The impact of preventive activities on the economics of production systems: Modeling and application

In this paper, the impact of preventive activities on the economics of production systems has been discussed. A defective production system has been used to evaluate the financial return of a system with and without preventive activity. A mathematical model has been developed to simulate the situation. A practical case in the automotive industry has been used to verify the model. According to this research, it has been found that preventive activities will affect the return of the production system, and the effect depends on the cost of the action that has been taken.     

On One method for the numerical solution of a system of parabolic equations

An algorithm for the numerical solution of a system of two parabolic equations of a special form has been presented, and its stability has been proved. Estimates of the numerical solutions obtained have been made. Conditions guaranteeing the applicability of the sweep method are determined, and the time step at which the iterative method has the inner convergence has been estimated. An example of the application of the algorithm in soil science has been presented.     

Solvent extraction studies of indium

Solvent extraction of indium from malonic acid medium by Primene JM-T has been studied. The extraction has been studied as a function of pH and concentrations of malonic acid and sodium malonate. The nature of the acid-amine complex has been established by chemical analysis and by the application of the method of Hogfeldt and Fredlund. The equilibrium constant for the reaction has also been calculated. The nature of the indium complexes getting extracted has also been discussed.     

Dirichlet Problem for a Fractional-Order Ordinary Differential Equation with Retarded Argument

A solution of the Dirichlet problem for a fractional-order ordinary differential equation has been found. Green’s function has been constructed for the problem concerned. The problem solution has been written in terms of Green’s function. A theorem on the existence and uniqueness of a solution of the posed problem has been proved, and a condition for its unique solvability has been derived. It is shown that the condition of solvability may only be violated a finite number of times.     

Antiperiodic oscillations in a forced Duffing oscillator

Regularity has always been attributed to periodicity. However, there has been a spurt of interest in another unique type of regularity called anitperiodicity. In this paper we have presented results of antiperiodic oscillations obtained from a forced duffing equation with negative linear stiffness wherein the increase in the number of peaks in antiperiodic oscillation with the forcing strength has been observed. Similarity function has been used to identify the antiperiodic oscillation and further the bifurcation diagram has been plotted and stability analysis of the fixed points have been carried out to understand its dynamics. An analog electronic circuit governed by the forced Duffing equation has been designed and developed to investigate the dynamics of the antiperiodic oscillations. The circuit is quite robust and stable to enable the comparison of its analog output with the numerically simulated data. Power spectrum analysis obtained by fast Fourier transform has been corroborated using a nonlinear statistical technique called rescale range analysis method. By this technique we have estimated the Hurst exponents and detected the coherent frequencies present in the system.     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

Dark spatial soliton interaction in nonlinear Kerr medium

The dark spatial soliton interaction in nonlinear Kerr medium has been studied in this paper. The problem has been solved by the use of the slowly varying envelope approximation in solving coupled nonlinear Schrödinger equations. The perturbation nature of dark spatial soliton interaction has been described and some of their key properties has been discussed as well in the paper.     

矩阵LU分解定理的简单证明及其数值实现

用简单的方法证明了矩阵LU分解定理,讨论了定理的推广以及定理相应的数值实现,并对《数值分析》课程教学方法改革进行了思考.     

Fuzzy periodic review system with fuzzy random variable demand

In this paper, a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously. A model has been developed with customer demand assumed to be a fuzzy random variable. The lead-time has been assumed to be a constant. The lead-time demand and the lead-time plus one period’s demand have also been assumed to be fuzzy random variables. A methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized. A numerical example has been presented to illustrate the model.     

供应链营销渠道体系的研究

从供应链管理协调、优化的角度出发,探讨营销渠道的建设.以移动通讯行业为背景,提出了渠道协同应用的多目标规划模型,探讨了模型求解的方法,并以某移动分公司的数掘进行了算例分析.     

病态线性方程组的判定方法

针对用条件数来衡量方程组的性态将随阶数增大而变得异常困难这一问题,分析了病态线性方程组产生的原因,提出了一种判定方法,探讨了对一定精度要求的解的可允许扰动的数量级,实例证明了这种方法的有效性.     

On Quasivector Spaces of Convex Bodies and Zonotopes

In this work the theory of quasivector spaces has been briefly outlined and applied for computation with zonotopes. An approximation problem for zonotopes in the plane has been formulated and an algorithm for its solution has been proposed.     

Extraction of indium,cadmium and thallium by dinonylnaphthalene sulfonic acid

The extraction of indium, cadmium and thallium by dinonylnaphthalene sulfonic acid (HD) from acid media has been studied. HD extracts the metal ion by an ion exchange mechanism. The nature of the species and the extent of aggregation has been evaluated. The effect of diluents on the extraction has also been studied and the results interpreted on the basis of aggregation of HD. A comparative study with solid ion exchangers has also been made.     

Spectra and ionization potential of cyanoacetylene

The spectrum of cyanoacetylene has been photographed in the vacuum ultraviolet region and its analysis made. The ionization potential has been calculated from an observed Rydberg series to be 11.6 eV. The first Rydberg band has been compared with the photoelectron spectrum of the molecule and conclusions about the initial orbital have been drawn.     

A nonlinear model for footings on granular bed–stone column reinforced earth beds

In the present study, an attempt has been made to model and analyze a combined footing supporting column, which is to be constructed on very soft soil. In view of small bearing capacity and very large deflections, foundations are constructed after improving the original ground. Here, the ground has been improved by providing the stone columns in the soft soil and on top of this improved ground; a granular fill layer has been placed just below the footing. The footing has been modeled as a beam having finite flexural rigidity. Granular fill layer, soft soil and stone columns have been represented by Pasternak shear layer, Kelvin–Voigt body and the Winkler springs, respectively. Nonlinear behavior of these has been considered by means of hyperbolic constitutive relationships. Governing differential equations for response of the system have been derived and presented in non-dimensional form. These equations have been solved using appropriate boundary conditions by means of an iterative Gauss Elimination technique.     

The relationship between the Box dimension of the Besicovitch functions and the orders of their fractional calculus

The relationship between the Box dimension of the Besicovitch functions and the orders of their fractional calculus has been investigated. On some special conditions, the linear connection between them has been proved, and the other case has also been discussed.     

Terminal motion of a thin elliptical plate over a horizontal plane with orthotropic friction

The problem on the terminal motion of a thin elliptic plate over a horizontal plane taking into account orthotropic friction forces has been considered. Differential equations of the movement of the plate have been derived. The system of equations has been numerically solved under various initial conditions. It has been shown that sliding and spinning cease simultaneously. It has been found that the limiting behavior of the plate is governed not only by the ratio of the moment of inertia to the coefficient of friction, but also by the orientation of the plate. A comparison of the behaviors of the elliptic and circular plates has been carried out. The results of the calculations can be used to describe the phenomena that occur in a rail–wheel contact in more detail.     

Introducing a modified gradient vector method for optimization of accident prediction non-linear functions

In this paper, a new optimization method has been proposed for accident prediction non-linear models. This has been achieved by eliminating the Hessian matrix from the equation of optimal pace length in the gradient vector method. One advantage is that it is independent of the starting point in optimization processes and it provides convergence at the highest top as well. This method has been tested on an accident prediction model and its preference over the gradient vector method has been proven.     

A fuzzy random periodic review system with variable lead-time and negative exponential crashing cost

In the present model a fuzzy random periodic review system has been investigated with the annual demand assumed to be a discrete fuzzy random variable with associated imprecise probabilities. Keeping in mind the widespread application of the Just-In-Time manufacturing philosophy and lead-time management being one of its most effective methods of implementation, the lead-time has been assumed to be an added control parameter. Also as it may not be always possible to resolve the lead-time into all its components and estimate their individual crashing costs, the crashing cost has been introduced as a negative exponential function of the lead-time. A methodology has been developed in this regard such that the total inventory cost is minimized and the optimal period of review, the optimal target inventory level and the optimal lead-time are determined in the process. An algorithm has been provided to encapsulate the methodology and it has been illustrated by way of a numerical example.     

Some Applications of the “Branch-and-Bound” Algorithm to the Machine Scheduling Problem

The "branch-and-bound" algorithm for the exact solution of a three-machine scheduling problem proposed by Lomnicki has been generalized to the case of an arbitrary number of machines (under the assumption of an identical order on all the machines) and it has been adapted for an electronic computer. The flow chart of this algorithm used in the programming of calculations has been given and the efficiency of the method has been illustrated by some experimental evaluations of optimum job sequencing.