求解二维Fisher-KPP方程的一类保正保界差分格式及其Richardson外推法

本文研究求解二维Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP)方程的一类保正保界差分格式.运用能量分析法证明了当网格比满足$R_{x}+R_{y}+[b\tau (p-1)]/2\leq\frac{1}{2}$时差分解具有一系列数学性质,包括保正性、保界性和单调性,且在无穷范数意义下有$O (\tau+h_{x}^{2}+h_{y}^{2})$的收敛阶.然后通过发展Richardson外推法得到收敛阶为$O (\tau^{2}+h_{x}^{4}+h_{y}^{4})$的外推解.最后数值实验表明数值结果与理论结果相吻合.值得提及的是在运用本文构造的Richardson外推法时对时空网格比没有增加更严格的条件.     

A Multi-Scale Method for Distributed Convex Optimization with Constraints

Journal of Optimization Theory and Applications - This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using...     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A Space-Time Polynomial Collocation Method for Solving 3D Burgers Equations北大核心CSCD

Burgers方程是一类应用广泛的非线性偏微分方程,方程中的非线性项难以处理。该文提出一种新的时空多项式配点法——多项式特解法求解三维Burgers方程。求解过程分为两步:第一步,对三维Burgers方程中的线性导数项(包括时间导数项),求出相应的多项式特解。第二步,将求出的多项式特解作为基函数,对三维Burgers方程中剩余的非线性项进行迭代求解。与时空多项式函数作为基函数对三维Burgers方程进行直接求解相比,该算法简单易行,得到的近似解精度非常高,算法极其稳定,对于教学过程中提高学生的编程能力,加深对高维Burgers方程的理解能力以及Burgers方程的实际应用具有重要意义。     

绿色产品零售企业与市场消费者策略选择演化分析

线上线下结合营销模式有效缓解了流通渠道不畅和营销方式单一的问题,进而促进绿色产品消费。在相关假设的基础上,通过构建绿色产品零售企业和市场消费者的演化博弈模型,重现博弈主体的动态演进过程。研究结果表明,在线上线下结合营销模式中,绿色产品零售企业与消费者演化博弈系统存在两个可能的均衡状态,分别是O{维持传统营销策略,使用传统渠道购买产品}、C{建立线上营销策略,使用线上渠道购买产品}。演化博弈系统的演进受到9个相关因素的干扰,这些因素通过影响博弈主体的收益、成本及潜在的风险损失等发生作用。在理论推导的基础上,以被调研的A绿色产品零售企业为样本进行数值模拟,验证理论推导的正确性,给出上述影响因素的作用强度。     

汽车制造商分时租赁模式采用及产品线策略研究

考虑自有平台和第三方平台两种分时租赁方式,将汽车质量划分为性能质量和环境质量,构建销售模式、纯分时租赁模式和混合模式下的产品线策略模型,研究制造商产品线策略与商业模式之间的相互作用。研究发现,同品牌产品间竞争和合并效应是分时租赁模式影响产品线策略的两个关键因素。同品牌产品间竞争的加剧和合并效应的增大都会激励企业选择性能更好的车型而忽略其环境表现。分时租赁模式能同时改进利润与产品环境表现,但存在条件:当消费者价格敏感性较低时,使用成本高且合并效应小是实现同时改进的条件;当消费者价格敏感较高时,使用成本低且合并效应小则是同时改进的条件。     

Electrooxidation Mechanism of Methanol at Pt-Ru Catalyst Modified GC Electrode in Electrolytes with Different pH Using Electrochemical and SERS Techniques

The electrochemical and in-situ surface-enhanced Raman spectroscopy （SERS） techniques were used to investigate the electrooxidation behavior of methanol in acidic, neutral and alkaline media at a Pt-Ru nanoparticle modified glassy carbon （Pt-Ru/GC） electrode. The results showed that methanol could be dissociated spontaneously at the Pt-Ru/GC electrode to produce a strongly adsorbed intermediate, CO. It was found that CO could be oxidized more easily in the alkaline medium than in the acidic and neutral media. The peak potential of methanol oxidation was shifted from 0.663 and 0.708 V in the acidic and neutral media to -0.030 V in the alkaline medium, which is due to that the adsorption strength of CO on the Pt surface in the alkaline medium is weaker than that in the acidic and neutral media. The final product of the methanol oxidation is CO2. However, in the alkaline medium, CO2 produced would form CO3^2- and HCO3^- resulting in the decrease in the alkaline concentration and then in the decrease in the performance of DMFC. Therefore, the performance of the alkaline DMFC is not Stable.     

Determination of Pesticide Ethion by Linear Sweep Stripping Voltammetry

IntroductionOrganophosphorus pesticides( OPPs) are widelyused in agriculture as insecticides, but they are foundto contaminate agricultural products such as fruits andvegetables to variable extents. Because of their toxicproperties[1,2]and the potential r…     

青钱柳中多糖的测定

建立了一种测定青钱柳中多糖的方法. 青钱柳样经80%乙醇回流除去单糖、双糖、低聚糖、多酚、氨基酸等杂质后用水提取, 得青钱柳多糖, 其含量采用蒽酮-硫酸法比色测定, 用精制青钱柳多糖测得青钱柳多糖对葡萄糖的换算因子. 采用该方法测定简便可行, 供试液在8 h内显色稳定, 重现性较好, 平均回收率为100.8%, RSD为1.9% (n=3). 所测江西修水青钱柳中多糖含量为4.39%.     

制备方法对负载型纳米ZrO2/Al2O3复合载体性能的影响

采用浸渍-沉淀法制备了负载型纳米ZrO2/Al2O3复合载体.采用X射线衍射、N2物理吸附、差示扫描量热(DSC)和程序升温脱附等技术考察了浸渍方式和干燥方法对复合载体的表面性能、热稳定性和晶相结构的影响.结果表明,ZrO2/Al2O3复合载体中没有生成ZrO2-Al2O3复合氧化物或固溶体,纳米ZrO2仅负载在Al2O3的表面.微波干燥法制备的ZrO2/Al2O3复合载体的比表面积(158.7 m2/g)较大,最可几孔径为19.4 nm,ZrO2的粒度为4.2 nm,晶相结构为四方相ZrO2.微波诱导作用使ZrO2/Al2O3复合载体表面产生了新的酸碱中心,微波干燥法制备的ZrO2/Al2O3复合载体具有较强的热稳定性,在873~1 073 K范围内DSC曲线没有出现吸热峰,而其它干燥方法制备的复合载体在903~1 023 K范围内出现了较明显的吸热峰,表明复合载体表面的部分四方相ZrO2转变为单斜相ZrO2(m-ZrO2).对超声波处理过的复合载体进行微波干燥能进一步提高纳米ZrO2与Al2O3之间的相互作用,纳米粒子的粒度(3.4 nm)更小,分布更均匀,但没有改变ZrO2的晶相结构.