The roots of a polynomial have many applications in various sciences. If the polynomial under study has a degree of 4 or more, it will be impossible to find its roots through the coefficients. In this situation, most researchers use numerical methods to find the roots. The purpose of this research is to introduce a relatively simple method for calculating the real roots of a polynomial. In fact, the proposed approach emphasizes the ability of operation research science in the area of finding roots. In the end, some numerical examples are solved with the help of lingo software to better understand the proposed method. The results indicated that the proposed method is remarkably effective in finding the roots of a polynomial. پرونده مقاله

We consider a class of fuzzy stochastic differential equations (FSDE), in which the integrands of thestochastic integrals are not adapted to the duration generated by a Wiener process. Such equations with randomness, fuzziness, and non-adapted processes can be applied in financial models. We discuss the existence and uniqueness of strong solutions.We consider a class of fuzzy stochastic differential equations (FSDE), in which the integrands of thestochastic integrals are not adapted to the duration generated by a Wiener process. Such equations with randomness, fuzziness, and non-adapted processes can be applied in financial models. We discuss the existence and uniqueness of strong solutions. پرونده مقاله

The quadratic assignment problem (QAP) is one of the combinatorial optimization problems belonging to the NP-hard problems’ class and has a wide application in the placement of facilities. Thus far, many efforts have been made to solve this problem and countless algorithms have been developed to achieve optimal solutions, one of which is the Genetic Algorithm (GA). This paper aims at finding a suitable layout for the facilities of an industrial workshop by using a developed genetic algorithm and Taguchi Method (TM). The research method in the current study is mathematical modeling and data was analyzed using genetic algorithm in Minitab and MATLAB. The results show that the Developed Genetic Algorithm (DGA) is highly efficient, as it has the power to discover many optimal solutions. Therefore, according to the obtained results, it is recommended that when the genetic algorithm (GA) is used to solve problems, it is better to run this algorithm several times; because the proposed method increases the variety of answers in the genetic algorithm and power for discovering the optimal solution becomes more. پرونده مقاله

Chemistry is undoubtedly the most practical science in our life, if we pay attention to the nature around us from the moment we wake up until the day ends, we will find that at the moment of the day and night, we are surrounded by different chemicals. And we have work. In fact, many of our daily activities are related to chemical processes. This has caused the expansion of chemistry and has caused the emergence of various problems. This study aims to analyze a classical chemistry problem known as the chemical reaction equilibrium, which has no uniform solution in different scenarios. In other words, different types of chemical reactions may require diverse methods for establishing equilibrium. This paper proposes a simple system for each chemical reaction through the law of conservation of mass (LCM) and basic mathematical concepts. Optimization algorithms (e.g., the genetic algorithm) are then employed to find a solution to this system. پرونده مقاله