Electro-optic pulse response of ferroelectric liquid crystals

The electro-optic response of ferroelectric smectic C* liquid crystals has been studied. Anomalous switching behaviour of such materials which possess a negative dielectric anisotropy has been reported. These materials show a minimum in response time at a sufficiently high field. We present results showing the dependency of this minimum upon spontaneous polarisation and the effect of AC bias. Calculations based upon the equation of motion of the director around the cone are presented which describe this effect and its dependence on the relative magnitudes of the spontaneous polarization and dielectric anisotropy of the material. Good agreement with the experimental results is found.     

Thermal desorption of interacting molecules from mixed adlayers

A Monte Carlo simulation method is used to study thermal desorption of gas molecules from mixed adlayers containing two species. The effects of lateral interactions among adatoms and initial surface coverage on the desorption spectra are examined. It is shown that attractive lateral interactions lead to sharper peaks and that desorption occurs at high temperatures, whereas repulsive interactions lead to multiple peak spectra. It is found that interactions between unlike molecules affect the spectra for species with lower desorption energy only, and that the two species desorb together only in certain cases. Lateral interactions also affect the desorption kinetics significantly and very different behavior for the two species may be obtained.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

Risk and quality control in a supply chain: competitive and collaborative approaches

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.     

Global Parametric Sufficient Optimality Conditions for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized （η,ρ）-invex Functions

In this paper,we discuss a large number of sets of global parametric sufficient optimality condi-tions under various gcneralized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programmingproblem.     

A fluid system with coupled input and output,and its application to bottlenecks in ad hoc networks

This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c/(n+1), where the remaining c/(n+1) is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can be regarded as a system with Markov fluid input. The rationale behind studying this queue lies in ad hoc networks: bottleneck links have roughly this type of sharing policy. We consider four performance metrics: (i) the stationary workload of the queue, (ii) the queueing delay, i.e., the delay of a ‘packet’ (a fluid particle) that arrives at the queue at an arbitrary point in time, (iii) the flow transfer delay, i.e., the time elapsed between arrival of a flow and the epoch that all its traffic has been put into the queue, and (iv) the sojourn time, i.e., the flow transfer time increased by the time it takes before the last fluid particle of the flow is served. For each of these random variables we compute the Laplace transform. The corresponding tail probabilities decay exponentially, as is shown by a large-deviations analysis. F. Roijers’ work has been carried out partly in the SENTER-NOVEM funded project Easy Wireless.     

Spectral Properties of Four-Dimensional Compact Flat Manifolds

We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the heat trace of the Laplacian acting on p-forms, we determine all p-isospectral and L-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on p-forms for all values of p are equivalent to each other. The list shows for any p, 1 ≤ p ≤ 3, many p-isospectral pairs that are not isospectral on functions and have different lengths of closed geodesics. We also determine all length isospectral pairs (i.e. with the same length multiplicities), showing that there are two weak length isospectral pairs that are not length isospectral, and many pairs, p-isospectral for all p and not length isospectral. Mathematics Subject Classifications (2000): 58J53, 58C22, 20H15.