On maximum norm contractivity of second order damped single step methods

In this paper we consider A(θ)-stable finite difference methods for numerical solutions of dissipative partial differential equations of parabolic type. Combining two rational approximation methods with different orders of accuracy, where the lower order method is applied n ₀ times (n ₀ fixed) at each time step, we prove the existence of a second order method which is contractive for all time steps. Moreover, we shed light on the conditions on the lower order method which are sufficient (and sometimes necessary) to obtain the optimal order of accuracy. For the one-dimensional heat equation we construct a family of numerical methods which are contractive in the maximum norm for all values of the discretization parameters. We also present numerical examples to illustrate our results. Received: May 2002 / Accepted: January 2003     

Kinetics of chlorination of tantalum pentoxide in mixture with sucrose carbon by chlorine gas

The mechanism and kinetics of β-Ta₂O₅ chlorination, mixed with sucrose carbon, have been studied by a thermogravimetric technique. The investigated temperature range was 500 °C to 850 °C. The reactants and reaction residues were analyzed by scanning electronic microscopy (SEM), X-ray diffraction (XRD), and Brunauer-Emmett-Teller method for surface area (BET). The effect of various experimental parameters was studied, such as carbon percentage, temperature, chlorine partial pressure, and flow, use of the multiple sample method, and carbon previous oxidation. The carbon percentage and previous treatment have an effect on the system reactivity. The temperature has a marked effect on the reaction rate. In the 500 °C to 600 °C temperature interval, the apparent activation energy is 144 kJ/mol of oxide, while at higher temperatures, the activation energy decreases. With high chorine partial pressures, the order of reaction is near zero. The kinetic contractile plate model, X=kt, considering carbon oxidation as the controlling stage, is the one with the best fit to the experimental data. A probable mechanism for the carbochlorination of β-Ta₂O₅ is proposed: (1) activation of chlorine on the carbon surface, (2) chlorination of Ta₂O₅, (3) oxidation of carbon, and (4) recrystallization of β-Ta₂O₅.     

Formal techniques for performance analysis: blending SAN and PEPA

In this paper we consider two performance modelling techniques from the perspectives of model construction, generation of an underlying continuous time Markov process, and the potential for reduction in the Markov process. Such careful comparison of modelling techniques allows us to appreciate the strengths and weaknesses of different approaches, and facilitates cross-fertilization between them. In the present case we take a characteristic of one formalism, functional rates in Stochastic Automata Networks, and introduce it to the other formalism, Performance Evaluation Process Algebra. We investigate the benefits of this cross-fertilization, particularly from the perspectives of Markov process generation and reduction.     

Simultaneous translation of lectures and speeches

With increasing globalization, communication across language and cultural boundaries is becoming an essential requirement of doing business, delivering education, and providing public services. Due to the considerable cost of human translation services, only a small fraction of text documents and an even smaller percentage of spoken encounters, such as international meetings and conferences, are translated, with most resorting to the use of a common language (e.g. English) or not taking place at all. Technology may provide a potentially revolutionary way out if real-time, domain-independent, simultaneous speech translation can be realized. In this paper, we present a simultaneous speech translation system based on statistical recognition and translation technology. We discuss the technology, various system improvements and propose mechanisms for user-friendly delivery of the result. Over extensive component and end-to-end system evaluations and comparisons with human translation performance, we conclude that machines can already deliver comprehensible simultaneous translation output. Moreover, while machine performance is affected by recognition errors (and thus can be improved), human performance is limited by the cognitive challenge of performing the task in real time.