In 2015, Shijun Liao introduced a new method of directly defining the inverse mapping (MDDiM) to approximate analytically a nonlinear differential equation. This method, based on the Homotopy Analysis Method (HAM) was proposed to reduce the time it takes in solving a nonlinear equation. Very recently, Dewasurendra, Baxter and Vajravelu (Applied Mathematics and Computation 339 (2018) 758–767) extended the method to a system of two nonlinear differential equations. In this paper, we extend it further to obtain the solution to a system of three nonlinear differential equations describing the HIV infection of CD4+ T-cells. In addition, we analyzed the advantages of MDDiM over HAM, in obtaining the numerical results. From these results, we noticed that the infected CD4+ T-cell density increases with the number of virions N; but decreases with the blanket death rate μI.
In this article, the three-dimensional Magnetohydrodynamics flow of a nanofluid over a horizontal non-linearly stretching sheet in bilateral directions under boundary layer approximation is addressed. A two-phase model has been used for the nanofluid. The influences of thermophoresis, Brownian motion and thermal radiation on heat and mass transfers are considered. Two different cases for the heat and mass transfers are studied. In the first case, uniform wall temperature and zero nanoparticles flux due to thermophoresis are considered. In the second case, prescribed heat and mass fluxes at the boundary are considered. By using the appropriate transformations, a system of non-linear partial differential equations along with the boundary conditions is transformed into coupled non-linear ordinary differential equations. Numerical solutions of the self-similar equations are obtained using a Runge–Kutta method with a shooting technique. Our results for special cases are compared with the available results in the literature, and the results are found to be in good agreement. It is observed that the pertaining parameters have significant effects on the characteristics of flow, heat and mass transfer. The results are presented and discussed in detail through illustrations.
A large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. The procedure starts by reducing both equations to related ODEs by compatible travelling wave transforms. The balance between the highest degree nonlinear and highest order derivative terms gives the degree of the finite series. Substitution of the assumed solution and some algebra results in a system of equations are found. The relation between the parameters is determined by solving this system. The solutions of travelling wave forms determined by the application of the approach are represented in explicit functions of some generalized trigonometric and hyperbolic functions and exponential function. Some more solutions with different characteristics are also found.
Photovoltaic power system is taking a significant percentage of power system and the demands for accurate forecasting of the power outputs is surging. In prior works, the forecasting problem was formulated as a regression problem, however, which most cannot guarantee that the forecasted outputs is nonnegative. To solve this problem, we proposed a novel probabilistic model by using nonlinear regression and Bayesian learning method. In the paper, we present the detailed theoretical derivations and interpretations. The simulation results show the validity and feasibility of the proposed algorithm by comparing with the traditional SVM algorithm.
How to reduce the hardware cost and high power consumption of RF link of communication device is the key problem to be solved for multi-transmitting antenna and multi-receiving antenna system (MIMO). Always choose the best antennas connection a limited number of RF circuits, which is called antenna selection technology (AS), are a perfect solution to the problem, Assuming that the spatial range of the antenna meets the requirements of signal multiplexing and based on the maximum capacity criterion of the selected MIMO system, the manuscript proposes a low computational complexity (CC) and high performance joint transmitting and receiving antenna selection technique (JTRAS). Starting from the traditional capacity formula and the full matrix of MIMO channel, we utilize a simplified channel capacity expression through repeatedly iterating to delete a row and a column of the equivalent decrement channel matrix, which is to remove a pair of transmitting and receiving antennas. Based on the decreasing JTRAS (DJTRAS) algorithm, the capacity results of simulating calculation indicate that its median capacity overtakes other ones, such as optimum selection (OS), AS based on Frobenius 2 norm (NBS), and concise joint AS criterion (CJAS) etc., and the novel DJTRAS scheme can significantly reduce computational complexity (CC) compared to the exhaustive search method with maximum capacity, which defined as optimal algorithm in the curve graphs. This new technology of the AS is particularly suited to large number of selected antennas, such as Lt ≥ NT/2,Lr ≥ NR/2.
The mathematical algorithm of zero order optimization is a general function approach optimization method. Based on this method, many sets of analytical procedures are developed using ANSYS to study the design of 600m scale concrete arch bridge and the optimal arch axis coefficient, change mode and cross section sizes are obtained and verified. Results show: the mathematical algorithm of zero order optimization can effectively study the design of 600m arch bridge. The rich conclusions about design parameters can be a significant reference for design and further research of 600 m scale concrete arch bridge.
This paper studies Inventory location routing problem in supply chain distribution network planning under vendor inventory management while considering customer inventory holding cost. In order to minimize the total cost of supply chain, an optimization model is established and an improved tabu search algorithm is used to solve the problem. From the analysis, it shows that the total cost decreases as the total vehicles capacity increases, and the maximum utilization of alternative vehicles and the minimum cost of the system don’t occur at the same time in some cases.
This paper uses the law of one price (LOP) and the DCC-GARCH method based on ten-day price sequences. The findings indicate that, compared with the international refined oil markets with mature market-oriented pricing mechanisms, only in the Chinese market do gasoline and diesel prices meet the LOP. This finding shows that, in the context of the gradual integration of the global refined oil market, the international level of China's refined oil price is still quite low. The price reforms pertaining to China's refined oil products still need to be pushed forward in the direction of marketization and internationalization.
With the continuous development of China's Internet economy, the model of grasping Internet economy benefit is diversified. Since 2016, the online celebrity economy has formed a trend of Internet marketing, and the online celebrity economic industry chain further has established along with the further development of MCN institutions. The relationship among the overall industry upstream and downstream sectors become closer and closer and even appear the trend of vertical cooperation. This paper is aimed at expressing the pricing mechanism of the online celebrity industrial chain and applies game theory and mathematical analysis to propose a reasonable pricing model
In the present manuscript, Crank Nicolson finite difference method is going to be applied to get the approximate solutions for the fractional Burgers equation. The fractional derivative used in this equation is going to be taken into consideration in the Caputo sense. The L1 type discretization formula is going to be applied to this equation. For checking the efficiency of proposed methods, the error norms L2 and L∞ have at the same time been calculated. Those newly got solutions using the presented method illustrate the easy usage and efficiency of the approach presented in this manuscript.