Optimal portfolio selection and how to invest in, is one of the key issues which is considered in the capital market and should be paid attention by investors. In this regard, investors studies in selecting optimal portfolio accords to risk and return level. What has been done in the field of financial calculations and portfolio selection should prioritize existing investments in terms of risk and return respectively, until investors be able to constitute their optimal portfolio according to the finance and their level of risk-taking. Hence, measuring risk is considered as a major issue in the investment of portfolio. So in this research which was done in a capital market of Iran, it is presented a multi objective single - period MATHEMATICAL MODEL for measuring the risk of portfolio which integrates measure of return and two measures of risk (semivariance, Cvar). This MODEL enables investors to measure the risk of portfolio carefully under transactions cost constrains and invest in a portfolio with maximum rate of return and minimum rate of risk Results show that using integraed risk measure can increase the carefulness of investors in capital market for optimal portfolio selection.

A numerical MODEL for simulating Residence Time Distribution (RTD) of turbulent flows in helical static mixers is proposed and developed to improve the understanding of static mixers. The results of this MODEL is presented in terms of different volumetric flow rate to illustrate the complicated flow patterns that drive the mixing process in helical static mixers. The computed results are also used to predict the amount of mixing that occurs within a mixing device. Such theoretical estimates need, however, always to be thoroughly checked against observations in static mixer. To check the reliability of the theoretically estimated RTD from the simulation by the application of the MODEL equation, a comparison of the same with those obtained from observed data experiments in static mixer using statistical characteristics is done. Comparison between RTD curves shows that motionless mixture can improve the performance of reactor.

Nowadays, the systematic transfer of customers, demands and comments and converting them to practical measures in line with the modification or correction of the product have become of immense importance for the companies in order to achieve success and competitive primacy. In this regard, companies have proceeded to seek higher levels of quality for their products and services as well as to improve them continually in order to keep up with the rapid pace of progress and change all over the world. The present survey attempts to present a MATHEMATICAL MODEL for quality function development (QFD) based on fuzzy approach which can consider customers’ demands and comments. For this purpose, first the demand and desired technical properties were identified by using QFD method. Then, by ANP method, we specified the demands and weighed technical properties as well as the rate of the correlation of demand and technical properties. Finally, the idealistic programming MODEL was presented which includes different level of importance of technical needs through the use Fuzzy ANP method, such as limitation of financial resource, rate of feasibility, and degree of competitiveness, which should be considered in the designing phase. In conclusion, in order to test the presented MODEL, we have shown the result of applying the MODEL in a case study related to the production line of “Axel” in “X” industrial manufacturing company.

In this paper, parametric technology display and a MATHEMATICAL MODEL of technology spillover as a different approach based on the technology changes would be discussed. The recently action that will be accomplished through formation matrices of technological changes, measure of technology spillover and other concepts along with a variety of matrices types. Several examples are given and the result would be helpful in mathematics, management and technology fields.

Product development process has its specific complexity. This complexity can also be due to overlapping and dependent relationships (coupling) amongst activities in a product development process. On one hand overlapping may reduce duration of a project on the other, it engenders rework risk. In addition, coupled activities are another reason for rework risk too. This iteration and rework caused by overlapping and coupling of activities results in increasing time and cost of the project. In this article, a MATHEMATICAL MODEL is presented to study the characteristics of the product development process and also to balance the duration and cost of it. According to the overlapping and the amount of dependent relationships among activities, four types of time MODELs have been formulated. Furthermore to verify the process, the MODEL has been implemented in MATLAB and an example has been solved. It is observed that the proposed MODEL is easily able to calculate the time and cost of the process in all four types.

Plant development can be defined as a programmed qualitative change in plant form, which leads plant to maturity, and researchers call it as phasic development or phenology. Recognizing the timing of occurring each development stage is necessary for managing system in order to yield increment. The timing of occurring development stages depend on climate, genotype specifications and sowing date then determination of these times in different regions is difficult and it is only possible through the using of crop simulation MODELs which can predict the timing of occurrence each development stage by integrating effective factors. The MODEL was constructed based on linear equation of plant temperature response. In order to MODEL evaluation two experiments were carried out in agricultural and natural resources research center of Khuzistan in 2003-2004 and 2004-2005 cropping years. Wheat development stages were determined based on Kirby and Appleyard’s scale by stereoscopic microscope and required GDD for each development stage as well. The constructed MODEL was calibrated and run for simulation. Comparison of simulated and observed data showed that the MODEL can strongly predict wheat development stages.