Variational upper and lower bounds for the correction of the second order energy in 1/Z expansions for two-electron atoms

1969 ◽  
Vol 4 (1) ◽  
pp. 45-47 ◽  
Author(s):  
Yu.Yu. Dmitriev ◽  
M.S. Yuriev
Keyword(s):  
Lower Bounds ◽  
Second Order ◽  
Upper And Lower Bounds ◽  
Order Energy

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

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.

scholarly journals Expansion of the spectrum in the weak disorder regime for random operators in continuum space

2017 ◽  
Vol 20 (01) ◽  
pp. 1750008 ◽  
Author(s):  
Denis Borisov ◽  
Francisco Hoecker-Escuti ◽  
Ivan Veselić
Keyword(s):  
Differential Operator ◽  
Lower Bounds ◽  
Second Order ◽  
Upper And Lower Bounds ◽  
Random Operators ◽  
Elliptic Differential Operator ◽  
Weak Disorder ◽  
Schrödinger Type Operators

We study the spectrum of random ergodic Schrödinger-type operators in the weak disorder regime. We give upper and lower bounds on how much the spectrum expands at its bottom for very general perturbations. The background operator is assumed to be a periodic elliptic differential operator on [Formula: see text], not necessarily of second order.

scholarly journals Second order Dehn functions and HNN-extensions

1999 ◽  
Vol 67 (2) ◽  
pp. 272-288 ◽  
Author(s):  
X. Wang ◽  
S. J. Pride
Keyword(s):  
Lower Bounds ◽  
Infinite Number ◽  
Second Order ◽  
Upper And Lower Bounds ◽  
Dehn Functions ◽  
Open Questions ◽  
Hnn Extensions

AbstractIn previous work [2] calculations of subquadratic second order Dehn functions for various groups were carried out. In this paper we obtain estimates for upper and lower bounds of second order Dehn functions of HNN-extensions, and use these to exhibit an infinite number of different superquadratic second order Dehn functions. At the end of the paper several open questions concerning second order Dehn functions of groups are discussed.

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.

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