Point contact tunnelling spectroscopy of the density of states in Tb-Mg-Zn quasicrystals

According to theoretical predictions the quasicrystalline (QC) electronic density of states (DOS) must have a rich and fine spiky structure which actually has resulted elusive. The problem with its absence may be related to poor structural characteristics of the studied specimens, and/or to the non-existence of this spike characteristic. Recent calculations have shown that the fine structure indeed exists, but only for two dimensional approximants phases. The aim of the present study is to show our recent experimental studies with point contacts tunnel junction spectroscopy performed in samples of very high quality. The studies were performed in icosahedral QC alloys with composition Tb$_9$Mg$_{35}$Zn$_{56}$. We found the presence of a pseudogap feature at the Fermi level, small as compared to the pseudogap of other icosahedral materials. This study made in different spots on the QC shows quite different spectroscopic features, where the observed DOS was a fine non-spiky structure, distinct to theoretical predictions. In some regions of the specimens the spectroscopic features could be related to Kondo characteristics due to Tb magnetic atoms acting as impurities. Additionally, we observed that the spectroscopic features vanished under magnetic field.Comment: 9 pages, 8 figures, accepted in Journal of Non-Crystalline Solid

Stochastic stability of sectional-Anosov flows

A {\em sectional-Anosov flow} is a vector field on a compact manifold inwardly transverse to the boundary such that the maximal invariant set is sectional-hyperbolic (in the sense of \cite{mm}). We prove that any $C^2$ transitive sectional-Anosov flow has a unique SRB measure which is stochastically stable under small random perturbations.Comment: 10 page

Fixed point theorems for a class of mappings depending of another function and defined on cone metric spaces

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.Comment: 11 pages, submitte

Cone metric spaces and fixed point theorems of T-Kannan contractive mappings

The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Kannan type mappings on complete cone metric spaces depended on another function.Comment: 9 page

On the Existence of Fixed Points of Contraction Mappings Depending of Two Functions on Cone Metric Spaces

In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.Comment: 9 pages, submitte

T-Zamfirescu and T-weak contraction mappings on cone metric spaces

The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Zamfirescu and T-weak contraction mappings in the framework of complete cone metric spaces.Comment: 9 pages, submitte

Common fixed points for a pair of commuting mappings in complete cone metric spaces

This paper is devoted to prove the S. L. Singh's common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of Generalized Kannan Con- traction, Generalized Zamfirescu Contraction and Generalized Weak Contraction for a pair of mappings, proving afterward their respective fixed point results.Comment: submitte

Searching for spiral shocks

Spiral shocks in cataclysmic variables (CVs) are the result of tidal interactions of the mass donor star with the accretion disc. Their study is fundamental for our understanding of angular momentum transfer in discs. In our quest to learn how widespread amongst binaries spiral shocks are, and how their presence depends upon orbital period and mass ratio (as they are created by direct interaction with the donor star), we have obtained spectra of a large sample of CVs during their high-mass-transfer states. We find that 24 out of the 63 systems observed are candidates for containing spiral shocks. 5 out of those 24 CVs have been confirmed as showing shocks in the disc during outburst.Comment: 2 pages. Proceedings of the Goettingen conference on Cataclysmic Variable Stars, Goettingen, August 200

Tilting Theory and Functor Categories III. The Maps Category

In this paper we continue the project of generalizing tilting theory to the category of contravariant functors $Mod(C)$, from a skeletally small preadditive category $C$ to the category of abelian groups. We introduced the notion of a a generalized tilting category $T$, and extended Happel's theorem to $Mod(C)$. We proved that there is an equivalence of triangulated categories $D^b (Mod(C))\cong Db (Mod(T))$. In the case of dualizing varieties, we proved a version of Happel's theorem for the categories of finitely presented functors. We also proved in this paper, that there exists a relation between covariantly finite coresolving categories, and generalized tilting categories. Extending theorems for artin algebras. In this article we consider the category of maps, and relate tilting categories in the category of functors, with relative tilting in the category of maps. Of special interest is the category $mod(mod \Lambda)$ with $\Lambda$ an artin algebra

Applying the Inverse Average Magnitude Squared Coherence Index for Determining Order-Chaos Transition in a System Governed by H\'enon Mapping Dynamics

The quantitative determination of the order-chaos transition in a nonlinear dynamical system described by H\'enon mapping defined as $x[n+1]=1.0-A*x[n]^2+B*y[n], y[n+1]=B*x[n]$, where $B=0.3$, and $A$ is an adjustable control parameter, was made. This was achieved by applying the Inverse Average Magnitude-Squared Coherence Index (IAMSCI). This method is based on the Welch average periodogram technique and it has the advantage respect to nonlinear dynamical methods that it may be applied to any stationary signal by using discrete Fourier transform (DFT) representation which allows to operate on a short discrete-time series. Its effectiveness was demonstrated by comparing the results obtained by applying IAMSCI method with those obtained by calculating the largest Lyapounov exponent (LLE), both applied to the same discrete-time series set derived from the H\'enon mapping.Comment: 20 pages, 7 figure