Optimal Control of an <Emphasis Type="Italic">M/E</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript>/1 Queueing System with a Removable Service Station

This paper studies the optimal operation of an M/E _k /1 queueing system with a removable service station under steady-state conditions. Analytic closed-form solutions of the controllable M/E _k /1 queueing system are derived. This is a generalization of the controllable M/M/1, the ordinary M/E _k /1, and the ordinary M/M/1 queueing systems in the literature. We prove that the probability that the service station is busy in the steady-state is equal to the traffic intensity. Following the construction of the expected cost function per unit time, we determine the optimal operating policy at minimum cost.     

An Algorithm for the Economic Design of <Emphasis Type="Italic">np</Emphasis> Charts for a Multiplicity of Assignable Causes

Chiu, in 1976, studied the economic design of np charts for processes subject to a multiplicity of assignable causes. Chiu developed a two-step minimization procedure to obtain the three control variables, namely, the sampling interval, the sample size and the acceptance number. Although Chiu's two-step minimization procedure is simple, applicable and down to earth, it is rather inefficient and has some drawbacks. This paper presents an algorithm to overcome these drawbacks. The results and the execution times of all numerical examples show that the accuracy and the efficiency of the algorithm is reasonably good.     

A Heuristic Decomposition Algorithm for Scheduling Problems on Mixed Graphs

We consider a scheduling problem where a set of n jobs has to be processed on a set of m machines and arbitrary precedence constraints between operations are given. Moreover, for any two operations i and j values a _ij >0 and a _ji >0 may be given where a _ij is the minimal difference between the starting times of operations i and j when operation i is processed first. Often, the objective is to minimize the makespan but we consider also arbitrary regular criteria. Even the special cases of the classical job shop problem J//C_max belong to the set of NP-hard problems. Therefore, approximation or heuristic algorithms are necessary to handle large-dimension problems. Based on the mixed graph model we give a heuristic decomposition algorithm for such a problem, i.e. the initial problem is partitioned into subproblems that can be solved exactly or approximately with a small error bound. These subproblems are obtained by a relaxation of a subset of the set of undirected edges of the mixed graph. The subproblems are successively solved and a proportion of the results obtained for one subproblem is kept for further subproblem definitions. Numerical results of the algorithm presented here are given.     

Availability Analysis of Repairable <Emphasis Type="Italic">N</Emphasis>-Server <Emphasis Type="Italic">n</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>-Replicated Systems

We develop an exact closed-form expression for the steady-state availability of a repairable, N-server system in which the ith server contains n _i identical, reconfigurable, breakdown-prone units. Our approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. We illustrate this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system.     

Spectrophotometric determination of ziram (dithiocarbamate fungicide) by thiocyanate and rhodamine 6G method

A sensitive spectrophotometric method has been developed for the determination of ziram in water, vegetables and grains. The method is based on the dissociation of dithiocarbamate complex of zinc with thiocyanate and rhodamine 6G at pH 4 to form a pink coloured complex that is stabilized by gelatin. The method is simple and Beer's law is obeyed over the concentration range of 0.05-1 ppm of ziram. The method is free from interference of similar dithiocarbamate fungicides containing Mn(2+) and Fe(3+) ions.     

Preparation and analytical properties of a chelating resin containing bicine groups

A polystyrene divinyl benzene based resin containing bicine groups has been prepared and its analytical properties investigated. The pH dependence of sorption of metal on the resin has been determined for Cu(II), Fe(II), Ni(II), Co(II), Zn(II), Hg(II) and Pb(II). The important characteristics of the resin are fast equilibrium, high selectivity and small volume change between its hydrogen and metal forms. These enable it to be applied to the rapid concentration of trace amounts of these metal ions. It shows promise for the separation of lead from other metal ions.     

Extractive spectrophotometric determination of some fluoroquinolone derivatives in pure and dosage forms

Two simple and sensitive extractive spectrophotometric methods for the determination of some fluoroquinolone derivatives (norfloxacin, NRF; ciprofloxacin, CPF; ofloxacin, OFL; and enrofloxacin, ERF) with Supracene Violet 3B (SV 3B, method A) and tropaeolin 000 (TP 000, method B) are described. The methods are based on the formation of ion-association complexes of fluoroquinolones with these dyes, which are extracted into chloroform and have absorption maxima at 575 nm (SV 3B) and 485 nm (TP 000). The methods obey Beer's law and the precision and accuracy of the methods were checked by UV reference methods. The detection limits were 5.0 mug/ml for NRF and 2.5 mug/ml for CPF in method A and 2.5 mug/ml for OFL and ERF in methods A and B.     

Clumping Data in 2-Way Tables: A User-Orientated Perspective

Following a critique of existing algorithms, an algorithm is presented which will re-organize a 2-way data table to bring like rows together, and like columns together. Extensions of the method are described, and justified, to accommodate distances measured in modular arithmetic, and with bipolar columns/rows, as in repertory grid analysis. One value of the algorithms is that the user can see relationships in the tables without the data in the cells themselves ever having been transformed. Thus, users will continue to feel they own their data.     

Refining the Diffusion Approximation for the <Emphasis Type="Italic">GI</Emphasis><Superscript><Emphasis Type="Italic">x</Emphasis></Superscript><Emphasis Type="Italic">/G/c</Emphasis> Queue

This paper deals with the GI ^x /G/c queueing system in a steady state. We refine a diffusion approximation method incorporating the constraint of traffic conservation for general queueing systems. An approximate expression for the distribution of the number of customers is obtained. Numerical results are presented to show that the refined model provides improved performance.     

Photoelasticity in quasicrystals

The maximum number of non-vanishing and independent second order photoelastic coefficients required by the seven pentagonal and the two icosahedral point groups 5(C₅), (S₁₀), (C_5h ), m2(D_5h ), 52(D₅), 5m(C_5v ), 2m(D_5d ); 235(I), 2/m (I _h )—that describe the quasicrystals symmetry groups in two and three dimensions—is obtained. The schemes of non-vanishing and independent coefficients have been calculated and listed. Finally the results of this group-theoretical study are briefly discussed.