A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
Due to the ability to model various complex phenomena where classical calculus failed, fractional calculus is getting enormous attention recently. There are several approaches available for numerical approximations of...Due to the ability to model various complex phenomena where classical calculus failed, fractional calculus is getting enormous attention recently. There are several approaches available for numerical approximations of various types of fractional differential equations. For fractional diffusion equations spectral collocation is one of the efficient and most popular ap-proximation techniques. In this research, we introduce spectral collocation method based on Lagrange’s basis polynomials for numerical approximations of two-dimensional (2D) space fractional diffusion equations where spatial fractional derivative is described in Riemann-Liouville sense. We consider four different types of nodes to generate Lagrange’s basis polynomials and as collocation points in the proposed spectral collocation technique. Spectral collocation method converts the diffusion equation into a system of ordinary differential equations (ODE) for time variable and we use 4th order Runge-Kutta method to solve the resulting system of ODE. Two examples are considered to verify the efficiency of different types of nodes in the proposed method. We compare approximated solution with exact solution and find that Lagrange’s spectral collocation method gives very high accuracy approximation. Among the four types of nodes, nodes from Jacobi polynomial give highest accuracy and nodes from Chebyshev polynomials of 1st kind give lowest accuracy in the proposed method.展开更多
针对传统D-S证据理论中基于识别率和误识率构造的基本概率赋值函数(Basic Probability Assignment,BPA)没有考虑训练样本分布的缺点,提出了一种将整体错误率分配给除了正确判别命题以外各个焦元的BPA构造新方法.针对传统D-S证据理论中...针对传统D-S证据理论中基于识别率和误识率构造的基本概率赋值函数(Basic Probability Assignment,BPA)没有考虑训练样本分布的缺点,提出了一种将整体错误率分配给除了正确判别命题以外各个焦元的BPA构造新方法.针对传统D-S证据理论中所采用的基于正交和运算的合成规则不能融合矛盾证据的缺陷,提出一种能融合矛盾证据的大概率赋值法.在此改进D-S证据理论的基础上,给出了两分类器决策层融合流程和多分类器决策层融合系统.在ORL和Yale数据库上的实验结果表明,对几种典型分类器的决策层融合提高了系统人脸识别的正确率,且改进D-S证据理论比传统D-S和投票融合方法的正确率更高.展开更多
基金Supported by the Natural Science Foundation of Hubei Province!(992P0 30 7) the National Natural Science Foun-dation of Chi
文摘A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
文摘Due to the ability to model various complex phenomena where classical calculus failed, fractional calculus is getting enormous attention recently. There are several approaches available for numerical approximations of various types of fractional differential equations. For fractional diffusion equations spectral collocation is one of the efficient and most popular ap-proximation techniques. In this research, we introduce spectral collocation method based on Lagrange’s basis polynomials for numerical approximations of two-dimensional (2D) space fractional diffusion equations where spatial fractional derivative is described in Riemann-Liouville sense. We consider four different types of nodes to generate Lagrange’s basis polynomials and as collocation points in the proposed spectral collocation technique. Spectral collocation method converts the diffusion equation into a system of ordinary differential equations (ODE) for time variable and we use 4th order Runge-Kutta method to solve the resulting system of ODE. Two examples are considered to verify the efficiency of different types of nodes in the proposed method. We compare approximated solution with exact solution and find that Lagrange’s spectral collocation method gives very high accuracy approximation. Among the four types of nodes, nodes from Jacobi polynomial give highest accuracy and nodes from Chebyshev polynomials of 1st kind give lowest accuracy in the proposed method.
文摘针对传统D-S证据理论中基于识别率和误识率构造的基本概率赋值函数(Basic Probability Assignment,BPA)没有考虑训练样本分布的缺点,提出了一种将整体错误率分配给除了正确判别命题以外各个焦元的BPA构造新方法.针对传统D-S证据理论中所采用的基于正交和运算的合成规则不能融合矛盾证据的缺陷,提出一种能融合矛盾证据的大概率赋值法.在此改进D-S证据理论的基础上,给出了两分类器决策层融合流程和多分类器决策层融合系统.在ORL和Yale数据库上的实验结果表明,对几种典型分类器的决策层融合提高了系统人脸识别的正确率,且改进D-S证据理论比传统D-S和投票融合方法的正确率更高.
