All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 65

Showing per page

Confining quantum particles with a purely magnetic field

Yves Colin de Verdière, Françoise Truc (2010)

Annales de l’institut Fourier

We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These...

Contact between elastic bodies. I. Continuous problems

Jaroslav Haslinger, Ivan Hlaváček (1980)

Aplikace matematiky

Problems of a unilateral contact between bounded bodies without friction are considered within the range of two-dimensional linear elastostatics. Two classes of problems are distinguished: those with a bounded contact zone and with an enlargign contact zone. Both classes can be formulated in terms of displacements by means of a variational inequality. The proofs of existence of a solution are presented and the uniqueness discussed.

Continuum spectrum for the linearized extremal eigenvalue problem with boundary reactions

Futoshi Takahashi (2014)

Mathematica Bohemica

We study the semilinear problem with the boundary reaction - Δ u + u = 0 in Ω , ∂ u ∂ ν = λ f ( u ) on ∂ Ω , where Ω ⊂ ℝ N , N ≥ 2 , is a smooth bounded domain, f : [ 0 , ∞ ) → ( 0 , ∞ ) is a smooth, strictly positive, convex, increasing function which is superlinear at ∞ , and λ > 0 is a parameter. It is known that there exists an extremal parameter λ * > 0 such that a classical minimal solution exists for λ < λ * , and there is no solution for λ > λ * . Moreover, there is a unique weak solution u * corresponding to the parameter λ = λ * . In this paper, we continue to study the spectral properties of u * and show...

Control of networks of Euler-Bernoulli beams

Bertrand Dekoninck, Serge Nicaise (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the exact controllability problem by boundary action of hyperbolic systems of networks of Euler-Bernoulli beams. Using the multiplier method and Ingham's inequality, we give sufficient conditions insuring the exact controllability for all time. These conditions are related to the spectral behaviour of the associated operator and are sufficiently concrete in order to be able to check them on particular networks as illustrated on simple examples.

Controllability of partial differential equations on graphs

Sergei Avdonin, Victor Mikhaylov (2008)

Applicationes Mathematicae

We study boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in L₂-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the heat equation...

Convergence de la métrique de Fubini-Study d'un fibré linéaire positif

Thierry Bouche (1990)

Annales de l'institut Fourier

Soit E , un fibré linéaire positif au-dessus d’une variété complexe compacte. Nous montrons que la fonction de distorsion définie par le rapport entre la métrique initiale et la métrique de Fubini-Study de E ⊗ k admet un équivalent lorsque k tend vers l’infini. Ceci améliore les encadrements de Kempf et Ji sur les variétés abéliennes, et les étend à toute variété projective. La démonstration repose sur le calcul d’un équivalent pour le noyau de la chaleur, avec contrôle de la convergence par rapport...

Convergence of approximation methods for eigenvalue problem for two forms

Teresa Regińska (1984)

Aplikace matematiky

The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space X . We investigate some approximation methods generated by sequences of forms a n and b n defined on a dense subspace of X . The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn’s method.

Converging self-consistent field equations in quantum chemistry – recent achievements and remaining challenges

Konstantin N. Kudin, Gustavo E. Scuseria (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper reviews popular acceleration techniques to converge the non-linear self-consistent field equations appearing in quantum chemistry calculations with localized basis sets. The different methodologies, as well as their advantages and limitations are discussed within the same framework. Several illustrative examples of calculations are presented. This paper attempts to describe recent achievements and remaining challenges in this field.

Convex shape optimization for the least biharmonic Steklov eigenvalue

Pedro Ricardo Simão Antunes, Filippo Gazzola (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The least Steklov eigenvalue d1 for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the L2-norm of harmonic functions. These applications suggest to address the problem of minimizing d1 in suitable classes of domains. We survey the existing results and conjectures about this topic; in particular, the existence of a convex domain...

Currently displaying 41 – 60 of 65