Several statistical physics models on random planar hexagonal lattice

从20世纪40年代起，在统计物理大量粒子系统的研究中就出现了组合学方法的踪影，2006年Fields奖获得者Okounkov的获奖成果之一就与这方面的工作密切相关.石墨烯(grapheme)即为``单层石墨片"，是构成石墨的基本结构单元.石墨烯是真正意义上的二维晶体结构，它具有可与碳纳米管相媲美或更优异的特性，``二维空间材料石墨烯方面的开创性实验"使得AndreGeim和KonstantinNovoselov成为2010年诺贝尔物理学奖的获得者.石墨烯的数学模型为六角系统(源于苯类碳氢化合物的分子图)，它是不具有割点的有限连通平面图，其每一个内面的边界是边长为1的正六边形.六角系统是理论化学...Since the 1940's, combinatorial methods has appeared in the study of systems of large number of particles in statistical physics. One of the achievements of 2006 Fields medal winner Okounkov is closely related to this topic. Graphene, i.e, monolayer graphite piece, constitute the basic structure unit of graphite. Graphene is a two-dimensional crystal structure in the real world which is an allot...学位：理学博士院系专业：数学科学学院_应用数学学号：1902011015399

On the Minimum Roots of the Adjoint Polynomials of Unicyclic Graphs

引入伴随多项式是为了从补图的角度研究色多形式,图的伴随多项式的极小根可用于判定色等价图.β(g)表示图g的伴随多项式的极小根.n表示n个顶点的单圈图的集合.分别确定了具有MAX{β(g)|g∈Ωn}和MIn{β(g)|g∈Ωn}的所有单圈图.The adjoint polynomial was introduced for solving the chromaticity problem of the complements of graphs.The minimum roots of the adjoint polynomials of graphs can be applied to sort out graphs that are not chromatically equivalent.Let β(G) be the minimum root of the adjoint polynomial of the graph G.Denote by n the set of all unicyclic graphs on n vertices.All graphs with max{β(G)|G ∈Ωn}(resp.min{β(G)|G ∈Ωn}) are determined.supportedbyNSFC(11061027;11161037); theNaturalScienceFoundationofQinghaiProvince(2011-Z-907;2011-Z-911

Dimer coverings on random multiple chains of planar honeycomb lattices

We study dimer coverings on random multiple chains. A multiple chain is a planar honeycomb lattice constructed by successively fusing copies of a 'straight' condensed hexagonal chain at the bottom of the previous one in two possible ways. A random multiple chain is then generated by admitting the Bernoulli distribution on the two types of fusing, which describes a zeroth-order Markov process. We determine the expectation of the number of the pure dimer coverings (perfect matchings) over the ensemble of random multiple chains by the transfer matrix approach. Our result shows that, with only two exceptions, the average of the logarithm of this expectation (i.e., the annealed entropy per dimer) is asymptotically nonzero when the fusing process goes to infinity and the length of the hexagonal chain is fixed, though it is zero when the fusing process and the length of the hexagonal chain go to infinity simultaneously. Some numerical results are provided to support our conclusion, from which we can see that the asymptotic behavior fits well to the theoretical results. We also apply the transfer matrix approach to the quenched entropy and reveal that the quenched entropy of random multiple chains has a close connection with the well-known Lyapunov exponent of random matrices. Using the theory of Lyapunov exponents we show that, for some random multiple chains, the quenched entropy per dimer is strictly smaller than the annealed one when the fusing process goes to infinity. Finally, we determine the expectation of the free energy per dimer over the ensemble of the random multiple chains in which the three types of dimers in different orientations are distinguished, and specify a series of non-random multiple chains whose free energy per dimer is asymptotically equal to this expectation.NSFC [10831001, 11061027

厦门市海沧区成年人高血压与糖尿病流行现状及其影响因素

目的 分析海沧区成年人高血压与糖尿病流行现状及其影响因素,为做好慢性病健康管理提供依据。方法采取多阶段整群随机抽样方法抽取2015年3—6月海沧区4个镇(街)13个村(居)共3 079名18岁以上居民作为调查对象,进行一般情况调查、身体测量、实验室检测及比较高血压、糖尿病患病率。结果 18岁及以上居民高血压总体患病率为18.35%,男性患病率为18.86%,女性患病率为18.10%,差异无统计学意义(χ~2=0.26,P>0.05);糖尿病总体患病率为11.01%,男性患病率为8.94%,女性患病率为12.03%,差异有统计学意义(χ~2=6.66,P<0.05)。对高血压和糖尿病的影响因素进行logistic回归分析,年龄(OR=1.58,95%CI:1.47~1.70)、吃薯类食物(OR=1.00,95%CI:1.00~1.01)为高血压的危险因素,吃牛羊肉(OR=0.99,95%CI:0.99~1.00)、水果(OR=0.99,95%CI:0.99~1.00)、奶类(OR=0.99,95%CI:0.99~1.00)、果汁(OR=0.99,95%CI:0.99~1.00)为高血压的保护因素;年龄(OR=1.76,95%CI:1.59~1.95)、性别(OR=1.50,95%CI:1.26~1.79)均为糖尿病的危险因素。结论 海沧区18岁及以上成年人高血压患病率相对较低,但是海沧区18岁及以上成年人糖尿病患病率较高,防治形势则较为严峻,应加大对糖尿病防治的力度,多做有针对性的健康宣教

冬凌草甲素作用PI3K/AKT通路诱导HeLa细胞凋亡

【目的】研究冬凌草甲素诱导HeLa细胞凋亡的作用及其机制。【方法】MTT法测定冬凌草甲素对HeLa细胞的生长抑制实验,Hoechst 33342荧光染色等观察细胞核形态学变化;LDH法研究细胞死亡的途径。流式细胞仪检测细胞的凋亡,免疫印迹实验检测相关蛋白的表达。【结果】25μmol/L以上的冬凌草甲素对宫颈癌HeLa细胞具有明显的生长抑制作用,并能诱导细胞发生凋亡,随着药物浓度的增加和作用时间的延长,细胞的生长抑制率及细胞凋亡率均明显升高,冬凌草甲素抑制细胞生长及诱导细胞发生凋亡的过程中,细胞端粒酶Akt、FKHRL、GSK3表达水平及活性显著降低。【结论】冬凌草甲素能够通过诱导人子宫颈癌HeLa细胞发生凋亡而发挥抑制HeLa细胞生长作用,抑制Akt和GSK3的活性是冬凌草甲素体外诱导人子宫颈癌HeLa细胞发生凋亡的重要作用机制之一

光分组交换网的TCP性能研究

与传统光网络相比,光分组交换（OPS）网络具有高速、大吞吐量、低时延和能高效地承载IP业务等突出优点。而作为支撑下一代Internet发展的最有希望的骨干光网络,OPS网与传输控制协议/互联网协议（TCP/IP）的兼容性和支持度是一个值得深入研究的课题。文章以光突发交换（OBS）网为模型,对OPS网络中的TCP传输性能进行了研究