Energy decay estimates for the Bernoulli–Euler-type equation with a local degenerate dissipation

In this paper, we study the decay property of the solutions to the Bernoulli–Euler-type equation with a local degenerate dissipation.     

A π‐stacked and conjugated hybrid based on poly(N‐vinylcarbazole) postfunctionalized with terfluorene for stable deep‐blue hole‐transporting materials

The combination of π‐stacked with π‐conjugated building blocks offers an essential strategy to construct multifunctional organic semiconductors (MOSs) with the unique optoelectrical properties. Covalent hybrids can efficiently avoid the intrinsic phase‐separation defects in corresponding blend system. In this contribution, poly(vinylcarbazole) tethered with terfluorene, PVK‐TF, as a double‐channeled π‐stacked and π‐conjugated hybrid (SCH), has been constructed via Friedal‐Crafts click postmodification (FCCP). The chemical structure and optoelectrical property were determined by GPC, UV–vis, PL, TGA, DSC, and CV. Its PL spectra in the annealing thin film at N₂ atmosphere without low‐energy emission bands centered at the 530 nm indicates that no π‐stacks between carbazole and TF or among TFs dominate the whole condensed phase, which is in agreement with the intrachain T‐shaped π‐pitched motifs in molecular modeling simulation due to steric hindrance effect in complicated diarylfluorenes (CDAFs). A supporting prototype stable deep‐blue PLED was successfully obtained with an Internationale de l'Eclairage (CIE) coordinates of (0.20, 0.10) and a width at half maximum (FWHM) of about 60 nm at high current density of 100 mA/cm² (35 V). Deep‐blue PVK‐TF is a promising MOS for hole‐transporting and host materials. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5221–5229, 2009     

Analyzing linear mergers

Mergers are functions that transform k (possibly dependent) random sources (distributions) into a single random source, in a way that ensures that if one of the input sources has min‐entropy rate δ then the output has min‐entropy rate close to δ. Mergers have proven to be a very useful tool in explicit constructions of extractors and condensers, and are also interesting objects in their own right. In this work we give a refined analysis of the merger constructed by [Raz, STOC'05] (based on [Lu, Reingold, Vadhan, and Wigderson, STOC'03 pp. 602–611, 2003]). Our analysis uses min‐entropy instead of Shannon's entropy to derive tighter results than the ones obtained in [Raz STOC'05]. We show that for every constant r and k it is possible to construct a merger that takes as input k strings of length n bits each, and outputs a string of length n/r bits, such that if one of the input sources has min‐entropy b, the output will be close to having min‐entropy b/(r + 1). This merger uses a constant number of additional uniform bits. One advantage of our analysis is that b (the min‐entropy of the “good” source) can be as small as a constant (this constant depends on r and k), while in the analysis given in [Raz STOC'05], b is required to be linear in n. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Influence of substituents in the salicylaldehyde‐derived Schiff bases on vanadium‐catalyzed asymmetric oxidation of sulfides

A series of chiral Schiff bases ( L ¹ – L ⁵ ) with different substituents in the salicylidenyl unit were prepared from condensation of 3‐aryl‐5‐ tert ‐butylsalicylaldehyde derivatives and optically active amino alcohols. Bromination of 3‐phenyl‐5‐ tert ‐butylsalicylaldehyde gave an unexpected product 3‐(4‐bromophenyl)‐5‐bromosalicylaldehyde, from which the corresponding Schiff base ligands L ⁶ and L ⁷ , derived from (S)‐valinol and (S)‐ tert ‐leucinol, respectively, were prepared. Ligands L ¹ – L ⁷ were applied to the vanadium‐catalyzed asymmetric oxidation of aryl methyl sulfides. Under the optimal conditions, the oxidation of the thioanisole with H₂O₂ as oxidant in CH₂Cl₂ catalyzed by VO(acac)₂‐ L ¹ – L ⁷ gives good yields (74–83%) with moderate enantioselectivity (58–77% ee). Ligand L ⁷ , containing a 4‐bromophenyl group on the 3‐position and a Br atom on the 5‐position of the salicylidenyl moiety, displays an 80–90% ee for vanadium‐catalyzed oxidation of methyl 4‐bromophenyl sulfide and methyl 2‐naphthyl sulfide. Copyright © 2008 John Wiley & Sons, Ltd.     

一类椭圆型随机偏微分方程弱解的存在性

设$D$是$R^N$ ($N>1$)中有界开集,$(\Omega, {\cal F}, P)$是一个完备的概率空间.该文研究了下列随机边值问题弱解的存在性问题\[\left\{\begin{array}{ll}-{\rm div} A(x,\omega,u, \nabla u)=f(x,\omega, u),\,\, &;(x,\omega)\in D\times \Omega,\\u=0, &;(x,\omega)\in \partial D\times \Omega,\end{array}\right.\]其中, div与 $\nabla $ 表示仅对 $x$求微分. 首先,作者引入了弱解的概念; 然后,作者转化随机问题为高维确定性问题;最后,作者证明了该问题弱解的存在性.     

气体-表面相互作用中动量和能量分量间转化机制的分子动力学研究

气体分子与壁面之间的相互作用是影响稀薄气体流动状态的主要因素,但是由于其物理上的复杂性和微观性,这一过程的机理并没有得到充分揭示.本文利用分子束法对Ar分子在金属Pt表面的碰撞过程进行了分子动力学模拟,并探究了入射速度、角度和壁面粗糙度对动量、能量转化机制的影响.结果表明,当气体分子以5o的极角入射时,分子的法向速度分量占主导因素,在与壁面发生碰撞之后,分子的切向和法向动量都会损失,法向动能会向切向转移,并且当分子速度不低于2.0时,切向和法向动能的比值会稳定在一个很小的区间,而粗糙度对动量和能量转化的影响不明显.与小角度入射时不同,当气体分子以75o的极角与金属表面碰撞时,粗糙度的影响就不能再被忽略了.大极角入射的气体分子在光滑壁面散射之后,其运动规律基本符合Maxwell所假设的镜面反射,动量和能量分量的变化都不明显.而粗糙度的引入则会促进气体分子切向动量和能量向法向转移,并且会使分子总能量的损失更加显著.     

Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes

Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.     

Synthesis and properties of allyloxy-based tolane liquid crystals with high negative dielectric anisotropy

A series of tolane liquid crystals (LCs) containing 2,3-difluorophenyl and allyloxy terminal groups have been synthesised via multi-step reactions. Their thermotropic mesophases, birefringences and dielectric anisotropy properties are discussed by comparison with the non-fluorinated analog. The results show that the allyloxy-based tolane LC 3TOV reveals a high value of the birefringence (0.29), negative dielectric anisotropy (?4.44) and a broad nematic mesophase with a low melting point and high clearing point. The effects of the terminal alkyl chains, the lateral fluoro substituents, the allyloxy terminal group and alkyne bridge on the mesomorphic and physical properties were also discussed. Meanwhile, Density Functional Theory (DFT) calculations of molecular conformation and polarisability were used to correlate the experimental findings.     

99mTc-AMD3100: A novel potential receptor-targeting radiopharmaceutical for tumor imaging

<正>The chemokine CXCR4 receptor is over-expressed in a wide variety of tumors.In this study,AMD3100,which was a prototype non-peptide antagonist of CXCR4 receptor,was labeled with ~(99m)Tc.~(99m)Tc-AMD3100 was verified by thin layer radio chromatography(TLRC).The tumor-localizing properties of ~(99m)Tc-AMD3100 were evaluated and proved in mice bearing Hep-G2 tumor xenograft.~(99m)Tc-AMD3100 was a promising,novel receptor-specific radiopharmaceutical with potential application in the imaging of human tumors.     

A deuterium-palladium electrode as a new sensor in non-aqueous solutions: potentiometric titration of weak acids in acetonitrile and benzonitrile

A deuterium-palladium electrode was employed as a new indicator electrode for the titration of weak acids in acetonitrile and benzonitrile. The investigated electrode showed a linear dynamic response for p-toluenesulfonic acid in the concentration range from 0.001 M to 0.1 M with a Nernstian slope of 48 mV in acetonitrile. Sodium methylate, potassium hydroxide and tetrabutylammonium hydroxide proved to be very suitable titrating agents for these titrations. The response time was less than 10-11 s and the lifetime of the electrode was limitless. Advantages of the electrode are: long-term stability, fast response, reproducibility, easy preparation and low cost.