Structural properties of Markov chains with weak and strong interactions

Markov chains have been frequently used to characterize uncertainty in many real-world problems. Quite often, these Markov chains can be decomposed into a vector consisting of fast and slow components; these components are coupled through weak and strong interactions. The main goal of this work is to study the structural properties of such Markov chains. Under mild conditions, it is proved that the underlying Markov chain can be approximated in the weak topology of L² by an aggregated process. Moreover, the aggregated process is shown to converge in distribution to a Markov chain as the rate of fast transitions tends to infinity. Under an additional Lipschitz condition, error bounds of the approximation sequences are obtained.     

A stochastic model for risk management in global supply chain networks

With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau–Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives.     

Moran's genetics model via electric networks

Using the electric approach, we derive exact and asymptotic closed form formulas for hitting times in symmetric cases of the Moran's genetics model.     

β-环糊精与环氧氯丙烷共聚物的13C-NMR研究

¹³C NMR测定了一个系列的环氧氧丙烷与β-环糊精的共聚物,进行了谱峰归属和DEPT谱验证,实验测得2,3-丙二醇基在β-环糊精C(2)-O-位、C(3)-O-位和C(6)-O-位取代的¹³C NMR化学位移α-取代效应参数,描述了该共聚物分子链的组成和链化学结构特征.     

On the computation of the optimal cost function for discrete time Markov models with partial observations

We consider several applications of two state, finite action, infinite horizon, discrete-time Markov decision processes with partial observations, for two special cases of observation quality, and show that in each of these cases the optimal cost function is piecewise linear. This in turn allows us to obtain either explicit formulas or simplified algorithms to compute the optimal cost function and the associated optimal control policy. Several examples are presented.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-86-0029, in part by the National Science Foundation under Grant ECS-8617860, in part by the Advanced Technology Program of the State of Texas, and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-86-C-0045.     

一般状态空间跳过程不变测度的存在性和唯一性

本文利用一般状态空间马氏链关于不变测度的有关结果和跳过程的性质，研究了一般状态空间跳过程不变测度的存在性和唯一性。     

Thermal Disorder, Fluctuations, Growth and Fragmentation of Finite One-Dimensional Atomic Chains

Ordering in one-dimensional atomic chains is studied using computer simulation. We find that dense ordered chains may exist if the system is cold enough and not macroscopically long. Growth of finite length chains from the vapor and by vapor exchange between chains begins rapidly, then slows down exponentially in time. As temperature rises density fluctuations increase, causing the chains to fragment. Independent of fragmentation, disordering begins at the ends, a condition similar to the precursor of edge and surface melting in two and three dimensions. The chemical potential of finite ordered chains is a function of length and temperature, due to the competition between attraction and internal thermal excitation. Equilibrium of chains coexisting with one-dimensional vapor produces a distribution of sizes, peaked at a temperature dependent chain length. Several results may be relevant to experimental studies of adsorption on carbon nanotubes     

Improving the impact property and heat‐resistance of PLA/PC blends through coupling molecular chains at the interface

The influences of both the molecular structure and the melt viscosity differences between Poly(lactic acid) (PLA) and polycarbonate (PC) on the interpenetration of molecular chains at the interface were investigated by comparing the dynamic mechanical properties and morphologies of the as‐prepared PLA/PC solution‐casting blends with those of their corresponding annealed (180°C, 8 h) samples or PLA/PC melt blends. Additionally, two chain extenders containing epoxy groups (ADR and TGDDM) were used to improve the interfacial strength. Subsequently, the interpenetration of PLA and PC molecular chains at the interface was also surveyed. Finally, the effects of the morphology formed by after adding ADR or TGDDM on the impact property, and heat resistance were discussed. The results showed that there was no interpenetration of molecular chains at the interface in PLA/PC melt blends because of the serious hindrance of the molecular structure and the melt viscosity differences. Although the interfacial strength achieved significant increase after adding ADR or TGDDM, the increase of the interfacial strength should be caused by the connection of ADR or TGDDM molecules with PLA and PC molecules at the interface through chemical bonds rather than the entanglements of PLA and PC molecular chains because of no interpenetration of PLA and PC molecular chains at the interface. Thus, the morphology formed after adding ADR or TGDDM is still the type of complete phase separation, which may be the most suitable morphology for achieving high impact and heat resistance PLA/PC blends because these two properties strongly depend on the crystallinity of PLA phase. Copyright © 2015 John Wiley & Sons, Ltd.     

Partitioning Solvophobic and Dispersion Forces in Alkyl and Perfluoroalkyl Cohesion

Fluorocarbons often have distinct miscibility properties compared to their nonfluorinated analogues. These differences may be attributed to van der Waals dispersion forces or solvophobic effects, but their contributions are notoriously difficult to separate in molecular recognition processes. Here, molecular torsion balances were used to compare cohesive alkyl and perfluoroalkyl interactions in a range of solvents. A simple linear regression enabled the energetic partitioning of solvophobic and van der Waals forces in the self‐association of apolar chains. The contributions of dispersion interactions in apolar cohesion were found to be strongly attenuated in solution compared to the gas phase, but still play a major role in fluorous and organic solvents. In contrast, solvophobic effects were found to be dominant in driving the association of apolar chains in aqueous solution. The results are expected to assist the computational modelling of van der Waals forces in solution.