Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Invariant Characterization of Neural Systems

It is shown that the invariant integral, viz., the Kolmogorov second entropy, is eminently suited to characterize EEG quantitatively. The estimation obtained for a "clinically normal" brain is compared with a previous result obtained from the EEG of a person under epileptic seizure.

Financial crisis: theory and practice

In the last 50 years, we have had approximately 40 events with characteristics related to financial crisis. The most severe crisis was in 1929, when the financial markets plummet and the US gross domestic product decline in more than 30 percent. Recently some years ago, a new crisis developed in the United States, but instantly caused consequences and effects in the rest of the world. This new economic and financial crisis has increased the interest and motivation for the academic community, professors and researchers, to understand the causes and effects of the crisis, to learn from it. This is the one of the main reasons for the compilation of this book, which begins with a meeting of a group of IAFI researchers from the University of Barcelona, where researchers form Mexico and Spain, explain causes and consequences of the crisis of 2007. For that reason, we believed this set of chapters related to methodologies, applications and theories, would conveniently explained the characteristics and events of the past and future financial crisis This book consists in 3 main sections, the first one called "State of the Art and current situation", the second named "Econometric applications to estimate crisis time periods" , and the third one "Solutions to diminish the effects of the crisis". The first section explains the current point of view of many research papers related to financial crisis, it has 2 chapters. In the first one, it describe and analyzes the models that historically have been used to explain financial crisis, furthermore, it proposes to used alternative methodologies such as Fuzzy Cognitive Maps. On the other hand , Chapter 2 , explains the characteristics and details of the 2007 crisis from the US perspective and its comparison to 1929 crisis, presenting some effects in Mexico and Latin America. The second section presents two econometric applications to estimate possible crisis periods. For this matter, Chapter 3, studies 3 Latin-American countries: Argentina, Brazil and Peru in the 1994 crisis and estimates the multifractal characteristics to identify financial and economic distress. Chapter 4 explains the crisis situations in Argentina (2001), Mexico (1994) and the recent one in the United States (2007) and its effects in other countries through a financial series methodology related to the stock market. The last section shows an alternative to prevent the effects of the crisis. The first chapter explains the financial stability effects through the financial system regulation and some globalization standards. Chapter 6, study the benefits of the Investor activism and a way to protect personal and national wealth to face the financial crisis risks.

Multiple edges of a quantum Hall system in a strong electric

In this paper we show that if the electrons in a quantum Hall sample are subjected to a constant electric field in the plane of the material, comparable in magnitude to the background magnetic field on the system of electrons, a multiplicity of edge states localized at different regions of space is produced in the sample. The actions governing the dynamics of these edge states are obtained starting from the well-known Schrödinger field theory for a system of nonrelativistic electrons, where on top of the constant background electric and magnetic fields, the electrons are further subject to slowly varying weak electromagnetic fields. In the regions between the edges, dubbed as the "bulk," the fermions can be integrated out entirely and the dynamics expressed in terms of a local effective action involving the slowly varying electromagnetic potentials. It is further shown how the bulk action is gauge noninvariant in a particular way, and how the edge states conspire to restore the U(1) electromagnetic gauge invariance of the system. In the edge action we obtain a heretofore unnoticed gauge-invariant term that depends on the particular edge. We argue that this term may be detected experimentally as different edges respond differently to a monochromatic probe due to this term

Vertically coupled quantum dots in the local spin-density functional theory

We have investigated the structure of double quantum dots vertically coupled at zero magnetic field within local-spin-density functional theory. The dots are identical and have a finite width, and the whole system is axially symmetric. We first discuss the effect of thickness on the addition spectrum of one single dot. Next we describe the structure of coupled dots as a function of the interdot distance for different electron numbers. Addition spectra, Hund's rule, and molecular-type configurations are discussed. It is shown that self-interaction corrections to the density-functional results do not play a very important role in the calculated addition spectra

Freezing of 4He and its liquid-solid interface from density functional theory

We show that, at high densities, fully variational solutions of solidlike types can be obtained from a density functional formalism originally designed for liquid 4He . Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased density functional (DF) methods to study highly nonhomogeneous systems, like 4He interacting with strongly attractive impurities and/or substrates, or the nucleation of the solid phase in the metastable liquid.

Optical response of two-dimensional few-electron concentric double quantum rings: A local-spin-density-functional theory study

We have investigated the dipole charge- and spin-density response of few-electron two-dimensional concentric nanorings as a function of the intensity of a erpendicularly applied magnetic field. We show that the dipole response displays signatures associated with the localization of electron states in the inner and outer ring favored by the perpendicularly applied magnetic field. Electron localization produces a more fragmented spectrum due to the appearance of additional edge excitations in the inner and outer ring.

Helium in polygonal nanopores at zero temperature: Density functional theory calculations

We investigate adsorption of helium in nanoscopic polygonal pores at zero temperature using a finite-range density functional theory. The adsorption potential is computed by means of a technique denoted as the elementary source method. We analyze a rhombic pore with Cs walls, where we show the existence of multiple interfacial configurations at some linear densities, which correspond to metastable states. Shape transitions and hysterectic loops appear in patterns which are richer and more complex than in a cylindrical tube with the same transverse area.