Products and transforms of white-noise functionals (in general setting)

Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled Products and Transforms of White-Noise Functionals (preprint, 1990).     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Residual stress/strain analysis in thin films by X-ray diffraction

Residual stresses are found in the majority of multilayer thin film structures used in modem technology. The measurement and modeling of such stress fields and the elucidation of their effects on structural reliability and device operation have been a “growth area” in the literature, with contributions from authors in various scientific and engineering disciplines.

In this article the measurement of the residual stresses in thin film structures with X-ray diffraction techniques is reviewed and the interpretation of such data and their relationship to mechanical reliability concerns are discussed.     

Direct analysis of thin-layer chromatographic spots of narcotics by means of diffuse reflectance Fourier transform infrared spectroscopy

The technique of diffuse reflectance Fourier transform infrared spectrometry (DRIFT) as an in situ detection method was used for the qualitative and quantitative analysis of drugs (heroin, cocaine and codeine) separated by thin layer chromatography.It was found that at a given interferometer throughput and detector sensitivity the quality of the spectrum depends strongly in the type of the chromatographic thin layer used. A detection limit of approx. 2 g was attained on a microcrystalline cellulose thin layer with a dynamically aligned Bio-Rad Digilab FTS 60A/896 type interferometer and room temperature DTGS detector. A reliable qualitative analysis can be made with as little as 10 to 15 g drug per spot.     

Quantitative determination of chloride by means of flow injection analysis with spectrophotometric detection in the UV/VIS range

Chloride is determined indirectly by Spectrophotometric flow injection analysis. Two systems are compared, both based on the principle of ion exchange of easily detectable anions versus chloride from suitable mercury salts. The first method is based on the exchange of chloride with chloranilate which is detected at 332 nm or at 306 nm in neutral or in acidic medium respectively. In the second case, chloride reacts with Hg(SCN)₂. The liberated thiocyanate forms a strongly coloured complex with Fe(III) in acidic solution with an absorption maximum at 460 nm. Both methods have a detection limit of about 5 mol Cl^–/l (175 ng/ml). In the case of the thiocyanate method, the relative standard deviation is about 2% (7 measurements) in the range of 5 to 150 mol/l and decreases significantly to a value of approximately 0.2% at higher concentrations; for the chloranilate method it is 10% for lower and about 1% for higher concentrations respectively.     

Parallelism across the steps in iterated Runge-Kutta methods for stiff initial value problems

For the parallel integration of stiff initial value problems (IVPs) three main approaches can be distinguished: approaches based on parallelism across the problem, on parallelism across the method and on parallelism across the steps. The first type of parallelism does not require special integration methods can be exploited within any available IVP solver. The methodparallel approach received some attention in the case of Runge-Kutta based methods. For these methods, the required number of processors is roughly half the order of the generating Runge-Kutta method and the speed-up with respect to a good sequential IVP solver is about a factor 2. The third type of parallelism (step-parallelism) can be achieved in any IVP solver based on predictor-corrector iteration. Most step-parallel methods proposed so far employ a large number of processors, but lack the property of robustness, due to a poor convergence behaviour in the iteration process. Hence, the effective speed-up is rather poor. The step-parallel iteraction process proposed in the present paper is less massively parallel, but turns out to be sufficiently robust to solve the four-stage Radau IIA corrector used in our experiments within a few effective iterations per step and to achieve speed-up factors up to 10 with respect to the best sequential codes.The research reported in this paper was partly supported by the Technology Foundation (STW) in the Netherlands.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Perturbation analysis of theGI/GI/1 queue

We examine a family ofGI/GI/1 queueing processes generated by a parametric family of service time distributions,F(x,), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect to. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions for the corresponding second derivatives (as well as partial second derivatives involving both interarrivai and service time parameters) are also obtained. Finally, we present perturbation analysis algorithms based on these expressions along with simulation results demonstrating their performance.     

An existence result for linear partial differential equations with coefficients in an algebra of generalized functions

We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.

     

An algebraic approach to the vector ε-algorithm

The vector -algorithm is obtained from the scalar -algorithm by taking the pseudo-inverse of a vector instead of the inverse of a scalar. Thus the vector -algorithm is known only through its rules contrarily to the scalar -algorithm and some other extrapolation algorithms.The aim of this paper is to provide an algebraic approach to the vector -algorithm.