In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc ...function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions. Based on this approach, some optimal approximations of the sinc function are derived by determining the corresponding minimax approximants.
This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals ...using the Maclaurin series to approximate the exponential function precisely. Additionally, we discuss the relation between MEPs and stratified families of functions from 1 through two applications, referring to inequalities from papers 2 and 3.
In this paper, we generalize Cristinel Mortici’s results on Wilker-Cusa-Huygens inequalities using stratified families of functions and SimTheP – a system for automated proving of MTP inequalities.
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc ...function are obtained. This extension of Jordan's inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions. Based on this approach, some optimal approximations of the sinc function are derived by determining the corresponding minimax approximants.
This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals ...using the Maclaurin series to approximate the exponential function precisely. Additionally, we discuss the relation between MEPs and stratified families of functions from Malesevic_Mihailovic_2021 through two applications, referring to inequalities from papers Wu_Zhang_2004 and Chesneau_Bagul_Dhaigude_2022.
U ovom radu prikazan je jedan edukativni softver za računanje korena realnih i kompleksnih polinoma stepena manjeg od pet. Dat je opšte poznat postupak za računanje korena polinoma stepena dva. Zatim ...je napravljena generalizacija za polinome stepena tri i četiri (Kardanove i Ferarijeve formule, respektivno). Napravljene su tri interaktivne Jupyter sveske koje omogućavaju korisniku da menja vrednosti koeficijenata polinoma i da prati sve korake u simboličkom računanju korena polinoma.
In this paper, we generalize Cristinel Mortici's results on Wilker-Cusa-Huygens inequalities using stratified families of functions and SimTheP - a system for automated proving of MTP inequalities.
In this paper, a parametric method for proving inequalities is described. The method is based on associating a considered inequality with the corresponding stratified family of functions. Many ...inequalities from the theory of analytic inequalities can be interpreted using families of functions that are stratified with respect to some parameter. By discussing the sign of the functions from the family by the parameter according to which the family is stratified, inequalities are obtained that contain the best possible constants, if they exist. The application of this method is demonstrated for four inequalities: the Cusa–Huygens inequality, the Wilker-type inequality and the two Mitrinović–Adamović-type inequalities. Significantly simpler proofs and improvements of all these inequalities are provided.
Open surgical aortic valve replacement (SAVR) is a viable alternative to transcatheter implantation in low-risk patients. In this light, we evaluated the safety and effectiveness of SAVR performed ...through conventional and less invasive surgical approaches in a high-volume center. We retrospectively reviewed the records of 395 consecutive patients who underwent open SAVR from January 2019 through December 2019 in our center. We evaluated and compared the operative results and postoperative major adverse outcomes of 3 surgical approaches: full median sternotomy (n=267), upper ministernotomy (ministernotomy) (n=106), and right anterior thoracotomy (minithoracotomy) (n=22). Overall, the 30-day all-cause mortality rate was 0.8% (3 patients). Stroke occurred in 8 patients (2%), disabling stroke in 4 patients (1%), myocardial infarction in 1 (0.2%), and surgical site infection in 13 (3.2%). There was no difference in 30-day mortality rate or incidence of postoperative major adverse events among the 3 surgical groups. Stroke and surgical site infection occurred more frequently, but not significantly so, in the full-sternotomy group. The mean hospital stay was longer after full sternotomy (9.1 ± 5.5 d) than after ministernotomy (7.5 ± 2.9 d) or minithoracotomy (7.4 ± 1.9 d) (P=0.012). Our findings suggest that open SAVR performed in a high-volume center is associated with a low early mortality rate and that less invasive approaches result in faster postoperative recovery and shorter hospital stays.
Temperature distribution in the metallic plate influenced by high frequency electromagnetic wave depends on thermal and electrical properties of the plate material. The goal of the paper is to ...present the significance of the temperature dependence of the electrical resistivity and its influence on the plate heating. A mathematical model of the problem was established and an analytical closed-form solution the problem was presented. The active power of the electromagnetic wave was calculated by Poynting vector. Temperature field was obtained by integral-transform technique. Numerical examples were presented for three different materials (copper, aluminum, and steel). Calculated results show the large influence of temperature dependent electrical resistance on heating of the metallic plate.
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