A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

球磨-溶剂热诱导法合成WS2纳米棒及其摩擦性能

采用行星式高能球磨机，将WS₂与S粉末混合球磨，得到纳米片状结构的前驱体，然后添加分散剂聚乙二醇(PEG)用溶剂热诱导的方法使纳米片状前驱体发生结构转变，制备了棒状结构的WS₂纳米材料。用XRD、SEM、TEM等方法对WS₂纳米棒进行了形貌和结构表征，并对其作为润滑油添加剂的摩擦性能进行了初步的研究。     

Influence of branch length asymmetry on the electrophoretic mobility of rigid rod-like DNA

The electrophoretic mobility of three-arm asymmetric star DNA molecules, produced by incorporating a short DNA branch at the midpoint of rigid-rod linear DNA fragments, is investigated in polyacrylamide gels. We determine how long the added branch must be to separate asymmetric star DNA from linear DNA with the same total molecular weight. This work focuses on two different geometric progressions of small DNA molecules. First, branches of increasing length were introduced at the center of a linear DNA fragment of constant length. At a given gel concentration, we find that relatively small branch lengths are enough to cause a detectable reduction in electrophoretic mobility. The second geometric progression starts with a small branch on a linear DNA fragment. As the length of this branch is increased, the DNA backbone length is decreased such that the total molar mass of the molecule remains constant. The branch length was then increased until the asymmetric branched molecule becomes a symmetric three-arm star polymer, allowing the effect of molecular topology on mobility to be studied independent of size effects. DNA molecules with very short branches have a mobility smaller than linear DNA of identical molar mass. The reason for this change in mobility when branching is introduced is not known, however, we explore two possible explanations in this article. (i) The branched DNA could have a greater interaction with the gel than linear DNA, causing it to move slower; (ii) the linear DNA could have modes of motion or access to pores that are unavailable to the branched DNA.     

Mg／Mgl．8La0．2Ni纳米复合材料的吸放氢性能研究

应用高能球磨法制备Mg-x％Mg1.8La0.2Ni（x=10、20和30）纳米复合储氢材料．X射线衍射（XRD）、透射电镜（TEM）和选区电子衍射（SAED）测试表明，该复合材料具有纳米晶和非晶态混合结构的性质，吸氢温度降低，较好的吸放氢动力学性能，在423K，2．5MPa氢压的条件下，50s内即可达到最大吸氢量．     

锂离子电池高比容量FeSn2-C复合负极材料的合成与性能

Sn基合金负极材料具有高达990 mAh·g^-1的理论比容量,但其也存在因脱嵌锂过程发生巨大的体积变化而导致循环性能较差的问题. 本文以Sn、Fe、石墨为原料利用简易的高能球磨法成功制备了具有核壳结构的FeSn₂-C复合物,系统研究了球磨时间、FeSn₂相含量对材料物相结构及电化学性能的影响,并分析了电极的失效机理. 研究表明,球磨时间的增加有利于FeSn₂金属间化合物相的形成及材料颗粒的细化,进而有利于材料比容量的增加及循环性能的提升;FeSn₂相含量的增加能够提高FeSn₂-C材料的比容量,但会降低FeSn₂-C电极的循环稳定性. 经工艺优化及组分调节,球磨24 h合成的Sn₂₀Fe₁₀C₇₀材料具有最优的电化学性能,材料的比容量在540 mAh·g^-1左右,并能稳定循环100次,是一种非常有发展前途的锂离子电池高比容量负极材料.     

Topological effect on MO energies,IV. The total π-electron energy ofS- andT-isomers

A novel general property of theS- andT-isomers (a concept which has been introduced and elaborated elsewhere^{1, 2}) of alternant hydrocarbons is demonstrated, namely that due to the HMO total -electron energy theS-isomer should always be more stable than theT-isomer. Some other classes of conjugated isomers are also constructed, for which similar inequalities are derived.

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Topologischer Effekt bei MO-Energien, 4. Mitt.: Die -Elektronen-Gesamtenergie vonS- undT-Isomeren

Zusammenfassung Es wird allgemein gezeigt, daß bei einemS-T-Isomerenpaar (beschrieben in^{1, 2}) eines alternierenden Kohlenwasserstoffes infolge der HMO -Elektronen-Gesamtenergie dasS-Isomere stets stabiler sein sollte als dasT-Isomere. Weitere Klassen konjugierter Isomere werden konstruiert und ähnliche Ungleichungen angegeben.

     

The topology of energy hypersurfaces III. The fundamental group of reaction mechanisms on potential energy hypersurfaces

The family of all possible reaction mechanisms on a potential surface has an algebraic structure with potential applications in quantum chemical molecular design and synthesis planning.Transformation properties and equivalence relations of reaction paths on potential energy hypersurfaces lead to a topological definition of reaction mechanisms. The family of all fundamental reaction mechanisms on the hypersurface has a group structure,the fundamental group of an appropriately defined topological space. Isomorphism and homomorphism relations between fundamental groups of reaction mechanisms are used to characterize the chemically important topological properties of various subsets of a hypersurface, or those of different excited state hypersurfaces.     

Topological Space of the Chemical Elements and its Properties

We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table     

Use of blowing catalysts for integral skin polyurethane applications in a controlled molecular architectural environment: Synthesis and impact on ultimate physical properties

Polyurethane elastomers of a controlled molecular architecture were synthesized using a two‐step polymerization technique. The building blocks of the elastomeric materials included urea–urethane prepolymers end‐capped with diisocyanate groups and had an exact number of urea groups at both ends. Two‐dimensional bifurcated hydrogen‐bonding networks incorporating the urea groups were, with differential scanning calorimetric and dynamic mechanical thermal analyzer techniques, responsible for the increase in the glass‐transition temperature (T_g) of the hard block and sharp interface morphology between the pure “hard” domains and pure “soft” domains. The higher extent of the phase separation between the two phases contributed to higher elastic moduli for the hard blocks and higher tensile strength for the elastomeric samples. Higher elongation values were attributed to the liberation of the elastomeric chain ends that otherwise would have been constrained in the interface region. The higher T_g values of the hard blocks corresponded to an increase in the hardness values and a decrease in the tear‐strength values. The increase in the amount of urea groups within the hard segments, as a result of the increased amount of water and blowing catalyst, resulted in elastomeric foams with higher open‐cell content. This resulted in lower resilience values as measured using the pendulum rebound test and was attributed to the ability of the open cells to absorb and dissipate energy. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2526–2536, 2002     

Simulations of the active transport of a neutral solute based on a kinase-channel-phosphatase topology

Simulations of coupled interactions involving two opposite enzymatic reactions, solute diffusions, and electrostatic interactions between membrane charges and charged solutes were conducted under a fixed kinase-channel-phosphatase (KCP) topology oriented from the outside to the inside of a porous membrane structure. Depending on the kinase and phosphatase locations, we recently demonstrated that an active transport of a phosphorylated substrate may occur via the opposite topology, that is, a PCK topology. The present analysis demonstrates that, under a KCP membrane topology, which also behaves as a specific ATP-dependent transporter, the active transport of a neutral substrate may occur. This analogous active transport appears to be dependent on the phosphatase location and on the membrane surface potentials. A broad analysis of the role played by the main parameters taken into account in the model was conducted in order to define precisely the physico-chemical conditions and the membrane topology needed for the highest active transports within the shortest time.