Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equationy (4n)=f(t,y,y′,y″,...,y (4n-1))(a)with the boundary conditions g 2i(y (2i)(a),y (2i+1...Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equationy (4n)=f(t,y,y′,y″,...,y (4n-1))(a)with the boundary conditions g 2i(y (2i)(a),y (2i+1)(a))=0,h 2i(y (2i)(c),y (2i+1)(c))=0,(i=0,1,...,2n-1)(b) where the functions f, g i and h i are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equationy (n)=f(t,y,y′,y″,...,y (n-1))many results have been given at the present time. But the existence of solutions of boundary value problem (a),(b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, i.e. existence of solutions of the boundary value problem.y (4n)=f(t,y,y′,y″,...,y (4n-1)) a 2iy (2i)(a)+a 2i+1y (2i+1)(a)=b 2i,c 2iy (2i)(c)+c 2i+1y (2i+1)(c)=d 2i,(i=0,1,...2n-1)has not been dealt with in previous works.展开更多
针对高维数据分类问题的特点,提出一种基于改进型局部线性嵌入LLE(Locally Linear Embedding)算法的数据降维算法,结合支持向量机SVM(Support Vector Machine)算法实现数据分类。首先,通过LLE算法降维后的数据集,按照数据集内的离差最小...针对高维数据分类问题的特点,提出一种基于改进型局部线性嵌入LLE(Locally Linear Embedding)算法的数据降维算法,结合支持向量机SVM(Support Vector Machine)算法实现数据分类。首先,通过LLE算法降维后的数据集,按照数据集内的离差最小化,数据集间的离差最大化的原则,计算得到最优化邻近点个数;其次,将最优邻近点个数所得的降维数据作为最优结果,按一定比例选取训练集,输入SVM算法建立数据分类器;最后,将测试集输入训练完成的分类器中,实现最优化数据分类。选取Iris flower,Yale等多类数据集与传统算法进行对比实验,验证算法的可行性。实验结果表明:所提出的算法可以有效地完成数据分类,针对低维数据和高维数据分类问题具有较好的适用性和优越性,在人脸检测中也取得较好的结果。展开更多
文摘Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equationy (4n)=f(t,y,y′,y″,...,y (4n-1))(a)with the boundary conditions g 2i(y (2i)(a),y (2i+1)(a))=0,h 2i(y (2i)(c),y (2i+1)(c))=0,(i=0,1,...,2n-1)(b) where the functions f, g i and h i are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equationy (n)=f(t,y,y′,y″,...,y (n-1))many results have been given at the present time. But the existence of solutions of boundary value problem (a),(b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, i.e. existence of solutions of the boundary value problem.y (4n)=f(t,y,y′,y″,...,y (4n-1)) a 2iy (2i)(a)+a 2i+1y (2i+1)(a)=b 2i,c 2iy (2i)(c)+c 2i+1y (2i+1)(c)=d 2i,(i=0,1,...2n-1)has not been dealt with in previous works.
