ChemInform Abstract: A STUDY OF THE UPPER AND LOWER BOUNDS OF THE SECOND-ORDER PERTURBATION ENERGY

1974 ◽  
Vol 5 (40) ◽  
pp. no-no
Author(s):  
TOKIO YAMABE ◽  
KAZUYOSHI TANAKA ◽  
SHINGO ISHIMARU ◽  
KENICHI FUKUI
Keyword(s):  
Lower Bounds ◽  
Second Order ◽  
Order Perturbation ◽  
Upper And Lower Bounds ◽  
Perturbation Energy

scholarly journals A Study of the Upper and Lower Bounds of the Second-order Perturbation Energy

1974 ◽  
Vol 47 (7) ◽  
pp. 1578-1581 ◽  
Author(s):  
Tokio Yamabe ◽  
Kazuyoshi Tanaka ◽  
Shingo Ishimaru ◽  
Kenichi Fukui
Keyword(s):  
Lower Bounds ◽  
Second Order ◽  
Order Perturbation ◽  
Upper And Lower Bounds ◽  
Perturbation Energy

Force Reconstruction for Uncertain Structure Based on Interval Model and Second-Order Perturbation Theory

2019 ◽  
Vol 18 (01) ◽  
pp. 1950040
Author(s):  
Xiaowang Li ◽  
Haitao Zhao ◽  
Jiping Huang ◽  
Ji’an Chen
Keyword(s):  
Perturbation Theory ◽  
Lower Bounds ◽  
Second Order ◽  
Order Perturbation ◽  
Upper And Lower Bounds ◽  
Order Perturbation Theory ◽  
Uncertain Parameters ◽  
Interval Model ◽  
Uncertain Structure ◽  
Second Order Perturbation Theory

In order to reconstruct the upper and lower bounds of dynamic excitations applied on the uncertain structure, an algorithm based on interval model and second-order perturbation theory is presented in this paper. First, interval model is built up by expressing the uncertain parameters of structure in interval form. Next according to second-order perturbation theory, structure characteristic matrices and input force vector are approximated as second-order Taylor polynomial expansion at the midpoint of uncertain parameters. After that the input force’s midpoint, first-order and second-order partial derivatives are respectively calculated by existing step-by-step integration method. Then addition and subtraction of the three components obtained in previous step are operated. Ultimately the upper and lower bounds of dynamic load can be identified. Numerical simulation results demonstrate this method is with the characteristic of high efficiency and precision. In addition, it is able to remain a relatively strong robustness under noise turbulence.

Remarks on the Use of Approximate Wavefunctions for the Second‐Order Perturbation Energy

1966 ◽  
Vol 45 (5) ◽  
pp. 1803-1804 ◽  
Author(s):  
T. J. Dougherty ◽  
T. Vladimiroff ◽  
S. T. Epstein
Keyword(s):  
Second Order ◽  
Order Perturbation ◽  
Perturbation Energy

Multiplicity results for systems of asymptotically linear second order equations

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Anna Capietto ◽  
Francesca Dalbono
Keyword(s):  
Lower Bounds ◽  
Second Order ◽  
Upper And Lower Bounds ◽  
Asymptotically Linear ◽  
Multiplicity Results ◽  
Number Of Zeros ◽  
Existence And Multiplicity ◽  
Abstract Continuation Theorem ◽  
Nodal Properties ◽  
Second Order Equations

AbstractWe prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.

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