扩展的Boussinesq系统Lax对的Bcklund变换和递推求解公式的导出

本文研究2+1维的扩展经典Boussinesq系统。首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Bcklund变换。然后,又导出了Lax对的特征函数的生成公式。最后,利用Bcklund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式。利用此递推公式,求出了一些Lax对的解。     

Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed on the interfaces. The approximate flux is sought in the lowest-order Raviart-Thomas space and the pressure field in the rotated- nonconforming space. Furthermore, we demonstrate that the present finite volume method can be interpreted as a rotated- nonconforming finite element method for the pressure with a simple local recovery of flux. Numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method.

     

金属纳米颗粒的热导率

本文使用统计模拟方法对金属纳米颗粒的电子平均自由程进行了计算,并考察了纳米颗粒的晶格比热和声子平均群速度,最后应用动力学理论对纳米颗粒的电子热导率和声子热导率分别进行了求解.研究结果表明:具有相同特征尺寸的方形、球形纳米颗粒的无量纲电子(或声子)平均自由程比较接近.金属纳米颗粒的电子热导率远大于声子热导率;电子、声子热导率随着直径减小呈现降低趋势,而电子热导率的颗粒尺度依赖性比声子热导率更为明显;随着颗粒直径进一步减小,声子热导率与电子热导率趋于同一数量级.当纳米颗粒特征尺寸大于4倍块材电子(或声子)平均自由程,其电子(或声子)热导率的颗粒尺度依赖性将减弱.     

Variations in the Concentrations of Cu and Zn and in the Ratio of Cu to Zn in Whole Blood and Hair Samples from Hepatocellular Carcinoma Patients and from Healthy Controls in Taiwan

An atomic absorption spectrophotometer was used to determine concentrations of copper and zinc and the ratio of Cu to Zn in samples of whole blood and hair from hepatocellular carcinoma (HCC) patients (n=51) and from healthy controls (n=50) in Taiwan. Our results indicate that the HCC patients have higher copper concentrations and higher ratios of Cu to Zn than do the healthy controls both in whole blood and hair samples, but only the concentration of copper and the ratio of Cu to Zn in whole blood were significantly different (p<0.001 and p<0.05). Conversely, a lower concentration of zinc was found in whole blood and hair samples of HCC patients. Similarly, only the concentration of zinc in whole blood showed a significant difference (p<0.001). We concluded that the whole blood concentrations of copper and zinc and the ratio of Cu to Zn seemed to have a higher correlation with HCC. Thus, we suggest that a sample of whole blood may be a more suitable diagnostic sample than is a hair sample for HCC.     

AN INVARIANCE OF CDF EQUATION

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SYMMETRIES AND GROUP-INVARIANT SOLUTIONS OF DIFFERENTIAL EQUATIONS

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Electro-optic mapping systems of electric-field using CW laser diodes

Two novel systems are proposed to perform the electro-optic (EO) mapping of the electric-field strength close to electrode structure using CW laser diodes. By these systems, mappings of both static (DC) and high-frequency electric-field can be obtained. For the static field, the field is chopped to increase the sensitivity performance. For the high-frequency field, an intensity modulation laser, instead of a pulse laser, is used to perform the mapping measurement in frequency domain, instead of in time domain. This approach greatly simplifies the system. An experiment set-up using a vertical cavity surface emitted laser diode (VCSEL) of a wavelength 850 nm and its mapping results for a coplanar waveguide (CPW) with the signal frequency around 1 GHz are reported.