The optimal portfolio selection is vital for investment. The risk of portfolio Selection and return is the most critical concern of investment companies and private investors. According to modern portfolio theory, diversification should cover the risk. This theory is based on the normality of assets return. Experimental findings indicate that the assets return non-normality. Higher moments are sed to upgrade traditional models with the primary presumption of a normal distribution in recent years. This study uses a higher moment and the entropy for diversification and selects a portfolio given a non-normality assumption. It is essential to use up-to-date information to increase the model's efficiency, and accordingly, we used the Rolling window for new price information. For the financial information method, we use the total index return in the last five working days and weigh the shares of the banking, insurance, and leasing industries on the next working day and evaluate this for three years. Python, math, and NumPy libraries were used to analyze the data. The results show that a much higher moment model can provide better portfolio selection results in most cases.

Influential parameters of the planetary Rolling process for the production of copper pipes were initially defined as the reduction of area, feed (α) and inclination (β) angles, material entry rate or input rate, roller’s shape and the rotational speed of the rollers. For evaluating the effects of these parameters, finite element method was selected as the best choice of continuum simulation procedures to reduce costs and save time. Extensive simulations revealed that for any specific reduction of area, feed and inclination angles, there should be a positive correlation between the rotational speed of the rollers and the material input rate for production of geometrically sound copper pipes. This finding brought the possibility of determining the suitable combinations of the influential variables for the production of geometrically sound pipe. These combinations can be summarized as the planetary Rolling process windows at different area reductions, varying feed and inclination angles. These process windows show that by increasing the area reduction, the production range of the pipe becomes confined to the limited ranges.

Inability to identify asset price bubbles and their types (single and multiple) causes adverse effects on economy. New economic instruments make, not only the analysis of mild explosive behavior but also the determination of origination and termination of bubbles possible, of bubbles possible. The present study aims to detect price bubbles of Tehran stock exchange and OTC, and determine date of origination, burst, and complete deletion of bubbles in the period of 2010.03 to 2016.03. To this end, the study uses total index, industry index, index of 50 firms and total OTC index. The results show that the stock market and OTC have experienced 2 and 5 bubble periods, respectively. The results also show that stock and OTC markets were bubbling in 59% and 57% of sample period, respectively. Therefore, these markets have had bubbles in more than half of the study period indicating the great instability in the stock prices.

Abstract: The forging model for cold Rolling is one of the Rolling models which is used in Rolling calculations. In this model, the final Rolling pressure is an average value and it is not as accurate for actual and industrial cases. Also, by using forging model, friction hill curves are plotted due to the central point of Rolling bite length while frictional stresses intersect at the neutral point of Rolling bite. In this study, a new model based on the forging model is presented to determine the Rolling pressure during cold Rolling process for using in a reversing tandem mill, where this is called “Improved forging model”. In the proposed model, the intersection of the frictional forces is the neutral point. Finally, the computing results from this new model coincide well with the precedent investigations.