Journal of the
Korean Mathematical Society
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ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2023-07-01
Computations and conservativeness of traces of one-dimensional diffusions
Ali BENAMOR, Rafed MOUSSAAbstract : We compute explicitly traces of one-dimensional diffusion processes. The obtained trace forms can be regarded as Dirichlet forms on graphs. Then we discuss conditions ensuring the trace forms to be conservative. Finally, the obtained results are applied to the Bessel process of order $\nu$.
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2023-01-01
Weak Herz-type Hardy spaces with variable exponents and applications
Souad Ben SeghierAbstract : Let $\alpha\in(0,\infty)$, $p\in(0,\infty)$ and $q(\cdot): {{\mathbb R}}^{n}\rightarrow[1,\infty)$ satisfy the globally log-H\"{o}lder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator $M$ and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley $g$-function and the Littlewood-Paley $g^{\ast}_{\lambda}$-function.
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2023-09-01
On non-displaceable Lagrangian submanifolds in two-step flag varieties
Yoosik KimAbstract : We prove that the two-step flag variety $\mathcal{F}\ell(1,n;n+1)$ carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to $S^3 \times T^{2n-4}$ and a continuum family of non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when $n > 2$.
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2024-01-01
Gorenstein $FP_{n}$-injective modules with respect to a semidualizing bimodule
Zhiqiang Cheng, Guoqiang ZhaoAbstract : Let $S$ and $R$ be rings and $_{S}C_{R}$ a semidualizing bimodule. We introduce the notion of $G_C$-$FP_n$-injective modules, which generalizes $G_C$-$FP$-injective modules and $G_C$-weak injective modules. The homological properties and the stability of $G_C$-$FP_n$-injective modules are investigated. When $S$ is a left $n$-coherent ring, several nice properties and new Foxby equivalences relative to $G_C$-$FP_n$-injective modules are given.
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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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2022-11-01
A new optimal eighth-order family of multiple root finders
Dejan \'Cebi\'c
, Neboj\v sa M. Ralevi\'cAbstract : This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.
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2022-11-01
$(\mathcal{F}, \mathcal{A})$-Gorenstein flat homological dimensions
V\'ictor BecerrilAbstract : In this paper we develop the homological properties of the Gorenstein $(\mathcal{L}, \mathcal{A})$-flat $R$-modules $\mathcal{GF}_{(\mathcal{F} (R), \mathcal{A})}$ proposed by Gillespie, \linebreak where the class $\mathcal{A} \subseteq \mathrm{Mod} (R^{\mathrm{op}})$ sometimes corresponds to a duality pair $(\mathcal{L}, \mathcal{A})$. We study the weak global and finitistic dimensions that come with the class $\mathcal{GF}_{(\mathcal{F} (R), \mathcal{A})}$ and show that over a $(\mathcal{L}, \mathcal{A})$-Gorenstein ring, the functor $-\otimes _R-$ is left balanced over $\mathrm{Mod} (R^{\mathrm{op}}) \times \mathrm{Mod} (R)$ by the classes $\mathcal{GF}_{(\mathcal{F} (R^{\mathrm{op}}), \mathcal{A})} \times \mathcal{GF}_{(\mathcal{F} (R), \mathcal{A})}$. When the duality pair is $(\mathcal{F} (R), \mathcal{FP}Inj (R^{\mathrm{op}}))$ we recover the G. Yang's result over a Ding-Chen ring, and we see that is new for $(\mathrm{Lev} (R), \mathrm{AC} (R^{\mathrm{op}}))$ among others.
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2024-01-01
Complete noncompact submanifolds of manifolds with negative curvature
Ya Gao, Yanling Gao, Jing Mao , Zhiqi XieAbstract : In this paper, for an $m$-dimensional ($m\geq5$) complete noncompact submanifold $M$ immersed in an $n$-dimensional ($n\geq6$) simply connected Riemannian manifold $N$ with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of $M$, the norm of its weighted mean curvature vector $|\textbf{\emph{H}}_{f}|$ and the weighted real-valued function $f$, we can obtain:$\bullet$ several one-end theorems for $M$; $\bullet$ two Liouville theorems for harmonic maps from $M$ to complete Riemannian manifolds with nonpositive sectional curvature.
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2024-01-01
Periodic surface homeomorphisms and contact structures
Dheeraj Kulkarni, Kashyap Rajeevsarathy, Kuldeep SahaAbstract : In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.
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2023-09-01
Summability in Musielak--Orlicz Hardy spaces
Jun Liu, Haonan XiaAbstract : Let $\varphi: \mathbb{R}^n\times[0,\infty)\to[0,\infty)$ be a growth function and $H^{\varphi}(\mathbb{R}^n)$ the Musielak--Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called $\theta$-summability is considered for multi-dimensional Fourier transforms in $H^{\varphi}(\mathbb{R}^n)$. Precisely, with some assumptions on $\theta$, the authors first prove that the maximal operator of the $\theta$-means is bounded from $H^{\varphi}(\mathbb{R}^n)$ to $L^{\varphi}(\mathbb{R}^n)$. As consequences, some norm and almost everywhere convergence results of the $\theta$-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner--Riesz, Weierstrass and Picard--Bessel summations, are also presented.
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Schur convexity of $L$-conjugate means and its applications
Chun-Ru Fu
, Huan-Nan Shi, Dong-Sheng WangJ. Korean Math. Soc. 2023; 60(3): 503-520
https://doi.org/10.4134/JKMS.j220039 -
Sharp Ore-type conditions for the existence of an even $[4,b]$-factor in a graph
Eun-Kyung Cho, Su-Ah Kwon, Suil O
J. Korean Math. Soc. 2022; 59(4): 757-774
https://doi.org/10.4134/JKMS.j210605 -
Weak Herz-type Hardy spaces with variable exponents and applications
Souad Ben Seghier
J. Korean Math. Soc. 2023; 60(1): 33-69
https://doi.org/10.4134/JKMS.j210764 -
Birkhoff's ergodic theorems in terms of weighted inductive means
Byoung Jin Choi, Jae Hun Kim
J. Korean Math. Soc. 2022; 59(3): 549-570
https://doi.org/10.4134/JKMS.j210239
Most Downloaded
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Schur convexity of $L$-conjugate means and its applications
Chun-Ru Fu
, Huan-Nan Shi, Dong-Sheng WangJ. Korean Math. Soc. 2023; 60(3): 503-520
https://doi.org/10.4134/JKMS.j220039 -
Thomas algorithms for systems of fourth-order finite difference methods
Soyoon Bak, Philsu Kim, Sangbeom Park
J. Korean Math. Soc. 2022; 59(5): 891-909
https://doi.org/10.4134/JKMS.j210701 -
The Bongartz's theorem of Gorenstein cosilting complexes
Hailou Yao, Qianqian Yuan
J. Korean Math. Soc. 2023; 60(6): 1337-1364
https://doi.org/10.4134/JKMS.j230208 -
Low rank orthogonal bundles and quadric fibrations
Insong Choe, George H. Hitching
J. Korean Math. Soc. 2023; 60(6): 1137-1169
https://doi.org/10.4134/JKMS.j220125
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