NCD系统的数学理论

无索赔折扣系统(No Claim Discount system,简记为NCD系统)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.本文尝试建立了NCD系统严谨的数学理论, 重点讨论了NCD系统的数学建模和稳态分析.此外,作为本文必要的数学前提,首先在第2节着重探讨了随机矩阵间的随机优序关系,并将所得结论运用至齐次不可约且遍历的马尔科夫链的研究中,这些内容也有其独立的数学上的兴趣.     

Dendrimers as scaffolds for multifunctional reversible addition–fragmentation chain transfer agents: Syntheses and polymerization

The synthesis and characterization of novel first‐ and second‐generation true dendritic reversible addition–fragmentation chain transfer (RAFT) agents carrying 6 or 12 pendant 3‐benzylsulfanylthiocarbonylsulfanylpropionic acid RAFT end groups with Z‐group architecture based on 1,1,1‐hydroxyphenyl ethane and trimethylolpropane cores are described in detail. The multifunctional dendritic RAFT agents have been used to prepare star polymers of poly(butyl acrylate) (PBA) and polystyrene (PS) of narrow polydispersities (1.4 < polydispersity index < 1.1 for PBA and 1.5 < polydispersity index < 1.3 for PS) via bulk free‐radical polymerization at 60 °C. The novel dendrimer‐based multifunctional RAFT agents effect an efficient living polymerization process, as evidenced by the linear evolution of the number‐average molecular weight (M_n) with the monomer–polymer conversion, yielding star polymers with molecular weights of up to M_n = 160,000 g mol^?1 for PBA (based on a linear PBA calibration) and up to M_n = 70,000 g mol^?1 for PS (based on a linear PS calibration). A structural change in the chemical nature of the dendritic core (i.e., 1,1,1‐hydroxyphenyl ethane vs trimethylolpropane) has no influence on the observed molecular weight distributions. The star‐shaped structure of the generated polymers has been confirmed through the cleavage of the pendant arms off the core of the star‐shaped polymeric materials. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5877–5890, 2004     

Synthesis and characterization of well‐defined diblock and triblock copolymers of poly(N‐isopropylacrylamide) and poly(ethylene oxide)

Well‐defined diblock and triblock copolymers composed of poly(N‐isopropylacrylamide) (PNIPAM) and poly(ethylene oxide) (PEO) were successfully synthesized through the reversible addition–fragmentation chain transfer polymerization of N‐isopropylacrylamide (NIPAM) with PEO capped with one or two dithiobenzoyl groups as a macrotransfer agent. ¹H NMR, Fourier transform infrared, and gel permeation chromatography instruments were used to characterize the block copolymers obtained. The results showed that the diblock and triblock copolymers had well‐defined structures and narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight < 1.2), and the molecular weight of the PNIPAM block in the diblock and triblock copolymers could be controlled by the initial molar ratio of NIPAM to dithiobenzoate‐terminated PEO and the NIPAM conversion. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4873–4881, 2004     

Permeability of N2, Ar,He, O2, and CO2 through as‐extruded amorphous and biaxially oriented polyester films: Dependence on chain mobility

For as‐extruded amorphous and biaxially orientated polyester films based on poly(ethylene terephthalate), poly(ethylene naphthalate), and copolymers containing poly(ethylene terephthalate) and poly(ethylene naphthalate) moieties, permeability, diffusion, and solubility coefficients are interpreted in terms of chain mobility. The influence of polymer morphology is determined by comparison of the data for as‐extruded amorphous sheets and materials produced with different biaxial draw ratios. The crystallinities of the samples were assessed using differential scanning calorimetry and density measurements. Changes in mobility at a molecular level were investigated using dielectric spectroscopy and dynamic mechanical thermal analysis. The study, in conjunction with our earlier work, leads to the conclusion that the key to understanding differences in gas transport is the difference in local chain motions rather than in free volume. This was illustrated by the permeability results for He, Ar, N₂, and O₂ in the range of polyesters. However, the permeability of CO₂ was found to require alternative explanations because of polymer–penetrant interactions. For biaxially oriented samples, the differences in diffusivity are not only due to differences in local chain motions, but also additional constraints resulting from the increased crystallinity and chain rigidity—which also act to hinder segmental mobility. The effectiveness of the reduction in permeability in the biaxially oriented films is consequently determined by the ability of the polymer chains to effectively align and form crystalline structures. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2916–2929, 2004     

Addition–fragmentation chain transfer: Molecular weight distributions and retardation in the system methyl methacrylate/methyl α‐(bromomethyl)acrylate

A detailed investigation of addition–fragmentation chain transfer (AFCT) in the free‐radical polymerization of methyl methacrylate (MMA) in the presence of methyl α‐(bromomethyl)acrylate (MBMA) was carried out to elucidate mechanistic details with efficient macromonomer synthesis as an underlying goal. Advanced modeling techniques were used in connection with the experimental work. Curve fitting of simulated and experimental molecular weight distributions with respect to the rate coefficient for addition of propagating radicals to MBMA (k_add) over 60–120 °C resulted in E_add = 21.7 kJ mol^?1 and A_add = 2.18 × 10⁶ M^?1 s^?1 and a very weak temperature dependence of the chain‐transfer constant (E_add ≈ E_p). The rate coefficient for fragmentation of adduct radicals at 60 °C was estimated as k_f ≈ 39 s^?1 on the basis of experimental data of the MMA conversion and the concentration of 2‐carbomethoxy‐2‐propenyl end groups. The approach developed is generic and can be applied to any AFCT system in which copolymerization does not occur and in which the resulting unsaturated end groups do not undergo further reactions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2640–2650, 2004     

THE CLASSIFICATION AND PERIOD OF STATES FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a “class property” ,i.e. two states x and y belong to same class implies the period of x is equal to the period of y.     

一个强极限定理

设是可列非齐次马氏链，本文通过利用［１］中提出的在Ｗｉｅｎｅｒ概率空间的一种实现，而给出了一个对任意可列非齐次马氏链普遍成立的强极限定理。     

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．