1. On PDE Problem Solving Environments for Multidomain Multiphysics Problems

   Christos Antonopoulos, Manolis Maroudas, and Manolis Vavalis

   Abstract: This paper presents the design, the prototype implementation and the preliminary evaluation of an enhanced meta-computing environment based on the FEniCS Project and focused on multi-domain multi-physics problems modeled with partial differential equations. It is based on scripting languages and their practices, and on the Service Oriented Architecture paradigm and the associated web services technologies. Our design is generic, covering a wide range of problems but our proof of concept implementation is restricted to elliptic PDEs in two or three dimensions.

   Keywords: problem solving environments, numerical solution of PDEs, scientific high performance meta-computing, numerical software.

   Pages: 111 – 123 | Full PDF Paper

2. Comparison of Estimation Methods for the Parameters of Poisson-Lomax Distribution under Progressive Type-II Censoring

   Alaa H. Abdel-Hamid and Atef F. Hashem

   Abstract: The Poisson-Lomax distribution, with decreasing and upside down shapes of failure rate, is considered as a lifetime distribution. Its genesis may appear in the complementary risks model and parallel systems. Based on progressive type-II censoring, the maximum likelihood, unweighted least squares, weighted least squares and Bayes (using linear-exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. The performance of these methods is compared through an extensive numerical simulation, based on mean squared errors and relative absolute biases of the estimates. Two real data sets are used to compare the Poisson-Lomax distribution with the exponentiated Lomax distribution, exponentiated Weibull Poisson distribution, exponentiated exponential geometric distribution, exponentiated exponential Poisson distribution and Lomax distribution which have showed that the former distribution is better to fit the data than the other five distributions.

   Keywords: Complementary risks model; Poisson-Lomax distribution; Progressive type-II censoring; Maximum likelihood estimation; Unweighted and weighted least squares estimations; Bayes estimation; Simulation.

   Pages: 124 – 153 | Full PDF Paper

3. Groups with Fuzzy Operations (F-groups)

   S. S. Davidov and J. Hatami

   Abstract: In this paper, we are going to develop the notion of groups with fuzzy operations (F-groups). An F-group is a set equipped with a fuzzy equality and a binary fuzzy operation. In the rest, we investigate the notions of fuzzy subgroup, fuzzy normal subgroup and isomorphism theorems in F-groups setting.

   Keywords: F-algebra, F-group, Fuzzy subgroup, Fuzzy normal subgroup, Isomorphism theorems.

   Pages: 154 – 165 | Full PDF Paper

4. Correlation of Quantitative and Qualitative Evaluation Methods of Modern Transborder Processes

   Dr. habil. Serhii Ustych, Dr. Alex Rovt, Dr. Svitlana Piasetska-Ustych

   Abstract: The presentation examines system-methodological issues of quantitative (primarily statistical) and qualitative analysis of the phenomenon of modern transborder processes, in particular, at the new Eastern EU border. In it has been substantiated the necessity of introducing to the scientific circulation the notion “transborder system” and via it to identify the main components in the number of transborder phenomena. Are offered the basic techniques for expert’ qualitative and quantitative assessment of those components that have been included by the authors of the system for indexation and monitoring of transborder processes. Is also analyzed the value of the system statistical toolkit in the process of empirical sociological research of the borders and transborder phenomena.

   Keywords: qualitative and quantitative methods for assessing social phenomena; transborder processes; transborder system; indexation and monitoring; empirical sociological research.

   Pages: 166 – 177 | Full PDF Paper

5. An Efficient Dual to Ratio and Product Estimator of Population Variance in Sample Surveys

   Subhash Kumar Yadav, Sheela Misra, Ravendra Kumar, Shailendra Verma, Shailendra Kumar

   Abstract: The present manuscript deals with the estimation of population variance using auxiliary variable. Here we proposed an efficient dual to ratio and product type estimator of population variance of study variable utilizing auxiliary information in the form of coefficient of kurtosis and the population mean of the auxiliary variable. To the first order of approximations, the bias and the mean squared error of the proposed variance have been obtained. The optimum value of the characterizing scalar has been obtained. This optimum value of characterizing scalar minimizes the mean squared error of the proposed estimator. The minimum value of the mean squared error has been obtained for this optimum value of the characterizing scalar. A comparison of the proposed estimator has been made with the mentioned existing estimators of population variance. Through an empirical study, the performances of different estimators of population variance are judged by calculating mean squared errors of different estimators. It has been seen that the proposed estimators has minimum mean squared error among all mentioned estimators.

   Keywords: Main variable, auxiliary variable, bias, mean squared error, efficiency.

   Pages: 178 – 188 | Full PDF Paper