Error analysis of collocation method based on reproducing kernel approximation

Solving partial differential equations (PDE) with strong form collocation and nonlocal approximation functions such as orthogonal polynomials, trigonometric functions, and radial basis functions exhibits exponential convergence rates; however, it yields a full matrix and suffers from ill conditioning. In this work, we discuss a reproducing kernel collocation method, where the reproducing kernel (RK) shape functions with compact support are used as approximation functions. This approach offers algebraic convergence rate, but the method is stable like the finite element method. We provide mathematical results consisting of the optimal error estimation, upper bound of condition number, and the desirable relationship between the number of nodal points and the number of collocation points. We show that using RK shape function for collocation of strong form, the degree of polynomial basis functions has to be larger than one for convergence, which is different from the condition for weak formulation. Numerical results are also presented to validate the theoretical analysis. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 554–580, 2011     

NMR and X‐ray structural studies on 3‐benzyl‐8‐bromoadenine

8‐Bromoadenine was benzylated in the presence of base to give a mixture of two regioisomers. One was easily recognized as 9‐benzyl‐8‐bromoadenine, but the other structure could not be determined with absolute certainty by NMR. Therefore, X‐ray crystallography was used to prove that the benzyl group was attached to N‐3. Furthermore, it is shown that the 3‐benzyl adenine derivative exists as the amine tautomer both in the crystalline state as well as in solution (DMSO‐d₆), with restricted rotation around the N⁶? C6 bond. J. Heterocyclic Chem., (2011).     

Effect of Nonsolvent on the Formation of Polymer Nanomaterials in the Nanopores of Anodic Aluminum Oxide Templates

We study the effect of nonsolvent on the formation of polymer nanomaterials in the nanopores of porous templates. Water (nonsolvent) is added into a poly (methyl methacrylate) (PMMA) solution in dimethylformamide (DMF) confined in the nanopores of an anodic aluminum oxide (AAO) template. Water forms a wetting layer on the pore wall and causes the PMMA solution to be isolated in the center of the nanopore, resulting in the formation of PMMA nanospheres or nanorods after the solvent is evaporated. The formation of the polymer nanomaterials induced by nonsolvent is found to be driven by the Rayleigh‐instability‐type transformation. Without adding the nonsolvent, PMMA chains precipitate on the walls of the nanopores after the solvent is evaporated, and PMMA nanotubes are obtained.     

Advent of the cancer methylome

DNA hypermethylation of CpG islands plays an important role in gene regulation during cancer development. Many techniques have been developed to detect global DNA methylation in cancer cells compared to normal tissues. This knowledge helps us to better understand cancer progression and also aids in the development of new biomarker for early cancer detection. New prognostic tools for monitoring drug efficacy during cancer treatment can also be developed. In this review, we will examine the different techniques that have been used to study DNA methylation, as well as the emerging high resolution, high throughput techniques for identification of methylated regions to defining cancer related genes in the cancer methylome.     

Synthesis of uniform layered protonated titanate hierarchical spheres and their transformation to anatase TiO2 for lithium-ion batteries

Layered protonated titanates (LPTs), a class of interesting inorganic layered materials, have been widely studied because of their many unique properties and their use as precursors to many important TiO(2)-based functional materials. In this work, we have developed a facile solvothermal method to synthesize hierarchical spheres (HSs) assembled from ultrathin LPT nanosheets. These LPT hierarchical spheres possess a porous structure with a large specific surface area and high stability. Importantly, the size and morphology of the LPT hierarchical spheres are easily tunable by varying the synthesis conditions. These LPT HSs can be easily converted to anatase TiO(2) HSs without significant structural alteration. Depending on the calcination atmosphere of air or N(2), pure anatase TiO(2) HSs or carbon-supported TiO(2) HSs, respectively, can be obtained. Remarkably, both types of TiO(2) HSs manifest excellent cyclability and rate capability when evaluated as anode materials for high-power lithium-ion batteries.     

Electrogenerated Chemiluminescence of Pure Polymer Films and Polymer Blends

We recently reported the discovery of soliton‐like electrogenerated chemiluminescence (ECL) waves from pure conjugated polymer films and gold‐nanoparticles‐doped polymer films. In addition to a more detailed study of these polymer systems by changing the film thickness and the distribution of local leaks, we also apply the ECL wave phenomenon to polymer blends of conjugated and nonconjugated polymers. Poly(9,9‐dioctylfluorene‐co‐benzothiadiazole) (F8BT) is used as the active material that is oxidized and produces ECL with the presence of a co‐reactant, tri‐n‐propylamine (TPA). Several factors such as film thickness, artificial leaks, and solubility of doped polymers are examined for their effects on the ECL behavior. When polystyrene (PS), less soluble in the electrolyte, is blended with F8BT, dotted ECL signals are observed and transported as waves. When poly(methyl methacrylate) (PMMA), more soluble in the electrolyte, is blended with F8BT, PMMA serves as local scratches and ECL waves are triggered simultaneously from the whole film.

     

A practical authentication protocol with anonymity for wireless access networks

The use of anonymous channel tickets was proposed for authentication in wireless environments to provide user anonymity and to probably reduce the overhead of re‐authentications. Recently, Yang et al. proposed a secure and efficient authentication protocol for anonymous channel in wireless systems without employing asymmetric cryptosystems. In this paper, we will show that Yang et al.'s scheme is vulnerable to guessing attacks performed by malicious visited networks, which can easily obtain the secret keys of the users. We propose a new practical authentication scheme not only reserving the merits of Yang et al.'s scheme, but also extending some additional merits including: no verification table in the home network, free of time synchronization between mobile stations and visited networks, and without obsolete anonymous tickets left in visited networks. The proposed scheme is developed based on a secure one‐way hash function and simple operations, a feature which is extremely fit for mobile devices. We provide the soundness of the authentication protocol by using VO logic. Copyright © 2010 John Wiley & Sons, Ltd.     

Hypervalent Iodine(III) Sulfonate Mediated Synthesis of 2‐Arylimidazo[1,2‐a]Pyrimidines in Liquid PEG‐400

PEG‐400[poly(ethylene glycol‐400)] is used as a “green” recyclable solvent in the one‐pot synthesis of 2‐arylimidazo[1,2‐a]pyrimidines by reaction with ketones, [hydroxyl(2,4‐dinitrobenzenesulfonyloxy)‐iodo]benzene (HDNIB), and 2‐aminopyrimidine. Significant rate enhancements and improved yields have been observed.     

Calibration of the WCT‐100 photoconductance instrument at low conductance

The WCT‐100 photoconductance instrument is used throughout the photovoltaic industry providing a relatively simple and inexpensive means to assess recombination parameters. This paper presents a method to determine its output voltage V _WCT over the conductance range, S = 0·002–20 mS, a range not easily attained by the conventional calibration method. The relationship between V _WCT and S is found to transition from being non‐linear to linear at S ∼ 1 mS, which equates to the conductance of a 300 µ m thick 30 Ω‐cm silicon wafer. For samples whose dark conductance is lower than the transition conductance, the non‐linear relationship between V _WCT and S must be taken into account to prevent a gross underestimation of recombination rate. The method we describe can equally well be used to investigate the calibration of other photoconductance instruments. It involves the simultaneous measurement of a device's electrical conductance and the instrument's output voltage under a range of steady‐state illumination intensities. Copyright © 2008 John Wiley & Sons, Ltd.     

SF6-N2混合气激光触发延迟抖动特性研究

 研究了SF₆-N₂混合气在四倍频Nd:YAG激光脉冲作用下的触发特性。实验结果表明：充SF₆-N₂混合气的火花隙的触发延迟和抖动、最低可触发阈值随充气压力及混合气中SF₆含量上升而上升，随激光波长减小而减小，火花隙的触发延迟和抖动随焦距的减小而减小。由于SF₆-N₂混合气的介电强度、触发延迟和抖动与混合气中SF₆含量之间均存在非线性关系，作为开关工作介质，SF₆-N₂混合气的综合性能较好的SF₆含量范围是5%～45%。