GW invariants relative to normal crossing divisors

In this paper we introduce a notion of symplectic normal crossing divisor V and define the GW invariant of a symplectic manifold X relative to such a divisor. Our definition includes normal crossing divisors from algebraic geometry. The invariants we define in this paper are key ingredients in symplectic sum type formulas for GW invariants, and extend those defined in our previous joint work with T.H. Parker [16], which covered the case V   was smooth. The main step is the construction of a compact moduli space of relatively stable maps into the pair (X,V)$(X,V)$ in the case V is a symplectic normal crossing divisor in X.     

Comparative DFT study of Raman spectra of phosphorus-containing dendrimers built from thiophosphoryl,cyclotriphosphazene and phthalocyanine cores

The FT Raman spectra of the zero and first generations of phosphorus-containing dendrimers built from thiophosphoryl, cyclotriphosphazene and phthalocyanine core with terminal oxybenzaldehyde groups have been recorded and analyzed. The structural optimization and normal mode analysis were performed for dendrimers on the basis of the density functional theory (DFT). The calculated geometrical parameters, harmonic vibrational frequencies and Raman scattering activities are predicted in a good agreement with the experimental data. The experimental Raman spectra of dendrimers were interpreted by means of potential energy distribution. Relying on DFT calculations the lines of the cores, repeating units and terminal groups of dendrimers were assigned.The influence of the encirclement on the line frequencies and intensities was studied and due to the predictable, controlled and reproducible structure of dendrimers the information, usually inaccessible is obtained. The strong line at 1600 cm⁻¹ show marked changes of intensity in dependence of aldehyde (CHO) or azomethyne (CHN) substituents in the aromatic ring. The polarizabilities and lipophilicity of dendrimers were estimated.     

涉及分担函数与分担值的正规定则

研究了涉及分担函数的正规定则,证明了:设F为定义在区域D内的一族亚纯函数,n,k是两个正整数,满足n≥k+3.如果对于F中任意一个函数f,(fn)(k)-z至多有一个不同的零点,则F在D内正规.此结论说明在(fn)(k)具有不动点的情形下,1990年杨乐在Notre Dame大学举行的学术会议上提出的断言仍然成立.     

CH2Cl2分子中CH的摇摆振动与伸缩和弯曲振动的耦合

Infrared absorption spectra of gaseous CH2Cl2 in the regions of 1200-12000 cm-1 were measured using a Bruker IFS 120HR Fourier transform spectrometer in conjunction with a multipass cell. 47 vibrational levels of overtone and combinational spectral lines of the CH stretching (v1, v6), bending (v2), and rocking(v8) modes were analyzed and assigned. Utilizing the normal mode model and considering the coupling among CH stretching, bending and rocking vibrations, values of the harmonic frequency ωi, the anharmonic constant xij, and the coefficients of Fermi and the Darling-Dennison resonances of v1, v6, v2 and v8 modes were also determined from experimental spectral data with nonlinear least-square fitting. These spectral constants reproduced the experimental levels very well. These results showed that Fermi resonance between CH stretching and rocking vibrations (ki88=-254.63 cm-1) is stronger than that between CH stretching and bending vibrations (k122 = 54.87 cm-1); and that Darling-Dennison resonances between CH stretching and bending vibrations (k1166=-215.28 cm-1) is also much stronger than that between CH bending and rocking vibrations (k2288=-5.72 cm-1).     

Splitting of coupled bright solitons in two-component Bose-Einstein condensates under parametric perturbation

We analyze the dynamics of bright-bright solitons in two-component Bose-Einstein condensates (BECs) subject to parametric perturbations using the variational approach and direct numerical simulations. The system is described by a vector nonlinear Schrödinger equation (NLSE) appropriate to coupled multi-component BECs. A periodic variation of the inter-component coupling coefficient is used to explore nonlinear resonances and splitting of the coupled bright solitons. The analytical predictions are confirmed by direct numerical simulations of the vector NLSE.     

基于相移偏折法的高反射表面面形测量技术

利用单相机所采集的图像实现了对光滑高反射表面面形的直接检测.首先利用相机获取参考平面在标准平面镜中的镜像,然后通过参考平面上的点与归一化成像平面上图像点之间的密集折返对应关系,求得待测镜面的深度距离,从而实现对高反射表面面形的测量.通过光线追迹将该测量过程转化为求解物空间中关于两对应光线束之间的相交问题.以相位为载体获取面形梯度分布,求得该表面的法向量场,并求解相应的反射光线束.通过光线追迹对该光线束与相应入射光线束求“交点”检测高反射表面.对标准平面镜进行实验检测,测量得到的面形平面度为0.19 mm.采用传统方法与本文所提方法对汽车后视镜进行检测,所得检测结果对应点之间的平均距离为0.15 mm,验证了本文方法检测镜面面形的有效性.     

寒热中药微量元素的比较与分析

对28种温热中药及28种寒凉中药所测定的12种微量及常量元素进行了比较分析，发现温热药中Mn、Cu、Na、K含量显著高于寒凉药，而寒凉药中的Ca含量显著高于温热药，结果提示微量元素及常量元素含量的差异是中药寒凉温热性质的物质基础之一。     

钛-锆氧化物复合填料的正相色谱性能评价

采用油乳法制备了钛锆复合氧化物并系统评价了该填料的正相色谱性能。研究结果表明，该填料对碱性化合物有良好的分离选择性，峰形对称；但对酚类化合物强烈保留，峰形较差；中性化合物和碱性化合物的色谱行为均符合Snyder吸附顶替模型。     

A Normal Criterion Concerning Omitted Holomorphic Function

In this paper, we continue to discuss the normality concerning omitted holomorphic function and get the following result. Let F be a family of meromorphic functions on a domain D, k ≥ 4 be a positive integer, and let a(z) and b(z) be two holomorphic functions on D, where a(z) 0 and f(z) ≠ ∞ whenever a(z)=0. If for any f ∈ F, f'(z) -a(z)f^k(z) ≠ b(z), then F is normal on D.     

Stability and bifurcation analysis in the delay-coupled van der Pol oscillators

In this paper, the dynamics of a system of two van der Pol equations with a finite delay are investigated. We show that there exist the stability switches and a sequence of Hopf bifurcations occur at the zero equilibrium when the delay varies. Using the theory of normal form and the center manifold theorem, the explicit expression for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.