Photoinitiated curing of mono‐ and bifunctional epoxides by combination of active chain end and activated monomer cationic polymerization methods

Photoinitiated cationic polymerization of mono‐ and bifunctional epoxy monomers, namely cyclohexeneoxide (CHO), 4‐epoxycyclohexylmethyl‐3′,4′‐epoxycyclohexanecarboxylate (EEC), respectively by using sulphonium salts in the presence of hydroxylbutyl vinyl ether (HBVE) was studied. The real‐time FTIR spectroscopic, gel content determination, and thermal characterization studies revealed that both hydroxyl and vinyl ether functionalities of HBVE take part in the polymerization. During the polymerization, HBVE has the ability to react via both active chain end (ACE) and activated monomer mechanisms through its hydroxyl and vinyl ether functionalities, respectively. Thus, more efficient curing was observed with the addition of HBVE into EEC‐containing formulations. It was also demonstrated that HBVE is effective in facilitating the photoinduced crosslinking of monofunctional epoxy monomer, CHO in the absence of a conventional crosslinker. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4914–4920, 2007     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.      

关于任意随机变量序列泛函的强极限定理

本文在k是固定的正整数，{fn}是R^k 1上的Borel可测函数列时，得到了任意随机变量序列{Xrn≥0}的泛函{fn(Xn-k,…,Xn)}的强极限定理，它是Chung的关于独立随机变量序列的强大数律的推广，作为推论，得到了k重非齐次马尔科夫链的一类强极限定理．     

Variational Formulation of the Schrödinger Field

The variational formulation of the Schrödinger field was investigated and the applicability of the chain method was analyzed. Using Batalin-Fradkin-Tyutin formalism a gauge invariant theory was constructed.     

Synthesis of β-phenyl-δ,ε-unsaturated amino acids and stereoselective introduction of side chain groups into [4,3,0]-bicyclic β-turn dipeptides

(2S,3S)- and (2R,3R)-2-amino-3-phenyl-5-hexenoic acids have been synthesized in large scale by using Ni(II)-complexes as a template. The amino acids were used in the synthesis of [4,3,0]-bicyclic β-turn mimetics by a convergent methodology. The unique advantage of this strategy is the convenience of introducing side chain groups with predetermined chiralities on both the five- and six-membered heterocyclic rings.     

Capacity Constrained Transit Assignment with Common Lines

This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be able to board because of the absence of sufficient space. The model also handles the common lines problem, where choice of route depends on frequency of arrivals. The mathematical formulation of the problem is presented together with a numerical example. This revised version was published online in July 2006 with corrections to the Cover Date.     

三量子位Heisenberg XX 链中杂质对纠缠的影响

研究了有杂质时三量子位Heisenberg-XX链中正常格点之间的热纠缠情况，给出了Concurrence的解析表达式.进一步的讨论发现，杂质对正常格点的热纠缠有着重要的影响，甚至能够改变纠缠在反铁磁区的特性.理论表明，可以通过调节温度和杂质参数来控制纠缠. 关键词： Heisenberg -XX链 热纠缠 杂质格点     

Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme

In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of orderk and leads us a new type of geneses of the discrete distributions.     

Fully-angular polyhex chains with minimal total π-electron energy

By Hückel molecular orbital (HMO) theory, the calculation of the total energy of all π-electrons in conjugated hydrocarbons can be reduced to that of E(G)=|λ₁|+|λ₂|+?+|λn|, where λi are the eigenvalues of the corresponding graph G. Denote by Ψn the set of all fully-angular polyhex chains with n hexagons. In this paper, we show that Hn has the minimum total π-electron energy among chains in Ψn, where Hn is the helicene chain.