The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moo...The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T+ is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T+ will be given, and some properties of T+ will be investigated in this paper.展开更多
Lee discrepancy has been employed to measure the uniformity of fractional factorials.In this paper,we further study the statistical justification of Lee discrepancy on asymmetrical factorials.We will give an expressio...Lee discrepancy has been employed to measure the uniformity of fractional factorials.In this paper,we further study the statistical justification of Lee discrepancy on asymmetrical factorials.We will give an expression of the Lee discrepancy of asymmetrical factorials with two-and three-levels in terms of quadric form,present a connection between Lee discrepancy,orthogonality and minimum moment aberration,and obtain a lower bound of Lee discrepancy of asymmetrical factorials with two-and three-levels.展开更多
The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field i...The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.展开更多
基金the National Natural Science Foundation of China(No.19971023)the Heilongjiang Provincial Natural Science Foundation of China.
文摘The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T+ is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T+ will be given, and some properties of T+ will be investigated in this paper.
基金supported by Research Fund for the Doctoral Program of Higher Education of China (RFDP) (Grant No. 20090144110002)
文摘Lee discrepancy has been employed to measure the uniformity of fractional factorials.In this paper,we further study the statistical justification of Lee discrepancy on asymmetrical factorials.We will give an expression of the Lee discrepancy of asymmetrical factorials with two-and three-levels in terms of quadric form,present a connection between Lee discrepancy,orthogonality and minimum moment aberration,and obtain a lower bound of Lee discrepancy of asymmetrical factorials with two-and three-levels.
基金supported by the Natural Science Foundation of Shanxi Province (Grant No. 2011011021-3)
文摘The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.
