Vol. 2 No. 2 (2024)

  • 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; 142 Views, 52 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.

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  • 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; 95 Views, 48 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.

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  • 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; 90 Views, 41 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.

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