Comparative behavior of polybutadiene and polynorbornene‐based latices prepared by dispersion ring‐opening metathesis polymerization with a poly(ethylene oxide) macromonomer

This study critically examines the similarities and differences between poly(ethylene oxide) (PEO) stabilized latices of polynorbornene and polybutadiene. Features such as the kinetics of copolymerization of norbornene and cyclooctadiene with a macromonomer of PEO, the particles' size and morphology, the type of copolymer formed, and the stability of these latices were investigated and the results obtained are considered. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2705–2716, 2004     

Thermal behavior of metallodendrimers possessing bis(terpyridinyl)Ru(II) connectivity and different surface functionality

A series of metallodendrimers, assembled by means of bis(terpyridinyl)Ru^(II) connectivity on poly(propylene imine) dendrimer scaffolds, with homogeneous or heterogeneous surfaces, were prepared. Differential scanning calorimetry and thermogravimetric analysis were used to determine their thermal behavior, glass‐transition temperatures, and the decomposition kinetics and temperatures; no synergy effects for these properties were observed for the heterogeneously surfaced constructs in contrast to the corresponding homogeneously coated materials, which exhibited different values depending on their surface functionalities. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1487–1495, 2004     

Dynamic boundary stabilization of a Reissner–Mindlin plate with Timoshenko beam

This paper is concerned with well‐posedness results for a mathematical model for the transversal vibrations of a two‐dimensional hybrid elastic structure consisting of a rectangular Reissner–Mindlin plate with a Timoshenko beam attached to its free edge. The model incorporates linear dynamic feedback controls along the interface between the plate and the beam. Classical semigroup methods are employed to show the unique solvability of the coupled initial‐boundary‐value problem. We also show that the energy associated with the system exhibits the property of strong stability. Copyright © 2004 John Wiley & Sons, Ltd.     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.     

初-边值问题驻波解的渐近稳定性

本文考虑一带有人工粘性的二维定常等熵无旋平面流方程组的初-边值问题. 在一定的假设下,我们证明其驻波解是渐近稳定的.     

The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations

We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. We prove the convergence and stability of the scheme in L ₂ and C norms. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005.     

Control Policy for a Manufacturing System with Random Yield and Rework

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.     

On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.     

On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.     

Stability control of the electrooptic effect with new maleimide copolymers containing photoreactive tricyanopyrrolidene‐based chromophores

New photocrosslinkable maleimide copolymers have been synthesized by the attachment of a tricyanopyrrolidene‐based chromophore. The 2‐(3‐cyano‐4‐(2‐{4‐[hexyl‐(6‐hydroxy‐hexyl)‐amino]‐phenyl}‐vinyl)‐5‐oxo‐1‐{4‐[4‐(3‐oxo‐3‐phenyl‐propenyl)‐ phenoxy]‐butyl}‐1,5‐dihydro‐pyrrol‐2‐ylidene)‐malononitrile chromophore exhibits nonlinear optical activity and contains a chalcone moiety that is sensitive to UV light (λ = 330–360 nm) for crosslink formation. The maleimide monomers have also been functionalized with chalcone moieties. The resultant copolymers exhibit great processability, and one of them shows a maximum electrooptic coefficient of 90 pm/V at 1300 nm. We could control the thermal stability of the electrooptic coefficient with the newly synthesized photoreactive copolymers successfully. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 531–542, 2007