Delocalization of slowly damped eigenmodes on Anosov manifolds

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a "strip" of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.Comment: 28 pages; compared with version 1, minor modifications, add two reference

Benign breast diseases: experience at a teaching hospital in rural India

Background: Though benign breast diseases are very common with nearly 1/3 of women suffering some time during their life time, not many studies have focused on this entity, especially in rural areas. Our teaching hospital situated amongst the villages in rural part of India provided the right background for the study.  Objective: To determine the frequency of benign breast diseases in a teaching hospital situated in the rural setting and to analyze the role of triple assessment in assessing benign breast diseases.Study design: Prospective, descriptive study.Setting: MVJ Medical College and Research Hospital, Hoskote, Bangalore Rural district, Karnataka, India.Method of study: Data including age, complaints, clinical examination, radiological investigations and histopathological diagnosis was collected from patients presenting to the department of surgery with breast complaints. Patients with carcinoma of the breast were excluded from the study.Results: A total of 110 patients were studied between November 2009 to March 2011. Mean age of patients was 28.6 years. Fibroadenoma was the most common diagnosis in 56.4% followed by fibroadenosis in 20.9%. There was one case each of lipoma, tuberculosis and duct ectasia and two cases of atypical ductal hyperplasia. The sensitivity of clinical diagnosis in our study was 91.1% and FNAC was 100% accurate in all patients with fibroadenoma but had a sensitivity of only 78% in the diagnosis of fibroadenosis. Only 3.3% of cases of fibroadenoma were treated conservatively

Experiences with Mycobacterium leprae soluble antigens in a leprosy endemic population

Rees and Convit antigens prepared from armadillo-derived Mycobacterium leprae were used for skin testing in two leprosy endemic villages to understand their use in the epidemiology of leprosy. In all, 2602 individuals comprising 202 patients with leprosy detected in a prevalence survey, 476 household contacts and 1924 persons residing in non-case households were tested with two antigens. There was a strong and positive correlation ( r = 0.85) between reactions to the Rees and Convit antigens. The distribution of reactions was bimodal and considering reactions of 12 mm or more as ‘positive’, the positivity rate steeply increased with the increase in age. However. the distributions of reactions to these antigens in patients with leprosy. their household contacts and persons living in non-case households were very similar. These results indicate that Rees and Convit antigens are not useful in the identification of M. leprae infection or in the confirmation of leprosy diagnosis in a leprosy endemic population with a high prevalence of nonspecific sensitivity

Semiclassical measures and the Schroedinger flow on Riemannian manifolds

In this article we study limits of Wigner distributions (the so-called semiclassical measures) corresponding to sequences of solutions to the semiclassical Schroedinger equation at times scales $\alpha_{h}$ tending to infinity as the semiclassical parameter $h$ tends to zero (when $\alpha _{h}=1/h$ this is equivalent to consider solutions to the non-semiclassical Schreodinger equation). Some general results are presented, among which a weak version of Egorov's theorem that holds in this setting. A complete characterization is given for the Euclidean space and Zoll manifolds (that is, manifolds with periodic geodesic flow) via averaging formulae relating the semiclassical measures corresponding to the evolution to those of the initial states. The case of the flat torus is also addressed; it is shown that non-classical behavior may occur when energy concentrates on resonant frequencies. Moreover, we present an example showing that the semiclassical measures associated to a sequence of states no longer determines those of their evolutions. Finally, some results concerning the equation with a potential are presented.Comment: 18 pages; Theorems 1,2 extendend to deal with arbitrary time-scales; references adde

Entropy of semiclassical measures for nonpositively curved surfaces

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2

Extended metal-organic solids based on benzenepolycarboxylic and aminobenzoic acids

This article describes the recent results obtained in our laboratory on the interaction of polyfunctional ligands with divalent alkaline earth metal ions and a few divalent transition metal ions. Treatment of MC12·nH2O (M = Mg, Ca, Sr or Ba) with 2-amino benzoic acid leads to the formation of complexes [Mg(2-aba)2] (1), [Ca(2-aba)2(OH2)3]∞ (2), [{Sr(2-aba)2(OH2)2}2·H2O)]∞ (3), [Ba(2-aba)2(OH2)]∞ (4), respectively. While the calcium ions in 2 are hepta-coordinated, the strontium and barium ions in 3 and 4 reveal a coordination number of nine apart from additional metal-metal interactions. Apart from the carboxylate functionality, the amino group also binds to the metal centres in the case of strontium and barium complexes 3 and 4. Complexes [{Mg(H2O)6}(4-aba)2·2H2O] (5), [Ca(4-aba)2(H2O)2] (6) prepared from 4-aminobenzoic acid reveal more open or layered structures. Interaction of 2-mercaptobenzoic acid with MCl2·6H2O (M = Mg, Ca), however, leads to the oxidation of the thiol group resulting in the disulphide 2,2' -dithiobis(benzoic acid). New metal-organic framework based hydrogen-bonded porous solids [{M(btec) (OH2)4}n·n(C4H12N2)·4nH2O] (btec = 1,2,4,5-benzene tetracarboxylate) (M = Co9; Ni10; Zn11) have been synthesized from 1,2,4,5-benzene tetracarboxylic acid in the presence of piperazine. These compounds are made up of extensively hydrogen-bonded alternating layers of anionic M-btec co-ordination polymer and piperazinium cations. Compounds 2- 11 described herein form polymeric networks in the solid-state with the aid of different coordinating capabilities of the carboxylate anions hydrogen bonding interactions

Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\beta)$--KMS states and eigenmeasures of $\mathcal{L}_{-\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--isomorphic to the given Cuntz--Krieger algebra. Finally, we apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups $G$ which may have parabolic elements. We show that for the Cuntz--Krieger algebra arising from $G$ there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen--Series map associated with $G$. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of $G$. If $G$ has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with $G$.Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact