BMAP|SM⥻1 model with Markov modulated retrials

This paper deals with the single server queueing system with a Batch Markovian Arrival Process (BMAP), the semi-Markovian (SM) service process, and the retrial process of a MMPP (Markov Modulated Poisson Process) type. The stationary distribution of orbit size at the embedded and arbitrary epochs is the subject of research. We appreciate the INTAS program for the financial support of this research via project #96-828.     

Aggregate production planning for process industries under oligopolistic competition

We consider a competitive version of the traditional aggregate production planning model with capacity constraints. In the general case, multiple products are produced by a few competing producers (oligopoly) with limited capacities. Production quantities, prices and consequently profits depend on production and allocation decisions of each producer. In addition, there is competition for the raw material whose supplies are limited, and where prices reflect these limitations. Such situations have recently occurred in several process industry settings including petro-refining, petrochemicals, basic chemicals, cement, fertilizers, pharmaceuticals, rubber, paper, food processing and metals. We use a successive “Bertrand–Cournot” framework to address this problem and to determine optimal production quantities, prices and profits at the producers and at the raw material supplier. Our analysis allows a new way to understand and evaluate the marginal value of additional capacity when there is competition for the market and raw materials.     

Applications of the deferred standard technique in process gas chromatography

Three applications of the deferred standard (DS) technique in on-line gas chromatographic analysis with a rotary injection valve are reported. It is demonstrated how both absolute and relative measurements are affected by several deviations of the experimental conditions, such as atmospheric pressure, sample injection during either flow or stopped-flow conditions and instrumental settings (carrier gas flow-rate, column oven temperature, detector bridge current) of the analytical system. It is shown that the relative DS concept provides an excellent means of improving the reliability of the analytical equipment. Under standard conditions, accurate results were obtained with a relative standard deviation < 1%. Significant deviations in the instrumental settings affected the accuracy of the final analytical results by less than 4%. It is further shown how the DS technique can be applied to obtain early information on maintenance requirements of the system. A diagnostic table is included that relates observed changes with time of the signals, obtained with a thermal conductivity detector, to possible maintenance requirements.     

A generalized geometric-programming solution to “An economic production quantity model with flexibility and reliability considerations”

The classical economic production quantity (EPQ) model assumes that items are produced by a perfectly reliable production process with a fixed set-up cost. While the reliability of the production process cannot be perfected cost-free, the set-up cost can be reduced by investment in flexibility improvement. In this paper, we propose an EPQ model with a flexible and imperfect production process. We formulate this inventory decision problem using geometric programming (GP), establish more general results using the arithmetic-geometric mean inequality, and solve the problem to obtain a closed-form optimal solution. Following the theoretical treatment, we provide a numerical example to demonstrate that GP has potential as a valuable analytical tool for studying a certain class of inventory control problems. Finally we discuss some aspects of sensitivity analysis of the optimal solution based on the GP approach.     

Nonaxiomatisability of equivalences over finite state processes

This paper considers the existence of finite equational axiomatisations of behavioural equivalences over a calculus of finite state processes. To express even simple properties such as μxE = μxE[E/x] some notation for substitutions is required. Accordingly, the calculus is embedded in a simply typed lambda calculus, allowing such schemas to be expressed as equations between terms containing first order variables. A notion of first order trace congruence over such terms is introduced and used to show that no finite set of such equations is sound and complete for any reasonable equivalence finer than trace equivalence. The intermediate results are then applied to give two nonaxiomatisability results over calculi of regular expressions.     

EXISTENCE AND UNIQUENESS OF THE ENTROPY SOLUTION TO A NONLINEAR HYPERBOLIC EQUATION

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INVARIANCE PRINCIPLE FOR THE INTEGRAL PERIODOGRAM OF A MULTIPLE TIME SERIES

Many authers have studied the asymptotic behavior of the integral periodogram of a Gaussian stationary series. In this paper, the invariance principle for the integral periodogram of a multiple time series is investigated. We have obtained the following theorem:Let X, be a real M -dimensional stationary time series with spectral density matrix f(λ) which satis-fies the conditions:M,and X, can be represented in theform: Xn =whereξ, is the M-dimensional fourth order moment existedstationary martingale series, thenweakly converges to a Gauss process η(λ) withEη(λ) = 0,where V and Q are the second and fourth moment of the martingale seriesξ , respectively.From this theorem, two corollaries have been given, which cover some results of [2][5][6].     

An economic¯X-chart approach to the joint control of the means of independent quality characteristics

Summary In controlling the mean of a multivariate normally distributed quality characteristic the main disadvantage of the globalT ²-control charts is that they don't indicate the component of the quality characteristic which gives rise to an alarm. To avoid this disadvantage the joint use of¯x-charts is proposed in this paper, where — for the sake of simplicity — the investigations are restricted to the case of independent components and to one-sided¯x-charts. On the basis of an economic objective function an approximation to the optimal design of the¯x-charts procedure is derived and discussed. It turns out that at least in the bivariate case the nearly optimal economic design is very close to the exact solution.Supported by the Deutsche Forschungsgemeinschaft (DFG).     

Poisson过程作为更新过程的若干新的特征刻画

本文将给出Poisson过程作为更新过程的一系列新的特征刻画．这些刻画是借助于更新过程中所有关键量的条件概率分布或条件期望来表述的．所给的条件是至任一指定时刻发生的抵达敷为已知．     

Reversed‐phase liquid chromatography with electrospray mass detection and 1H and 13C NMR characterization of new process‐related impurities,including forced degradants of Efavirenz: Related substances correlated to the synthetic pathway

In this study, a stability‐indicating reversed‐phase liquid chromatographic electrospray mass spectrometric method was developed and validated for the determination of process‐related impurities and forced degradants of Efavirenz in bulk drugs. Efavirenz was subjected to acid, alkaline hydrolysis, H₂O₂ oxidation, photolysis, and thermal stress. Significant degradation was observed during alkaline hydrolysis, and the degradants were isolated on a mass‐based purification system and characterized by high‐resolution mass spectrometry, positive electrospray ionization tandem mass spectrometry, and ¹H and ¹³C NMR spectroscopy. Accurate mass measurement and NMR spectroscopy revealed the possible structure of process‐related impurities and degradant under stress conditions. The acceptable separation was accomplished on Waters bondapak C₁₈ column (250 mm × 4.6 mm; 5 μm), using 5 mM ammonium acetate and acetonitrile as a mobile phase in a gradient elution mode at a flow rate of 1.0 mL/min. The eluents were monitored by diode array detector at 247 nm and quantitation limits were obtained in the range of 0.1–2.5 μg/mL for Efavirenz, degradants, and process‐related impurities. The liquid chromatography method was validated with respect to accuracy, precision, linearity, robustness, and limits of detection and quantification as per International Conference on Harmonization guidelines.