Search results for "Functional analysis"
showing 10 items of 1059 documents
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…
Input-to-State Stability of Lur’e Hyperbolic Distributed Complex-Valued Parameter Control Systems: LOI Approach
2013
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/364057 Open access In this work, input-to-state stability of Lur'e hyperbolic distributed complex-valued parameter control systems has been addressed. Using comparison principle, delay-dependent sufficient conditions for the input-to-state stability in complex Hilbert spaces are established in terms of linear operator inequalities. Finally, numerical computation illustrates our result.
About the reliability, efficiency, and meaning of the error estimates of a LAOCOON3-type NMR analysis system
1977
Abstract The statistical error estimates of a LAOCOON3-type system are tested. The analyzabilities of a spectrum and spectral parameters are described by a new measure. The variation in the uncertainties of the parameters can be explained by correlation coefficients. According to the calculations made, the error estimates are normally quite reliable if the accuracy of the observed spectrum is known. In some cases the Newton-Raphson type of iteration does not converge or the confidence limits of the parameters are enormous or both; an example is discussed. It seems clear that one cannot avoid differing uncertainties of the parameters by changing the method of analysis, or that one can avoid …
FATIGUE FAILURE CRITERIA FOR MATERIALS UNDER RANDOM TRIAXIAL STATE OF STRESS
1984
SUMMARY Five fatigue failure criteria are formulated for a random triaxial state of stress whose components have zero mean values. It is assumed that fatigue failure is determined by the stress and strain components that act on an expected fracture plane. It is shown that in some special cases the proposed failure theories reduce to classical theories applied for sinusoidal stresses.
An evaluation framework and a benchmark for multi/hyperspectral image compression
2011
International audience; This paper benchmarks three multi/hyperspectral image compression approaches: the classic Multi-2D compression approach and two different implementations of 3D approach (Full 3D and Hybrid). All approaches are combined with a spectral PCA decorrelation stage to optimize performance. These three compression approaches are compared within a larger comparison framework than the conventionally used PSNR, which includes eight metrics divided into three families. The comparison is carried out with regard to variations in bitrates, spatial, and spectral dimensions variations of images. The time and memory consumption difference between the three approaches is also discussed…
Characterizations of convex approximate subdifferential calculus in Banach spaces
2016
International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale
2002
L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur Terre ou programme d'exploration de Mars). Le système décrivant les trajectoires est de dimension 6, le contrôle est l'angle de gîte cinématique et le coût est l'intégrale du flux thermique. Par ailleurs il y a des contraintes sur l'état (flux thermique, accélération normale et pression dynamique). Notre étude est essentiellement géométrique et fondée sur une évaluation de l'ensemble des états accessibles en tenant compte des contraintes sur l'état. On esquisse une analyse des extrémales du Principe du …
A note on Hilbert’s weak nullstellensatz
2015
In this article, through a suitable generalization of the well-known notion of spectrum of an element of an arbitrary normed algebra of Operator Theory, it will be possible to give another simple proof of the Hilbert’s Weak Nullstellensatz.
On Gelfand-Mazur Theorem
2015
From a suitable extension of the notion of spectrum drew from normed algebra theory, it will be possible, among other things, to provide some generalizations of the well-known Gelfand-Mazur theorem. In this brief research report, we wish to pursue one of these, as achieved in I,4.
Can there be a general nonlinear PDE theory for existence of solutions ?
2010
Updated version of the 2004 paper arxiv:math/0407026; Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the respective PDEs. The method can also deal with associated initial and/or boundary value problems. The solutions obtained can be assimilated with usual measurable functions or even with Hausdorff continuous functions on the respective Euclidean domains. It is important to note that the use of the or…