Theoretical model of crack branching in magnetoelectric thermoelastic materials

Thermomagnetoelectroelastic crack branching of magnetoelectro thermoelastic materials is theoretically investigated based on Stroh formalism and continuous distribution of dislocation approach. The crack face boundary condition is assumed to be fully thermally, electrically and magnetically impermeable. Explicit Green’s functions for the interaction of a crack and a thermomagnetoelectroelastic dislocation (i.e., a thermal dislocation, a mechanical dislocation, an electric dipole and a magnetic dipole located at a same point) are presented. The problem is reduced to two sets of coupled singular integral equations with the thermal dislocation and magnetoelectroelastic dislocation densities along the branched crack line as the unknown variables. As a result, the formulations for the stress, electric displacement and magnetic induction intensity factors and energy release rate at the branched crack tip are expressed in terms of the dislocation density functions and the branch angle. Numerical results are presented to study the effect of applied thermal flux, electric field and magnetic field on the crack propagation path by using the maximum energy release rate criterion.     

Long‐chain‐branched polyethene by the copolymerization of ethene and nonconjugated α,ω‐dienes

Ethene was copolymerized (1) with 1,5‐hexadiene with rac‐ethylenebis(indenyl)zirconium dichloride/methylaluminoxane (MAO) used as a catalyst and (2) with 1,7‐octadiene with bis(n‐butylcyclopentadienyl)zirconium dichloride/MAO and rac‐ethylenebis(indenyl)hafnium dichloride (Et[Ind]₂HfCl₂)/MAO used as catalysts at 80 °C in toluene. The copolymer microstructure and the influence of diene incorporation on the rheological properties were examined. Ethene and 1,5‐hexadiene formed a copolymer in which a major fraction of the 1,5‐hexadiene was incorporated into rings and a small fraction formed 1‐butenyl branches. The copolymerization of ethene with 1,7‐octadiene resulted in a higher selectivity toward branch formation. Some of the branches formed long‐chain‐branching (LCB) structures. The ring formation selectivity increased with decreasing ethene concentration in the polymerization reactor. Melt rheological properties of the diene copolymers resembled those of metallocene‐catalyzed LCB homopolyethenes and depended on the vinyl content, the catalyst, and the polymerization conditions. At high diene contents, all three catalysts produced crosslinked polyethene. This was especially pronounced with Et[Ind]₂HfCl₂, where only 0.2 mol % 1,7‐octadiene in the copolymer was required to achieve significantly modified rheological properties. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3805–3817, 2001     

保费和索赔到达率与余额相依的最优有界分红率问题

研究保费和索赔到达率与余额相依的最优有界分红问题,目标是最大化破产前的累积期望折现分红。首先,给出一个策略是平稳马氏策略的充分必要条件,运用测度值生成元的理论得到测度值动态规划方程（DPE）,并且给出了验证定理的证明。最后,讨论了测度值DPE和相应拟变分不等式（QVI）之间的关系,并且证明了最优分红策略为具有波段结构的平稳马氏策略。     

Fixed points of smoothing transformation in random environment

At each time n\in \mathbb{N},\mathrm{l}\mathrm{e}\mathrm{t}{\overline{Y}}^{(n)}(\xi )=(y_1^{(n)}(\xi ),y_2^{(n)}(\xi ),\cdots ) be a random sequence of non-negative numbers that are ultimately zero in a random environment\xi \text{=}（{\xi }_n{）}_{n\in \mathbb{N}}. The existence and uniqueness of the nonnegative fixed points of the associated smoothing transformation in random environment are considered. These fixed points are solutions to the distributional equation for a.e.\xi ,Z(\xi )\stackrel{\text{d}}{=}{\sum }_{i\in \mathbb{N}+}{y}_i^{(\mathrm{0})}(\xi )Z_i^{(\mathrm{1})}(\xi ),where ｛Z_i^{(\mathrm{1})}:i\in {\mathbb{N}}_{+}｝ are random variables in random environment which satisfy that for any environment\xi; under P_{\xi }; ｛Z_i^{(\mathrm{1})}:i\in {\mathbb{N}}_{+}｝are independent of each other and {\bar{Y}}^{(\mathrm{0})}(\xi ), and have the same conditional distribution P_{\xi }(Z_i^{(1)}(\xi )\in \cdot )=P_{T\xi }(Z(T\xi )\in \cdot ) where T is the shift operator. This extends the classical results of J. D. Biggins [J. Appl. Probab., 1977, 14: 25-37] to the random environment case. As an application, the martingale convergence of the branching random walk in random environment is given as well.     

Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line

In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.     

Computer‐Aided Optimization of Conditions for Fast and Controlled ICAR ATRP of n‐Butyl Acrylate

The potential of initiators for continuous activator regeneration atom transfer radical polymerization (ICAR ATRP) for the synthesis of well‐defined poly(n‐butyl acrylate) is analyzed by means of simulations. The kinetic model accounts for reactivity differences between secondary and tertiary macrospecies and considers the possible influence of diffusional limitations. CuBr₂ is used as transition metal salt and the commercially available N,N,N′,N″,N″‐pentamethyldiethylenetriamine as ligand. For targeted chain lengths (TCLs) up to 1000, the ICAR ATRP can be performed relatively quickly, and with ppm levels of ATRP catalyst. For moderate TCLs, slightly higher ppm levels are required if excellent control over chain length is also desired. In all cases, limited loss of end‐group functionality (EGF) results.

     

集值局部平方可积鞅

介绍集值类（D）过程和集值局部鞅的概念和有关性质，进而讨论了集值局部平方可积鞅的概念和性质。