Tohoku Mathematical Journal最新文献

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Cheng's maximal diameter theorem for hypergraphs 超图的Cheng最大直径定理

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2021-02-19 DOI: 10.2748/tmj.20211202

Yu Kitabeppu, Erina Matsumoto

We prove that Cheng maximal diameter theorem for hypergraphs with positive coarse Ricci curvature.

证明了具有正粗Ricci曲率的超图的Cheng极大直径定理。

引用次数: 2

Structures of sets of solutions to the Hartree-Fock equation Hartree-Fock方程解集的结构

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-12-17 DOI: 10.2748/tmj.20210922

Sohei Ashida

The Hartree-Fock equation which is the Euler-Lagrange equation corresponding to the Hartree-Fock energy functional is used in many-electron problems. Since the Hartree-Fock equation is a system of nonlinear eigenvalue problems, the study of structures of sets of all solutions needs new methods different from that for the set of eigenfunctions of linear operators. In this paper we prove that the sets of all solutions to the Hartree-Fock equation associated with critical values of the Hartree-Fock energy functional less than the first energy threshold are unions of a finite number of compact connected real-analytic spaces. The result would also be a basis for the study of approximation methods to solve the equation.

Hartree-Fock方程是与Hartree-Fock能量泛函相对应的欧拉-拉格朗日方程，用于许多电子问题。由于Hartree-Fock方程是一个非线性特征值问题系统，研究所有解的集的结构需要不同于研究线性算子的特征函数集的结构的新方法。本文证明了Hartree-Fock方程与小于第一能量阈值的Hartree-Fock能量泛函临界值相关的所有解的集合是有限个紧连通实解析空间的并。这一结果也将为求解该方程的近似方法的研究奠定基础。

引用次数: 1

Kolmogorov operator with the vector field in Nash class 纳什类中具有向量场的Kolmogorov算子

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-12-04 DOI: 10.2748/tmj.20210825

D. Kinzebulatov, Y. Semenov

We establish sharp two-sided heat kernel bounds, Harnack inequality and H"{o}lder continuity of bounded solutions for divergence-form parabolic equation with measurable uniformly elliptic matrix and the first-order term in a large class of locally unbounded vector fields containing $L^p$, $p>d$ as well as some vector fields $notin L_{loc}^p$, $p>2$.

我们建立了尖锐的双侧热核界、Harnack不等式和H“{o}lder具有可测一致椭圆矩阵的发散型抛物方程的有界解的连续性和一大类局部无界向量场的一阶项，该向量场包含$L^p$，$p>d$以及L_｛loc｝^p$中的一些向量场$not，$p>2$。

引用次数: 3

Characterizations of Sobolev spaces with variable exponent via averages on balls 基于球平均的变指数Sobolev空间的刻画

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-12-01 DOI: 10.2748/tmj.20191018

Jingshi Xu

In this paper we generalize the characterization for Sobolev spaces with constant exponent via averages on balls to the variable exponent setting. This method can be used to define Sobolev spaces with variable exponent on metric spaces.

本文将常指数Sobolev空间的特征化通过球上的平均推广到变指数集。该方法可用于定义度量空间上的变指数Sobolev空间。

引用次数: 0

Characterizations of heat kernel estimates for symmetric non-local Dirichlet forms via resistance forms 通过电阻形式刻画对称非局部Dirichlet形式的热核估计

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-12-01 DOI: 10.2748/tmj.20190625

Sheng-Hui Chen, Jian Wang

Motivated by [5], we obtain new equivalent conditions for two-sided heat kernel estimates of symmetric non-local Dirichlet forms in terms of resistance forms. Characterizations for upper bounds of heat kernel estimates as well as near diagonal lower bounds of Dirichlet heat kernel estimates are also established. These results can be seen as a complement of the recent studies on heat kernel estimates and parabolic Harnack inequalities for symmetric non-local Dirichlet forms in [10, 11].

受[5]的启发，我们获得了对称非局部Dirichlet形式的电阻形式的双侧热核估计的新的等价条件。还建立了热核估计上界和Dirichlet热核估计的近对角线下界的特征。这些结果可以被视为[10，11]中关于对称非局部Dirichlet形式的热核估计和抛物型Harnack不等式的最新研究的补充。

引用次数: 0

Generalized Cartan-Behnke-Stein's theorem and $q$-pseudoconvexity in a Stein manifold Stein流形中的广义Cartan-Behnke-Stein定理和$q$-伪凸性

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-12-01 DOI: 10.2748/tmj.20190808

Shun Sugiyama

引用次数: 0

Convergence theorems of a modified iteration process for generalized nonexpansive mappings in hyperbolic spaces 双曲空间中广义非扩张映射的一个修正迭代过程的收敛性定理

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-12-01 DOI: 10.2748/tmj.20191210

Preeyalak Chuadchawna, A. Farajzadeh, A. Kaewcharoen

In this paper, we introduce a modified Picard-Mann hybrid iterative process for a finite family of mappings in the framework of hyperbolic spaces. Furthermore, we establish $Delta$-convergence and strong convergence results for a sequence generated by a modified Picard-Mann hybrid iterative process involving mappings satisfying the condition $(E)$ in the setting of hyperbolic spaces which more general than one mapping in the setting of CAT(0) spaces in Ritika and Khan [19]. Our results are the extension and improvement of the results in Ritika and Khan [19]. Moreover, in the numerical example we also illustrate an example for supporting our main result.

本文给出了双曲空间框架下有限族映射的一种改进的Picard-Mann混合迭代过程。在此基础上，我们进一步建立了由一个改进的Picard-Mann混合迭代过程生成的序列的$Delta$收敛性和强收敛性结果，该序列包含满足条件$(E)$的映射，该映射在Ritika和Khan[19]的双曲空间设置下比在CAT(0)空间设置下的一个映射更一般。我们的结果是Ritika和Khan[19]结果的推广和改进。此外，在数值算例中，我们还举例来支持我们的主要结果。

引用次数: 2

Structure of minimizers of Cafarelli-Kohn-Nirenberg inequality Cafarelli-Kohn-Nirenberg不等式极小子的结构

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-12-01 DOI: 10.2748/tmj.20190917b

J. Chern, Chih-Her Chen, Gyeongha Hwang

In this article, we are concerned with radial solutions for the best constant of the Cafarelli-Kohn-Nirenberg inequality. Firstly, we classify the radial solutions according to its asymptotic behavior as $r to 0$ and $r to infty$. Secondly, we investigate the structure of radial singular solutions. Lastly, we briefly discuss the Neumann problem related to the Cafarelli-Kohn-Nirenberg inequality.

本文研究了Cafarelli-Kohn-Nirenberg不等式的最佳常数的径向解。首先，我们根据径向解的渐近行为将其分类为$rto0$和$rtoinfty$。其次，我们研究了径向奇异解的结构。最后，我们简要讨论了与Cafarelli-Kohn-Nirenberg不等式有关的Neumann问题。

引用次数: 0

Predictive risk factors for post-traumatic stress symptoms among nurses during the Italian acute COVID-19 outbreak. 意大利急性 COVID-19 爆发期间护士出现创伤后应激症状的预测风险因素。

IF 2 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-11-27 eCollection Date: 2021-01-01 DOI: 10.5114/hpr.2020.101249

Jessica Ranieri, Federica Guerra, Dina Di Giacomo

Background: The aim of the study was to investigate the posttraumatic stress disorder risk in nurses, detecting the relationship between distress experience and personality dimensions in the Italian acute COVID-19 outbreak. The study is an observational study conducted in March 2020.

Participants and procedure: Mental screening was carried out in the Laboratory of Clinical Psychology on N = 36 nurses in the age range 22-64 years (M = 37.30, SD = 12.60). 76.3% were working in nursing care with confirmed COVID-19 patients; 47.4% of nurses worked in a high COVID-19 rate environment, whereas 52.6% worked in a low COVID-19 rate environment.

Results: The results confirm relation between anxiety and peritraumatic dissociation and posttraumatic stress; also anxiety is positively correlated with the agreeableness variable. Our finding was obtained in an acute Italian COVID-19 outbreak and measured and quantified the psychological response of nurses in terms of anxiety as an early reaction for emotional distress and high risk for posttraumatic stress disorders; the personality dimensions did not mediate the emotional distress or the probable risk for post-traumatic stress disorder. Nurses appeared to be exposed to mental distress and needed help.

Conclusions: The results evidenced the need to carry out a mental health program for health workers (especially nursing professionals).

研究背景本研究的目的是调查护士创伤后应激障碍的风险，检测意大利急性 COVID-19 疫情中痛苦经历与人格维度之间的关系。该研究是一项观察性研究，于 2020 年 3 月进行：临床心理学实验室对 N = 36 名护士进行了心理筛查，他们的年龄在 22-64 岁之间（M = 37.30，SD = 12.60）。76.3%的护士从事护理工作，护理确诊的 COVID-19 患者；47.4%的护士在 COVID-19 高发环境中工作，52.6%的护士在 COVID-19 低发环境中工作：结果：研究结果证实了焦虑与创伤周围解离和创伤后应激之间的关系；焦虑还与宜人性变量呈正相关。我们的研究结果是在意大利 COVID-19 急性疫情中得出的，测量并量化了护士的心理反应，即焦虑是情绪困扰的早期反应，也是创伤后应激障碍的高危因素；人格维度并不介导情绪困扰或创伤后应激障碍的可能风险。护士似乎面临精神压力，需要帮助：结论：研究结果表明，有必要为医务工作者（尤其是护理专业人员）实施心理健康计划。

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引用次数: 24

A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups 一些幂零李群上左不变洛伦兹度量的分类

IF 0.5 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal

Pub Date : 2020-11-18 DOI: 10.2748/tmj.20211122

Yuji Kondo, H. Tamaru

It has been known that there exist exactly three left-invariant Lorentzian metrics up to scaling and automorphisms on the three dimensional Heisenberg group. In this paper, we classify left-invariant Lorentzian metrics on the direct product of three dimensional Heisenberg group and the Euclidean space of dimension $n-3$ with $n geq 4$, and prove that there exist exactly six such metrics on this Lie group up to scaling and automorphisms. Moreover we show that only one of them is flat, and the other five metrics are Ricci solitons but not Einstein. We also characterize this flat metric as the unique closed orbit, where the equivalence class of each left-invariant metric can be identified with an orbit of a certain group action on some symmetric space.

已知在三维海森堡群上存在精确到标度的三个左不变洛伦兹度量和自同构。本文对三维Heisenberg群与具有$ngeq4$的维数为$n-3$的欧氏空间的直积上的左不变Lorentzian度量进行了分类，并证明了在这个Lie群上精确存在六个这样的度量，直到标度和自同构。此外，我们还证明了它们中只有一个是平坦的，其他五个度量是Ricci孤子，而不是Einstein。我们还将这个平坦度量刻画为唯一的闭合轨道，其中每个左不变度量的等价类可以用某个对称空间上的某个群作用的轨道来识别。

引用次数: 7

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