Abstract: In this paper, we present a new numerical technique based on Block-pulse functions to solve two-dimensional Volterra-Fredholm integral equations of the second kind. To produce Block-pulse functions, the orthogonal Legendre polynomials is used. Furthermore, operational matrix is applied to convert two-dimensional Volterra-Fredholm integral equations to a linear algebraic system. The convergence analysis of the new method is discussed. Finally, some numerical examples are given to confirm the applicability and efficiency of the new method for solving two-dimensional Volterra-Fredholm integral equations of the second kind.
Abstract: In this paper, a two layer recurrent neural network (RNN) is shown for solving nonsmooth pseudoconvex optimization . First it is proved that the equilibrium point of the proposed neural network (NN) is equivalent to the optimal solution of the orginal optimization problem. Then, it is proved that the state of the proposed neural network is stable in the sense of Lyapunov, and convergent to an exact optimal solution of the original optimization. Finally two examples are given to illustrate the effectiveness of the proposed neural network.
Abstract: The purpose of this paper is to locate and estimate the eigenvaluesof stochastic tensors. We present several estimation theorems about the eigen-values of stochastic tensors. Meanwhile, we obtain the distribution theorem forthe eigenvalues of tensor product of two stochastic tensors. We will concludethe paper with the distribution for the eigenvalues of generalized stochastictensors.
Abstract: Tensors as vector fields structures and manifolds as great geometrical-topological structures have many applications in the fields of big data analysis. Types of norms, metrics and scalable structures have been defined from various aspects. Nowadays, the hybrid methods between tensorial algorithms and manifold learning (MaL) methods have been attracted some attention. In image and signal processing, from image recovery to face recognition, these methods have appeared very excellent. According to our experiments by MATLAB R2021a, the hybrid algorithms are powerful other than algorithms based on the efficient popular parameters.
Abstract: In this paper we introduce concepts of pseudo-triangular entropy as a supplement measure of uncertainty in the uncertain portfolio optimization. We first prove that logarithm entropy and triangular entropy for uncertain variables sometimes may fail to measure the uncertainty of an uncertain variable. Then, we propose a definition of pseudo-triangular entropy as a supplement measure to characterize the uncertainty of uncertain variables and we derive its mathematical properties. We also give a formula to calculate the pseudo-triangular entropy of uncertain variables via inverse uncertainty distribution. Moreover, we use the pseudo-triangular entropy to characterize portfolio risk and establish some uncertain portfolio optimization models based on different types of entropy. A genetic algorithm (GA) is implemented in MATLAB software to solve the corresponding problem. Numerical results show that pseudo-triangular entropy as a quantifier of portfolio risk outperforms logarithm entropy and triangular entropy in the uncertain portfolio optimization.
Abstract: ‎In this paper we study the covid-19 disease with treatment and control to spread it with different measures‎. ‎The model equations are analysed from the general MC Kendrick equations for age structured populations‎. ‎The existence,positiveness,boundedness and stability of equilibria are studied as they depend on the prey's natural carrying capacity‎. ‎The main result of this paper is the three age group population‎, ‎how to control and avoid to infect the disease from predator with local,global stability and Hopf bifurcation method also utilised.Finally the result of this model prey predator where numerical examples using maple software of Rossler type.
Abstract: A new class of exact solutions of the Einstein-Maxwell system is found in closed form for a static spherically symmetric anisotropic star in the presence of an electric field by generalizing earlier approaches. The field equations are integrated by specifying one of the gravitational potentials, the anisotropic factor and electric field which are physically reasonable. We demonstrate that it is possible to obtain a more general class of solutions to the Einstein-Maxwell system in the form of series with anisotropic matter. For specific parameter values it is possible to find new exact models for the Einstein-Maxwell system in terms of elementary functions from the general series solution. Our results contain particular solutions found previously including models of Thirukkanesh and Maharaj (2009) and Komathiraj and Maharaj (2007) charged relativistic models.
Abstract: In this paper, we have introduced a five‐parameter bivariate model by taking a geometric minimum of the modified exponential distributions. It is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters. A number of simulation experiments have been performed to determine the effectiveness of the proposed EM algorithm. We analyze two datasets for illustrative purposes, and it is observed that the proposed models and the expectation‐maximization algorithm perform at a satisfactory level.
Abstract: Since December 2019 that the coronavirus pandemic (COVID-19) has hit the world, with over 13 million cases recorded, only a little above 4.67 percent of the cases have been recorded in the continent of Africa. The percentage of cases in Africa rose significantly from 2 percent in the month of May 2020 to above 4.67 percent by the end of July 15, 2020. This rapid increase in the percentage indicates a need to study the transmission, control strategy, and dynamics of COVID-19 in Africa. In this study, a nonlinear mathematical model to investigate the impact of asymptomatic cases on the transmission dynamics of COVID-19 in Africa is proposed. The model is analyzed, the reproduction number is obtained, the local and the global asymptotic stability of the equilibria were established. We investigate the existence of backward bifurcation and we present the numerical simulations to verify our theoretical results. The study shows that the reproduction number is a decreasing function of detection rate and as the rate of re-infection increases, both the asymptomatic and symptomatic cases rise significantly. The results also indicate that repeated and increase testing to detect people living with the disease will be very effective in containing and reducing the burden of COVID-19 in Africa.
Abstract: By taking into account that the computation of the numerical radius is an optimization problem, we prove, in this paper, several refinements of the numerical radius inequalities for Hilbert space operators. It is shown, among other inequalities, that if $A$ is a bounded linear operator on a complex Hilbert space, then[omega left( A right)le frac{1}{2}sqrt{left {{left A right }^{2}}+{{left {{A}^{*}} right }^{2}} right +left left A right left {{A}^{*}} right +left {{A}^{*}} right left A right right },]where $omega left( A right)$, $left A right $, and $left A right $ are the numerical radius, the usual operator norm, and the absolute value of $A$, respectively. This inequality provides a refinement of an earlier numerical radius inequality due to Kittaneh, namely,[omega left( A right)le frac{1}{2}left( left A right +{{left {{A}^{2}} right }^{frac{1}{2}}} right).]Some related inequalities are also discussed.
Abstract: So far, the numerous methods for solving and analyzing differential equations are proposed. Meanwhile; the combined methods are beneficial; one of them is the Optimized MRA method (OMRA). This method is based on the Father wavelets (dependent on the invariant solutions obtained by the Lie symmetry method) and correspondent MRA. In this paper, we apply the OMRA on the generalized version of FKPP equation (GFKPP) with function coefficientbegin{eqnarray*}f u_{tt}(x,t) + u_t(x,t) = u_{xx}(x,t) + u(x,t) - u^2(x,t),end{eqnarray*}where $f$ is a smooth function of either $x$ or $t$.We will see that by the suitable Father wavelets, this method proposes attractive approximate solutions.
Abstract: In this paper, we consider a nonlinear non autonomous system of differential equations. We linearize this system by the Newton's method and obtain a sequence of linear systems of ODE. We are going to solve this system on [0,Nl] , for some positive integer N and a positive real l>0 . For this purpose, in the first step we solve the problem on [0,l]. By knowing the solution on [0,l], we solve the problem on [l,2l] and obtain the solution on [0,2l]. We continue this procedure until [0,Nl]. In each partial interval [(k-1)l,kl], first of all, we solve the problem by the extrapolation method and obtain an initial guess for the Newton-Taylor polynomial solutions. These procedures cause that the errors don’t propagate. The sequence of linear systems in Newton's method are solved by a famous method called Taylor polynomial solutions, which have a good accuracy for linear systems of ODE. Finally, we give a mathematical model of the novel corona virus disease and illustrate accuracy and applicability of the method by some examples from this model and compare them by similar work, that simulate the numerical solutions.
Abstract: The aim of this paper is to provide a stability analysis for models with a general structure and mass action incidence; which include stage progression susceptibility, differential infectivity as well, and the loss of immunity induced by the vaccine also. We establish that the global dynamics are completely determined by the basic reproduction number $R_0$. More specifically, we prove that when $R_0$ is smaller or equal to one, the disease free equilibrium is globally asymptotically stable; while when it is greater than one, there exist a unique endemic equilibrium. We also provide sufficient conditions for the global asymptotic stability of the endemic equilibrium.
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