广义线性系统平衡点的谱分析

从另一个角度研究线性广义系统Ex＝Ax的平衡点邻域的定性行为,并对正则性概念作了有益的推广.     

Dimers Belonging to Three Orientations on Plane Honeycomb Lattices

It is well known that there are three types of dimers belonging to the three different orientations in a honeycomb lattice, and in each type all dimers are mutually parallel. Based on a previous result, we can compute the partition function of the dimer problem of the plane (free boundary) honeycomb lattices with three different activities by using the number of its pure dimer coverings (perfect matchings). The explicit expression of the partition function and free energy per dimer for many types of plane honeycomb lattices with fixed shape of boundaries is obtained in this way (for a shape of plane honeycomb lattices, the procedure that the size goes to infinite, corresponds to a way that the honeycomb lattice goes to infinite). From these results, an interesting phenomena is observed. In the case of the regions of the plane honeycomb lattice has zero entropy per dimer—when its size goes to infinite—though in the thermodynamic limit, there is no freedom in placing a dimer at all, but if we distinguish three types of dimers with nonzero activities, then its free energy per dimer is nonzero. Furthermore, a sufficient condition for the plane honeycomb lattice with zero entropy per dimer (when the three activities are equal to 1) is obtained. Finally, the difference between the plane honeycomb lattices and the plane quadratic lattices is discussed and a related problem is proposed.     

具收获项的Ⅱ类功能反应的捕-食系统的定性分析~Ⅰ

在文[7][8]的基础上，分析一类食饵具常数收获项的Ⅱ类功能反应的捕食系统．通过对两鞍点分界线相互位置仔细的分析，得到了比较完备的定性结论，特别是第一次在生态系统的讨论中得到了三个极限环的存在性．     

微积分中值定理间的关系

直观地阐述从微分中值定理到积分中值定理,乃至第二积分中值定理的演绎过程,指出积分中值定理的实质仍是微分中值定理,并在经典积分中值定理的条件下,得到更强的结论。     

ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR GENERALIZED SYSTEMS

§ 1　IntroductionAs compared with the ODEs system,the generalized system is of many distinctiveproperties[1 ] ,forexam ple,the level structural problem of system state solutions,the uncon-sistent initial value problem,the uniqueness of initial value problem and so on.The asymp-totic stability problem of zero solution of generalized system involves the tractability andunimpulsivity.These properties are of great importance in engineering applications.Theconclusion on the ODEs system can not …     

A simple proof of Graham and Pollak's theorem

Graham and Pollak [Bell System Tech. J. 50 (1971) 2495-2519] obtained a beautiful formula on the determinant of distance matrices of trees, which is independent of the structure of the trees. In this paper we give a simple proof of Graham and Pollak's result.     

Some Two-Point Resistances of the Sierpinski Gasket Network

In this paper, we use the principle of substitution to replace sub-gaskets of the Sierpinski gasket network by an equivalent Y-network which enables the use of only the Delta–Wye transformation and the series and parallel principles to derive some two-point resistances of the Sierpinski gasket network with dimension two.     

绍兴市区中学生情绪障碍与生命早期应激相关性研究

目的调查绍兴市区中学生生命早期应激及情绪障碍的发生情况,并探讨两者的相关性。方法对绍兴市区6所中学的518例初中生和468例高中生以生命早期应激问卷（ELSQ）调查生命早期应激发生情况;根据有无生命早期应激及其数量,共分成6组：初中生高应激组（应激数量≥3个,75例）、低应激组（应激数量1~2个,279例）、对照组（无应激,164例）和高中生高应激组（应激数量≥3个,92例）、低应激组（应激数量1~2个,260例）、对照组（无应激,116例）,以抑郁自评量表（SDS）和焦虑自评量表（SAS）分别评定各组的情绪障碍情况。结果绍兴市中学生焦虑、抑郁症状等情绪障碍的发生率分别为16.73%和31.54%,初中生的抑郁症状发生率高于高中生,而高中生的焦虑症状发生率高于初中生;绍兴中学生生命早期应激发生率为71.60%,以家庭暴力、遭受欺凌、与父母分离及家庭冲突发生率最高;初中生经历自己患重大疾病、遭受欺凌、情感虐待或忽视、家庭暴力、家庭灾祸等应激事件容易出现焦虑、抑郁,而高中生在经历家庭冲突、与父母分离、家庭暴力、遭受欺凌、亲人死亡、情感虐待或忽视及家庭成员重大疾病等应激事件时更易出现焦虑、抑郁;生命早期应激与中学生情绪障碍的发生有相关性,特别是抑郁情绪与ELS数量更有显著相关性。结论高达2/3以上的青少年存在生命早期应激,生命早期应激与中学生焦虑、抑郁密切相关,生命早期应激可能是导致中学生出现情绪障碍的重要影响因素。