Heat conduction on the ring: Interface problems with periodic boundary conditions

The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuity at the interface is imposed.     

球形Dirac方程的空间格点求解及假态问题

本文在空间格点上利用虚时间步长方法求解了球形Dirac方程, 着重研究了出现的假态问题. 利用三点数值导数公式离散方程中一阶导数项, 可以证明对于量子数为 κ 和 -κ的单粒子能级能量是完全相同的, 其中一个为物理解, 另一个为假态. 通过在径向Dirac方程中引入Wilson 项, 可以解决假态问题, 得到全部物理解. 文章以 Woods-Saxon 势为例, 考虑 Wilson 项后, 得到与打靶法一致的结果.     

Stability in Probability of Nonlinear Stochastic Volterra Difference Equations with Continuous Variable

Abstract

The general method of Lyapunov functionals construction, that was proposed by Kolmanovskii and Shaikhet and successfully used already for functional-differential equations, difference equations with discrete time, difference equations with continuous time, and is used here to investigate the stability in probability of nonlinear stochastic Volterra difference equations with continuous time. It is shown that the investigation of the stability in probability of nonlinear stochastic difference equation with order of nonlinearity more than one can be reduced to investigation of the asymptotic mean square stability of the linear part of this equation.     

Expansion of analytic functions in q-orthogonal polynomials

A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey–Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.      

二维正方晶格光子晶体禁带特性

基于平面波展开法,以碳化硅构成二维正方晶格光子晶体,数值模拟了TE模、TM模二维光子晶体的禁带特性,结果表明,TE模更容易形成光子禁带。同时设计了以碳化硅构成二维正方晶格光子晶体波导,数值模拟了TE模、TM模波导的传输特性和禁带特性,结果表明,TE模构成的波导电磁波能够较好的传播,它们的光子禁带都没有出现。研究结论为光子晶体波导器件的开发提供参考。     

绞股蓝种子中α-桐酸的定性和定量分析

用RTX-5MS弹性石英毛细管柱(0.25mm×30m×0.25μm)气相色谱-质谱法(GC-MS)分析绞股蓝种子中的α-桐酸。用相对保留时间和质谱对α-桐酸进行定性分析,用内标法对α-桐酸进行定量分析。结果表明,绞股蓝种子中含有α-桐酸,在0.34—1.37mg/mL范围内线性关系良好(R2=0.9996),平均回收率为99.91%,且绞股蓝种子中α-桐酸的含量为66.9mg/g。实验结果为以后的绞股蓝种子中α-桐酸的开发与利用提供理论依据。     

波士顿矩阵法在河南承接产业转移中的应用

承接产业转移是加速区域经济发展的"助推器",提升产业集聚能力是提高区域产业竞争力的关键,如何科学地选择承接产业,并提升产业集聚能力是河南亟待解决的问题.选取2010年和2014年两个时点,运用产业梯度系数和产业动态集聚指数对工业进行分行业分析,并借鉴波士顿矩阵分析法将其划分为明星、金牛、问题、瘦狗和衰退等产业.根据河南的自然资源、劳动力、区位条件、市场需求等比较优势,并考虑产业集聚发展的能力,来确定河南承接产业转移的重点产业.     

Development and validation of high-performance liquid chromatography method for analysis of β-CCT and its related substances

Compound 2β-carbomethoxy-3β-(4-chlorophenyl)tropane (β-CCT) is a key intermediate for the synthesis of some clinical dopamine transporter (DAT) imaging agents. Potential impurities from synthesis process of β-CCT and degradation during storage might have detrimental effect on the final imaging agents. Thus, it is necessary to guarantee the quality of β-CCT. In this study, a rapid, sensitive and accurate high-performance liquid chromatography (HPLC) method was developed and validated for the analysis of β-CCT and its related substances. The chromatographic separation was achieved on a reverse-phase phenomenex? Gemini C18 column with an isocratic mobile phase consisted of methanol, water and TFA (30:70:0.1 v/v/v). The flow rate was 1.0 mL/min at 30 °C and samples were monitored at 220 nm. The method was validated concerning system suitability, linearity, accuracy, precision, specificity, robustness and stability. The limit of detection (LOD) and the limit of quantification (LOQ) of β-CCT were 0.5 and 1.5 μg/mL, respectively. The linearity range of β-CCT was 1.5–450 μg/mL with a good linear correlation coefficient (R² = 0.9999) between the peak response and concentration. Specificity investigation through forced degradation experiments displayed that β-CCT was stable in acidic, thermal and photolytic degradation conditions, but significantly unstable in alkaline and oxidative conditions. With the developed chromatographic method, possible impurity α-CCT from synthetic process and potential degradation products could be well separated from β-CCT. Good recovery and precision were manifested in the assay method. These results indicated that the present method would be suitable for not only the quality assurance of β-CCT in regular production sample assays but also the monitoring and determination of its related substances.     

Multidisciplinary green approaches (ultrasonic,co-precipitation,hydrothermal, and microwave) for fabrication and characterization of Erbium-promoted Ni-Al2O3 catalyst for CO2 methanation

The dispersion of nickel catalysts is crucial for the catalytic ability of CO₂ methanation, which can be influenced by the fabrication method and the operation process of the catalysts. Therefore, a series of fabrication methods, including ultrasonic, hydrothermal, microwave, and co-precipitation, have been applied to prepare 25Ni-5Er-Al₂O₃ catalysts. The fabrication method can partially influence the structural and catalytic activity of the nickel aluminate catalysts. Among the catalysts modified by Erbium prepared with various methods, the catalyst fabricated by ultrasonic pathway exhibited better catalytic performance and CH₄ selectivity especially, at a temperature (400 ℃). The impact of the temperature of the reaction (200–500 °C) was examined under a stoichiometric precursor ratio of (H₂:CO₂) = 4: 1, atmospheric pressure, and space velocity (GHSV) of 25000 mL/gcath. The results demonstrate that the ultrasonic method is strongly efficient for fabricating Ni-based catalysts with a high BET surface area of about 190.33 m²g^?1. The catalyst composed via the ultrasonic technique has 69.38 % carbon dioxide conversion and 100 % methane selectivity at 400 °C for excellent catalytic performance in CO₂ methanation reactions. The fabrication effect can be associated with its high surface area, which is achieved via the hot spot mechanism. Besides, the addition of Erbium promotes the Ni dispersion on the supports and stimulates the positive reaction because of the erbium oxygen vacancies.     

重量法测定土壤水溶性盐总量的优化

土壤水溶性盐是表征土壤盐碱化程度的重要指标,也是评价耕地地力的重要参数,被纳入第三次全国土壤普查（“三普”）监测指标体系中。重量法是测定土壤水溶性盐总量的最常用方法,其测定过程易受多种因素影响,导致其测定结果不准。鉴于此,本文设计试验分别验证了水溶性盐浸提和浸提液固液分离这两个过程对测定结果的影响,结果表明浸提液固液分离是影响土壤水溶性盐总量测定准确度和精密度的主要因素。基于此进一步探究4种不同固液分离方式（布氏漏斗过滤、滤膜真空抽滤、离心、滤纸组合过滤）对测定结果的影响,结果表明相较于其它方式,滤纸组合过滤测定结果准确度高,适用于土壤水溶性盐总量的测定。对改进后的重量法测定土壤水溶性盐总量进行方法学确认,结果表明其检出限为0.01 g/kg,测定下限为0.04 g/kg;方法的准确度和精密度、适用范围等均符合相关要求。本文推荐的土壤水溶性盐总量测定方法为：土壤样品采用1:5土水比浸提,180 r/min振荡3 min,浸提液采用滤纸组合自然过滤;其测定结果的准确度和精密度符合相关要求。本文旨在为“三普”内业检测提供参考和借鉴,为全面摸清不同区域土壤水溶性盐含量水平及土壤盐渍化程度提供技术支撑。