Search results for "Names"
showing 10 items of 6843 documents
Noether’s Early Contributions to Modern Algebra
2020
As described in preceding chapters, Noether’s work on invariant theory broke new ground that led the Gottingen mathematicians, but first and foremost Hilbert, to invite her to habilitate there.
Multiplication of Distributions in One Dimension: Possible Approaches and Applications to δ-Function and Its Derivatives
1995
We introduce a new class of multiplications of distributions in one dimension merging two different regularizations of distributions. Some of the features of these multiplications are discussed in detail. We use our theory to study a number of examples, involving products between Dirac delta functions and its successive derivatives. © 1995 Academic Press. All rights reserved.
Spectrum and Pseudo-Spectrum
2019
In this book all Hilbert spaces will be assumed to separable for simplicity. In this section we review some basic definitions and properties; we refer to Kato (Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer, New York, 1966), Reed and Simon (Methods of modern mathematical physics. I. Functional analysis, 2nd edn. Academic, New York, 1980; Methods of modern mathematical physics. II. Fourier analysis, self adjointness. Academic, New York, 1975; Methods of modern mathematical physics. IV. Analysis of operators. Academic, New York, 1978), Riesz and Sz.-Nagy (Lecons d’analyse fonctionnelle, Quatrieme edition. Academie des Sciences d…
Analytic vectors, anomalies and star representations
1989
It is hinted that anomalies are not really anomalous since (at least in characteristic examples) they can be related to a lack of common analytic vectors for the Hamiltonian and the observables. We reanalyze the notions of analytic vectors and of local representations of Lie algebras in this light, and show how the notion of preferred observables introduced in the deformation (star product) approach to quantization may help give an anomaly-free formulation to physical problems. Finally, some remarks are made concerning the applicability of these considerations to field theory, especially in two dimensions.
Current Algebras as Hilbert Space Operator Cocycles
1994
Aspects of a generalized representation theory of current algebras in 3 + 1 dimensions axe discussed. Rules for a systematic computation of vacuum expectation values of products of currents are described. Their relation to gauge group actions in bundles of fermionic Fock spaces and to the sesquilinear form approach of Langmann and Ruijsenaars is explained. The regularization for a construction of an operator cocycle representation of the current algebra is explained. An alternative formula for the Schwinger terms defining gauge group extensions is written in terms of Wodzicki residue and Dixmier trace.
Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics
2010
Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz pro…
An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation
2007
A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross-section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower freq…
Modeling of copper fixed-bed biosorption from wastewater by Posidonia oceanica
2009
Biosorption of copper from aqueous solutions by Posidonia oceanica was investigated in batch and fixed-bed experiments. Batch experiments were conducted to evaluate the removal equilibrium at pH 5.0 and 6.0; experimental data were fitted to Langmuir model with maximum uptake capacities of 56.92 and 85.78 mg g(-1), respectively. Five column experiments were carried out at different feed concentrations. Breakthrough times and continuous sorption isotherm were obtained from breakthrough curves. Differences among batch and continuous isotherms were observed; the maximum uptake capacity in dynamic conditions was found in 56.70 mg g(-1) for final pH between 5.0 and 5.5. The biosorbent was regener…
Isomerization of C5–C7 n-alkanes on unidirectional large pore zeolites: activity, selectivity and adsorption features
2001
Abstract The hydroisomerization–hydrocracking of nC5–nC7 is studied with a 12MR unidirectional zeolite (ITQ-4). Selectivity and kinetic parameters indicate that differences in pore topology are more important than acidity for determining isomerization selectivity. The adsorption of the paraffins is determined by van der Waals interactions.
<title>Fibers supporting super-Gaussian beams: cladding effects</title>
1996
We define a matching function that describes the amplitude variations produced over supergaussian beams, by cladding optical fibers that, if uncladded, can sustain this type of beams as Eigenmodes.