Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2023-07-01
Generalized hexagons embedded in metasymplectic spaces
Sebastian Petit, Hendrik Van MaldeghemAbstract : We consider thick generalized hexagons fully embedded in metasymplectic spaces, and we show that such an embedding either happens in a point residue (giving rise to a full embedding inside a dual polar space of rank 3), or happens inside a symplecton (giving rise to a full embedding in a polar space of rank 3), or is isometric (that is, point pairs of the hexagon have the same mutual position whether viewed in the hexagon or in the metasymplectic space--these mutual positions are \emph{equality, collinearity, being special, opposition}). In the isometric case, we show that the hexagon is always a Moufang hexagon, its little projective group is induced by the collineation group of the metasymplectic space, and the metasymplectic space itself admits central collineations (hence, in symbols, it is of type $\mathsf{F_{4,1}}$). We allow non-thick metasymplectic spaces without non-thick lines and obtain a full classification of the isometric embeddings in this case.
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2023-07-01
Preresolving subcategories in extriangulated categories
Songsong Liu, Jiaqun WeiAbstract : In this paper, we introduce and study preresolving subcategories in an extriangulated category~$\mathscr{C}$. Let $\mathcal{Y}$ be a $\mathcal{Z}$-preresolving subcategory of $\mathscr{C}$ admitting a $\mathcal{Z}$-proper $\xi$-generator $\mathcal{X}$. We give the characterization of $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution dimension of an object in $\mathscr{C}$. Next, for an object $A$ in $\mathscr{C}$, if the $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution~dimension of $A$ is at most $n$, then all ``$n$-$\mathcal{X}$-syzygies" of $A$ are objects in $\mathcal{Y}$. Finally, we prove that $A$ has a $\mathcal{Z}$-proper $\mathcal{X}$-resolution if and only if $A$ has a $\mathcal{Z}$-proper $\mathcal{Y}$-resolution. As an application, we introduce $(\mathcal{X},\mathcal{Z})$-Gorenstein~subcategory $\mathcal{GX}_{\mathcal{Z}}(\xi)$ of $\mathscr{C}$ and prove that $\mathcal{GX}_{\mathcal{Z}}(\xi)$ is both $\mathcal{Z}$-resolving subcategory and $\mathcal{Z}$-coresolving subcategory of $\mathscr{C}$.
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2023-03-01
Relative Rota-Baxter systems on Leibniz algebras
Apurba Das, Shuangjian GuoAbstract : In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.
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2023-01-01
Two-weighted conditions and characterizations for a class of multilinear fractional new maximal operators
Rui Li, Shuangping TaoAbstract : In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator $\mathcal{M}_{\varphi,\beta}$ are established. Meanwhile, we introduce the $S_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ conditions and obtain the characterization of two-weighted inequalities for $\mathcal{M}_{\varphi,\beta}$. Finally, the relationships of the conditions $S_{(\vec{p},q),\beta}(\varphi)$, $\mathcal{A}_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ and the characterization of the one-weight $A_{(\vec{p},q),\beta}(\varphi)$ are given.
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2023-01-01
Geometry of bilinear forms on a normed space $\mathbb{R}^n$
Sung Guen KimAbstract : For every $n\geq 2$, let $\mathbb{R}^n_{\|\cdot\|}$ be $\mathbb{R}^n$ with a norm $\|\cdot\|$ such that its unit ball has finitely many extreme points more than $2n$. We devote to the description of the sets of extreme and exposed points of the closed unit balls of ${\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ and ${\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$, where ${\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ is the space of bilinear forms on $\mathbb{R}^n_{\|\cdot\|}$, and ${\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$ is the subspace of ${\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ consisting of symmetric bilinear forms. Let ${\mathcal F}={\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ or ${\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$. First we classify the extreme and exposed points of the closed unit ball of ${\mathcal F}$. We also show that every extreme point of the closed unit ball of ${\mathcal F}$ is exposed. It is shown that ${ext}B_{{\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})}={ext}B_{{\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})}\cap {\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$ and ${exp}B_{{\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})}={exp}B_{{\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})}\cap {\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$, which expand some results of \cite{18, 23, 28, 29, 35, 38, 40, 41, 43}.
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2022-09-01
Bailey pairs and strange identities
Jeremy LovejoyAbstract : 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.
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2022-05-01
Construction of a solution of split equality variational inequality problem for pseudomonotone mappings in Banach spaces
Getahun Bekele WegaAbstract : The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.
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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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2023-07-01
Classification of solvable lie algebras whose non-trivial coadjoint orbits of simply connected lie groups are all of codimension 2
Hieu Van Ha, Vu Anh Le, Tu Thi Cam Nguyen, Hoa Duong QuangAbstract : We give a classification of real solvable Lie algebras whose non-trivial coadjoint orbits of corresponding to simply connected Lie groups are all of codimension 2. These Lie algebras belong to a well-known class, called the class of MD-algebras.
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2023-03-01
The Harbourne-Hirschowitz condition and the anticanonical orthogonal property for surfaces
Abel Castorena, Juan Bosco Fr\'ias-MedinaAbstract : In this paper we give the first steps toward the study of the Harbourne-Hirschowitz condition and the anticanonical orthogonal property for regular surfaces. To do so, we consider the Kodaira dimension of the surfaces and study the cases based on the Enriques-Kodaira classification.
Most Read
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On uniformly $S$-absolutely pure modules
Xiaolei Zhang
J. Korean Math. Soc. 2023; 60(3): 521-536
https://doi.org/10.4134/JKMS.j220055 -
Time periodic solution for the compressible magneto-micropolar fluids with external forces in $\mathbb{R}^3$
Qingfang Shi, Xinli Zhang
J. Korean Math. Soc. 2023; 60(3): 587-618
https://doi.org/10.4134/JKMS.j220285 -
A Neumann type problem on an unbounded domain in the Heisenberg group
Shivani Dubey, Mukund Madhav Mishra, Ashutosh Pandey
J. Korean Math. Soc. 2022; 59(3): 635-648
https://doi.org/10.4134/JKMS.j210462 -
Two new recurrent levels and chaotic dynamics of $\mathbb{Z}^d_+$-actions
Shaoting Xie, Jiandong Yin
J. Korean Math. Soc. 2022; 59(6): 1229-1254
https://doi.org/10.4134/JKMS.j220202
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Simple zeros of $L$-functions and the Weyl-type subconvexity
Peter Jaehyun Cho
, Gyeongwon OhJ. Korean Math. Soc. 2023; 60(1): 167-193
https://doi.org/10.4134/JKMS.j220242 -
The automorphism groups of Artin groups of edge-separated CLTTF graphs
Byung Hee An, Youngjin Cho
J. Korean Math. Soc. 2023; 60(6): 1171-1213
https://doi.org/10.4134/JKMS.j220343 -
On the $\eta$-parallelism in almost Kenmotsu $3$-manifolds
Jun-ichi Inoguchi, Ji-Eun Lee
J. Korean Math. Soc. 2023; 60(6): 1303-1336
https://doi.org/10.4134/JKMS.j230105 -
Erratum to ``Pseudo-Riemannian Sasaki solvmanifolds'' [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115--141]
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
J. Korean Math. Soc. 2023; 60(5): 1135-1136
https://doi.org/10.4134/JKMS.j230073
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