On Higher Order Pyramidal Finite Elements

In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four sub-tetrahedra that form a given pyramidal element.     

生物组织光学参数的离体和在体无损测量

利用漫反射无损测量装置对实际生物组织的光学性质进行了测量,同时对人体前臂进行了在体测量,利用漫射近似所得到的两个解析表达式,对实验数据进行非线性拟合得到了两组光学特性参数,与其它文献中的结果相比较,一方面证实了我们实验设计的可行性,另一方面验证了漫射近似所得到的两个解析表达式之一更准确一些.     

Approximate wφ - Ωφ Relations in Quintessence Models

Quintessence field is a widely-studied candidate of dark energy. There is ＂tracker solution＂ in quintessence models, in which evolution of the field φ at present times is not sensitive to its initial conditions. When the energy density of dark energy is negleetable （Ωφ 〈〈 1）, evolution of the tracker solution can be well analysed from ＂tracker equation＂. In this paper, we try to study evolution of the quintessence field from ＂full tracker equation＂, which is valid for all spans of Ωφ. We get stable fixed points of we and wφ （noted as wφ and Ωφ） from the ＂full tracker equation＂, i.e., we and ωφ will always approach ωφ and Ωφ respectively. Since wφ and Ωφ are analytic functions of φ, analytic relation of φ can be obtained, which is a good approximation for the we φ relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities ωφ 〈 we and 〈ωφ are statisfied if the we （or ωφ） decreases with time. In this way, the potentiai U（φ） can be constrained directly from observations, by no need of solving the equations of motion numerically.     

Optimization of extinction efficiency of gold‐coated polystyrene bead substrates improves surface‐enhanced Raman scattering effects by post‐growth microwave heating treatment

We report a novel post‐growth microwave treatment approach to selectively modify the surface morphologies of gold (Au) films coated on the polystyrene (PS) bead substrates for effectively improving the surface‐enhanced Raman scattering (SERS) effect on the analytes. The discrete dipole approximation (DDA) model was introduced to evaluate the enhancement effects by calculating the localized electromagnetic field distribution and extinction efficiency based on the sizes of the trenches and voids, and the surface roughness of the modified Au–PS bead substrates. The SERS performance of microwave‐modified Au–PS substrates on rhodamine 6G (Rh 6G) and saliva yields at least 10‐fold improvements in SERS intensities compared to the as‐grown substrates, which is also in agreement with theoretical predictions by DDA modeling. This work demonstrates both experimentally and theoretically the efficacy of the microwave heating treatment on modifying the Au–PS bead substrates for the realization of high SERS performance in biomedical applications. Copyright © 2009 John Wiley & Sons, Ltd.     

Deriving Energy-Gap of Some Nonlinear Hamiltonians by Invariant Eigen-operator Method

By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for some Hamiltonians describing nonlinear processes in particle physics. In this way the energy-gap of the Hamiltonians can be naturally obtained. The characteristic polynomial theory has been fully employed in our derivation.     

Comparative study between dispersive and non-dispersive dielectric permittivity in spectral remittances of chiral sculptured zirconia thin films

The transmission and reflection spectra from a right-handed chiral sculptured zirconia thin film are calculated using the piecewise homogeneity approximation method and the Bruggeman homogenization formalism using both dispersive and non-dispersive functions for axial and non-axial states. The comparison of spectral results shows that the dispersion of the dielectric function has a considerable effect on the results. In axial excitation of cross-polarized reflectances and co-polarized transmittances the dispersion effect becomes more pronounced at wavelengths further away from the homogenization wavelength. This is also true in the case of non-axial excitation of circular transmittances, while there are considerable differences for cross-polarized reflectances where (wavelength) the first Bragg peak occurs. At wavelengths in the vicinity of the homogenization wavelength the dispersion effect of the dielectric function in R_RR becomes more significant.     

Singular perturbation of first boundary value problem for higher order elliptic equations (II)

In this paper we discuss singular perturbations of first boundary value problem for higher order elliptic equations of two parameter and obtain the asymptotic expression for the formal solution containing two-parameter as well as the estimation of its remainder term. These results are the extensions of (2) and (3).     

用A238U超核聚变检验裂变机制的可行性探讨

超核_A²³⁸U的裂变的剪断过程,用不断上升的势垒模拟,对不同的剪断过程(恒速或加速),对A末态激发几率(布居于轻裂块的几率)作了计算,分别为27%或31%。有待实验检验。     

球面散布数据点插值的误差估计

讨论球面上散布数据点插值的误差估计问题．一方面用深刻的新概念——正规生成集对插值节点集的特性进行刻画,同时给出它与基本系统、网格范数间的关系;另一方面得到了插值误差及导数的点态估计．