elnaz hosseini

In this paper, two new methods are presented to find the optimal control of systems described by linear differential equations that have interval coefficients. In these methods, the given interval optimal control problem is transformed into a non-interval (deterministic) optimal control problem so that it is possible to use the optimal control theory to solve it. By considering the variation limits for the control signal, the optimal solution of the main problem is obtained.

In this research, two methods are presented to solve the deterministic sub-models of linear interval optimal control problems and find a good approximation for the optimal solution of them. In the first method, by using the center of intervals, the given interval optimal control problem becomes a deterministic optimal control problem and it is possible to use the Pontriagin conditions to solve it. By considering a resilience variable for the resulting solution, the limits of the control signal changes and the interval optimal solution for the main problem are obtained. In the second method, we first solve the optimal control problem for the beginning and the end of the interval, and at any time we consider the lowest value as the lower bound and the highest value as the upper bound of the interval solution. Then, by applying the constraints of the problem, we calculate the resilience of the state variable and the control signal. We also used Hokuhara's difference to reduce the error in interval calculations.

Solving optimization problems using the interval optimal control approach, show that the optimal solution of the submodel that is solved by any of these two methods is within the range of the solution of the main problem. In addition, the solutions of these problems are also presented as interval values.

Originality/Value:

 To obtain the numerical results, MATLAB software and INTLAB software package of interval calculations have been used. These approaches are categorized into indirect methods for solving optimal control problems, while it is far from their defects, e.g. curse of burdensome computational load, so that interval approach is applied to simply solve the problems.

Sclerosing stromal tumor of the ovary is believed to be a rare, benign, sex cord stromal tumor occurring predominantly in younger women in the 2nd and 3rd decades of their life. The prevalent clinical presentations include pelvic or abdominal pain, mass, or menstrual changes. Even though it is occasionally accompanied by hormonal manifestations, virilization as a result of androgen production by the tumor is rare. The present research was conducted to present a rare case of bilateral sclerosing stromal ovarian tumor in a 20-year-old patient with irregular menstruation and pelvic pain. All of the sclerosing stromal tumors were benign and were treated successfully with enucleation or unilateral oophorectomy.

Studying the biographies of great scientists can lead to more effectively understanding their intellectual path. As we learn how other people made novel discoveries, we learn new ways of thinking that might allow us to make our own new discoveries. In addition, through learning about the history of science, we read about great scientists who thought outside the box. We also see how science is influenced by the culture. In this way, we discover the history of science. In this study, the biographies of Razi and Avicenna, two great Iranian scientists and Newton and Pasteur, two great Western scientists have been studied. In this paper, in addition to mentioning the discoveries and inventions of these great scientists, their moral highlights have been addressed. Some of the opinions and thoughts of these scientists are summarized: Razi was the first physician to free himself from the unquestioning beliefs. He chose experimental and practical methods, and he rejected what seemed wrong in practice. He imported experimental methods in natural sciences (especially medicine and chemistry) 1500 years ago. Razi was one of the pioneers of Alchemy knowledge as he wrote a book entitled Al-Asrar or Secrets of the Alchemy Industry. Razi's opinion about animals, plants, and living things is as follows: It is not permissible to harm a living thing unless we have removed the most severe suffering from it. One of the important issues at corona virus(COVID-19) time knows about quarantine ruled by Avicenna. Avicenna announced the first rules of quarantine and hygiene regarding the plague, including: wash your hands with water and vinegar, stay at home, do not go to the mosque, keep your distance, shops are closed only grocery stores and basic necessities should be open. One of his most important tips was to be completely hygienic but not afraid of the plague. Fear causes the plague to come to you. One of Avicenna's views was that prejudice in science and philosophy, like any other prejudice, is a sign of crudeness and futility and always ends up to the detriment of truth. Newton said: he made most of his discoveries during the 18-month quarantine period due to the outbreak of the plague, which he called the Golden Age until many years later. Another great quote from Newtown: You can never do great things with small people. Pasteur achieved remarkable achievements such as disinfectant for the room and surgical instruments, anthrax vaccine and rabies vaccine, which undoubtedly changed human life, and after him, the principles of its foundation were shared with other scientists. It was very effective in treating typhus, cholera, diphtheria and yellow fever. One of Pasteur's great quotes: The role of infinitesimal beings in nature is infinitely large.

There are different methods for the killing of animals around the world. The Islamic method of animal slaughtering, called halal slaughter. Several studies have shown that different type of slaughtering was influenced on post-mortem quality, chemical and biochemical composition such as iron, heme and glucose levels in blood, as well as physical properties such as color and water holding capacity of the meat and its antimicrobial properties. In this Study, a comparative of halal slaughtering to other types of slaughtering was performed. In this paper, safety and quality of halal meat and other killings are examined from the perspective of biochemistry, biophysics and microbial biology.