Desorption behavior of a surfactant in a linear low‐density polyethylene blend at elevated temperatures

The desorption behavior of a surfactant in a linear low‐density polyethylene (LLDPE) blend at elevated temperatures of 50, 70, and 80 °C was studied with Fourier transform infrared spectroscopy. The composition of the LLDPE blend was 70:30 LLDPE/low‐density polyethylene. Three different specimens (II, III, and IV) were prepared with various compositions of a small molecular penetrant, sorbitan palmitate (SPAN‐40), and a migration controller, poly(ethylene acrylic acid) (EAA), in the LLDPE blend. The calculated diffusion coefficient (D) of SPAN‐40 in specimens II, III, and IV, between 50 and 80 °C, varied from 1.74 × 10^?11 to 6.79 × 10^?11 cm²/s, from 1.10 × 10^?11 to 5.75 × 10^?11 cm²/s, and from 0.58 × 10^?11 to 4.75 × 10^?11 cm²/s, respectively. In addition, the calculated activation energies (E_D) of specimens II, III, and IV, from the plotting of ln D versus 1/T between 50 and 80 °C, were 42.9, 52.7, and 65.6 kJ/mol, respectively. These values were different from those obtained between 25 and 50 °C and were believed to have been influenced by the interference of Tinuvin (a UV stabilizer) at elevated temperatures higher than 50 °C. Although the desorption rate of SPAN‐40 increased with the temperature and decreased with the EAA content, the observed spectral behavior did not depend on the temperature and time. For all specimens stored over 50 °C, the peak at 1739 cm^?1 decreased in a few days and subsequently increased with a peak shift toward 1730 cm^?1. This arose from the carbonyl stretching vibration of Tinuvin, possibly because of oxidation or degradation at elevated temperatures. In addition, the incorporation of EAA into the LLDPE blend suppressed the desorption rate of SPAN‐40 and retarded the appearance of the 1730 cm^?1 peak. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1114–1126, 2004     

A Characterisation of Posets that Are nearly Antichains

We present a characterisation of posets of size n with linear discrepancy n − 2. These are the posets that are “furthest” from a linear order without being an antichain. This revised version was published online in September 2006 with corrections to the Cover Date.     

Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

Boundary position feedback control of Kirchhoff's non‐linear strings

This paper is concerned with global stabilization of an undamped non‐linear string in the case where any velocity feedback is not available. The linearized system has an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by linear boundary control. Copyright © 2003 John Wiley & Sons, Ltd.     

Pointwise stabilization of strings with non‐linear feedback

We consider an initial and boundary value problem for a homogenous string subject to an internal pointwise control. The solution resulting from a non‐linear feedback is studied. We give various explicit decay estimates depending on the control position and the feedback non‐linearity. Copyright © 2004 John Wiley & Sons, Ltd.     

Existence and uniform decay for Euler–Bernoulli beam equation with memory term

In this article we prove the existence of the solution to the mixed problem for Euler–Bernoulli beam equation with memory term. The existence is proved by means of the Faedo–Galerkin method and the exponential decay is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik. Copyright © 2004 John Wiley & Sons, Ltd.     

Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. 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.     

Hyperspaces of Normed Linear Spaces with the Attouch–Wets Topology

Let Cld _AW (X) be the hyperspace of nonempty closed subsets of a normed linear space X with the Attouch–Wets topology. It is shown that the space Cld _AW (X) and its various subspaces are AR's. Moreover, if X is an infinite-dimensional Banach space with weight w(X) then Cld _AW (X) is homeomorphic to a Hilbert space with weight 2 ^w(X).     

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.