Spectral collocation and radial basis function methods for one-dimensional interface problems

Differential equations with singular sources or discontinuous coefficients yield non-smooth or even discontinuous solutions. This problem is known as the interface problem. High-order numerical solutions suffer from the Gibbs phenomenon in that the accuracy deteriorates if the discontinuity is not properly treated. In this work, we use the spectral and radial basis function methods and present a least squares collocation method to solve the interface problem for one-dimensional elliptic equations. The domain is decomposed into multiple sub-domains; in each sub-domain, the collocation solution is sought. The solution should satisfy more conditions than the given conditions associated with the differential equations, which makes the problem over-determined. To solve the over-determined system, the least squares method is adopted. For the spectral method, the weighted norm method with different scaling factors and the mixed formulation are used. For the radial basis function method, the weighted shape parameter method is presented. Numerical results show that the least squares collocation method provides an accurate solution with high efficacy and that better accuracy is obtained with the spectral method.     

δ-Jordan李超代数的交换扩张

通过δ-Jordan李超代数T的表示和上同调理论,构造δ-Jordan李超代数T■V.证明了δ-Jordan李超代数的等价交换扩张给出相同的表示.通过δ-Jordan李超代数的表示和其交换扩张得到2-上圈.     

Intrinsic tunneling study of underdoped Bi2Sr2-xLaxCuO6+δ superconductors

We report on a tunneling study of underdoped submicron Bi₂Sr_2-xLa_xCuO_6+δ (La-Bi2201) intrinsic Josephson junctions (IJJs), whose self-heating is sufficiently suppressed. The tunneling spectra are measured from 4.2 K up to the pseudogap opening temperature of T^* = 260 K. The gap value found from the spectral peak position is about 35 meV and has a weak temperature dependence both below and above the superconducting transition temperature of T_c = 29 K. Since the superconducting gap should have a value of 10-15 meV, our results indicate that the pseudogap (～35 meV) plays an important role in the underdoped La-Bi2201 intrinsic tunneling spectroscopy down to the lowest temperature of 4.2 K. However, the contribution of the superconducting gap can be separated by normalizing the spectra to the one near and above T_c, which shows that the IJJs can be a useful tool for the study of the electronic properties of the La-Bi2201 cuprate superconductors.     

全能近似分析简介

根据无限的“无有终了”的事实,应当把无尽小数看作无穷数列简写,采用这种观点就可以得到实数的运算法则;如果用康托（Cantor,G）的“无限是现实的、完成了的、存在着的整体”的“实无限”观点就得不到这个法则．点是针对误差界的足够小,其中没有大小的点叫做理想点,有大小的点叫做近似点．理想点具有无法点出的性质．近似点的集合能够组成线段,但理想点的集合不能组成线段．绝对准确地讨论没有大小的理想瞬时上的速度没有实际意义,理想的瞬时速度依赖于近似瞬时的速度．对于点、线、面、实数、函数、导数、积分、积分变换、实数集等数学名词都需要提出近似、理想、全能近似三类技术术语,应用对立统一法则去阐述数学理论．     

AlGaAs／InGaAs功率PHEMT用异质材料的计算机优化与器件实验结果

借助一新的工艺模拟与异质器件模型用ＣＡＤ软件──ＰＯＳＥＳ（Ｐｏｉｓｓｏｎ－ＳｃｈｒｏｅｄｉｎｇｅｒＥｑｕａｔｉｏｎＳｏｌｖｅｒ），对以ＡｌＧａＡｓ／ＩｎＧａＡｓ异质结为基础的多种功率ＰＨＥＭＴ异质层结构系统（传统、单层与双层平面掺杂）进行了模拟与比较，确定出优化的双平面掺杂ＡｌＧａＡｓ／ＩｎＧａＡｓ功率ＰＨＥＭＴ异质结构参数，并结合器件几何结构参数的设定进行器件直流与微波特性的计算，用于指导材料生长与器件制造。采用常规的ＨＥＭＴ工艺进行ＡｌＧａＡｓ／ＩｎＧａＡｓ功率ＰＨＥＭＴ的实验研制。对栅长０．８μｍ、总栅宽１．６ｍｍ单胞器件的初步测试结果为：ＩＤｓｓ２５０～４５０ｍＡ／ｍｍ；ｇｍ０２５０～３２０ｍＳ／ｍｍ；Ｖｐ－２．０－２．５Ｖ；ＢＶＤＳ５～１２Ｖ。７ＧＨｚ下可获得最大１．６２Ｗ（功率密度１．０Ｗ／ｍｍ）的功率输出；最大功率附加效率（ＰＡＥ）达４７％。     

弱磁场下低温中和法制备亚微米非晶态δ-FeOOH的研究

利用XRD和SEM分别对在弱磁场下通过低温中和法制备的羟基铁氧化物进行相成分和颗粒形貌分析. 试验结果表明: 无磁场下, 产物是由部分球形和部分针状的α-FeOOH组成. 0.1 T磁场下, 产物是纺锤形的γ-FeOOH, 但是, 其粒度分布很不均匀. 0.3 T磁场下, 产物是球形的Fe_1.833(OH)_0.5O_0.25. 0.5 T磁场下, 产物是100 nm左右的球形的非晶态δ-FeOOH. Fe_1.833(OH)_0.5O_0.25是无磁场下制备的α-FeOOH向弱磁场下制备的δ-FeOOH转变的中间产物. 并且, 亚微米球形Fe_1.833(OH)_0.5O_0.25和亚微米非晶态球形δ-FeOOH的粒度分布都很均匀. 此外, 弱磁场影响羟基铁氧化物的结晶度.     

利用甾体皂甙元氧化降解废弃物(R)-4-甲基-δ-戊内酯合成松叶蜂主要性信息素(2S,3S,7S)-3,7-二甲基-2-十五醇乙酸酯和丙酸酯

首次利用甾体皂甙元氧化降解废弃物(R)-4-甲基-δ-戊内酯合成了松叶蜂性信息素(2S,3S,7S)-3,7-二甲基-2-十五醇乙酸酯(2)和丙酸酯(3). 甾体皂甙元氧化降解废弃物(R)-4-甲基-δ-戊内酯首先被转化成为性质稳定易保存的(R)-5-溴-4-甲基戊酸甲酯(5), 化合物5经过偶联、还原、溴代、环氧加成开环和酰化反应给出目标分子. 本研究结果不仅为松叶蜂性信息素化合物2和3提供了一个简洁有效的合成方法, 同时也丰富了资源化学(即基于资源性化合物合理利用的有机合成化学)的内涵.     

Validation of the membrane composition effect on the flow-injection signal profile of chalcogenide-based ion-selective sensors: a model study using electrochemical approach: Hg(II) flow-injection detector case

The membrane composition effect on signal profile of the combined ISE-flow-injection system is examined on the example of Hg(II) flow-injection potentiometric (FIP) detector based on the secondary response to Hg(II) of different thin layer silver chalcogenide membranes, obtained by cathodic electrodeposition at controlled potential. The potential of the electrochemical approach to produce a great diversity of membrane compositions and the possibility for fine tuning of their stoichiometry made it possible to select the stoichiometry with respect to silver (intrinsic defects factor) and the inclusion of dopant (extrinsic defects factor) as the two variable composition parameters. The following membranes have been tested: Ag₂Se_1−xTe_x, Ag₂Se, Ag_2+δSe and Ag_2+δSe_1−xTe_x (δ=0.24). The experimental conditions have been varied in a wide range to include four flow-rates (within the 2.5-6 ml min⁻¹ interval), and three typical carrier compositions to which either Ag(I) or Hg(II) have been added as pilot ions. The results obtained in this study show unambiguously that the membrane composition factors are an important figure of merit, the weight of which in some particular cases can be co-measurable with that of the flow manifold factors. A new important information concerning the active role of the “pilot ion” added to the carrier in controlling the rising part of the signal, through changing the membrane response rate order, is also provided.     

Co3−δO4 paracrystal: 3D assembly of nanosize defect clusters in spinel lattice

Paracrystalline array of defect clusters ca. five times the lattice spacing of the average Co_3−δO₄ spinel structure occurred more or less in a relaxed manner when the sintered Co_1−xO polycrystals were air-quenched below the Co_1−xO/Co_3−δO₄ transition temperature to activate oxy-precipitation of cube-like Co_3−δO₄ at dislocations. The same paracrystalline spacing was obtained for Co_3−δO₄ when formed via oxidizing/sintering the Co_1−xO powders at 800°C in air, suggesting a nearly constant δ value for Co_3−δO₄ in the T-P_O2 conditions encountered. The extra cobalt vacancies and Co³⁺ interstitials, as a result of δ value, may form additional 4:1-derived defect clusters for further paracrystalline distribution in the spinel lattice. The nanosize defect clusters self-assembled by columbic interactions and lattice relaxation in ionic crystal may have potential applications as step-wise sensor of oxygen partial pressure at high temperatures.     

Novel rare-earth borosilicide RE1−xB12Si3.3−δ (RE=Y, Gd-Lu) (0?x?0.5, δ≈0.3): synthesis, crystal growth, structure analysis and properties

New rare-earth boron-rich compounds with the formula of RE_1−xB₁₂Si_3.3−δ (RE=Y, Gd-Lu) (0?x?0.5,δ≈0.3) have been synthesized. They belong to a new type of rhombohedral structure with the space group of R-3m (No. 166) and z=9. The lattice constants were measured from powder XRD data. Crystal structure solved from powder XRD data for Tb_0.68B₁₂Si₃ as a representative has been compared with that of YB_17.6Si_4.6 (or Y_0.68B₁₂Si_3.01), whose structure was solved from single-crystal reflection data. The structure model is confirmed by high-resolution transmission microscope analysis. The vibrational modes of the new crystals were measured by Raman spectroscopy. Temperature dependence of magnetic susceptibility which was measured for RE_1−xB₁₂Si_3.3−δ single crystals by SQUID revealed that they are paramagnetic materials down to 2.0 K.