Mathematical Analysis and its Contemporary Applications
https://www.macajournal.com/
Mathematical Analysis and its Contemporary Applicationsendaily1Fri, 01 Mar 2024 00:00:00 +0330Fri, 01 Mar 2024 00:00:00 +0330Some Analytical Properties of the Hyperbolic Sine Integral
https://www.macajournal.com/article_711543.html
By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational bounds for the hyperbolic tangent function.Some inequalities of the Edmundson-Lah-Ribarič type for 3-convex functions with applications
https://www.macajournal.com/article_711906.html
In this paper, we study 3-convex functions, which are characterized by the third-order divided differences, and for them, we derive a class of inequalities of the Jensen and Edmundson-Lah-Ribarič type involving positive linear functionals that do not require convexity in the classical sense. A great number of theoretic divergences, i.e. measures of distance between two probability distributions, are special cases of Csisz&aacute;r f-divergence for different choices of the generating function f. In the second part of this paper, we apply our main results to the generalized f-divergence functional to obtain lower and upper bounds. Examples of Zipf&ndash;Mandelbrot law are used to illustrate the results. In addition, the obtained results are utilized in constructing some families of exponentially convex functions and Stolarsky-type means.Stability of two multi-quadratic mappings by a fixed point method
https://www.macajournal.com/article_711907.html
In this paper, the Gavruta stability of two multi-quadratic functional equations is established by a known fixed point theorem. As an example, the Hyers-Ulam, and Rassias stability and hyperstability of the mentioned mappings are proved in the setting of Banach spaces.Jafari variation iteration method for solving one-dimensional fractional diffusion equation
https://www.macajournal.com/article_712323.html
H. Jafari proposed a new integral transform recently, namely, the Jafari transform, which covered all classes of integral transforms in the class of Laplace transform, such as Laplace, Sumudu, Elzaki, Aboodh, natural, Shehu transformation, etc. In this paper, we utilize a semi-analytical technique, namely the Jafari variational iteration method, abbreviated JVIM, and we apply this technique to resolve one-dimensional diffusion equations with fractional order type using the Caputo fractional derivative. The results are compared with the homotopy analysis Shehu transform method (HASTM). Also, the results show the suggested algorithm is efficient, accurate and a powerful technique for solving a wide variety of linear and non-linear problems arising in various scientific areas.Fixed point theorems in intuitionistic fuzzy 2-metric spaces
https://www.macajournal.com/article_709204.html
In the paper, we find some fixed point theorem in intuitionistic fuzzy 2-metric spaces on four mappings and six mappings with the help of the theory of sub-compatibility of type (A).Optimizing airfoil efficiency for offshore turbines through aerodynamic geometry enhancement
https://www.macajournal.com/article_711544.html
Initially, the optimal Thickness-to-Camber ratio (t/c) of the SG6043 airfoil was examined across Reynolds numbers (Re) ranging from 10,000 to 500,000, typical for Small Wind Turbines (SWTs) using QBLADE software. The ideal t/c increased between 0.5 and 1.50, surpassing the SG6043 airfoil in peak Lift-to-Drag ratio coefficient (CL/CD). Subsequently, three modified airfoils were developed within the t/c range of 0.5 to 1.5. Results demonstrated improved aerodynamic coefficients in the modified airfoils as Re increased. Notably, the Case 3 airfoil exhibited the highest maximum CL/CD of 176.97 at Re 500,000. Furthermore, Case 1 and Case 2 yielded maximum CL/CD values of 172.43 and 171.08, respectively. The airfoils in Cases 2, 1, and 3 achieved peak Lift Coefficients (CL) of 1.847, 1.82, and 1.77, respectively. Specifically, at Re except for 100,000, the Case 2 airfoil outperformed the other modified and SG6043 airfoils in terms of CL. At Re &le;100,000, the Case 1 airfoil demonstrated a higher maximum CL/CD compared to other modified and SG6043 airfoils. Across the Re range of 10,000 to 500,000, the Case 2 airfoil consistently achieved the highest peak CL/CD. This research was validated through experimental work and compared with the EYO-Series airfoils.