Search results for "Vectors"
showing 10 items of 601 documents
Probabilities, States, Statistics
2016
In this chapter we clarify some important notions which are relevant in a statistical theory of heat: The definitions of probability measure, and of thermodynamic states are illustrated, successively, by the classical Maxwell-Boltzmann statistics, by Fermi-Dirac statistics and by Bose-Einstein statistics. We discuss observables and their eigenvalue spectrum as well as entropy and we calculate these quantities for some examples. The chapter closes with a comparison of statistical descriptions of classical and quantum gases.
Pseudo-bosons and Riesz Bi-coherent States
2016
After a brief review on D-pseudo-bosons we introduce what we call Riesz bi-coherent states, which are pairs of states sharing with ordinary coherent states most of their features. In particular, they produce a resolution of the identity and they are eigenstates of two different annihilation operators which obey pseudo-bosonic commutation rules.
Three-mode two-boson Jaynes–Cummings model in trapped ions
2006
In this paper, we analyse a two-boson three-mode Jaynes–Cummings model which can be implemented in the context of trapped ions. The symmetries of the Hamiltonian are brought to light and analysed in detail in order to solve the eigenvalue problem. The calculation of the time evolution operator shows the possibility of realizing interesting applications, such as the generation of nonclassical states.
On the hyperbolicity of certain models of polydisperse sedimentation
2012
The sedimentation of a polydisperse suspension of small spherical particles dispersed in a viscous fluid, where particles belong to N species differing in size, can be described by a strongly coupled system of N scalar, nonlinear first-order conservation laws for the evolution of the volume fractions. The hyperbolicity of this system is a property of theoretical importance because it limits the range of validity of the model and is of practical interest for the implementation of numerical methods. The present work, which extends the results of R. Burger, R. Donat, P. Mulet, and C.A. Vega (SIAM Journal on Applied Mathematics 2010; 70:2186–2213), is focused on the fluxes corresponding to the …
Aryl hydrocarbon receptor activation by cAMP vs. dioxin: divergent signaling pathways.
2005
Even before the first vertebrates appeared on our planet, the aryl hydrocarbon receptor ( AHR ) gene was present to carry out one or more critical life functions. The vertebrate AHR then evolved to take on functions of detecting and responding to certain classes of environmental toxicants. These environmental pollutants include polycyclic aromatic hydrocarbons (e.g., benzo[ a ]pyrene), polyhalogenated hydrocarbons, dibenzofurans, and the most potent small-molecular-weight toxicant known, 2,3,7,8-tetrachlorodibenzo- p -dioxin (TCDD or dioxin). After binding of these ligands, the activated AHR translocates rapidly from the cytosol to the nucleus, where it forms a heterodimer with aryl hydroc…
A navigation and control algorithm for the position tracking of underwater vehicles
2014
In this paper we consider position control of underwater vehicles through inversion of differential kinematics based on uncalibrated, relative to the water, velocity sensors and unknown marine current. An estimation algorithm, based on the above measurements, estimates calibration parameters and marine current, assuring convergence of the estimated velocities to the true quantities. A kinematic control algorithm assures convergence to zero of the position tracking error. An extension of the basic estimation algorithm has been considered, in which position measurements are considered sampled at low rate and randomly spaced in time. Computer simulations are given of the proposed position trac…
On the numerical solution of some finite-dimensional bifurcation problems
1981
We consider numerical methods for solving finite-dimensional bifurcation problems. This paper includes the case of branching from the trivial solution at simple and multiple eigenvalues and perturbed bifurcation at simple eigenvalues. As a numerical example we treat a special rod buckling problem, where the boundary value problem is discretized by the shooting method.
On Boundary Conditions for Wedge Operators on Radial Sets
2008
We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.
A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter
2021
The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalueλβwith negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer forλβand the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.
Evolution of Worldwide Stock Markets, Correlation Structure and Correlation Based Graphs
2011
We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, corre…