Markov chains with replacement

The following modification of a general state space discrete-time Markov chain is considered: certain transitions are supposed “forbidden” and the chain evolves until there is such a transition. At this instant the value of the chain is “replaced” according to a given rule, and, starting from the new value, the chain evolves normally until there is a forbidden transition again; the cycle is then repeated. The relationship of this modified process to the original one is studied in general terms, with particular emphasis being given to invariant measures. Examples are given which illustrate the results obtained.     

Application of dye-partition technique to the determination of the rates of initiation in radical polymerization

Summary Dye-partition technique as an useful method of measuring kinetic chain length (v), rate of initiation (R _i ), initiator efficiency (f), and the parameter [=(2k _t)^1/2 k _p] etc. in radical polymerization using styrene and methylmethacrylate as monomers in dimethyl formamide medium and 4,4 azobis-4-cyanopentanoic acid as the initiator to produce dye responsive carboxyl ended polymers has been discussed. The values ofR _p,f and obtained by this method compare fairly well with those obtained by a standard method, viz., molecular weight method. The magnitude off much less than unity and constancy in its value under different concentrations of monomers and initiator indicate that almost all radicals surviving geminate recombination is captured by the monomers. The precautions necessary for applying this method have also been discussed.

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Zusammenfassung Farbstoff-Verteilungstechnik als nützliche Methode zur Messung der kinetischen Kettenlänge (v), Initiationsgeschwindigkeit (R _i ), des Initiator-Wirkungsgrades (f), und des Kennwertes (2k,^1/2 k _p ) (=) etc. bei der radikalischen Polymerisation von Styrol und Methylmethacrylat in Dimethylformamid-Medium mit 4,4'-Azobis-4-cyanopentansäure als Initiator zur Bildung von mit Farbstoffen reagierenden Carboxylatendgruppen in den Polymeren, wurde diskutiert. Die durch obengenannte Methode festgestellten Werte vonR _p ),f und sind ungefähr mit den durch übliche Methoden festgestellten Werten vergleichbar (durch Molekulargewicht-Methode).Die konstante Größenordnung von 'f, die viel weniger als eins beträgt, weist darauf hin, daß alle die paarweise Rekombination überlebenden Radikale von den Monomeren abgefangen werden. Die zur Anwendung dieser Methode nötigen Vorsichtsmaßnahmen sind auch diskutiert worden.

     

Statistical Thermodynamic Properties of Linear Protein Solutions

利用统计力学理论结合格点模型,讨论了链状蛋白质分子溶液的热力学性质. 结果表明,对于稀溶液来说,溶液的吉布斯函数随蛋白质浓度的增加而降低,蛋白质分子化学势随其浓度增加而升高. 还分析了蛋白质分子链长及温度对溶液吉布斯函数和蛋白质分子化学势的影响. 并且计算讨论了几种第一类抗冻蛋白的化学势.     

Analysis and design of electromagnetic band gap structures with stratified and inhomogeneous media

In this study, a generalized and easy to use method based on Hill's equation and chain matrix concept is used to analyze the electromagnetic wave propagation in stratified dielectric and inhomogeneous media with arbitrary profiles.Numerical simulations are performed to compute the reflection and transmission of several Electromagnetic Bandgap (EBG) structures for various permittivity profiles and given polarization as well as incidence angles of driving fields.Multilayer structures are analyzed and optimized to enhance their selectivity performances. Obtained results agree excellently well with other published data.     

Duals of constacyclic codes over finite local Frobenius non-chain rings of length 4

Duals of constacyclic codes over a finite local Frobenius non-chain ring of length 4, the length of which is relatively prime to the characteristic of the residue field of the ring are determined. Generators for the dual code are obtained from those of the original constacyclic code. In some cases self-dual codes are determined.     

基于Markov Chain Monte Carlo模型对医院出院病人调查表数据缺失的填补与分析

目的对医院出院病人调查表普遍存在的数据缺失进行填补与分析,以保证统计调查表的质量,为医院以及上级卫生部门了解现状,进行预策和决策提供技术支持和质量保证。方法运用SAS9.1,采用多重填补方法Markov Chain Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果MCMC填补10次的结果最优。结论(Multiple Imputation)MI方法在解决医院出院病人调查表数据缺失时有优势,发挥空间较大,且填补效率较高。     

Tree maps having chain movable fixed points

In this paper we discuss some basic properties of chain reachable sets and chain equivalent sets of continuous maps. It is proved that if f:T→T is a tree map which has a chain movable fixed point v, and the chain equivalent set CE(v,f) is not contained in the set P(f) of periodic points of f, then there exists a positive integer p not greater than the number of points in the set End([CE(v,f)])−Pv(f) such that fp is turbulent, and the topological entropy . This result generalizes the corresponding results given in Block and Coven (1986) [2], Guo et al. (2003) [6], Sun and Liu (2003) [10], Ye (2000) [11], Zhang and Zeng (2004) [12]. In addition, in this paper we also consider metric spaces which may not be trees but have open subsets U such that the closures are trees. Maps of such metric spaces which have chain movable fixed points are discussed.     

Fractionation and Crystal Morphology of Rigid Polymer,Poly(p‐Phenylene Benzobisthiazole)

Abstract

Fractionation of the rigid polymer, poly(p‐phenylene benzobisthiazole) (PBZT), was carried out in dilute solution in concentrated methane sulfuric acid (MSA) using silica gels as packing material of a column. Several combinations of the average chain length of the fractionating materials and the average pore diameter of the gels were examined to improve fractionation resolution. The gels with average pore diameter near the average chain length resulted in high fractionation resolution. Single crystals of the fractionated and unfractionated PBZTs were observed by transmission electron microscopy (TEM). Both single crystals were fundamentally composed of rod crystals with the chain orienting normal to the rods. The unfractionated PBZT made a cluster of parallel rod crystals, where longer chains penetrated a few rod crystals leaving their chain ends within the crystalline core. On the contrary, with the fractionated polymer, extended‐chain rod‐like crystals were dispersed, isolated from each other. This morphology enables us to estimate the chain length visibly by TEM, for which a few milligrams of the material is enough for the observation.     

A Markov Chain Monte Carlo comparison of variance estimators for the sampling of particulate mixtures

During the sampling of particulate mixtures, samples taken are analyzed for their mass concentration, which generally has non‐zero sample‐to‐sample variance. Bias, variance, and mean squared error (MSE) of a number of variance estimators, derived by Geelhoed, were studied in this article. The Monte Carlo simulation was applied using an observable first‐order Markov Chain with transition probabilities that served as a model for the sample drawing process. Because the bias and variance of a variance estimator could depend on the specific circumstances under which it is applied, Monte Carlo simulation was performed for a wide range of practically relevant scenarios. Using the ‘smallest mean squared error’ as a criterion, an adaptation of an estimator based on a first‐order Taylor linearization of the sample concentration is the best. An estimator based on the Horvitz–Thompson estimator is not practically applicable because of the potentially high MSE for the cases studied. The results indicate that the Poisson estimator leads to a biased estimator for the variance of fundamental sampling error (up to 428% absolute value of relative bias) in case of low levels of grouping and segregation. The uncertainty of the results obtained by the simulations was also addressed and it was found that the results were not significantly affected. The potentials of a recently described other approach are discussed for extending the first‐order Markov Chain described here to account also for higher levels of grouping and segregation. Copyright © 2013 John Wiley & Sons, Ltd.