Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.     

丙烯和甲苯的超共轭效应的理论研究

用从头算对丙烯和甲苯2个超共轭体系进行计算,结果表明甲基上氢原子参与超共轭时,其碳氢键键长增大,氢上集居数减少,丙烯、甲苯的甲基旋转势垒为7.61及0.096 kJ/mol.超共轭基作用相当于一带有孤对电子参与共轭之杂原子,超共轭体系不同构型稳定性可用M=sum from i=1 to 3(sinθ_i[sin(θ_i-α)+sinα])来表征。     

三线摆实验中摆角偏大产生的误差及修正方法

研究了三线摆实验中摆角偏大(5°θ20°)时对测量转动惯量产生的误差和修正办法。实验发现随着摆角的增大,测得的圆盘转动惯量也会相应偏大,从而导致测量误差增大。文章通过进一步的理论分析解释了这一现象,并对测量结果进行了系统误差修正。     

Z 2-equivariant cubic system which yields 13 limit cycles

For the planar Z_2-equivariant cubic systems having two elementary focuses,the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved.The necessary and sufficient conditions for the existence of the bi-center are obtained.On the basis of this work,in this paper,we show that under small Z_2-equivariant cubic perturbations,this cubic system has at least 13 limit cycles with the scheme 16∪6.     

一类光滑凸规划的牛顿法

给出了一个求解一类光滑凸规划的算法,利用光滑精确乘子罚函数把一个光滑凸规划的极小化问题化为一个紧集上强凸函数的极小化问题,然后在给定的紧集上用牛顿法对这个强凸函数进行极小化．     

酸式邻苯二甲酸铜的合成与晶体结构的研究

采用固 -液反应法 ,用氧化铜和邻苯二甲酸酐合成了二水合酸式邻苯二甲酸铜Cu( HPht) 2 · 2 H2 O,研究了反应条件 ,测定了晶体结构和配位结构。结构分析发现 ,中心金属离子位于分子的对称中心位置 ,铜离子与来自 2个水分子和 2个邻苯二甲酸根中的4个氧原子形成近似正方形平面配位 ,邻苯二甲酸根是以 1个 O( 1 )与 Cu2 + 离子形成单齿配体 ,O( 2 )和 Cu2 +之间没有形成配位键     

煤矸石堆积模型

本文就煤矿堆积煤矸石费用问题建立数学模型 ,就不同的征地方式 (建矿初期一次性征完 2 0年所需用地和分批征地方式 )和煤矸石堆数进行了分析讨论 ,得出结论 :在建矿初期一次性征完所需用地 ,且所有煤矸石全堆成一堆的方案是最优的 ,并就不同的出矸率计算出该最优方案的总费用 ,最后给出对不同的出矸率处理矸石的最低年度平均费用公式     

Antitumor activity of transition metal(II) complexes with all- trans retinoic acid

Five complexes of transition metals with all-trans retinoic acid (HRA) have been prepared and characterized by elemental analysis, molar conductance, t.g.–d.t.a, i.r., and u.v.-vis. spectroscopy, and 1H-n.m.r. spectrometry. The general formula of these complexes is ML2 ·nH2O where L=RA, M=MnII, CoII, NiII, CuII, ZnII, and n=3 or 4. They have been studied for their antitumour activity against human bladder cancer line EJ (EJ cells) with respect to proliferation, induce differentiation, P21 and mutation P53 expressions in vitro.     

青饲大豆主要品质参数的近红外光谱快速分析

饲料是畜牧生产的物质基础,饲草原料和饲料产品营养价值的检测与评估是饲料生产中的重要环节,面对饲草资源中粗蛋白含量低和大量依靠进口饲料的局面,大豆作为优质的高蛋白豆科饲草是畜牧业生产利用的重要资源.不同青饲大豆及其不同刈割期的饲用品质参数可以评价青饲大豆的饲用性能,但目前主要以化学方法进行检测,过程繁琐,试验周期长、易造...