Isoperimetric inequality from the poisson equation via curvature

In this paper, we establish an isoperimetric inequality in a metric measure space via the Poisson equation. Let (X,d,μ) be a complete, pathwise connected metric space with locally Ahlfors Q‐regular measure, where Q > 1, that supports a local L²‐Poincaré inequality. We show that, for the Poisson equation Δu = g, if the local L^∞‐norm of the gradient Du can be bounded by the Lorentz norm L^Q,1 of g, then we obtain an isoperimetric inequality and a Sobolev inequality in (X,d,μ) with optimal exponents. By assuming a suitable curvature lower bound, we establish such optimal bounds on $\||Du|\|_{L^\infty_{\rm loc}}$ . © 2011 Wiley Periodicals, Inc.     

Highly conductive free standing polypyrrole films prepared by freezing interfacial polymerization

Highly conductive free standing polypyrrole (PPy) films were prepared by a novel freezing interfacial polymerization method. The films exhibit metallic luster and electrical conductivity up to 2000 S cm(-1). By characterizing with SEM, FTIR, Raman and XRD, the high conductivity is attributed to the smooth surface, higher conjugation length and more ordered molecular structure of PPy.     

(E)-5-styryl-1H-indole and (E)-6-styrylquinoline derivatives serve as probes for β-amyloid plaques

We report the synthesis and biological evaluation of novel (E)-5-styryl-1H-indole and (E)-6-styrylquinoline derivatives as probes for imaging β-amyloid (Aβ) plaques. These derivatives showed binding affinities for Aβ???? aggregates with K(i) values varying from 4.1 to 288.4 nM. (E)-5-(4-iodostyryl)-1H-indole (8) clearly stained Aβ plaques in the brain sections of Alzheimer's disease (AD) model mice (APP/PS1). Furthermore, autoradiography for [12?I]8 displayed intense and specific labeling of Aβ plaques in the brain sections mentioned above with low background. In biodistribution experiments using normal mice [12?I]8 showed high initial brain uptake followed by rapid washout (4.27 and 0.64% ID/g at 2 and 30 min post injection, respectively). These findings suggests that [123I]8 may be a potential SPECT imaging agent for detecting Aβ plaques in AD brain.     

Measure-valued continuous curves and processes in total variation norm

Several equivalent characterizations of continuous curves in the total variation norm are given, which enable us to provide a sufficient condition for a purely atomic finite measure-valued stochastic process to possess a version with continuous sample paths in the total variation norm. Our criterion is in the form of Kolmogorov’s continuity theorem. As an application, we apply this criterion to study the sample path property of finite measure-valued diffusions with immigrations constructed by Shiga (1990).     

Mechanism of water oxidation to molecular oxygen with osmocene as photocatalyst: a theoretical study

In the present work, photoinduced O(2) evolution from the [Cp(2)Os-OH](+) complex in aqueous solution has been studied by the DFT, CASSCF, and CASPT2 methods. The CASPT2//CASSCF calculations predict that the S(3) state is initially populated and the subsequent deprotonation of [Cp(2)Os-OH](+) proceeds very easily along the T(1) pathway as a result of the efficient S(3) → T(1) intersystem crossing. It is found that the O-O bond is formed via the acid-base mechanism, which is different from the direct oxo-oxo coupling mechanism suggested in the experimental study. Formation of the O-O bond is the rate-determining step and has an activation energy and activation free energy of 81.3 and 90.4 kcal/mol, respectively. This is consistent with the low quantum yield observed for generating molecular oxygen upon irradiation at 350 nm (~ 82 kcal/mol). The O(2) release from an intermediate complex has to overcome a small barrier on the triplet pathway first and then pass through the triplet-singlet intersection, generating the O(2) molecules in either the lowest singlet or triplet state. The formed (3)O(2) molecule can be converted into the (1)O(2) molecule by the heavy atom effect in the Os complexes, which is probably the reason only the (1)O(2) molecule was detected experimentally.     

In situ formed white-light-emitting lanthanide-zinc-organic frameworks

Five novel 3D heterometallic lanthanide-zinc-organic frameworks, [H(H(2)O)(8)][LnZn(4)(imdc)(4)(Him)(4)] [Ln = La (1), Pr (2), Eu (3), Gd (4), Tb (5); H(3)imdc = 4,5-imidazoledicarboxylic acid; Him = imidazole], were synthesized via an in situ hydrothermal reaction, and tunable luminescence from yellow to white was obtained through the doping of Eu and Tb ions in the La-Zn framework.     

由Levy过程驱动的双边反射型倒向随机微分方程的一般结果

研究了由Levy过程驱动的双边反射型倒向随机微分方程,获得了该类方程全局解存在唯一的一些充分条件.主要的工具是局部解和链接法.作为应用,给出了比较定理.     

基于区间数度量的区间值模糊集合的归一化距离、相似度、模糊度和包含度的关系研究

区间值模糊集合的距离、相似度、模糊度和包含度及其关系研究是区间值模糊集合的一个研究热点.考虑到区间值模糊集合所表示信息的丰富性,本文使用区间数而非实数来刻画区间值模糊集合的距离,首先给出基于区间数度量的区间值模糊集合的归一化距离的公理化定义,然后通过五个定理详细研究了基于公理化定义的区间值模糊集合的归一化距离、相似度、模糊度和包含度之间的相互转换关系,最后,给出了若干公式来计算基于区间数度量的区间值模糊集合的相似度、模糊度和包含度.这些结论,一方面丰富了区间值模糊集合的信息测度(距离、相似度、模糊度和包含度)的内容,另一方面也为区间值模糊集合的近似推理、决策分析、模式识别等领域的应用提供了新方法和新理论.     

Homoclinic Solutions for a Class of Second Order Hamiltonian Systems

In this paper we consider the existence of homoclinic solutions for the following second order non-autonomous Hamiltonian system $${\ddot q}-L(t)q+\nabla W(t,q)=0, \quad\quad\quad\quad\quad\quad\quad (\rm HS)$$ where ${L\in C({\mathbb R},{\mathbb R}^{n^2})}$ is a symmetric and positive definite matrix for all ${t\in {\mathbb R}}$ , W(t, q)?=?a(t)U(q) with ${a\in C({\mathbb R},{\mathbb R}^+)}$ and ${U\in C^1({\mathbb R}^n,{\mathbb R})}$ . The novelty of this paper is that, assuming L is bounded from below in the sense that there is a constant M?>?0 such that (L(t)q, q)?≥ M |q|² for all ${(t,q)\in {\mathbb R}\times {\mathbb R}^n}$ , we establish one new compact embedding theorem. Subsequently, supposing that U satisfies the global Ambrosetti–Rabinowitz condition, we obtain a new criterion to guarantee that (HS) has one nontrivial homoclinic solution using the Mountain Pass Theorem, moreover, if U is even, then (HS) has infinitely many distinct homoclinic solutions. Recent results from the literature are generalized and significantly improved.