Search results for "Operator theory"

Flow measurement using circular portable flume

2018

Abstract The circular portable flume is a simple device to measure discharge in circular drainage networks. Since the unit can be easily installed and removed, it is helpful in water distribution measurement and management. First in this paper the available studies are reviewed for highlighting the effect of both the contraction ratio and the flume slope on the stage-discharge relationship. Then the Buckingham's Theorem of the dimensional analysis and the self-similarity theory are used to deduce the stage-discharge curve of the circular flume. The new theoretical stage-discharge equation is calibrated by the literature available experimental data and those obtained in this experimental inv…

The calculation of the first positive Lyapunov exponent in sleep EEG data

1993

To help determine if the EEG is quasiperiodic or chaotic we performed a new analysis by calculating the first positive Lyapunov exponent L1 from sleep EEG data. Lyapunov exponents measure the mean exponential expansion or contraction of a flow in phase space. L1 is zero for periodic as well as quasiperiodic processes, but positive in case of chaotic processes expressing the sensitive dependence on initial conditions. We calculated L1 for sleep EEG segments of 15 healthy male subjects corresponding to sleep stages I, II, III, IV and REM (according to Rechtschaffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor simple noise. Moreover…

Dynamics of differentiation and integration operators on weighted spaces of entire functions

2014

Invariance spectrale des algèbres d'opérateurs pseudodifférentiels

2002

We construct and study several algebras of pseudodifferential operators that are closed under holomorphic functional calculus. This leads to a better understanding of the structure of inverses of elliptic pseudodifferential operators on certain non-compact manifolds. It also leads to decay properties for the solutions of these operators. To cite this article: R. Lauter et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1095–1099.

Nonlocalization Properties of Time Operators Transformations

2014

It is presented a general approach to the problem of extension of time operators and the associated Lambda transformations on singular measures. It is also shown that Lambda transformations defined on function spaces having the Urysohn property are non localized. Particular attention has been devoted to time and Lambda operators associated with the Walsh-Paley system and to a characterization of their domain and non locality.

On many-sorted algebraic closure operators

2004

A theorem of Birkhoff-Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many-sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many-sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Integrability of the one dimensional Schrödinger equation

2018

We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.

Dissipative operators and differential equations on Banach spaces

1991

If we consider the initial value problem Inline Equation $$x'(t) = f(t,x(t)),{\text{ }}x(0) = {x_0}$$ on the real line, it is well known that one—sided bounds like Inline Equation $$\left[ {f(t,x) - f\left( {t,y} \right)} \right]\left( {x - {\text{y}}} \right) \leqslant \omega {\left( {x - y} \right)^2}$$ give much better information about the behaviour of solutions than the Lipschitz- type estimates Inline Equation $$ \left| {f\left( {t,x} \right) - f\left( {t,y} \right)} \right| \leqslant L\left| {x - y} \right|,$$ because ω, unlike L, may be negative.

Kernel manifold alignment for domain adaptation

2016

The wealth of sensory data coming from different modalities has opened numerous opportu- nities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. How- ever, multimodal architectures must rely on models able to adapt to changes in the data dis- tribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation proble…

Least-squares community extraction in feature-rich networks using similarity data

2021

We explore a doubly-greedy approach to the issue of community detection in feature-rich networks. According to this approach, both the network and feature data are straightforwardly recovered from the underlying unknown non-overlapping communities, supplied with a center in the feature space and intensity weight(s) over the network each. Our least-squares additive criterion allows us to search for communities one-by-one and to find each community by adding entities one by one. A focus of this paper is that the feature-space data part is converted into a similarity matrix format. The similarity/link values can be used in either of two modes: (a) as measured in the same scale so that one may …