PROBABILISTIC NORM OF OPERATORS AND RESONANCE THEOREMS

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (7): 781-788.

PROBABILISTIC NORM OF OPERATORS AND RESONANCE THEOREMS

肖建中¹, 朱杏华²

1. Department of Mathematics, Jiangsu Yancheng Educational Institute, Yancheng 224002, P. R. China;
2. Department of Mathematics, Jiangsu Yancheng Teachers College, Yancheng 224002, P. R. China

收稿日期:1997-01-23 修回日期:1999-01-21 出版日期:1999-07-18 发布日期:1999-07-18

PROBABILISTIC NORM OF OPERATORS AND RESONANCE THEOREMS

Xiao Jianzhong¹, Zhu Xinghua ²

1. Department of Mathematics, Jiangsu Yancheng Educational Institute, Yancheng 224002, P. R. China;
2. Department of Mathematics, Jiangsu Yancheng Teachers College, Yancheng 224002, P. R. China

Received:1997-01-23 Revised:1999-01-21 Online:1999-07-18 Published:1999-07-18

摘要/Abstract

摘要： In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilistic normed linear space was further studied. On probabilistic normed linear operator space, some resonance theorems dealing with probabilistic bounded sets, probabilistic semi-bounded sets, and probabilistic non-unbounded sets are obtained.

关键词: unsaturated soil, non-linear, elasto-plasticity, consolidation, finite element method

Abstract: In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilistic normed linear space was further studied. On probabilistic normed linear operator space, some resonance theorems dealing with probabilistic bounded sets, probabilistic semi-bounded sets, and probabilistic non-unbounded sets are obtained.

Key words: unsaturated soil, non-linear, elasto-plasticity, consolidation, finite element method

中图分类号:

O177.5

肖建中;朱杏华. PROBABILISTIC NORM OF OPERATORS AND RESONANCE THEOREMS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(7): 781-788.

Xiao Jianzhong;Zhu Xinghua . PROBABILISTIC NORM OF OPERATORS AND RESONANCE THEOREMS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(7): 781-788.

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