• Microbiology and Biotechnology Letters
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• v.27 no.3
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• pp.223-229
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• 1999

The two optimal control algorithms, singular approximation and minimum principle, were compared in this paper. The switching time with singular approximation was determined with mathematical derivation and the optimal control profile of specific growth rate was also calculated with minimum principle. The optimal control profiles were calculated by making simple model correlating the specific cell growth rate and specific product formation rate. The optimal control profiles calculated by singular approximation approach were similar to stepwise form of those calculatd by minimum principles. With the minimum principle, the product concentration was 8% more than that of singular approximation. This performance difference was due to a linearization of a nonlinear function with singular approximation. This optimal approaches were applicable to any system with different optimal cell growth and product formation.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.81-86
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• 1994

A Chi-square approximation to the distribution of product of independent Beta variates denoted by U is developed. The distribution is commonly used as a test criterion for the general linear hypothesis about the multivariate linear models. The approximation is obtained by fitting a logarithmic function of U to a Chi-square variate in terms of the first three moments. It is compared with the well known approximations due to Box(1949), Rao(1948), and Mudholkar and Trivedi(1980). It is found that the Chi-square approximation compares favorably with the other three approximations.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.3
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• pp.63-79
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• 2006

In this study we consider a CONWIP system in which the processing times at each station follow a Coxian distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied immediately are either backordered or lost according to the number of demands that exist at their arrival Instants. For this system we develop an approximation method to calculate performance measures such as steady state probabilities of the number of parts at each station, proportion of lost demands and the mean number of backordered demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product-form approximation method. A recursive technique is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method are compared with those obtained by simulation. Comparisons with simulation show that the approximation method provides fairly good results.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.3
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• pp.172-182
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• 2013

In this study we consider a flow line CONWIP system in which two types of product are produced. The processing times of each product type at each station follow an independent exponential distribution and the demands for the finished products of each type arrive according to a Poisson process. The demands that are not satisfied instantaneously are either backordered or lost according to the number of unsatisfied demands that exist at their arrival instants. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts of each product type at each station, mean waiting times of backordered demands and the proportion of backordered demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a two class closed queueing network with a synchronization station and analyze the closed queueing network using a product-form approximation method for multiple classes developed by Baynat and Dallery. In the approximation method, each subsystem is analyzed using a matrix geometric method. Comparisons with simulation show that the approximation method provides fairly good results for all performance measures.

• IE interfaces
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• v.11 no.3
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• pp.55-63
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• 1998

In this study we consider a CONWIP system in which the processing times at each station follow an exponential distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied instantaneously are assumed to be lost. We assume that the lot size at each station is greater than one. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts at each station, average number of parts at each station and the proportion of lost demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. A recursive technique is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method were compared with those obtained by simulation. Comparisons with simulation have shown that the accuracy of the approximate method is acceptable.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.3
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• pp.153-168
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• 1998

In this study we consider a CONWIP system in which the processing times at each station follow an exponential distribution and the demands for the finished Products arrive according to a compound Poisson process. The demands that are not satisfied instantaneously are assumed to be backordered. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts at each station, the proportion of backordered demands, the average number of backordered demands and the mean waiting time of a backordered demand. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. A matrix geometric method is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method were compared with those obtained by simulation. Comparisons with simulation have shown that the approximate method provides fairly good results.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.267-288
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• 2014

We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order $L^{\infty}((0, T];L^2({\Omega}))$-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.

• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.577-585
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• 2004

Storing and estimating the high order probability distribution of classifiers and class labels is exponentially complex and unmanageable without an assumption or an approximation, so we rely on an approximation scheme using the dependency. In this paper, as an extended study of the second-order dependency-based approximation, the probability distribution is optimally approximated by the third-order dependency. The proposed third-order dependency-based approximation is applied to the combination of multiple classifiers recognizing handwritten numerals from Concordia University and the University of California, Irvine and its usefulness is demonstrated through the experiments.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.1
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• pp.1-13
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• 2002

We study a multi-component production/inventory system in which individual components are made to meet various demand types. We assume that the demands arrive according to a Poisson process, but there is a fixed probability that a demand requests a particular kit of different components. Each component is produced by a flow line with several stations. The production of each component is operated by the CONWIP control mechanism. To analyse this system, we propose an approximation method based on aggregation method. In application of the aggregation method, a product-form approximation technique as well as a matrix-geometric method is used. Comparisons with simulation show that the approximation method provides fairly good results.