GREEN FUNCTIONS FOR A DECAGONAL QUASICRYSTALLINE MATERIAL WITH A PARABOLIC BOUNDARY

This investigation presents the Green functions for a decagonal quasicrystalline material with a parabolic boundary subject to a line force and a line dislocation by means of the complex variable method. The surface Green functions are treated as a special case, and the explicit expressions of displacements and hoop stress at the parabolic boundary are also given.Finally, the stresses and displacements induced by a phonon line force acting at the origin of the lower half-space are presented.     

各阶欺骗概率相等的最优认证码

本文研究各阶欺骗概率相等的、一般阶的最优认证码的构造。利用有限域上高次抛物线、M-序列和线性校验办法分别构造了一类保密最优认证码和两类Cartesian最优认证码。     

Crystal Growth Kinetics of Nanocrystalline ZnS under Surface Adsorption

The crystal growth mechanism,kinetics,and microstructure development play a fundamental role in tailoring the materials with controllable size and morphology. In this study,by introducing the strong surface adsorption of the concentrated NaOH,two-stage crystal growth kinetics of ZnS nanoparticles was observed. In the first stage,the primary particles grow into a size over a hundred times of the original volume and the growth is controlled by the crystal-lographically specific oriented attachment. The first stage data were fitted by the "multistep OA kinetic model" built based on the molecular collision and reaction. In the second stage,following the dispersal of nanoparticles,an abrupt transition from asymptotic to parabola growth kinetics occurs,which can be fitted by a standard Ostwald ripening volume diffusion model. The presence of surface adsorption causes the two-stage growth kinetics and permits an almost exclusive OA-based growth to dominate in the first stage.     

Optical terminal analysis of a multigrating tiled compressor in a PW-class CPA-laser

In the highest-power chirped-pulse amplification lasers, the pulse must be stretched in time, amplified, compressed in a grating compressor and subsequently focused by off-axis parabola to obtain a high peak power. In the optical terminal, the temporal and spatial effects of mismatched multigrating tiled compressor on the far-field pulse are critical factors to be analysed. In this paper, a k-space raytracing model is proposed for the temporal and spatial analyses of possible errors in a four-grating single-pass tiled compressor. The results show that the last grating affects mainly the partial focal spot, while the middle two gratings affect the temporal waveform, and the partial focal spot needs much higher error control than that in the temporal domain in a picosecond pulse compression.     

共轴抛物镜线聚焦性能的2维分析

 掠入射泵浦方式作为一种全新的X射线激光泵浦方式,采用了共轴抛物镜作为线聚焦器件。利用2维光路追踪程序,计算了高斯光束从5°掠入射角增加到7°时入射到共轴抛物镜上的线聚焦效果。研究发现,掠入射角从5°增加到7°过程中,线聚焦的尺寸随着掠入射角变大,线聚焦长度从6 mm逐渐变长到12 mm,线聚焦宽度从150 μm变到40 μm;掠入射角6.5°～7°可以实现符合实验要求的线聚焦效果,线聚焦尺寸约10 mm×20 μm(最小线聚焦宽度),7°掠入射可以实现较好的线聚焦,基本满足实验的要求。     

Aitken插值在几何作图中的应用

本文利用 Aitken插值 ,介绍一种过已知三点的抛物线的几何作图法 .     

从立方抛物线谈起(2)--余弦型行波,椭圆余弦型行波与孤立波

从立方抛物线的特性谈起，用较初浅的方法，借助于雅可比椭圆函数求椭圆方程的解，说明一类非线性波方程可用行波法求解析解．求得了许多非线性波的重要性质，特别是求得孤立波解．举KdV方程、正弦-Gordon方程(SG方程)、非线性薛定谔方程(NLS)及mKdV方程为典型实例．     

Semiempirical method of calculations of transition-state geometries for radical addition reactions

Transition-state geometries of the addition reactions of H^·, ^·CH₃, ^·NH₂, and ^·OCH₃ radicals to ethylene; H^· radical to acetylene, methyleneimine, acetonitrile, and formaldehyde; and ^·CH₃ radical to acetone and acetylene were determined by the density functional (B3LYP) method. The interatomic distances in the transition states of these reactions were also calculated from experimental data (enthalpies and activation energies) using the model of intersecting parabolas, the model of reduced intersecting parabolas (RIP), and the model of reduced intersecting parabola and Morse curve. The results obtained by different methods were compared and analyzed. An algorithm was elaborated for calculations of interatomic distances using experimental data, based on introduction of corrections to the RIP model. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 886–893, April, 2005.     

Nuclear mass parabola and its applications

We propose a method for extracting the properties of the isobaric mass parabola based on the total doubleβ-decay energies of isobaric nuclei.Two important parameters of the mass parabola,the location of the most β-stable nuclei Z_A and the curvature parameter b_A,are obtained for 251 A values,based on the total double β-decay energies of nuclei compiled in the AME2016 database.The advantage of this approach is that the pairing energy term P_A caused by the odd-even variation can be removed in the process,as well as the mass excess M(A,Z_A) of the most stable nuclide for the mass number A,which are employed in the mass parabolic fitting method.The Coulomb energy coefficient a_c=0.6910 MeV is determined by the mass difference relation for mirror nuclei,and the symmetry energy coefficient is also studied by the relation a_(sym)(A)=025 b_AZ_A.     

二次曲线方程的分类与化简

通过对二次曲线方程配方变形,利用直线与二次曲线相交时参数t的几何意义,以及仿射变换的性质,得到了二次曲线方程分类与化简的一种新方法,从而解决了二次曲线方程通过坐标系的平移、旋转进行分类、化简运算复杂,通过不变量进行化简,无法画出图形的具体位置等问题.