Model Assisted Statistics and Applications - Volume 6, issue 3

Authors: Topchishvili, Alexander | Lipovetsky, Stan

Article Type: Editorial

DOI: 10.3233/MAS-2011-0202

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 161-162, 2011

Authors: Mandel, Igor

Article Type: Research Article

Abstract: The current condition of knowledge about social world as reflected in political sciences, economics, management sciences, sociology, psychology, and their many derivatives is in deep disarray. It can be observed in the poor representation of the obtained results of scientific findings in practical issues as well as in the internal problems and inconsistencies within the respective branches of science. The exponentially growing volume of information in these areas is supplemented with less than linear growth of real knowledge, and even this one cannot be considered “hard knowledge” for many reasons. This phenomenon is not new, but the alarming gap between …two flows of symbolic realm on the one hand, and between these flows as a whole and real practices on the other hand, is growing faster with every year. Further scientific specialization seems just to widen this gap. A need for some unifying principles overcoming narrow boundaries of particular sciences and even their composites (like behavioral economics or social psychology) becomes more and more clear. The attempts to solve universal problems using such grand concepts as general theory of systems, cybernetics, sociophysics, statistics have yielded many brilliant results, but haven't proven to become the sought-after unifying frame in many aspects. One of the reasons for that was their orientation to specific types of models, which, applied to social reality, do not work as expected. In this article, I'll try to introduce some principles of a new science, sociosystemics, which will hopefully help to transform over the cross a time the enormous volume of social information into meaningful knowledge to be used for analysis, prediction, finding innovative solutions, and decision making. Show more

Keywords: Sociosystemics, social sciences, statistics, decision theory, economics, sociology, natural language processing, subject classification

DOI: 10.3233/MAS-2011-0203

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 163-217, 2011

Authors: Dolenko, Galyna | Konareva, Evgenia | Manovytska, Dariia

Article Type: Research Article

Abstract: The aim of this paper is the evaluation of effectiveness of economic development of organizational system with the help of the fuzzy sets theory and the elements of applied statistics. The model and the method of evaluation of effectiveness of economic development of organizational system are proposed to consideration. The methodology is illustrated through example of Ukraine. Statistical data over the years 2009–2010 is used for calculations.

Keywords: Economic development, regional politics, evaluation method, complex evaluation, result indicators, fuzzy set, applied statistics, multicriteria decision making, analytic hierarchy process

DOI: 10.3233/MAS-2011-0204

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 219-229, 2011

Authors: Molostvov, Vitaly

Article Type: Research Article

Abstract: The aim of this article is to attract researchers' attention to a “mixed” variant of Multiple Criteria Optimization (MCO) problem with incomplete information, namely to the case where stochastic distributions for some characteristics of an optimized system are known, but only up to the uncertain parameters. Applied examples are given to show how the combination of stochastic and maximin approaches makes it possible to reduce the problems of this type to MCO problems with uncertainty. Both problems are reduced to classical well studied Markowitz model (without uncertainty). Such elimination of uncertainty is possible due to only one criterion depends on …uncertainty. Further general case where uncertainty affects the values of all the criteria in an arbitrary manner is considered. For one of possible reasonable concept of P-optimal solution sufficient conditions are presented. They reduce the optimal solution calculation to maximin problem. Constructiveness of the suggested approach is illustrated by an example of multiple criteria linear programming with uncertain coefficients of linear criteria. If these coefficients satisfy given set of linear constraints, the computation of the optimal solutions is reduced to linear programming problem. Finally, some possible directions for future research are discussed. Show more

Keywords: Multiple criteria optimization, uncertainty, information incompleteness of mixed type, stochastic and maximin approaches combination, mixing problem, portfolio problem

DOI: 10.3233/MAS-2011-0205

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 231-237, 2011

Authors: Roychowdhury, Soma | Bhattacharya, Debasis

Article Type: Research Article

Abstract: This paper presents a probabilistic optimization problem of selecting the best system from a group of competing coherent systems with mutually dependent components by optimizing the probability that the system will meet a specified target lifetime and ranking the systems from best to worst according to the orders of those probability values from highest to lowest. The problem of comparing different system designs in search for the best configuration is of great concern to the reliability engineers, especially when the systems are of different orders and having mutually dependent components. Earlier works in this direction have discussed the problem for …systems with independent components. The problem becomes complicated if the component lives are mutually dependent. The paper attempts to find an approach to solving the issue of comparing coherent systems of different orders with mutually dependent components. Here we select a system by minimizing the probability that the system will fail to meet a specified target lifetime, where the component lifetimes are mutually dependent, using a stochastic ordering criterion. A technique based on stochastic ordering has been proposed to compare systems of different orders. Some complex systems have been used to show that the result derived in this paper can be used effectively to make comparison of the systems with dependent components and to find the best system from a group of competing systems of different orders. Show more

Keywords: Coherent system, mutually dependent component lives, minimal cut set, stochastic optimization, stochastic ordering, system life

DOI: 10.3233/MAS-2011-0206

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 239-247, 2011

Authors: Gogsadze, Robert | Prangishvili, Archil | Chikovani, Rafael | Goderdzishvili, Gela | Topchishvili, Alexander | Jibladze, Nodar

Article Type: Research Article

Abstract: The paper has been devoted to the development of a three-dimensional mathematical model of a diffusion-based technological process of fabrication of isoplanar semiconductor structure. Such structures with a definite accuracy describe functioning of various devices of micro and optoelectronics. The gradual complication of functions of electron devices by reduction of sizes of their elements requires calculations accuracy increasing and analysis of these elements during designing of devices, which leads to necessity to develop more perfect methods in mathematical modeling. The calculation of the atoms' concentration of a diffusate in a crystal during fabrication of microelectronics leads to solving …classical boundary problems for differential equations of parabolic type with variable coefficients. In the present paper we consider the particular kinds of boundary problems, which describe the diffusion process during fabrication of isoplanar structure. For practical solving of these boundary problems we have been using the classical methods of tensor analysis and Riemannian geometry, and the method of Green function (the so called Green's function method modeling) as well. Application of these methods allows us to determine the analytical image of the impurity concentration depending on time and space variables and on other topological, physical and technological parameters of the technological process and the crystal. The developed method of three-dimensional mathematical modeling has a sufficient importance and is quite promising for the creation of various semiconductor nanostructures. Show more

Keywords: Diffusion, differential equations, boundary problem, metric tensor, geodesic line, fundamental solution

DOI: 10.3233/MAS-2011-0207

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 249-260, 2011

Authors: Singh, Rajinder Pal | Singh, Tejwant

Article Type: Research Article

Abstract: Electrochemical methods have been found to be more efficient but of all the methods, which are vogue for treatment of effluent generated from various industries containing toxic substances like heavy metals, cyanide, organic compounds etc. Mathematical models play an important role in investigating the whole environmental management problems through statistical empirical modeling to more sophisticated statistical computer simulations. The mathematical model of mass transport for LSV under hydrodynamic conditions at tubular electrodes for ECE processes in which an irreversible chemical reaction is coupled between two reversible charge transfer reactions is considered. The resulting boundary value problem is converted into system …of two integral equations, which is solved numerically. The effect of electrons (n 2 / n 1 ) involved in two charge transfer reactions on cv-voltammograms are investigated and shown graphically. Show more

Keywords: Mass transport, linear sweep voltammetry, ECE process, optimization techniques

DOI: 10.3233/MAS-2011-0208

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 261-266, 2011

Authors: Vilge, Boris

Article Type: Research Article

Abstract: Numerous features, bifurcations and catastrophes (“jumps”) arise in problems of optimization, control and decision making. They can be detected by calculation extreme values of the respective functions. The selection of optimum control parameters for a number of technological processes is closely related to detection of initial and final moments of phase transitions of the first kind. This problem is based on the analysis of behavior of thermodynamic potentials and of their derivatives. Mathematical descriptions of phase transitions of the first kinds within the framework of phenomenological thermodynamics using the symplectic geometry formalism have indicated that in general they are accompanied …by a weak disruption, or “jump” of the first derivative of the thermodynamic potential with respect to extensive parameter. Changes in physical condition of the studied materials are accompanied by changes of electric impedances and temperatures. A method has been suggested for detection of phase transition moments in order to achieve optimum composition of materials and optimum control of their strengthening and hardening processes. A special case of such materials are samples of freshly-mixed concrete. They form the experimental basis for the researches. Statistical analysis has demonstrated high correlation between the moments of kinetic phase transition of the first kind and the concentration surface-active substances in chemically active materials. Show more

Keywords: Computation, optimization, thermodynamic, phase transition, chemically active materials, penetration resistance, correlation

DOI: 10.3233/MAS-2011-0209

Citation: Model Assisted Statistics and Applications, vol. 6, no. 3, pp. 267-277, 2011