Weak attractors for the dissipative fractional Heisenberg equation

In this short paper, we consider the long time behaviors of the fractional Heisenberg equation and the existence of a global weak attractor is proved for the shift dynamics in the path space. The key ingredient is some new type of commutator structure introduced in this paper, which seems indispensable in proving the compactness of the dynamics. The technique introduced in this paper may also be useful to other fractional order partial differential equations.     

问题视角浅析

文中通过多视角分析解决数学问题,向学习者渗透了数学思想的辩证性和学习方法的灵活性,体现了"以人为本"现代理念下的数学教育.     

弱Orlicz鞅空间的弱原子分解及其应用

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.     

Mathematical Analysis of a PDE System for Biological Network Formation

Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai [13 Hu , D. (2013). Optimization, Adaptation, and Initialization of Biological Transport Networks. Workshop on multiscale problems from physics, biology and material sciences. May 28–31st, 2014, Shanghai. Available at: http://math.sjtu.edu.cn/conference/multiscale2014/ (accessed 6 January 2015). [Google Scholar], 15 Hu , D. , Cai , D. ( 2013 ). Adaptation and optimization of biological transport networks . Phys. Rev. Lett. 111 : 138701 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. The model describes the pressure field thanks to Darcy's type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate D ≥ 0 representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behavior. It turns out that, by energy dissipation, steady states play a central role to understand the network formation capacity of the system. We show that for a large diffusion coefficient D, the zero steady state is stable, while network formation occurs for small values of D due to the instability of the zero steady state, and the borderline case D = 0 exhibits a large class of dynamically stable (in the linearized sense) steady states.     

Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems

We consider a general Euler-Korteweg-Poisson system in R ³, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-in-time weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which the Cauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Székelyhidi.     

Synthesis,spectroscopic and crystal structure analysis of 2-(4-fluorobenzyl)-6-(4-methoxyphenyl)imidazo[2,1-b][1,3,4]thiadiazole and its morpholinomethyl derivative

The preparation of 2-(4-fluorobenzyl)-6-(4-methoxyphenyl)-5-morpholin-1-ylmethyl imidazo[2,1-b][1,3,4]thiadiazole via the intermediate 2-(4-fluorobenzyl)-6-(4-methoxyphenyl)Imidazo[2,1-b][1,3,4] thiadiazole is described. Elemental analysis, IR spectrum, ¹H NMR and X-ray crystal structure analyses were carried out to determine the compositions and molecular structures of the two compounds. The crystal packing exhibits intermolecular C–H?O, C–H?N, C–H?F and π–π stacking interactions leading to the formation of the supramolecular network.     

Sc3C2@C80与[12]CPP纳米环之间非共价相互作用的理论研究

金属富勒烯嵌套于纳米环内形成主客体系, 二者产生的主客体作用可诱导内部金属团簇的取向, 影响分子的电子结构等性质. 本文基于密度泛函理论(DFT)计算, 对碳纳米环[12]CPP(CPP=环苯撑, 主体分子)与金属富勒烯Sc₃C₂@C₈₀(客体分子)形成的主客体配合物的结构和性质进行了研究. 计算结果表明, 在最稳定构型中, [12]CPP呈现椭圆形, Sc₃C₂@C₈₀与[12]CPP的质心不再重合. Sc₃C₂@C₈₀在[12]CPP内旋转对构型总体能量影响仅为13.51 kJ/mol. [12]CPP向Sc₃C₂@C₈₀转移了0.03 e, 主客体分子之间存在弱相互作用. 对二者相互作用的分析结果表明, 色散作用在弱相互作用中占主导地位.     

显化反应条件视角 发展反应调控意识——受控的燃烧

以波义耳研究燃烧的史实为背景,创新设计燃烧条件的探究实验,并提出“条件叠加式”燃烧条件探究新思路。以“燃灭控”为主线,一以贯之地显性化“条件是认识化学反应的一种基本视角”,落实“在一定条件下通过化学反应可以实现物质转化”的化学观念。基于调控化学反应思想创新设计“燃旺弱灭”反应控制视域,统整开展“情境”“活动”与“任务”三位一体的学习活动。重置教材实验的教学价值取向,结合燃烧的形式美、汉语言文字解读,将化学学科知识与美育、汉语言文化领域跨领域融合。     

Reprint of : Spin polarization induced by an electric field in the presence of weak localization effects

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.