Volume 8 (2016), Number 1

A Mathematical Model for the Universe Expansion

Author(s): MALVINA BAICA and MIRCEA CARDU

Abstract: In this paper we briefly introduce the Universe Expansion Phenomena and we comment about its graphical representation, in the spatial perspective, which appears in the specialized literature. Starting from this spatial representation, we trace the in plane representation of this phenomena. In order to find the mathematical model corresponding to the graphical representation of the Universe expansion we apply the paratrigonometric functions presented in [6]. Finally, we establish the needed mathematical model.

Weighted Reverse Inequalities of Jensen Type for Functions of Selfadjoint Operators

Author(s): S.S. DRAGOMIR

Abstract: On making use of the representation in terms of the Riemann-Stieltjes integral of spectral families for selfadjoint operators in Hilbert spaces, we establish here some weighted reverse inequalities of Jensen's type for convex functions of operators. Some applications for simple functions of operators are also provided.

On $(h-m)$-Convexity and Hadamard-Type Inequalities

Author(s): M. EMIN ÖZDEMIR, AHMET OCAK AKDEMIR and ERHAN SET

Abstract: In this paper, a new class of convex functions as a generalization of convexity which is called $(h-m)$-convex functions and some properties of this class is given. We also prove some Hadamard's type inequalities.

About Differential Sandwich Theorems Involving a Multiplier Transformation and Ruscheweyh Derivative

Author(s): ALB LUPAȘ ALINA

Abstract: In this work we study a new operator $I{R}_{\lambda ,l}^{m,n}$ defined as the Hadamard product of the multiplier transformation $I\left(m,\lambda ,l\right)$ and Ruscheweyh derivative $R^n$, given by $I{R}_{\lambda ,l}^{m,n}:\mathcal{A}\to \mathcal{A}$, $I{R}_{\lambda ,l}^{m,n}f\left(z\right)=\left(I\left(m,\lambda ,l\right)\ast R^n\right)f\left(z\right)$ and ${\mathcal{A}}_n=\{f\in \mathscr{H}\left(U\right):f\left(z\right)=z+a_{n+1}{z}^{n+1}+\mathrm{...,}z\in U\}$, is the class of normalized analytic functions with ${\mathcal{A}}_1=\mathcal{A}$. The purpose of this paper is to derive certain subordination and superordination results involving the operator $I{R}_{\lambda ,l}^{m,n}$ and we establish differential sandwich-type theorems.

Determining Thermoelastic Strains and Stresses Created by the Temperature Field and Constrictions Exerted on the Contours of the Reconditioned Cylindrical Piece

Author(s): DUMITRU ȘEREMET

Abstract: The main purpose of this article is to determine the distribution of displacements and thermal stresses in composite coatings applied as a compensating layer on reconditioned car parts by means of the squeeze technique. To achieve the purpose means to meet some objectives like: to obtain axial symmetrical displacements and stress fields that are distributed on the thickness of the composite material layer; to validate the received results by solving the boundary value problem by means of the direct integration method and the Green’s function method. As a result of mathematical modeling and theoretical analysis we propose a method to calculate displacements and stresses in different layers of the composite coating, taking into account their constraints too. Analytical expressions and graphs were built for both Green’s functions and heat fields and thermoelastic displacements and stresses for axial symmetrical boundary problems of heat conduction, elastic and thermoelastic theories. The graphic representation has been made using the Maple 15 software. The obtained data can be used for engineering design calculations and choosing appropriate interference fits renovated with composite materials.

In Memoriam Professor Doctor Docent SOLOMON MARCUS