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Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasti.city theory
  • ISSN号：1674-1056
  • 期刊名称：《中国物理B：英文版》
  • 时间：0
  • 分类：O343[理学—固体力学;理学—力学] O151.21[理学—数学;理学—基础数学]
  • 作者机构：[1]School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China, [2]College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
  • 相关基金：Project supported by the National Natural Science Foundation of China （Grant Nos. 10962004 and 11061019）, ＇Chunhui Program＇ Ministry of Education（Grant No. Z2009-1-01010）, the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 20070126002）, the Doctoral Foundation of Inner Mongolia （Grant No. 2009BS0101）, the Natural Science Foundation of Inner Mongolia （Grant No. 2010MS0110） and the Cultivation of Innovative Talent of ＇211 Project＇ of Inner Mongolia University.
作者： 黄俊杰[1], 阿拉坦仓[1], 王华[1,2]
关键词： 弹性理论, 展开定理, 矩阵类, 算子, 本征矢, 特征向量, 充分必要条件, 大肠杆菌, operator matrix, eigenvector, completeness, eigenvector expansion theorem
中文摘要：

This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory,i.e.,symplectic eigenvector expansion theorem.Under certain conditions,the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated.Based on this,a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given.Furthermore,the obtained results are tested for the free vibration of rectangular thin plates.

英文摘要：

This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.

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期刊信息
  • 《中国物理B：英文版》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国物理学会和中国科学院物理研究所
  • 主编：欧阳钟灿
  • 地址：北京 中关村 中国科学院物理研究所内
  • 邮编：100080
  • 邮箱：
  • 电话：010-82649026 82649519
  • 国际标准刊号：ISSN：1674-1056
  • 国内统一刊号：ISSN：11-5639/O4
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 被引量:406