Carrier dynamics and dispersive terahertz Bloch gain in semiconductor superlattices

We have directly determined the spectral shape of the complex conductivities of Bloch oscillating electrons by using time-domain terahertz (THz)-electrooptic sampling technique and presented an experimental evidence for a dispersive Bloch gain in superlattices. This unique dispersive gain without population inversion arises from a non-classical nature of Bloch oscillations; i.e., the phase of the Bloch oscillation is shifted by π/2 from that of the semi-classical charged harmonic oscillation when driven by the same AC field. By increasing the bias electric field, the gain bandwidth reached in our particular sample.     

Proper Orthogonal Decomposition of the mixing layer flow into coherent structures and turbulent Gaussian fluctuations

The Proper Orthogonal Decomposition is used to decompose fluctuating turbulent flows into a coherent non-Gaussian component and background fluctuations. An application is performed from 2D experimental data of a turbulent plane mixing layer flow. The analyses of the energy spectra and the Probability Density Function of the velocity field show that POD extracts an incoherent part approaching the quasi-Gaussian distribution properties. The background fluctuations are homogeneous with small amplitude. New future applications are then conceivable like the modeling of the incoherent part for particular inflow condition generation methodology and the analysis of the cyclic velocity field variabilities in Internal Combustion engine flow. To cite this article: Ph. Druault et al., C. R. Mecanique 333 (2005).     

Jacopo da Firenze and the beginning of Italian vernacular algebra

In 1307, a certain Jacopo da Firenze wrote in Montpellier a Tractatus algorismi that contains the earliest extant algebra in a European vernacular and probably, as is argued, the first algebra in vernacular Italian. Analysis of the text shows that it cannot descend from any of the algebras written in Latin, nor from any published Arabic treatise, for which reason it presents us with evidence for a so far unexplored level of Arabic algebra. Further, since it contains no Arabisms, it must build on an already existing Romance-speaking environment engaged in algebra. Comparison with other Italian algebras written during the next 40 years show that all are linked to Jacopo or to this environment (perhaps Catalan) and disconnected from Leonardo Fibonacci's Liber abbaci.     

Exponentially decaying wavelets with uncertainty constants uniformly bounded with respect to the smoothness parameter

We construct a family of wavelet functions whose scaling functions decay exponentially and have uncertainty constants uniformly bounded with respect to the smoothness parameter.     

Bloch constant of holomorphic mappings on the unit polydisk of ℂ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we give a definition of Bloch mappings defined in the unit polydisk D ⁿ , which generalizes the concept of Bloch functions defined in the unit disk D. It is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex variables. We shall establish the corresponding distortion theorems for subfamilies β(K) and β _loc(K) of Bloch mappings defined in the polydisk D ⁿ , which extend the distortion theorems of Liu and Minda to higher dimensions. As an application, we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloch mappings defined in D ⁿ . In particular, our results reduce to the classical results of Ahlfors and Landau when n = 1. This work was supported by the National Natural Science Foundation of China (Grant No. 10571164) and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (Grant No. 20050358052)     

Mutual-probability prediction and higher-order correlation effects among acoustic,light and electromagnetic waves in a video display terminal environment

A probabilistic signal processing method, with which is possible to get some methodological suggestion to the measurement method of correlative and/or accumulative effects in the compound environment of sound, light and electromagnetic (EM) waves is discussed. In order to extract various types of latent interrelation characteristics among wave environmental factors leaked from an actually operating video display terminal (VDT), an extended regression system model, hierarchically reflecting not only linear correlation information but also nonlinear correlation information, is first introduced, especially from a viewpoint of ‘relationism-first’. Then, through estimating each regression parameter of this model, some original evaluation methods for predicting a whole probability distribution form, from one another, are proposed. Finally, the effectiveness of the methods is experimentally confirmed, by applying them to the actual observed data leaked by a VDT with some television games. To cite this article: M. Ohta et al., C. R. Mecanique 333 (2005).     

Topological structures of the sets of composition operators on the Bloch spaces

We study properties of the topological sets of composition operators on Bloch and little Bloch spaces in the operator topology.     

Lie Point Symmetry Preserving Discretizations for Variable Coefficient Korteweg–de Vries Equations

A nonlinear evolution equationu _t + fuu _x + gu _xxx = 0, where f andg are functions of x and t isconsidered. These functions are so chosen that the equation has athree-dimensional Lie point symmetry group. An invariant differencemodel, i.e. a difference equation and a mesh, is presented, preservingall the Lie point symmetries of the original equation.