Stochastic systems with memory and jumps

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate $L^p$-type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation.     

Groups which do not admit ghosts

A ghost in the stable module category of a group is a map between representations of that is invisible to Tate cohomology. We show that the only non-trivial finite -groups whose stable module categories have no non-trivial ghosts are the cyclic groups and . We compare this to the situation in the derived category of a commutative ring. We also determine for which groups the second power of the Jacobson radical of is stably isomorphic to a suspension of .

     

Optimal replacement and allocation of multi‐state elements in k‐within‐m‐from‐r/n sliding window systems

This paper proposes a new model that generalizes the linear sliding window system to the case of multiple failures. The considered k ‐within‐ m ‐from‐ r / n sliding window system consists of n linearly ordered multi‐state elements and fails if at least k groups out of m consecutive groups of r consecutive multi‐state elements have cumulative performance lower than the demand W . A reliability evaluation algorithm is suggested for the proposed system. In order to increase the system availability, maintenance actions can be performed, and the elements can be optimally allocated. A joint element allocation and maintenance optimization model is formulated with the objective of minimizing the total maintenance cost subjected to the pre‐specified system availability requirement. Basic procedures of genetic algorithms are adapted to solve the optimization problem. Numerical experiments are presented to illustrate the applications. Copyright © 2015 John Wiley & Sons, Ltd.     

“Living” Free Radical Polymerization in Tubular Reactors. I. Modeling of the Complete Molecular Weight Distribution Using Probability Generating Functions

This is the first of a series of works aiming at developing a tool for designing “living” free radical polymerization processes in tubular reactors, in order to achieve tailor‐made MWDs. A mathematical model of the nitroxide‐mediated controlled free radical polymerization is built and implemented to predict the complete MWD. It is shown that this objective may be achieved accurately and efficiently by means of the probability generating function (pgf) transformation. Comparison with experimental data is good. The potential of the resulting model for optimization activities involving the complete MWD is also shown.

     

Branching and Crosslinking in Coordination Terpolymerizations

A general kinetic method, based upon population balances of generating functions, is applied to the prediction of the microstructure and molecular size of non‐linear terpolymers obtained through the coordination polymerization of two monovinyl monomers and a non‐conjugated diene. A rather complex kinetic scheme involving crosslinking and long‐chain branching is considered. It is shown that even in these conditions it is possible to carry out the prediction of molecular size and mass distributions, sequence size distributions, and z‐average mean‐square radius of gyration of the polymers. The influence of some kinetic parameters on the properties of the products is studied, considering a homogeneous operation in a semi‐batch reactor. The used simulation method is able to predict these properties before and after gelation whenever it occurs.

     

测度熵计算中映射不变分布的应用

构造计算测度熵(MetricEntropy)的马尔可夫划分(MarkovPartition)时,对于非线性映射采取等似然假设,影响精度。提出用计算映射的不变分布来进行改进;对逻辑映射导出映射不变分布的算式及迭代格式,进行了测度熵的计算;计算表明,迭代次数不多时即能得出较好结果。