disjoint cycles containing specified independent vertices

Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ₂(G)n+k-1. Let v₁,…,v_k be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C₁,…,C_k with v_iV(C_i) for all 1ik.Then G has k vertex-disjoint cycles such that

(i) for all 1ik.

(ii) , and

(iii) At least k-1 of the k cycles are triangles.

The condition of degree sum σ₂(G)n+k-1 is sharp.

Degree of branching of the hyperbranched polymers resulted from ab<Subscript>2</Subscript> polycondensation with substitution effect

The analytical expressions of the various structural units and the average degree of branching for the hyperbranched polymers resulted from AB₂ polycondensation with substitution effect were derived by the kinetic mechanism.The reactivity difference between the B group in linear unit and that in terminal group has great effect on the molecular parameters of the products obtained.The concentration of terminal units has a maximum with the increase of the conversion of A groups（x）.The higher the reactivity ratio（r） of linear B group to branched one is,the later the maximum appears and the larger it is.The degree of branching of the hyperbranched polymers obtained is controllable by adjusting the parameters of r and x,which increases with increasing both x and r.     

Relation between the permeability and the degree of coil overlap of polymer in the bulk state

Based on the expression of the index of coil interpenetration (i.e.,the degree of coil overlap,ξ_b) of amorphous polymers in the bulk state proposed by Qian,theξ_b was rewritten asξ_b=ρ_b[η]_θ/1.66 via Flory's intrinsic viscosity equation at them conditions.Theξ_b ofpoly (vinyl chloride) (PVC) dense membranes with different molecular weights and cellulose diacetate (CA) dense membranes prepared using different solvents were determined.The permeability,permeation coefficient (P) of nitrogen and permeation flux (J) of liquid through both membranes,respectively,was measured.P and J decreased exponentially with increasingξ_b for PVC and CA membranes were revealed.     

分子的模糊对称性

将模糊数学方法引入对分子对称点群的研究,建立描述具有不完整分子对称性的模糊点对称群(集合).建立具有模糊对称性分子轨道的模糊表示及其模糊特征标(模糊广义宇称).通过对典型的线状分子、平面分子以及非平面的立体分子等进行分析,展示了一个新的理论化学园地.初步探讨了具有模糊对称性的动态反应体系.从模糊对称性出发,探讨了分子轨道对称守恒原理的半定量特征.     

扑热息痛片剂药品的近红外光谱法非破坏定量分析

现代近红外光谱分析技术将近红外光谱 (NIR)法同计算机科学和化学计量学结合 ,实现了对样品进行无损非破坏性定量分析 .该法具有速度快、操作简单及所需样品少等特点 ,能够实现样品分析的时间同步、地点同步及无损非破坏分析 .为实现生产过程中即时、在线的质量控制提供了新的手段[1 ] .本文应用人工神经网络 [2 ]与近红外漫反射光谱相结合对扑热息痛片剂药品进行了非破坏快速定量分析 .用扑热息痛片剂药品的近红外漫反射光谱数据、一阶导数光谱数据及二阶导数光谱数据分别建立了 ANN模型 ,预测未知样品 ,讨论了影响网络的因素 ,使用了新…     

综合国力的数学建模

本文考虑社会文明与社会导恶现象的制约机制，建立一个综合国力的非线性数学模型，从数学上讨论了相应的二次微分系统的Ｈｏｐｆ分叉，中心与细焦点的判定，极限环的存在唯一性等问题，并对数学结论予以合理解释，把社会相平面划成社发展区域，社会动荡区域和社会崩溃区域，研讨社会走向，确定纳入社会发展区域的途径。     

About membership functions estimation

A logical approach to fuzzy sets method originated by Giles is developed. The infinitely many-valued logic t_ω is taken as basic. We accept, it is correct to use the strong conjunction by the logical analysis of the summation of fuzzy items. Under some broad conditions it is proved. that the sum of many fuzzy variables is a variable whose membership function is approximately equal to $\text{?(x) =}\text{max}\text{{1 ?}\text{1}\text{2}\text{c(x ? α)}{}^2\text{, 0}}$, where a and c are some constant parameters. A method of estimation of the unknown parameters is developed in a general case. The proposed fuzzy method coincides with the method of maximum likelihood if used in problems of classical mathematical statistics.     

Density of the Medvedev lattice of Π<Superscript>0</Superscript><Subscript>1</Subscript> classes

The partial ordering of Medvedev reducibility restricted to the family of ⁰₁ classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a ⁰₁ class, which we call a ``c.e. separating class'. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes. Mathematics Subject Classification (2000): 03D30, 03D25     

Polybenzimidazole dendrimer containing triazine rings-based high-temperature proton exchange membranes with high performances over a wide humidity range

A high-temperature proton exchange membrane with high proton conductivity over a wide humidity range still remains a challenge. PBI dendrimer containing triazine rings (TPBI) was synthesized to approach this aim considering its high content of hygroscopic terminal groups and of larger free volume. A novel proton conductor previously synthesized (zirconium 3-sulfopropyl phosphonate, ZrSP) was doped due to its good proton conductivity over a wide humidity range. TPBI was post-crosslinked with a tetrafunctional epoxy resin (N,N,N′,N′-tetraglycidyl-4,4′-diaminodiphenylmethane, TGDDM) to enhance the mechanical stability at low cross-linking degrees, which allowed high doping levels of ZrSP, and thus, high conductivity. The prepared membranes (TPBI-TGDDM/ZrSP) showed good thermal stability, high proton conductivity over wide humidity range, and good dimensional stability. At suitable degrees of branching, TPBI-TGDDM/ZrSP exhibited superior mechanical property, oxidative stability, methanol barrier property, and membrane selectivity than its linear analog (mPBI-TGDDM/ZrSP). As ZrSP instead of PA was applied as the proton conductor, TPBI-TGDDM/ZrSP showed good durability of proton conductivity, especially in comparison with TPBI-TGDDM/PA, which highly retarded decline in conductivity caused by PA leaking. The proton conductivity at 180 °C of TPBI(20)-TGDDM(10)/ZrSP(50) achieved 142, 84.2 and 23.6 mS cm^?1 at 100%, 50%, and 0 RH, respectively.     

叶片多角度偏振光谱特性影响因素的实验研究

通过测量绿萝、银杏、苹果三种叶片的多角度偏振光谱,采用斯托克斯矢量法计算了叶片的多角度光谱偏振度,并通过PROSPECT模型反演得到叶片的叶绿素、水分含量,进而分析了叶绿素、水分含量对叶片多角度光谱偏振度的影响,探索了观测几何条件与不同波段叶片偏振度间的关系。结果表明,相对于近红外波段,红光波段的偏振度受叶绿素含量变化的影响较小,而水分含量对这两个波段的偏振度基本均无明显影响。在反映叶片偏振度随观测几何变化方面,近红外波段较另外两个波段有着更好的敏感性和稳定性,但其偏振度值较另外两个波段偏小。