Journal of AppliedMath

A new definition of a variable order derivative is given. It is based on interpolation of integer order differentiation operators. An interpolation operator of the Hermite-Fejér type is built to jointly interpolate the function and its derivative of variable order. The upper estimate of the norm of this operator is obtained. This norm has been shown to be limited.

The objective of this paper is to study some properties of quasi-conformal and concircular tensor on (ϵ)-Kenmotsu manifold admitting the Schouten-van Kampen connection. Expressions of the curvature tensor, Ricci tensor and scalar curvature admitting Schouten-van Kampen connection have been obtained. Locally symmetric -Kenmotsu manifold admitting Schouten-van Kampen connection and quasicon formally flat as well as quasi-conformally semisymmetric -Kenmotsu manifolds admitting Schouten-van Kampen connection are studied.

As we know, the interpolation is one of the most basic and most useful numerical techniques in Mathematics. Newton’s forward interpolation method is one of most important of these methods. Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist to find roots. But in this paper, we introduce the interpolation technique for this purpose. The proposed method derived from the newton forward interpolation method and we compared the results with another existing method (Bisection Method (BM), Regula-Falsi Method (RFM), Secant Method (SM), Newton Raphson Method (NRM)) and the method proposed by J. Sanaullah (SJM). It’s observed that the proposed method has fast convergence but it has same order of convergence of the method (SJM). Maple software is used to solve problems by different methods.

Multi-attribute group decision-making (MAGDM) is very significant technique for selecting an alternative from the provided list. But the major problem is to deal with the information fusion during the information. Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN) are the most generalized and flexible t-norm (TN) and t-conorm (TCN) which is used for information processing. Moreover, the interval-valued T-spherical fuzzy set (IVTSFS) is the latest framework to cover the maximum information from the real-life scenarios. Hence, the major contribution of this paper is to deal the information while the MAGDM process by introducing new aggregation operators (AOs). Consequently, the interval-valued T-spherical fuzzy (IVTSF), Aczel-Alsina weighted averaging (IVTSFAAWA), IVTSF Aczel-Alsina (IVTSFAA) ordered weighted averaging (IVTSFAAOWA), IVTSFAA weighted geometric (IVTSFAAWG), IVTSFAA ordered weighted geometric (IVTSFAAOWG), and IVTSFAA hybrid weighted geometric (IVTSFAAHWG) operators are developed. It is shown that the proposed operators are the valid and the results obtained are reliable by discussing some basic properties. To justify the developed AOs, an example of the MAGDM is discussed. The sensitivity of these AOs is observed keeping in view of the variable parameter. To show the importance of the newly developed theory, a comparison of the proposed AOs is established with already existing operators.

The goal of the manuscript is to design a relatively best control structure for the noise suppression of a drone’s camera gimbal action. The gimbal’s movement can be simplified as a rest-to-rest reorientation system that can achieve the boundary result of a dynamic system. Six different control architectures are proposed and evaluated based on their ability to control the trajectory of the dynamic-system position and speed, their running time, and quadratic cost. The robustness of the control architecture to uncertainties in inertia and sensor noise is also analyzed. Monte Carlo figures are used to assess the performance of the six control systems. The conditions for applying different architectures are identified through this analysis. The analysis and experimental tests reveal the most suitable control of the drone’s camera gimbal rotation.

In nonparametric regression, the correlation of errors can have important consequences on the statistical properties of the estimators, but the focus is identification of the effect on Average Mean Squared Error (AMSE). This is performed by a Monte Carlo experiment where we use two types of correlation structures and examined with different correlation points/levels and different error distributions with different sample sizes. We concluded that if errors are correlated then distribution of error is important with correlation structures but correlation points/levels have a less significant effect, comparatively. When errors are uniformly distributed, then AMSE are smallest then any other distribution and if errors follow the Laplace distribution then AMSE are largest then other distributions also Laplace have some alarming effect. More keenly, kernel estimator is robust in case of simple correlation structure, and AMSEs attains their minimum when errors are uncorrelated.

Electronic tips systems have become very popular in the era of cashless payments. With the widespread use of such services, the problem of maximizing profits has arisen, which concerns both establishments using electronic tips services and the services themselves that provide such services. Identifying factors that influence guests’ economic behavior when leaving tips will allow for the creation of an optimal strategy to increase the efficiency of the system. This study used data on the profits of the electronic tips service in public catering establishments. A simulation model was created to evaluate and compare the effectiveness of different strategies, a methodology for finding the optimal strategy was described, and a clustering of establishments was performed using analysis of variance to customize the optimal strategy.

Covid-19 and its variants, have been a worst pandemic, the entire world has witnessed. Tens of millions of cases have been recorded in over 210 countries and territories as part of the ongoing global pandemic that is still going on today. In this paper, we propose a SEI mathematical model to investigate the impact of lockdown to the controlling and spreading of infectious disease COVID-19. The epidemic model incorporates constant recruitment, experiencing infectious force in the latent period and the infected period. The equilibrium states are computed. Under some conditions, results for local asymptotic stability and global stability of disease-free and endemic equilibrium are established by using the stability theory of ordinary differential equations. It is seen that when the basic reproduction number , the dynamical system is stable and diseases die out from the system and when , the disease persists in the dynamical system. When , trans critical bifurcation is appeared. The numerical simulations are carried out to validate the analytical results.

This article considers a boundary value problem for one non-linear second-order functional differential equation on the segment [0, 1] with an integral boundary condition at one of the ends of the segment. Using the well-known Go-Krasnoselsky theorem, sufficient conditions for the existence of at least one positive solution of the problem under consideration are established. A non-trivial example is given, illustrating the fulfillment of the conditions for the unique solvability of the problem posed.

We propose in this work to describe all the generalized-function solutions of the non-homogeneous first-order linear singular differential equation with  two real numbers, s and     , in the space of generalized functions K’. In the case of a second right-hand side consisting of an s-order derivative of the Dirac-delta function, we have completely investigated the considered equation when we look for the solution in the form of  with the unknown coefficients  which we have determined case by case, taking into account the relationship between the parameters inside. On the basis of what has been done, we focus our present research to apply the principle of superposition of the solutions that is conducting us to the awaited result when we also maintain the classical solutions of the homogeneous equation which remains the same.

In this experimental research paper, we investigate the potential enhancement of Co-doped Zn_0.5Ni_0.5Fe_2-xCo_xO₄ for (x = 0.0, and 0.0250) ferrites, synthesis by green synthesis method for applications in medicine. The structural analysis of the synthesized material is a crucial step in understanding its suitability for medical applications. X-ray Diffraction (XRD) is employed to elucidate the crystallographic structure of the Co-doped ZnNiFe₂O₄ ferrites. The results demonstrate that the doping process has a significant influence on the material’s crystal structure, which may impact its potential in various biomedical applications. The Co-doped ZnNiFe₂O₄ spinel ferrite materials become more suitable for medical applications as the decrease in X-ray density and simultaneous increase in bulk density can facilitate better tissue penetration and biocompatibility, making them ideal for non-invasive medical imaging and therapeutic applications, while minimizing potential health risks.

Einstein predicted a change in the energy of photons in the proximity of a gravitational field, the change being directly proportional with the distance from the gravitational source. In the early 60’s Pound and Rebka have set to verify Einstein’s prediction. The experiment was reprised with even higher precision by Pound and Snider. Later, Vessot reprised the experiment in space at a much improved precision. The standard explanation of gravitational redshift falls out straight from the Schwarzschild solution of the Einstein Field Equations (EFE). In the following, we will present an approach to the experiment relying on the Einstein Equivalence Principle and on the recently derived expressions of Doppler Effect for uniformly accelerated motion of the source and the receiver. We will conclude with a chapter on the numerical limits of applicability of the described method.

This research paper investigates the use of machine learning techniques in financial markets. The paper provides a comprehensive literature review of recent research on machine learning applications in finance, including stock price prediction, financial time series forecasting, and portfolio optimization. Various machine learning techniques, such as regression analysis, decision trees, support vector machines, and deep learning, are discussed in detail, with a focus on their strengths, weaknesses, and potential applications. The paper also highlights the challenges associated with machine learning in finance, such as data quality, model interpretability, and ethical considerations. Overall, the paper demonstrates that machine learning has significant potential in finance but calls for further research to address these challenges and fully explore its potential in financial markets.

Scientists began to study gyroscopic effects at the time of the Industrial Revolution. Famous mathematician L. Euler described only one gyroscopic effect, which is the precession torque that does not explain other ones. Since those times, scientists could not explain the physics of gyroscopic effects, Recent studies and the method of causal investigatory dependency demonstrated, that the nature of gyroscopic effects turned out that be more sophisticated than contemplated by researchers. The external torque acting on the spinning objects generates the system of the eight inertial torques and their interrelated motions around axes presented in the 3D coordinate system. The interrelated torques and motions of the spinning disc were described by mathematical models, and validated by practical tests that explain the physics of the gyroscopic effects based on the kinetic energy conservation law. The inertial torques generated by the centrifugal, and Coriolis forces, the change in the angular momentum, and the dependent motions of the spinning object around axes constitute the fundamental principles of the gyroscope theory. The derived gyroscopic theory opened a new chapter in the dynamics of rotating objects of classical mechanics that should be presented in all word encyclopedias.