Solution approximations for a mathematical model of relativistic electrons with beta derivative

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.

A New Mathematical Modeling of the COVID-19 Pandemic Including the Vaccination Campaign

In a short time, many illustrative studies have been conducted on the mathematical modeling and analysis of COVID-19. There are not enough studies taking into account the vaccine campaign among these studies. In this context, a mathematical model is developed to reveal the effects of vaccine treatment, which has been performed recently, on COVID-19 in this study. In the proposed model, as well as the vaccinated individuals, a five-dimensional compartment system including the susceptible, infected, exposed and recovered population is constructed. Moreover, besides the positivity, existence and uniqueness of the solution, biologically feasible region are provided. The basic reproduction number known as expected secondary infection which means that expected infection among the susceptible populations caused by this infection is evaluated. In the numerical simulations, the parameter values taken from the literature and estimated are used to perform the solutions of the proposed model. Fourth-order Runge-Kutta numerical scheme is applied to obtain the results.

Techniques of Remote Sensing and GIS as Tools for Visualizing Impact of Climate Change-Induced Flood in the Southern African Region

Flooding is a major problem facing Southern African region. The region has been experiencing flood for the past two decades. This flood event has been exacerbated in recent years by global weather pattern known as La Ni?a which cools ocean waters in the equatorial Pacific and changes rainfall patterns across the world. This change in weather pattern has resulted in increased rainfall over Southern Africa causing flash floods resulting in extensive socioeconomic loses, casualties and environmental damage. This study employs remote sensing and geographical information systems (GIS) data to visualize the impact of climate change caused by flooding in the Southern African region in order to assist decision makers’ plans for future occurrences. To achieve these objectives, the study used Digital Elevation Model (DEM), temporal Landsat Enhanced Thematic Mapper Plus (ETM+) and Moderate Resolution Imaging Spectroradiometer (MODIS) satellites data obtained from the United States Geological Survey (USGS) and NASA’s Earth Observatory websites in order to show the spatial dimensions of the damage and the flooded area. Results of the study revealed notable damages to social and natural environments as well as flood risk zones and watercourses in the study area. The paper concludes by outlining policy recommendations in the form of the need for building drainage ditches on the flat plains identified in this study to accommodate flood flows, the design of a comprehensive Regional Emergency Information System (REIS) with support from the governments in the study area and the neighboring countries. Building such system, the paper concludes could offer decision-makers access to the appropriate spatio-temporal data for monitoring climate change induced emergencies related to seasonal floods.

Solution and stability of mixed type functional equation in non-Archimedean random normed spaces

The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.

Weak and strong stabilization of linear systems

We study the problem of stabilizing a distributed linear system on a subregion of its geometrical domain. We are concerned with two methods： the first approach enables us to characterize a stabilizing control via the steady state Riccati equation, and the second one is based on decomposing the state space into two suitable subspaces and studying the projections of the initial system onto such subspaces. The obtained results are performed through various examples.

Mathematical Modelling and Simulation of <i>β</i>-Cell Mass, Insulin and Glucose Dynamics: Effect of Genetic Predisposition to Diabetes

Worldwide, diabetes is affecting 370 million people, causing nearly five million deaths and absorbing more than 471 billion USD per year. Mathematical models have been developed to simulate, analyse and understand the dynamics of β-cells, insulin and glucose. In this paper, we consider the effect of genetic predisposition to diabetes on dynamics of β-cells, glucose and insulin. We assume that the β-cell dynamics is governed by the differential equation: . The model indicates different behaviours according to the presence or absence of genetic predisposition. In presence of predisposition (ε = 1), the model shows three equilibrium points: a stable physiological equilibrium point (G = 100, I = 20, β = 600), a stable trivial pathological equilibrium point (G = 600, I = 0, β = 0) and a saddle point (G = 250, I = 9.8, β = 129.36). In absence of predisposition (ε = 0), the model has only two equilibrium points: an unstable pathological equilibrium point (G = 600, I = 0, β = 0) and a stable physiological equilibrium point (G = 82.6, I = 23, β = 900). In order to see how physical activity, obesity and other factors affect insulin sensitivity, simulations are carried out with different values of insulin induced glucose uptake rate (c), β-cell maximum insulin secretory rate (d) and environmental capacity (K).

Regional Controllability of Semi-Linear Distributed Parabolic Systems: Theory and Simulation

The aim of this brief paper is to give several results concerning the regional controllability of distributed systems governed by semi-linear parabolic equations. We concentrate on the determination of a control achieving internal and boundary regional controllability. The approach is based on an extension of the Hilbert Uniqueness Method (HUM) and Schauder’s fixed point theorem. We give a numerical example developed in internal and boundary sub region. These numerical illustrations show the efficiency of the approach and lead to conjectures.

A RECOGNITION OF SIMPLE GROUPS PSL(3,q) BY THEIR ELEMENT ORDERS

For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.

Calibrating Remotely Sensed Ocean Chlorophyll Data: An Application of the Blending Technique in Three Dimensions (3D)

In this article, the extension to three dimensions (3D) of the blending technique that has been widely used in two dimensions (2D) to calibrate ocean chlorophyll is presented. The results thus obtained revealed a very high degree of efficiency when predicting observed values of ocean chlorophyll. The mean squared difference between the predicted and observed values of ocean chlorophyll when 3D technique was used fell far below the tolerance level which was set to the difference between satellite and observed in-situ values. The resulting blended field did not only provide better predictions of the in situ observations in areas where bottle samples cannot be obtained but also provided a smooth variation of the distribution of ocean chlorophyll throughout the year. An added advantage is its computational efficiency since data that would have been treated at least four times would be treated only once. With the advent of these results, it is believed that the modelling of the ocean life cycle will become more realistic.

Contribution to the Mathematical Modeling of COVID-19 in Niger

We are interested in this paper in the modeling and analysis of the disease of COVID-19 applied to the capital of Niger: Niamey. The model we are presenting takes into account the strategy that the country has adopted to fight this pandemic. The spread of the infectious agent within the population is a dynamic phenomenon: the number of the healthy and sick individuals changes over time, depending on the contacts during which the pathogen passes from an infected individual to a healthy individual. We model this propagation phenomenon by a set of differential systems equations and determine its behavior through a numerical resolution.

Intrusion Detection System with Remote Signalling for Vehicles Using an Arduino Controller and Radio-Frequency Technology

Malicious activities or policy violations have been a concern for the past years. For example, many people have been victims of robbery on vehicles. A conceptual diagram of an Intrusion Detection System (IDS) [1] [2] for vehicles with remote signaling using an Arduino controller and radio-frequency technology is proposed in this paper. To address malicious activities on vehicles, two aspects are considered here, namely: notifier and detector. Firstly, an object-oriented C module that puts on and off a controller (installed inside the vehicle) and an anti-theft electronic editing that powered using an alternator and supported by a back-up battery are implemented. Secondly, a magnetic intrusion sensor, controlled by a proximity detector using radio-frequency technology, has been installed on each vehicle door. To enable IDS, a user needs to activate the monitoring system when leaving their vehicle. This is done using a remote system. In case the user does not activate the monitoring system while leaving the vehicle, a 5-meter-proximity detector will automatically lock the system and set off the monitoring system whenever the user is outside the detection zone. The detection zone is a 5-meter radius area centered at the controller. Here, monitoring consists of geolocating any intruders within the detection zone. This means, if any of the vehicle doors is opened while the system is still locked, the controller will activate the vehicle alarm for a few seconds, thereafter send an SMS notification to the owner. The system automatically unlocks as soon as the proximity detector is within the detection zone. The contribution of this paper, as compared to other similar work, is to reinforce the electronic implementation of IDS.

Solution of Modified Bergman Minimal Blood Glucose-Insulin Model Using Caputo-Fabrizio Fractional Derivative

Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an important model named-Bergman minimalmodel.In the present work,using Caputo-Fabrizio(CF)fractional derivative,we generalize Bergman’s minimal blood glucose-insulin model.Further,we modify the old model by including one more component known as diet D(t),which is also essential for the blood glucose model.We solve the modified modelwith the help of Sumudu transformand fixed-point iteration procedures.Also,using the fixed point theorem,we examine the existence and uniqueness of the results along with their numerical and graphical representation.Furthermore,the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied.Finally,we draw the graphs of G(t),X(t),I(t),andD(t)for different values ofτ.It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.

Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective

We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas. The main purpose in this work is the modeling of the aggressiveness of anopheles mosquitoes relative to the way humans use to protect themselves against bites of mosquitoes. This model is a system of several differential equations: the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number, and show that if, the disease free equilibrium (DFE) is globally asymptotically stable on the non-negative orthant. If, the system admits a unique endemic equilibrium (EE) that is globally and asymptotically stable. Numerical simulations are presented corresponding to scenarios typical of malaria-endemic areas, based on data collected in the literature. Finally, we discuss the relative effectiveness of different kinds of bed nets.

Nelson-Aalen and Kaplan-Meier Estimators in Competing Risks

In this paper, stochastic processes developed by Aalen [1]?[2] are adapted to the Nelson-Aalen and Kaplan-Meier?[3] estimators in a context of competing risks. We focus only on the probability distributions of complete downtime individuals whose causes are known and which bring us to consider a partition of individuals into sub-groups for each cause. We then study the asymptotic properties of nonparametric estimators obtained.

Note on the Linearity of Bayesian Estimates in the Dependent Case

This work deals with the relationship between the Bayesian and the maximum likelihood estimators in case of dependent observations. In case of Markov chains, we show that the Bayesian estimator of the transition probabilities is a linear function of the maximum likelihood estimator (MLE).

Investigation of electron beam effects on L-shell Mo plasma produced by a compact LC generator using pattern recognition

In this paper,the effects of an electron beam on X-pinch-produced spectra of L-shellMoplasma are investigated for the first time by principal component analysis(PCA);this analysis is compared with that of line ratio diagnostics.A spectral database for PCA extraction is arranged using a non-Local Thermodynamic Equilibrium(non-LTE)collisional radiative L-shell Mo model.PC vector spectra of L-shell Mo,including F,Ne,Na and Mg-like transitions are studied to investigate the polarization types of these transitions.PC1 vector spectra of F,Ne,Na and Mg-like transitions result in linear polarization of Stokes Q profiles.Besides,PC2 vector spectra show linear polarization of Stokes U profiles of 2p^(5)3s of Ne-like transitions which are known as responsive to a magnetic field[Trabert,Beiersdorfer,and Crespo Lo´pez-Urrutia,Nucl.InstrumMethods Phys.Res.,Sect.B 408,107–109(2017)].A 3D representation of PCA coefficients demonstrates that addition of an electron beam to the non-LTE model generates quantized,collective clusters which are translations of each other that follow V-shaped cascade trajectories,except for the case f=0.0.The extracted principal coefficients are used as a database for an Artificial Neural Network(ANN)to estimate the plasma electron temperature,density and beam fractions of the time-integrated,spatially resolved L-shellMoX-pinch plasma spectrum.PCA-based ANNs provide an advantage in reducing the network topology,with a more efficient backpropagation supervised learning algorithm.The modeled plasma electron temperature is about Te;660 eV and density n_(e)=1×10^(20) cm^(-3),in the presence of the fraction of the beams with f-0.1 and centered energy of 5 keV.

The Riccati Equation, Differential Transform, Rational Solutions and Applications

In this article, the Riccati Equation is considered. Various techniques of finding analytical solutions are explored. Those techniques consist mainly of making a change of variable or the use of Differential Transform. It is shown that the nonconstant rational functions whose numerator and denominator are of degree 1, cannot be solutions to the Riccati equation. Two applications of the Riccati equation are discussed. The first one deals with Quantum Mechanics and the second one deal with Physics.

Anti Aristotle—The Division of Zero by Zero

Today, the division of zero by zero (0/0) is a concept in philosophy, mathematics and physics without a definite solution. On this view, we are left with an inadequate and unsatisfactory situation that we are not allowed to divide zero by zero while the need to divide zero by zero (i.e. divide a tensor component which is equal to zero by another tensor component which is equal to zero) is great. A solution of the philosophically, logically, mathematically and physically far reaching problem of the division of zero by zero (0/0) is still not in sight. The aim of this contribution is to solve the problem of the division of zero by zero (0/0) while relying on Einstein’s theory of special relativity. In last consequence, Einstein’s theory of special relativity demands the division of zero by zero. Due to Einstein’s theory of special relativity, it is (0/0) = 1. As we will see, either we must accept the division of zero by zero as possible and defined, or we must abandon Einstein’s theory of special relativity as refuted.