Results 231 to 240 of about 47,542 (262)

Variational principles and thermodynamical perturbations

Journal of Physics A: Mathematical and General, 2004
Summary: Thermodynamical perturbation theory provides a method for calculating the partition function or the free energy of a system from the properties of another system. The first-order perturbation takes advantage of inequalities such as the Gibbs-Bogoliubov inequality in classical mechanics and the Peierls and Bogoliubov inequalities in quantum ...
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Perturbation expansion of variational principles at arbitrary order

Physical Review A, 1995
When perturbation theory is applied to a quantity for which a variational principle holds (eigenenergies of Hamiltonians, Hartree-Fock or density-functional-theory energy, etc.), different variational perturbation theorems can be derived. A general demonstration of the existence of variational principles for an even order of perturbation, when ...
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Limiting Absorption Principle for Singularly Perturbed Operators

Mathematische Nachrichten, 2001
Assume the limiting absorption principle for a selfadjoint operator \(H_1\). If \(H_2\) is another selfadjoint operator such that \((H_1- z)^{-p}- (H_2- z)^{-p}\), \(p\in\mathbb{R}\), is compact for some \(z\in \text{res }H_1\cap \text{res }H_2\), then the limiting absorption is valid also for \(H_2\). This result is applied to \(H_2\) which arise from
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Complementary variational principles in perturbation theory

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1968
Abstract Complementary upper and lower bounds are derived for second-order quantum-mechanical perturbation energies. The upper bound is equivalent to that of Hylleraas. The lower bound appears to be new, but reduces to that of Prager & Hirschfelder if a certain constraint is applied.
A. M. Arthurs, P. D. Robinson
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Maximum principle via singular perturbations

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2003
The paper is concerned with necessary optimality conditions for parabolic boundary control problems. Its main purpose is to provide a regularization technique via singular perturbations to obtain optimality conditions for the time optimal control problem. The considered system is nonlinear and consists of a controlled coupled ODE/PDE.
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On the integrability and perturbations of systems of Ode's with nonlinear superposition principles

Physica D: Nonlinear Phenomena, 1986
In this note - properly characterized as ''extended abstract'' by the authors themselves - the authors announce that they are currently investigating a variety of manifestations of chaotic behavior in different perturbations of systems of ODE's with nonlinear superposition principles.
Bountis, T. C., Papageorgiou, V., Winternitz, P.   +2 more
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Maximum Principle for a Hybrid System Via Singular Perturbations

SIAM Journal on Control and Optimization, 1999
This paper is on a boundary control problem for a linear parabolic equation coupled with an infinite dimensional ordinary differential equation. As the author points out, to obtain a Pontryagin maximum principle in the presence of pointwise state constraints, one needs an adjoint variational equation with measure boundary data.
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On Reduction Principle in Stability Theory for Systems with Random Perturbations

Ukrainian Mathematical Journal, 2001
The author considers a system of the form \[ \dot x=X(x,y),\quad \dot y=A(t)y+Y(t,x,y,\xi(t)),\tag{1} \] where \(X\in C(D_x\times D_y \mapsto \mathbb{R}^n)\), \(Y\in C([0,\infty)\times D_x\times D_y\times \mathbb{R}^k \mapsto \mathbb{R}^m)\), \(D_x\), \(D_y\) are domains in \(\mathbb{R}^n\) and \(\mathbb{R}^m\), respectively, and \(\xi(t)\) is an ...
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The Samoilenko Reduction Principle for Differential Equations with Random Perturbations

Differential Equations, 2001
Let \(x(t,t_0,x_0)\) be a solution to the randomly perturbed differential equation \[ dx/dt=F(x) +\sigma(t,x)\xi(f),\quad t\geq 0,\tag{*} \] with \(x\in \mathbb{R}^n\), \(\xi(t)\) a random process a.s. absolutely integrable on every finite interval, and \(F,\sigma \in\text{Lip}\). The set \(S_t\) is said to be positively invariant if \[ P\{x(t,t_0,x_0)\
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Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

Set-Valued Analysis, 2001
The author introduces the notions of flexible and tolerant perturbation functions and shows that for a flexible and tolerant perturbation function the set of parameters for which the corresponding minimization problem is well-posed is generic. Then he gives criteria for flexible (resp.\ tolerant) perturbations, obtaining so several genericity results ...
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