Optical and Acoustical Frequencies in a Nonlinear Helicoidal Model of DNA Molecules

We compare optical and acoustical frequencies in the Peyrard-Bishop-Dauxois model, i.e. an extended Peyrard-Bishop model, of DNA molecules. We discuss how ratio of those frequencies depends on a value of the harmonic constant of the helicoidal spring K. Also, we suggest that the most favourable mode could be a resonance mode.     

无介质微波作用下酮与稳定叶立德的反应

酮与稳定膦叶立德在家用微波炉中加热，在无任何溶剂或固体介质条件下，4．5min之内完成反应，得到了良好产率的Wittig反应产物，较之液相苯中回流反应的传统方法，此法具有时间短、操作步骤简单、无毒害等优点，同时使一些在传统方法中与稳定叶立德不反应或难反应的酮得以进行并有较好收率。此外，在得到α，β-不饱和酯的同时，还发现了少量重排产物β，γ-不饱和酯，并对其机理进行了推测与证明。     

纳米PIC-I分子聚集体的超辐射和Z-扫描研究

分子聚集体在非线性光学和集成光学等领域有潜在的应用前景。纳米结构一维染料分子J—聚集体有许多既不同于单个分子又不同于体材料的奇异性质，即超辐射和巨光学非线性。这种超辐射是由于在几个本征态内振于强度结合在一起，得到一巨跃迁偶极于，因而是超辐射的。跃迁速率与耦合分子个数N成正比。分子聚集体的J—吸收和超辐射发射是共振的。利用Z—扫描技术测量PIC在不同配比下的非线性折射率、非线性吸收系数和非线性极化率。观测到随着链长变短，样品的三阶非线性极化率增大。对这种非线性增强的机制进行了分析和讨论。     

Self-assembly behaviour of amphiphilic diblock copolymer in selective solvents studied by synchrotron small-angle x-ray scattering

The aggregation behaviour of styrene-vinyl benzoic acid (PSm-b-PVBAn) amphiphilic diblock copolymers in selective solvents with different m and n was investigated by synchrotron small-angle x-ray scattering (SAXS). We have carried out a detailed analysis of scattering intensity, dimension, shape and microstructure of the diblock copolymers of narrow distribution in water, methanol, ethanol and isopropanol selective solvents, respectively. We have found that the aggregation behaviour of the copolymer depends on the nature of the solvent and the micelle forms fiat disc objects with the ratio of radius ω=0.4. The average radius gyration Rg of the copolymer decreases as solvents change from isopropanol to ethanol and to methanol, and increases with increasing pH in aqueous solution, but decreases with the addition of COCl2 in ethanol solvent. The scattering intensity of diblock copolymer micelle follows I(h) ∝ h^-α in different selective solutions, suggesting that the PSm-b-PVBAn coils have self-similar structure behaviour or a fractal structure in the selective solvents. All of these revealed that the aggregation behaviour of the diblock copolymer changes dramatically with experimental condition in the selective solvent. The increase of mass fractal dimension (Dm) from 2.12 to 2.47 indicates that the copolymer chain changes from a swollen coil to a rather compact disc in the course of changing solvents, decreasing surface fractal dimension (Ds) from 2.98 to 2.58 indicates that the copolymer micelle change from a rather rough surface to a smooth form in the course of increasing pH in aqueous solutions, and increasing Dm and Ds from 2.29 to 2.35 and 2.70 to 2.90, respectively, indicates the shrinkage of copolymer micelle to a rather compact and rough disc form by adding COCl2 in ethanol solvents.     

关于气体中有无速率为无穷大分子的再讨论

本文以较简捷的方法讨论了气体分子速率问题，给出了计算分子最大速率的理论公式，通过这些讨论可更加深入地理解气体中分子的运动情况，准确地理解麦克斯韦速率分布函数。     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

Proton Fraction in Neutron Star Matter and Three-Body Force Effects

The three-body force effects on the equation of state and its iso-spin dependence of asymmetric nuclear matter and on the proton fraction in neutron star matter have been investigated[1] within Brueckner Hartree-Fock (BHF) approach by using a microscopic three-body force. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β=(N-Z)/A is fulfilled in the whole asymmetry range 0 ≤β ≤1 and also up to high density. The three-body force provides a strong enhancement of symmetry energy at high density in agreement with relativistic approaches. Thecalculated proton fraction in β stable neutron star matter is given in Fig.l, where the thick solid line is the BHF prediction using AV18 TBF, while the dotted one is the BHF result using AVis. The thin solid line is the prediction of the Dirac-Brueckner approach taken from Ref.[2]. The results extracted according to the phenomenological paramete rizations of the symmetry energy suggested in Ref.[3] are also plotted. It is seen from     

关于算子方程AX=XAX与AX=XA=XAX

用A的不变子空间作参数，给出了算子方程AX＝XAX的全部解。当A是单射或稠值域时，或者当A是正规算子时，给出了算子方程AX＝XA＝XAX的全部解。我们还给出正规算子X是算子方程AX＝XZ＝XAX的解的充分必要条件。     

Silane photoabsorption spectra mear the Si 2p thresholds：the geometry of Si 2p excited SiH4

Based on the multiple-scattering self-consistent-field method, we have studied the photoabsorption spectra near the Si 2p thresholds of silane. According to our calculations, the clear assignments of the inner-shell photoabsorption spectra are provided. In comparison with the high-resolution experimental spectra, the geometric structure of the Si 2p-excited SiH_{4}^{**} is recommended to be of a C_{2v} symmetry. More specifically, the Si 2p-excited SiH_{4}^{**} have two bond lengths of 2.50 a.u. and another two bond lengths of 2.77 a.u., and the corresponding two bond angles are 104.0° and 112.5° respectively.     

约束Hamilton系统的Poincaré-Cartan不变量

从正则形式作用量出发,导出了约束Hamilton系统(奇异拉氏量)的Poincaré-Cartan不变量,证明了该不变量与约束Hamilton系统的正则方程之间的等价性,纠正了某些作者工作中的错误。