一类凹与凸算子的推广

运用锥的性质以及单调迭代技巧给出了一类广义凹算子与凸算子正不动点的存在唯一性,并讨论了算子特征值方程的性质.作为应用,利用所获结果研究了一类积分方程正解的存在唯一性.     

Synthesis and thiol–ene photopolymerization of allyl‐ether functionalized dendrimers

Well‐defined, allyl‐ether functional, first‐generation dendrimers have been synthesized. The convergent growth approach was utilized, using the anhydride of the allyl‐ether terminated building block. Three different core moieties were used: trimethylolpropane, trisphenol, and ditrimethylolpropane. The coupling reactions proceeded in good yields and all compounds were characterized by NMR, MALDI‐TOF, and SEC. The allyl‐terminated dendrimers were crosslinked by thiol–ene chemistry, using a multifunctional thiol, TriThiol, to give clear and smooth films. The photopolymerization was conducted in the presence of a photoinitiator, Irgacure 651, and no traces of either allyl‐ether groups or thiols were observed by FT‐Raman after cure. All crosslinked films were characterized with respect to mechanical (DMA) and thermal (DSC) properties. It was found that homogeneous networks were formed and that the core functionality and structure had little effect on the network properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1339–1348, 2008     

对称排列的咔唑基树状分子的合成及其光物理性能和电化学性能(英文)

采用乌尔曼缩合反应合成了新型的咔唑基树状分子;利用核磁共振谱仪(1HNMR,13CNMR)和飞行时间质谱仪(MALDI-TOF-Mass)对其进行了表征;并评价了树状分子的荧光性能和电化学性能.结果表明,所合成的咔唑基树状化合物在394nm处发蓝光,同时具有低的HOMO能级.     

Self‐Assembly and Structural Evolvement of Polyoxometalate‐Anchored Dendron Complexes

A cationic dendritic molecule that has alkyl chains has been synthesized and employed to encapsulate anionic polyoxometalates through electrostatic interactions. The prepared surfactant‐encapsulated polyoxometalate (SEP) complexes were used as building blocks to fabricate self‐assemblies in solution and the solid state. Monodispersion, lamellar, and columnar assemblies of SEP complexes have been characterized in detail. With increasing the number of peripheral cationic dendrons on inorganic clusters, the SEPs undergo changes from globular assemblies to monodispersions in solution and from lamellar assemblies to hexagonal columnar structures in the solid state, depending on the amounts of cationic dendrons in the complexes. The structural evolvement was simulated through consideration of the size and shape of the cationic dendron and polyanionic clusters, and the experimental results are in good agreement with the interpretation of the simulations. The present research demonstrates a new kind of dendritic complex and provides a route for controlling their assembling states by simply alternating the number of cationic dendrons in the complexes.     

一种离轴计算全息图在凹非球面检测中的应用

为了精确检测大口径非球面面型质量,将CGH作为补偿器应用于凹非球面的离轴全息检测系统中.根据计算全息图的离轴全息检测系统检测凹非球面的基本原理,分析了离轴CGH的计算、制作过程,实现了对口径为150 mm,近轴半径为1499.7 mm,非球面系数为-1的凹非球面镜的检测.实验结果与轮廓仪检测结果吻合得很好.     

Existence and multiplicity results for singular quasilinear elliptic equation on unbounded domain

In this paper, we are interested in the existence and multiplicity results of solutions for the singular quasilinear elliptic problem with concave–convex nonlinearities (0.1) where is an unbounded exterior domain with smooth boundary ?Ω, 1 < p < N,0 ≤ a < (N ? p) ∕ p,λ > 0,1 < s < p < r < q = pN ∕ (N ? pd),d = a + 1 ? b,a ≤ b < a + 1. By the variational methods, we prove that problem 0.1 admits a sequence of solutions u_k under the appropriate assumptions on the weight functions H(x) and H(x). For the critical case, s = q,h(x) = | x | ^{? bq}, we obtain that problem 0.1 has at least a nonnegative solution with p < r < q and a sequence of solutions u_k with 1 < r < p < q and J(u_k) → 0 as k → ∞ , where J(u) is the energy functional associated to problem 0.1 . Copyright © 2013 John Wiley & Sons, Ltd.     

A converse of Loewner–Heinz inequality and applications to operator means

Let f(t)$f(t)$ be an operator monotone function. Then A?B$A?B$ implies f(A)?f(B)$f(A)?f(B)$, but the converse implication is not true. Let A?B$A?B$ be the geometric mean of A,B?0$A,B?0$. If A?B$A?B$, then B⁻¹?A?I$B^{-1}?A?I$; the converse implication is not true either. We will show that if f(λB+I)⁻¹?f(λA+I)?I$f{(\lambda B+I)}^{-1}?f(\lambda A+I)?I$ for all sufficiently small λ>0$\lambda >0$, then f(λA+I)?f(λB+I)$f(\lambda A+I)?f(\lambda B+I)$ and A?B$A?B$. Moreover, we extend it to multi-variable matrices means.     

RESEARCH ANNOUNCEMENTS ON "MODERATE DEVIATIONS FOR GRENANDER ESTIMATOR NEAR BOUNDARIES OF THE SUPPORT"

1 Introduction and Main Results Let f be a decreasing density with support[0,∞).Denote by Fn the empirical distribution function of a sample X_(1),...,X_(n) from f.Let F_(n) be the concave majorant of F_(n) on[0,∞),i.e.     

Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators

Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexificators to be minimal. A characterization of quasiconvexity of a continuous function is obtained in terms of the quasimonotonicity of convexificators.     

Multiple solutions for a class of biharmonic equations with a nonlinearity concave at the origin

In this paper, we investigate the existence of multiple solutions for a class of biharmonic equations where the nonlinearity involves a concave term at the origin. The solutions are obtained from the versions of mountain pass lemma and linking theorem.