Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

Using the new in–in method for the synthesis of polyisoprene/polystyrene heteroarm star polymers

The basis of the two‐step in–in method is as follows: star polymers with poly(divinyl benzene) cores, synthesized by the arm‐first method, include many unreacted double bonds in their core, and these double bonds can be attacked by the carbanions of some monomers such as styrene and dienes. In this work, linear polyisoprene chains were used to attack the double bonds existing in the poly(divinyl benzene) cores of polystyrene star polymers, so that a heteroarm star polymer with polystyrene and polyisoprene arms was synthesized. It was later well characterized with size exclusion chromatography, light scattering, viscometry, UV spectroscopy, dynamic mechanical thermal analysis, and ¹H NMR. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 135–142, 2003     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

Synthesis and characterization of poly(higher‐α‐olefin)s with a nickel(α‐diimine)/methylaluminoxane catalyst system: Effect of chain running on the polymer properties

Homopolymerization of octadecene‐1 at different reaction conditions has been studied. Significant chain running can be seen at higher polymerization temperatures. Interestingly, insertion of octadecene‐1 into a sterically hindered nickel‐cation/carbon (secondary) bond is observed. The microstructure of the polymer was established using NMR spectroscopy. The effects of chain running on polymer melting, crystallization behavior, and dynamic mechanical thermal properties were studied using DSC and DMTA. The extent of chain running (i.e., 2,ω‐, 1,ω‐enchainments) decreases with an increase in the carbon number of α‐olefins. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 191–210, 2007     

应用马尔科夫状态转移链的作战航空综合体效能评估

文章阐述了作战航空综合体的相关概念及组成,应用马尔科夫状态转移链建立了作战航空综合体完成典型作战任务时的数学模型,确定了作战效能的评估指标,最后通过具体算例检验了模型的正确性和可行性.     

马尔可夫域变模型在我国季度GDP增长率序列建模中的应用

本文建立了我国季度GDP同比增长率序列的马尔可夫域变模型,通过与线性AR(X)、LSTAR和ARCH等模型的比较,结果表明它更好地刻画了研究对象的均值、波动性和动态结构存在域变行为的非线性特征.     

Facile syntheses of surface-functionalized micelles and shell cross-linked nanoparticles

Block copolymer micelles and shell cross-linked nanoparticles (SCKs) presenting Click-reactive functional groups on their surfaces were prepared using two separate synthetic strategies, each employing functionalized initiators for the controlled radical polymerization of acrylate and styrenic monomers to afford amphiphilic block copolymers bearing an alkynyl or azido group at the α-terminus. The first route for the synthesis of the azide-functionalized nanostructures was achieved via sequential nitroxide-mediated radical polymerization (NMP) of tert-butyl acrylate and styrene, originating from a benzylic chloride-functionalized initiator, followed by deprotection of the acrylic acids, supramolecular assembly of the block copolymer in water and conversion of the benzylic chloride to a benzylic azide. In contrast, the second strategy utilized an alkynyl-functionalized reversible addition fragmentation transfer (RAFT) agent directly for the RAFT-based sequential polymerization of tetrahydropyran acrylate and styrene, followed by selective cleavage of the tetrahydropyran esters to give the α-alkynyl-functionalized block copolymers. These Click-functionalized polymers, with the functionality located at the hydrophilic polymer termini, were then self-assembled using a mixed-micelle methodology to afford surface-functionalized “Clickable” micelles in aqueous solutions. The optimum degree of incorporation of the Click-functionalized polymers was investigated and determined to be ca. 25%, which allowed for the synthesis of well-defined surface-functionalized nanoparticles after cross-linking selectively throughout the shell layer using established amidation chemistry. Functionalization of the chain ends was shown to be an efficient process under standard Click conditions and the resulting functional groups revealed a more “solution-like” environment when compared to the functional group randomly inserted into the hydrophilic shell layer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5203–5217, 2006     

Single electron transfer–degenerative chain transfer living radical polymerization of N‐butyl acrylate catalyzed by Na2S2O4 in water media

Living radical polymerization of n‐butyl acrylate was achieved by single electron transfer/degenerative‐chain transfer mediated living radical polymerization in water catalyzed by sodium dithionate. The plots of number–average molecular weight versus conversion and ln[M]₀/[M] versus time are linear, indicating a controlled polymerization. This methodology leads to the preparation of α,ω‐di(iodo) poly (butyl acrylate) (α,ω‐di(iodo)PBA) macroinitiators. The influence of polymerization degree ([monomer]/[initiator]), amount of catalyst, concentration of suspending agents and temperature were studied. The molecular weight distributions were determined using a combination of three detectors (TriSEC): right‐angle light scattering (RALLS), a differential viscometer (DV), and refractive index (RI). The methodology studied in this work represents a possible route to prepare well‐tailored macromolecules made of butyl acrylate in an environmental friendly reaction medium. Moreover, such materials can be subsequently functionalized leading to the formation of different block copolymers of composition ABA. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2809–2825, 2006