In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 ×...In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 × 2 infinite dimensional Hamiltonian operator is 1 and the ascent of a class of 4 × 4 infinite dimensional Hamiltonian operators that arises in study of elasticity is2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions.展开更多
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite...This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.展开更多
This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H）...This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11101200 and 11371185)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2013ZD01)
文摘In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 × 2 infinite dimensional Hamiltonian operator is 1 and the ascent of a class of 4 × 4 infinite dimensional Hamiltonian operators that arises in study of elasticity is2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions.
基金supported by the National Natural Science Foundation of China(Grant No 10562002)the Natural Science Foundation of Inner Mongolia,China(Grants No 200508010103 and 200711020106)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No 20070126002)
文摘This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.
基金Supported by the National Natural Science Foundation of China (No. 11061019, 10962004, 11101200)the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia (No. 2010MS0110, 2009BS0101)the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University
文摘This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.
