Multilevel a posteriori error analysis for reaction–convection–diffusion problems

We present a new approach to the a posteriori error analysis of stable Galerkin approximations of reaction–convection–diffusion problems. It relies upon a non-standard variational formulation of the exact problem, based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales. The associated norm, which is stronger than the standard energy norm, provides a robust (i.e., uniform in the convection limit) control over the streamline derivative of the solution. We propose an upper estimator and a lower estimator of the error, in this norm, between the exact solution and any finite dimensional approximation of it. We investigate the behaviour of such estimators, both theoretically and through numerical experiments. As an output of our analysis, we find that the lower estimator is quantitatively accurate and robust.     

Robustness and exponentiality in redundant repairable systems

A redundant system of independent repairable components with general failure time and repair time distributions is considered. It is shown that the system failure time has an expectation dependent only on the mean failure times and mean repair times of the components and not on their distributions. An intuitive argument is provided, based on the time of onset of the quasi-stationary distribution on the set of working states, to show that for highly reliable systems, the system failure time is exponentially distributed to good approximation. The argument also justifies a simple figure of merit for the quality of the exponential approximation. A key ingredient in the analysis is the system relaxation time, an informal review of which is provided.     

一类过程摄动系统的无阻塞鲁棒性

使用参数Dioid模块网络法,把含大量摄动参数的在普通极大代数意义下非线性状态空间模型在参数Dioid意义下线性化,在此基础上研究一类过程摄动系统的无阻塞鲁棒性.给出了有限缓冲串行生产系统在没有缓冲器下无阻塞的充要条件和充分条件.     

Robustly complete synthesis of sampled-data control for continuous-time nonlinear systems with reach-and-stay objectives

Formal methods are becoming favorable for control and verification of safety-critical systems because of the rigorous model-based computation. Relying on an over-approximated model of the original system behaviors, formal control synthesis algorithms are not often complete, which means that a controller cannot necessarily be synthesized even if there exists one. The main result of this paper shows that, for continuous-time nonlinear systems, a sample-and-hold control strategy for a reach-and-stay specification can be synthesized whenever such a strategy exists for the same system with its dynamics perturbed by small disturbances. Control synthesis is carried out by a fixed-point algorithm that adaptively partitions the system state space into a finite number of cells. In each iteration, the reachable set from each cell after one sampling time is over-approximated within a precision determined by the bound of the disturbances. To meet such a requirement, we integrate validated high-order Taylor expansion of the system solution over one sampling period into every fixed-point iteration and provide a criterion for choosing the Taylor order and the partition precision. Two nonlinear system examples are given to illustrate the effectiveness of the proposed method.     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

Uncertainty assessment from robustness testing applied on an LC assay for R-timolol and other related substances in S-timolol maleate

The robustness testing of a normal-phase liquid chromatographic (LC) method for the determination of R-timolol and other related substances in S-timolol maleate was performed applying a two-level Plackett-Burman design. Two qualitative and five quantitative factors were examined. Two types of responses were considered, qualitative, i.e. chromatographic performance criteria, and quantitative ones. The latter were taken into account to determine if the analytical procedure was robust. The quantitative responses were the contents of R-timolol in two S-timolol maleate samples. Even though some significant factor effects were observed on the qualitative responses, the R-timolol contents were not significantly different from those observed at nominal conditions, which demonstrated the robustness of the procedure.Since the experiments of the Plackett-Burman design can be assimilated to laboratories in an interlaboratory study, uncertainty can be evaluated using the robustness test data. The robustness test was set-up in such a way that the required variances could be estimated. It was shown that the robustness set-up allows estimating the reproducibility uncertainty without performing an interlaboratory study.     

Optimisation of a flow injection system with electrochemical detection using the desirability function: Application to the determination of hydroquinone in cosmetics

A procedure is proposed in which the determination of hydroquinone using a flow injection system with electrochemical detection is described. Size and coefficient of variation of the signal are optimised by a desirability function and a central composite design. The robustness of the optimum reached in the optimisation step is evaluated by means a Plackett-Burman design. The optimised FIA system is able to determine hydroquinone with a minimum detectable net concentration of 10 μg l⁻¹ with a false positive probability of 0.05 and a false negative probability less than 0.05. In samples of bleaching cream, the proposed procedure has a recovery of 102.2% with standard deviation of 4.4% and a relative error of 6.2%.     

Determination of the antifouling booster biocides irgarol 1051 and diuron and their metabolites in seawater by high performance liquid chromatography-diode array detector

A method for the simultaneous determination of two antifouling booster biocides, diuron (1-(3,4 dichlorophenyl) 3,3 dimethyl urea) and irgarol 1051 (2-methylthio-4-tert-butylamino-6-cyclopropylamino-s-triazine), and their metabolites, DCPMU (1-(3,4 dichlorophenyl)-3 methyl urea), DCPU (1-(3,4 dichlorophenyl) urea), DCA (3,4 dichloroaniline) and M1 (2-methylthio-4-tert-butylamino-s-triazine) in seawater by high performance liquid chromatography-diode array detector (HPLC-DAD) was developed. The optimization of the extraction procedure included the type of sorbent and the type of the organic solvent for the elution. Optimization of the liquid chromatography (LC) separation was also performed and the robustness of the developed separation was tested, in respect to the effect of three factors (column temperature, flow rate and initial strength of acetonitrile) on the retention times, peak resolution and peak area of the six compounds. The optimized procedure included off-line extraction of these compounds from seawater samples using C18 solid phase extraction (SPE) cartridges. The inter-day precision of the developed procedure was less than 14% (as R.S.D.s) for all the tested compounds. Satisfactory recoveries (higher than 82%) were obtained for all substances, except for DCA, for which low recovery was obtained (30.5%). The limits of detection (LODs) of the substances varied between 0.005 (DCPMU) and 0.026 (M1) μg L⁻¹.     

Cooperative schemes for path establishment in mobile ad-hoc networks under shadow-fading

The performance of routing protocols for multi-hop path-establishment in Mobile Ad-hoc NETworks (MANET) is examined when the individual radio links undergo shadow fading of parameterized severity. Such propagation modeling is typical of ground-level networking along with node mobility. The metrics of main interest are the probability of having a reliable multi-hop path plus the temporal statistics of such availability under a Markovian model. Such availability is an indicator for the suitability of the network to carry delay-sensitive applications (push-to-talk voice, streaming video) in uninterrupted manner. It is shown that high levels of diversity are necessary in such adverse environments, as obtained either by multiple independent paths or via concurrent cooperative transmission. Analytical and simulation comparisons of typical routing options are presented on the above metrics, plus on the required nodal engagement for supporting such diversity.     

Robustness of Pathwise Stability of Semilinear Perturbed Stochastic Evolution Equations

Abstract

The purpose of this paper is to investigate pathwise stability for certain Hilbert space-valued stochastic evolution equations. We are especially interested in the robustness analysis of perturbed stochastic differential equations in infinite dimensions. Sufficient conditions are established to ensure the almost surely stable decay of the given stochastic systems. Lastly, a corollary and corresponding example are studied to illustrate our theory.