Analysis of viscoelastic behavior and dynamic mechanical relaxation of copolyester based layered silicate nanocomposites using Havriliak–Negami model

The solid‐state viscoelastic properties are examined for intercalated nanocomposites based on a copolyester and (2‐ethyl‐hexyl)dimethyl hydrogenated‐tallow ammonium montmorillonite. The nanocomposites are prepared via the direct melt intercalation technique using a conventional twin‐screw extruder. Dynamic mechanical thermal analysis of the nanocomposites is conducted using two different test setups. The dynamic mechanical relaxation spectra show an increase in the storage modulus of the nanocomposite over the entire temperature range under study as compared to the pristine polymer (except in the transition region from 70 to 80 °C). These results are analyzed using the empirical Havriliak–Negami (HN) equation. The four temperature independent HN parameters (α, β, E₀, and E_∞) and one temperature dependent parameter (τ, the relaxation time) are determined by solving the HN equation for each temperature over the range of temperatures. The calculated moduli results fit well with the experimental values of the relaxation spectra for the nanocomposites. This study shows that the HN model can be applied to polymer layered silicate nanocomposites, and it can be used to predict their dynamic mechanical properties over a wide range of temperatures and frequencies a priori. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2657–2666, 2004     

Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems

In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.     

Integral Representation of Invariant Functions

We characterize those positive functions which are invariant for a bounded kernel, and which have a Choquet-type integral representation. Such a representation relies on the wellknown Choquet-type integral representation of measures which are invariant for a kernel. We apply our results to convolution kernels with spread-out measures on second countable locally compact Abelian groups.     

On a certain property of the BurkillSCP-integral

We establish a necessary condition for theSCP-integrability of a function and use it to construct an example of a function possessing a continuousSCP-majorant andSCP-minorant on a closed interval, but nonintegrable over this interval in the sense of theSCP-integral. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 599–606, April, 1999.     

Worst Traffic Passing Virtual Frame Regulation: Analysis with Dynamic Programming

This paper studies a discrete-time queueing system in which the traffic regulation places an upper bound on the number of arrivals in each of the non-overlapping time windows (virtual frames) of a fixed length. The worst traffic passing through this traffic regulation is characterized. As a criterion for traffic comparison, this paper employs the weighted sum of queueing delays with the weighting factors decaying geometrically over the time horizon. This paper uses dynamic programming techniques and convexity argument to characterize the worst traffic.     

On approximation of dual spaces and dual operators

We study the connection between equations which approximate an initial abstract linear equation and the adjoint one. We prove that the operator which is adjoint to the approximating one approximates the adjoint operator. As examples we consider adjoint linear integral equations and mutually dual linear programming problems.     

A case study of the MSA approach to quantized polarizable media

The mean spherical approximation (MSA) has proved to be a very general and flexible method to analyze equilibrium statistical mechanical systems. In this note we test its accuracy against a simple one-dimensional model, i.e., a lattice gas of polarizable molecules where the internal degree of freedom is treated as quantized harmonic oscillators which interact via harmonic forces. This model can be solved exactly. We find a very good agreement between the MSA and exact solutions.2 The corresponding classical problem of polarizable particles was first solved in a mean spherical approximation (MSA) by M. Wertheim [J. Chem. Phys. 26:1425 (1973)]. He considered the model with nonfluctuating dipole moments. Later L. Pratt [Mol. Phys. 40:347 (1980)] and J. S. Høye and G. Stell [J. Chem. Phys. 73:461 (1980)] solved the corresponding classical problem in the MSA for particles with fluctuating dipole moments.     

Lebesgue-stieltjes integral inequalities in several variables with retardation

The aim of this paper is to establish some new Lebesgue-Stieltjes integral inequalities inn independent variables with retardation which generalize and unify continuous and discrete inequalities of the Gronwall-Bellman-Bihari type inn independent variables.     

On the Differential Properties of Temlyakov-Type and Temlyakov-Bavrin-Type Integrals

We establish a formula that expresses the value of the density of the Temlyakov-type integral with defining domain of type A in terms of the integral itself by means of a differential operator. We extend this operator connection to the Temlyakov–Bavrin-type integral of order k. Our study bases on the method of linear differential operators with variable coefficients which is developed by A. V. Nelaev.