In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average...In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLP...In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.展开更多
In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were disc...In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.展开更多
The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally diffi...The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally difficult to handle the above problems simultaneously,such as the Track-Oriented marginal Multi-Bernoulli/Poisson(TOMB/P)and Measurement-Oriented marginal Multi-Bernoulli/Poisson(MOMB/P)filters.Based on the Arithmetic Average(AA)fusion rule,this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli(PMB)filter,which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence.In order to fuse the different PMB distributions,the Bernoulli components in different Multi-Bernoulli(MB)distributions are associated with each other by Kullback-Leibler Divergence(KLD)minimization.Moreover,an adaptive AA fusion rule is designed on the basis of the exponential fusion weights,which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT.Finally,by comparing with the TOMB/P and MOMB/P filters,the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.展开更多
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
文摘In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.
文摘In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.
基金supported by the National Natural Science Foundation of China(No.61871301)。
文摘The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally difficult to handle the above problems simultaneously,such as the Track-Oriented marginal Multi-Bernoulli/Poisson(TOMB/P)and Measurement-Oriented marginal Multi-Bernoulli/Poisson(MOMB/P)filters.Based on the Arithmetic Average(AA)fusion rule,this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli(PMB)filter,which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence.In order to fuse the different PMB distributions,the Bernoulli components in different Multi-Bernoulli(MB)distributions are associated with each other by Kullback-Leibler Divergence(KLD)minimization.Moreover,an adaptive AA fusion rule is designed on the basis of the exponential fusion weights,which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT.Finally,by comparing with the TOMB/P and MOMB/P filters,the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.
