tau)$. We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.
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2022-09-01
A generalization of Maynard's results on the Brun-Titchmarsh theorem to number fields
Jeoung-Hwan Ahn, Soun-Hi KwonAbstract : Maynard proved that there exists an effectively computable constant $q_1$ such that if $q \geq q_1$, then $\frac{\log q}{\sqrt{q} \phi(q)} {\rm Li}(x) \ll \pi(x;q,m) \!<\! \frac{2}{\phi(q)} {\mathrm{Li}}(x)$ 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 exist effectively computable constants $c_0$ and $d_1$ 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 $$\left| \pi_C(x) - \frac{|C|}{|G|} {\mathrm{Li}}(x) \right| \leq \left(1- c_0 \frac{\log d_L}{d_L^{7.072}} \right) \frac{|C|}{|G|} {\mathrm{Li}}(x).$$
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2022-07-01
Gorenstein quasi-resolving subcategories
Weiqing Cao, Jiaqun WeiAbstract : 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 $M$.
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2024-03-01
A note on Sobolev type trace inequalities for $s$-harmonic extensions
Yongrui Tang, Shujuan ZhouAbstract : In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.
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2022-09-01
New congruences for $\ell$-regular overpartitions
Ankita Jindal, Nabin K. MeherAbstract : 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 [15].
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2024-01-01
Stable automorphic forms for the general linear group
Jae-Hyun YangAbstract : In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.
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2023-03-01
On $S$-multiplication rings
Mohamed Chhiti, Soibri MoindzeAbstract : Let $R$ be a commutative ring with identity and $S$ be a multiplicatively closed subset of $R$. In this article we introduce a new class of ring, called $S$-multiplication rings which are $S$-versions of multiplication rings. An $R$-module $M$ is said to be $S$-multiplication if for each submodule $N$ of $M$, $sN\subseteq JM\subseteq N$ for some $s\in S$ and ideal $J$ of $R$ (see for instance [4, Definition 1]). An ideal $I$ of $R$ is called $S$-multiplication if $I$ is an $S$-multiplication $R$-module. A commutative ring $R$ is called an $S$-multiplication ring if each ideal of $R$ is $S$-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and $S$-$PIR$. Moreover, we generalize some properties of multiplication rings to $S$-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.
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The ideal class group of polynomial overrings of the ring of integers
Gyu Whan Chang
J. Korean Math. Soc. 2022; 59(3): 571-594
https://doi.org/10.4134/JKMS.j210419 -
Ricci-Bourguignon solitons and Fischer-Marsden conjecture on generalized Sasakian-space-forms with $\beta$-Kenmotsu structure
Sudhakar Kumar Chaubey, Young Jin Suh
J. Korean Math. Soc. 2023; 60(2): 341-358
https://doi.org/10.4134/JKMS.j220057 -
Weakly equivariant classification of small covers over a product of simplicies
Aslı Güçlükan İlhan, Sabri Kaan Gürbüzer
J. Korean Math. Soc. 2022; 59(5): 963-986
https://doi.org/10.4134/JKMS.j220104 -
Prime factorization of ideals in commutative rings, with a focus on Krull rings
Gyu Whan Chang, Jun Seok Oh
J. Korean Math. Soc. 2023; 60(2): 407-464
https://doi.org/10.4134/JKMS.j220271
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On non-displaceable Lagrangian submanifolds in two-step flag varieties
Yoosik Kim
J. Korean Math. Soc. 2023; 60(5): 1109-1133
https://doi.org/10.4134/JKMS.j230098 -
Gorenstein $FP_{n}$-injective modules with respect to a semidualizing bimodule
Zhiqiang Cheng, Guoqiang Zhao
J. Korean Math. Soc. 2024; 61(1): 29-40
https://doi.org/10.4134/JKMS.j220398 -
Two-weighted conditions and characterizations for a class of multilinear fractional new maximal operators
Rui Li, Shuangping Tao
J. Korean Math. Soc. 2023; 60(1): 195-212
https://doi.org/10.4134/JKMS.j220250 -
A new optimal eighth-order family of multiple root finders
Dejan \'Cebi\'c
, Neboj\v sa M. Ralevi\'cJ. Korean Math. Soc. 2022; 59(6): 1067-1082
https://doi.org/10.4134/JKMS.j210607
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