Search results for " Operator"
showing 10 items of 931 documents
Tensor Operators and the Wigner-Eckart Theorem
2007
In this chapter we pave the way to the use of the coupling methods of Chap. 1 for manipulating operators and their matrix elements. To enable smooth application of the angular momentum methods, we introduce so-called spherical tensor operators. Spherical tensors can be related to Cartesian tensors. A Cartesian tensor of a given Cartesian rank can be reduced to spherical tensors of several spherical ranks. There is a very convenient procedure, the so-called Wigner-Eckart theorem, to separate the part containing the projection quantum numbers from the rest of the matrix element of a spherical tensor operator. The remaining piece, called the reduced matrix element, is rotationally invariant an…
Théorie des spectres rovibroniques des molécules octaédriques : Hamiltonien et moments de transition
2002
This thesis is devoted to the treatment of rovibronic couplings of octahedral species for which the Born-Oppenheimer approximation is broken down. By using the octahedral formalism, a full effective rovibronic model is extended from works about molecules in a non-degenerate electronic state. This effective model is dedicated to molecules with an odd or an even number of electrons and it has been successfully applied to V(CO)6 and ReF6. For both of them we have four interacting vibronic sublevels attributed to a dynamical Jahn-Teller effect and giving rise to very complicated spectra. This model is validated by the overall agreement between predicted and observed band profiles. Moreover, an …
Weyl Type Theorems for Left and Right Polaroid Operators
2010
A bounded operator defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. In this paper we consider the two related notions of left and right polaroid, and explore them together with the condition of being a-polaroid. Moreover, the equivalences of Weyl type theorems and generalized Weyl type theorems are investigated for left and a-polaroid operators. As a consequence, we obtain a general framework which allows us to derive in a unified way many recent results, concerning Weyl type theorems (generalized or not) for important classes of operators.
Interventistica eco-guidata per l’articolazione d’anca
2013
Lo scopo di questo lavoro è di rivedere le principali applicazioni della interventistica eco-guidata d’anca, descrivendone le indicazioni e la metodologia. L’ecografia è una metodica considerata sicura per i pazienti, in quanto non è stato dimostrato un possibile danno dovuto all’energia trasmessa dagli ultrasuoni ai tessuti del paziente, contrariamente alle metodiche che fanno uso di radiazioni ionizzanti, come la radiografia convenzionale e la tomografia computerizzata. Inoltre, l’ecografia risulta rapida ed efficace nel guidare l’ago verso la sede voluta evitando di intercettare strutture vascolari e/o nervose, consentendo quindi una maggiore sicurezza, rispetto alle tecniche interventis…
A study on graph representations for genetic programming
2020
Graph representations promise several desirable properties for Genetic Programming (GP); multiple-output programs, natural representations of code reuse and, in many cases, an innate mechanism for neutral drift. Each graph GP technique provides a program representation, genetic operators and overarching evolutionary algorithm. This makes it difficult to identify the individual causes of empirical differences, both between these methods and in comparison to traditional GP. In this work, we empirically study the behavior of Cartesian Genetic Programming (CGP), Linear Genetic Programming (LGP), Evolving Graphs by Graph Programming (EGGP) and traditional GP. By fixing some aspects of the config…
A model of adaptive decision-making from representation of information environment by quantum fields
2017
We present the mathematical model of decision making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioral, and geo-political factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are of the purely informational nature. The QFT-model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantu…
Applications of Topological *-Algebras of Unbounded Operators
1998
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the time evolution of two interacting models of matter and bosons. We show that for all these systems it is possible to build up a common framework where the thermodynamical limit of the algebraic dynamics can be conveniently studied and obtained.
Boundedness and compactness of operators related to time-frequency analysis
2018
En esta tesis, estudiamos diferentes aspectos de los operadores relacionados con el análisis tiempo-frecuencia. Cada operador lineal y continuo de la clase de Schwartz en su dual, el espacio de distribuciones temperadas, se puede escribir como un operador integral con núcleo K, o también como un operador integral de Fourier (de hecho, pseudodiferencial). Las diferentes condiciones en el núcleo o el símbolo y la fase (en el caso de los operadores integrales de Fourier) permiten extender el operador a varios espacios de funciones y distribuciones. A continuación detallamos los contenidos de la memoria. En el primer capítulo presentamos la notación, las definiciones de algunos espacios, de suc…
Local maximal operators on fractional Sobolev spaces
2016
In this note we establish the boundedness properties of local maximal operators MG on the fractional Sobolev spaces Ws;p(G) whenever G is an open set in Rn, 0 < s < 1 and 1 < p < 1. As an application, we characterize the fractional (s;p)-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes. pq(G) whenever G is an open set in R n , 0 < s < 1 and 1 < p;q <1. Our main focus lies in the mapping properties of MG on a fractional Sobolev space W s;p (G) with 0 < s < 1 and 1 < p < 1, see Section 2 for the denition or (3) for a survey of this space. The intrinsically dened function space W s;p (G) on a given domain G coincides with the trace space F s …