International Journal of Science
Volume:6 Issue: 2, 2005

In this paper, we present and study the notion of firm θ -continuity toinvestigate θ -compactness.

Evaluation and selection of research projects are two important activities in decision making process of research and expertise panels and councils. They involved in participating a group of experts and decision-makers to evaluate the research projects with considering a set of criteria, then selecting a set of projects which better meet anorganizations'' objectives. On the one hand, research projects evaluation needs experts and decision-makers'' judgments. In many situations, experts and decision-makers have vague and uncertain knowledge about subjects and things, so they can not express themwith number values. In such situations, a realistic approach is linguistic one. According to this approach, experts can express their judgments and preferences by linguistic terms. Fuzzy set theory provides the requirement flexibility for representing uncertainty ariseof subjectivity of humans and their uncertain and vague knowledge. On the other hand, research projects portfolio selection involve using optimization models and techniques which meet multiple objectives of organization without exceeding available resources or violating other constraints. In this article, we have designed a model of mathematical programming based on integrating fuzzy set theory and Genetic algorithm optimization technique.

We present a multi-objective genetic algorithm for mining highly predictive and comprehensible classification rules from large databases. We emphasize predictive accuracy and comprehensibility of the rules. However, accuracy and comprehensibility of the rules often conflict with each other. This makes it an optimization problem that isvery difficult to solve efficiently. We have proposed a multi-objective evolutionary algorithm called Improved Niched Pareto Genetic Algorithm (INPGA) for this purpose. We have compared the rule generation by INPGA with that by simple genetic algorithm (SGA)and basic Niched Pareto Genetic Algorithm (NPGA). The experimental result confirms that our rule generation has a clear edge over SGA and NPGA.

In this paper we consider the periodically correlated first-order autoregressive (PCAR(1)) process with period T and periodic white noise. One problem in studying this model is to estimate periodic coefficients from an observed segment. For ordinary stationary AR(1) model, a median unbiased estimate of the coefficient is well-known. This paper is concerned with the median-unbiased (MU) estimation of the periodic coefficients of the PCAR(1) process with period T. Our median unbiased estimator is an adaptation with the periodic case of the well-known work of Zielinski. The method of estimation is illustrated by simulated data.

A fully Bayesian approach for sample size determination for a clinical trial is presented in which the final decision whether to use the newtreatment is taken by potential users and their medical advisers on the basis of the strength of the evidence provided by the trial. Data are assumed to come from two independent binomial distributions and theparameter of interest is 1 2 p = p − p, where 1 p and 2 p are two independent proportions. The optimal size is obtained by maximizing the expected net benefit function, which is the expected benefit from subsequent use of the new treatment minus the cost of the trial.

An extended model of asset price dynamics for modeling stochastic upward and downward jumps in asset prices is developed, and the modified Black-Scholes solution for value of vanilla options is derived. The change in volatility is identified in detail using the Itô integrals and Itô formulas.

The complex form of two first order real equations with a linear boundary condition, existence and uniqueness of the solution of the boundary value problem is studied using a function theoretic method. Keywords: Complex functions, System of partial differential equations in the plane, Non-Uniformly elliptic Lavrentiev type, Boundary values problem