C-wellposedness of the complete second order abstract cauchy problem and applications

In this paper, we first give a sufficient and necessary condition for to generate an exponentially bounded -semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem ((ACP₂) for short) in some sense. Then we use these results and those in [1] to discuss the C-(exponential) wellposedness of a kind of (ACP₂) with application backgrounds, and develop the results in [2]. This project is supported by the NNSF of China, and the Youth Science and Technique Foundation of Shanxi Province, China     

2-连通半无爪图的最长圈

A graph G is called quasi-claw-free if it satisfies the property:d(x,y)=2 there exists a vertex u∈N(x)∩N(y)such that N[u]■N[x]∪N[y].In this paper,we show that every 2-connected quasi-claw-free graph of order n with G■F contains a cycle of length at least min{3δ+2,n},where F is a family of graphs.     

Evolution of co-operation among mobile agents with different influence

Co-operation is a key factor in understanding the evolution of our society. Inspired by this issue, the individual mobility in game theory has been proved to be a very useful scenario. However, it is not realistic, as described in previous studies, that each agent has the same influence on its neighbour’s movement trait. In this work, we mainly focus on the weighted influence on the mobility of agents in the prisoner’s dilemma game. Here the weight is proportional to its degree with power exponent of λ$\lambda$, where λ$\lambda$ is the adjustable parameter to control the level of heterogeneity among individuals in the network. Through numerous simulations we find that co-operation level is promoted when the heterogeneous influence factor is considered. In particular, there is an intermediate value _λopt≈10${\lambda }_{opt}\approx 10$ to guarantee the optimal evolution of co-operation. Moreover, we also prove that the effect of influence weight on the enhancement of co-operation is only valid when the agent’s interaction radius is within a threshold value. We thus present a viable method of understanding the ubiquitous co-operative behaviour in nature and hope that it will inspire further studies to resolve social dilemmas.     

硬盘磁头-碟界面润滑剂失效机理及添加剂X-1P的性能研究

As a key part of Hard Disc（HDI）,the thin film of lube is possibly degraded and destroyed by the interaction between the magnetic head and disk during the hard disk working. Both TGA and FTIR are used to study lubes failure mechanism of HDI and investigate the function of X-1P as an additive in HDI lube. TGA experiment results show that the sample PFPE / X-1P / Al2O3 is much more stable than the sample PFPE / Al2O3 just as sample PFPE,and the sample PFPE / Al2O3 will degrade with high speed at enough high temperature. FTIR experiments present the results similar to that of TGA experiments. From IR sorption spectra at different heating times for the three samples,it can be found that the sample PFPE & the sample PFPE / X-1P / Al2O3 are similarly stable,but different from the sample PFPE / Al2O3 for which new CF = O absorption peak appeared after heated for 15 min and became stronger with the extending for heating time. FTIR experiment results further verifies that alumina is a catalyst for PFPE degradation reaction and X-1P can effectively passivate the catalyst and stabilize PFPE. In order to investigate X-1P's role to mechanical & tribological performances of HDI,the CSS experiment is also performed and the experiment results tell that the presence of X-1P dip-coated on the magnetic head can greatly reduce the friction between head and disk and improve CSS performance of HDI. In addition,the failure mechanism of HDI lube and X-1P's working principle as a HDI lube additive are analyzed and discussed respectively. The aluminum atom of alumina has empty orbits which can accept isolated electron pairs,and is a kind of Lewis acid with stronger electrophilic trend. Oxygen atom of PFPE has isolated electron pairs and shows nucleophilic trend. When the magnetic head contacts with the HDI lube,it is possible for alumina to induce PFPE to disproportionally degrade first from the ether bonding at enough high moment temperature. For X-1P,owing to its special molecule structure,not only has a good chemical stability but also shows stronger nucleophilic trend. When alumina contacts with the compounds of X-1P and PFPE,X-1P can be absorbed on the alumina surface prior to PFPE and keeps PFPE out of contact with alumina,and as such to protect PFPE out of degradation.     

完全二阶抽象柯西问题的温和C-存在族和解空间

本文中,我们定义了完全二阶抽象柯西问题的温和C-存在族.对指数有界的温和C-存在族,我们还给出了温和C-存在族的Hille-Yosida型的充要条件.对不完全二阶抽象柯西问题,我们定义了解空间和Hille-Yosida空间,我们还证明了不完全二阶抽象柯西问题在其Hille-Yosida空间上是自动适定的,把deLaubenfels文中关于一阶抽象柯西问题的相应结果推广到了二阶的情形.     

无$K_{1,4}$子图的图的路覆盖

For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of G. In this paper, we prove that if G is a K_(1,4)-free graph of order n and σ_(k+1)(G) ≥ n-k, then p(G) ≤ k, where σ_(k+1)(G) = min{∑v∈S d(v) : S is an independent set of G with |S| = k + 1}.     

HOLOMORPHIC INTERGATED MILD C-EXISTENCE FAMILIES

0IntroductionIn[1],deLaubenfelsdefilledexpollelltiitllyboullded11olonlorphicC-existeuccfalllilies,holomorpllicC-senhgroupsand11olonlorpllicilltegratedselnigroups.Healsodiscussedtheirrelationships,alldgavesomeHille-YOsidatypecollditiollsforalloperatortogenerateallyofthesefamiliesofoperatorsin[1].ZllengalldLetdefinedexpollelltiallyboulldedllololllorphiconceilltegratedC-semigroups,andpreselltedageueratiolltlleorelllill[2J.Moregelleral71-tilllesintegratedmildC-existencefamilieswereintroducedby…     

Hamiltonian Connectedness in Claw-Free Graphs

If every vertex cut of a graph G contains a locally 2-connected vertex, then G is quasilocally 2-connected. In this paper, we prove that every connected quasilocally 2-connected claw-free graph is Hamilton-connected.     

CeO_2:Eu~(3+)纳米晶的水热合成和光学性能

以硝酸铈(Ce(NO3)3·6H2O)、硝酸铕(Eu(NO3)3·6H2O)、氨水(NH3·H2O)为原料和十六烷基三甲基溴化铵(CTAB)为分散剂,采用水热法制备了CeO2:Eu3+纳米晶,用X射线衍射(XRD)、X射线光电子能谱分析(XPS)、透射电镜(TEM)、傅立叶红外(FT-IR)、拉曼光谱和荧光(FL)等手段对产品的结构和光学性能进行分析和表征。测试结果表明:CeO2:Eu3+是立方萤石结构的纳米晶体,铕以Eu3+形式进入CeO2晶格中致使其晶胞参数略增,晶粒尺寸减小。相比纯CeO2,CeO2:Eu3+的紫外-可见光吸收边发生些许红移,其中CeO2:Eu3+(9.0%)纳米晶的能带隙为2.84 e V。CeO2:Eu3+纳米晶在593,612和632 nm处发橙红光,其中非直接激发(356 nm)的CeO2:Eu3+(1.0%)的磁偶极跃迁(5D0→7F1)占主导,而直接激发(468 nm)的CeO2:Eu3+(5.0%)的电偶极跃迁(5D0→7F2)强度更大,两者均随焙烧温度升高而增强。