Open Access

Article

Article ID: 231

Pseudosymmetric normal paracontact metric space forms admitting (α, β)− type almost η−Ricci-Yamabe solitons

by Tuğba Mert, Mehmet Atçeken

Journal of AppliedMath, Vol.2, No.2, 2024; 175 Views, 78 PDF Downloads

In this paper, we have considered normal paracontact metric space forms ad- mitting (α, β) −type almost η−Ricci-Yamabe solitons by means of some curvature ten- sors. Ricci pseudosymmetry concepts of normal paracontact metric space forms admit- ting (α, β) −type almost η−Ricci-Yamabe soliton have introduced according to choos- ing of some special curvature tensors such as Riemann, concircular, projective, W1 curvature tensor. After that, according to choosing of the curvature tensors, necessary conditions are given for normal paracontact metric space form admitting (α, β) −type almost η−Ricci-Yamabe soliton to be Ricci semisymmetric. Then some characteriza- tions are obtained and some classifications are made under the some conditions.

Open Access

Article

Article ID: 451

H∞ hybrid control and MRD in a steel frame building subjected to excessive vibrations caused by the dynamic action of wind and earthquake

by Michael Dowglas de Gois Silva, Fábio Roberto Chavarette

Journal of AppliedMath, Vol.2, No.2, 2024; 115 Views, 64 PDF Downloads

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.

Open Access

Article

Article ID: 525

Mass-energy equivalence and the gravitational redshift: Does energy always have mass?

by Germano D'Abramo

Journal of AppliedMath, Vol.2, No.2, 2024; 114 Views, 53 PDF Downloads

One of the most widespread interpretations of the mass-energy equivalence establishes that not only can mass be transformed into energy (e.g., through nuclear fission, fusion, or annihilation) but that every type of energy also has mass (via the mass-energy equivalence formula). Here, we show that this is not always the case. With the help a few thought experiments, we show that, for instance, the electric potential energy of a charged capacitor should not contribute to the capacitor’s gravitational rest mass (while still contributing to its linear momentum). That result is in agreement with the fact that light (ultimately, an electromagnetic phenomenon) has momentum but not rest mass.

Open Access

Article

Article ID: 391

Computer visuality in mathematics teaching

by Laxmi Rathour, Dragan Obradovic, Lakshmi Narayan Mishra, Vishnu Narayan Mishra

Journal of AppliedMath, Vol.2, No.2, 2024; 54 Views, 24 PDF Downloads

The purpose of this study is to look at the changes that computers have made in mathematics itself and in the mathematics curriculum. The aim of the study is to investigate the various applications of computers in education in general, especially in mathematics education, and their application in the mathematics curriculum and in the teaching and learning of mathematics. The primary use of educational tools for mathematical purposes is the quality verification of results. There are various tools for developing student logic based on interactivity. Mathematics education tools are designed for innovative, interactive, and dynamic learning in different areas of mathematics. It is undeniable that the use of computers and mathematical software has great benefits that have been proven and presented in their works by numerous researchers of effective learning. It is also indisputable that one of the main tasks of teaching mathematics is the development of students’ constructive thinking. This work aims to describe the application of educational tools with which it can develop interactivity and help pupils and students to better and more clearly understand mathematics and to understand that it is all around us, that it is our everyday life.

Open Access

Article

Article ID: 405

Relativistic light clocks: Arbitrary orientation in uniform motion and hyperbolic motion analysis

by Adrian Sfarti

Journal of AppliedMath, Vol.2, No.2, 2024; 21 Views, 14 PDF Downloads

In this paper, we address the general case of a light clock in uniform translational motion parallel to itself and perpendicular to its uniform velocity v , as well as the case of the light clock in relativistic hyperbolic motion. Neither case has been previously addressed in the specialized literature, which typically restricts itself to canonical orientations where the light clock moves parallel to either the vertical or horizontal axis with uniform velocity, without acceleration. Therefore, it becomes interesting to study the more general case where the clock has an arbitrary orientation and/or is accelerated. Our paper is divided into two main sections. The first section deals with the light clock moving with constant velocity, oriented at an arbitrary angle with respect to the x-axis. We prove that the moving clock exhibits a standard time dilation, identical to that of a light clock moving in a canonical orientation. The second section deals with the light clock moving with constant acceleration, i.e., in hyperbolic motion. For the light clock in hyperbolic motion, we derive the period as measured from the perspective of an inertial frame and draw parallels with the case of uniform motion, outlining a term that is similar (but not identical) to the γ factor of uniform motion. We also point out that this factor depends not only on acceleration but also on the height of the light clock. This dependency on the dimension of the light clock distinguishes the accelerated case from the case of uniform motion. The first three sections deal with the theoretical aspects of light (optical) clocks, while the fourth section addresses the experimental implementations of optical clocks.