The natural algorithmic approach of mixed trigonometric-polynomial problems

The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to analyze some new rational (Pade) approximations of the function $\cos^2(x)$, and to improve a class of inequalities by Z.-H. Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities

Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type

About some exponential inequalities related to the sinc function

In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which these inequalities hold

WHAT ADVICE SHOULD BE GIVEN TO PEOPLE WITH EPILEPSY – PHYSICAL ACTIVITY, YES OR NO?

People with epilepsy (PWE) face numerous difficulties. Because of the complicity of the disease, a thorough treatment of those patients requires a multidisciplinary approach. One of the important aspects such approach should take into account is the quality of life of PWE. Apart from the pharmacological solutions, it is necessary to further search for non-pharmacological ones. In addition to raising education and level of awareness this means dealing with physical activity due to numerous benefits. Sometimes doctors themselves do not know how to assess risks and benefits, and in order to protect the patients, advise that it is best not to engage in any sport, thereby contributing to the vicious circle - fear - stigma - poor quality of life. The aim of this paper is to unify the experiences of various researchers on this topic, to point out the many difficulties that PWE meet, and to define guidelines in the workplace. We will try to answer a commonly posed question which sometimes in practice remain unclarified, that is - whether epilepsy patients should be involved in sports, if so - which sport, and what intensity of physical activity would be allowed, can they participate in the competitions. In order to provide patients with a decent life quality it is necessary to work on the education of patients and doctors, and the society as well. While giving recommendations, it is necessary to follow the guidelines, among which are the most comprehensive ones were created by the International League Against Epilepsy (ILAE) in 2016

Refinements and generalizations of some inequalities of Shafer-Fink’s type for the inverse sine function

Abstract In this paper, we give some sharper refinements and generalizations of inequalities related to Shafer-Fink’s inequality for the inverse sine function stated in Theorems 1, 2, and 3 of Bercu (Math. Probl. Eng. 2017: Article ID 9237932, 2017)

Contribution to improvement of the legalization of the work process of small-scale mines in the Republic of Serbia

In this study we focus our attention on the procedures of obtaining necessary permits for the opening of a mine. Our goal is during those conditionally speaking first steps in the process of activating a mine to point to the attention of the reader to the complexity of that process, as well as excessive administrative work when permits for small-scale mines are in question