Pyrolysis studies of aromatic polyesters

The products of pyrolysis, at 400°C in vacuo (1 Pa), of poly(ethyleneterephthalate) (PET) and poly(butyleneterephthalate) (PBT) were studied. The products were identified by gas chromatography/mass spectrometry technique. The highly volatile products of PET contained acetaldehyde, benzene, toluene, styrene and ethylbenzene and in the case of PBT, butadiene, tetrahydrofuran, vinylcyclohexene and ethylbenzene were the major products. A qualitative analysis of the products of low volatility revealed that the main components were benzoic acid, terephthalic acid, monovinyl esters of terephthalic acid and higher oligomers in the case of PET, whereas benzoic acid, monobutenyl esters of terephthalic acid and higher oligomers were the main products from PBT. The results obtained were in good agreement with those obtained from pyrolysis experiments, carried out directly in the mass spectrometer. Mechanisms to explain the occurrence of the different products are proposed.     

A fractional credit model with long range dependent default rate

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we start with a bivariate fractional Vasicek model for short and default rate, which allows for fairly explicit calculations. We calculate the prices of corresponding defaultable zero-coupon bonds by invoking Wick calculus. Applying a Girsanov theorem we derive today’s prices of European calls and compare our results to the classical Brownian model.     

On graphs having domination number half their order

In this paper we present a characterization of connected graphs of order 2n with domination numbern. Using this class of graphs, we determine an infinite class of graphs with the property that the domination number of the product of any two is precisely the product of the domination numbers.     

Column generation for vehicle routing problems with multiple synchronization constraints

Synchronization of workers and vehicles plays a major role in many industries such as logistics, healthcare or airport ground handling. In this paper, we focus on operational ground handling planning and model it as an archetype of vehicle routing problems with multiple synchronization constraints, coined as “abstract vehicle routing problem with worker and vehicle synchronization” (AVRPWVS). The AVRPWVS deals with routing workers to ground handling jobs such as unloading baggage or refuelling an aircraft, while meeting each job’s time window. Moreover, each job can be performed by a variable number of workers. As airports span vast distances and due to security regulations, workers use vehicles to travel between locations. Furthermore, each vehicle, moved by a driver, can carry several workers. We propose two mathematical multi-commodity flow formulations based on time-space networks to efficiently model five synchronization types including movement and load synchronization. Moreover, we develop a branch-and-price heuristic that employs both conventional variable branching and a novel variable fixing strategy. We demonstrate that the procedure achieves results close to the optimal solution in short time when compared to the two integer models.     

Gray codes extending quadratic matchings

Is it true that every matching in the n-dimensional hypercube can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey–Savage problem is affirmative for every matching of size at most . The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube by edges of into a Hamilton cycle of . On the other hand, we show that for every there is a balanced matching in of size that cannot be extended in this way.     

Elements of Design‐Based Science Activities That Affect Students' Motivation

The primary purpose of this study was to examine the ways in which a 12‐week afterschool science and engineering program affected middle school students' motivation to engage in science and engineering activities. We used current motivation research and theory as a conceptual framework to assess 14 students' motivation through questionnaires, structured interviews, and observations. Students reported that during the activities they perceived that they were empowered to make choices in how to complete things, the activities were useful to them, they could succeed in the activities, they enjoyed and were interested in the hands‐on activities and some presentations, they felt cared for by the facilitators and received help when they were stuck or confused, and they put forth effort. Based on our examination of data across our three data sources, we identified motivating opportunities that were provided to students during the activities. These motivating opportunities can serve as examples to help both formal and informal science educators better connect motivation theory to practice so that they can create motivating opportunities for students. Furthermore, this study provides a methodological example of how students' motivation can be examined during the context of authentic science and engineering instruction.     

Solution manifolds and submanifolds of parametrized equations and their discretization errors

Summary The paper concerns solution manifolds of nonlinear parameterdependent equations (1)F(u, )=y₀ involving a Fredholm operatorF between (infinite-dimensional) Banach spacesX=Z× andY, and a finitedimensional parameter space . Differntial-geometric ideas are used to discuss the connection between augmented equations and certain onedimensional submanifolds produced by numerical path-tracing procedures. Then, for arbitrary (finite) dimension of , estimates of the error between the solution manifold of (1) and its discretizations are developed. These estimates are shown to be applicable to rather general nonlinear boundaryvalue problems for partial differential equations.This work was in part supported by the U.S. Air Force Office of Scientific Research under Grant 80-0176, the National Science Foundation under Grant MCS-78-05299, and the Office of Naval Research under Contract N-00014-80-C-0455     

Quantum-to-classical transition in cavity quantum electrodynamics

The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupation-or effective temperature-is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantum-to-classical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements.