A Semigroup Crossed Product Arising in Number Theory

Recently Bost and Connes have studied an interesting C*-algebraicHecke algebra arising in number theory. Here it is shown thatthis algebra can be realised as a semigroup crossed product,and be profitably studied using methods developed by the authorsfor analysing Toeplitz algebras. One main result is a characterisationof faithful representations of the Hecke algebra.     

Isolation of three new naturally occurring compounds from the culture of Micromonospora sp. P1068

Bioassay guided isolation of an antibacterial extract prepared from the fermentation broth of a Micromonospora sp. P1068 led to the isolation of eight compounds identified as (3R) 3,4',7-trihydroxy-isoflavanone (1), 3-hydroxydehydrodaidzein, daidzein (2), 3-methyl-1H-indole-2-carboxylic acid (3), 1H-indole-3-carboxaldehyde (4), 3-(p-hydroxyphenyl)-N-methylpropionamide, N-methylphloretamide (5), phenyl acetic acid (6), 2-hydroxy phenyl acetic acid (7) and 4-hydroxy-5-methoxy-benzoic acid (8). Compounds 1 and 5 were found to be novel chemical entities while 3 was isolated from a natural source for the first time. All compounds were evaluated for their antimicrobial activities against a panel of clinically significant microorganisms. Compound 4 was active against Staphylococcus aureus (MIC, 32 microg/ml), Enterococcus faecium (MIC, 32 microg/ml) and Escherichia coli (MIC, 64 microg/ml).     

Fragmentation of water by heavy ions

Absolute cross sections for fragmentation of water molecules by C3+ and O5+ ions over an energy region where the Bragg peak maximizes were measured for ionization, electron capture, and electron loss channels. A collision regime where sigmaSigmaOq+> or =sigmaH2O+ was reached for the first time, producing large abundances of H+ and O+ fragments in comparison to proton impact. Our findings have straightforward implications in the subsequent fast chemistry at the ionization site and on the O production in the first stages of water radiolysis. An unexpected channel-independent relationship between the cross sections for the fragmentation products, which is also approximately independent of the particle type, energy, and charge state, is found. A model is presented to explain such behavior allowing the cross sections of all fragmentation products to be obtained from single and double electron removal cross sections.     

A Bernstein type theorem on a Randers space

We consider Finsler spaces with a Randers metric F=+, on the three-dimensional real vector space, where is the Euclidean metric and is a 1-form with norm b,0 b1. By using the notion of mean curvature for immersions in Finsler spaces, introduced by Z. Shen, we obtain the partial differential equation that characterizes the minimal surfaces which are graphs of functions. For each b, 0 b1/, we prove that it is an elliptic equation of mean curvature type. Then the Bernstein type theorem and other properties, such as the nonexistence of isolated singularities, of the solutions of this equation follow from the theory developped by L. Simon. For b 1/, the differential equation is not elliptic. Moreover, for every b, 1/b1 we provide solutions, which describe minimal cones, with an isolated singularity at the origin.Partially supported by CAPES/PROCAD.Partially supported by NSF grant DMS-0072242.Partially supported by CNPq and CAPES/PROCAD.     

A natural-product-inspired photonic logic gate based on photoinduced electron-transfer-generated dual-channel fluorescence

[structure: see text] Modified 1-benzylisoquinoline N-oxides can operate as molecular logic gates. The combination of dual-channel fluorescence emissions and the preferred interaction for selected chemical inputs allows one to design multifunction and self-reprogrammable molecular logic gates.     

Existence and asymptotic stability for evolution problems on manifolds with damping and source terms

One considers the nonlinear evolution equation with source and damping terms

     

Liquid-vapor isotherm in a closed single-component system with droplets or bubbles in smooth crevices

A thermodynamic model in order to study a single-component system where droplets or bubbles are inside smooth crevices is presented. Liquid-vapor interface curvature radius can change its sign as the droplet or bubble volume change. The results suggest that there is always dispersed phase inside smooth crevices of microscopic dimensions, even in the expected single-phase region. Thus, the occurrence of an anti-ripening phenomenon is predicted from a microscopic point of view; meanwhile the occurrence of a ripening phenomenon is energetically favorable at a macroscopic scale. The relevance of these results on the heterogeneous nucleation process is analyzed.     

From Endomorphisms to Automorphisms and Back: Dilations and Full Corners

When S is a discrete subsemigroup of a discrete group G suchthat G = S^–1S, it is possible to extend circle-valuedmultipliers from S to G, to dilate (projective) isometric representationsof S to (projective) unitary representations of G, and to dilate/extendactions of S by injective endomorphisms of a C*-algebra to actionsof G by automorphisms of a larger C*-algebra. These dilationsare unique provided they satisfy a minimality condition. The(twisted) semigroup crossed product corresponding to an actionof S is isomorphic to a full corner in the (twisted) crossedproduct by the dilated action of G. This shows that crossedproducts by semigroup actions are Morita equivalent to crossedproducts by group actions, making powerful tools available tostudy their ideal structure and representation theory. The dilationof the system giving the Bost–Connes Hecke C*-algebrafrom number theory is constructed explicitly as an application:it is the crossed product C₀(A_f)Q*₊, corresponding to the multiplicativeaction of the positive rationals on the additive group A_f offinite adeles.     

Low Dimension Dynamics in the EPRB Experiment with Random Variable Analyzers

The Einstein–Podolsky–Rosen–Bohm (EPRB) experiment performed with random variable and spatially separated analyzers is a milestone test in the controversy between Objective Local Theories (OLT) and Quantum Mechanics (QM). Only a few OLT are still possible. Some of the surviving OLT (specifically, the so called non-ergodic theories) would be undetectable in the averaged statistical values, but they may leave their trace in the time dynamics. For, while QM predicts random processes, the OLT of this kind predict the existence of regularities that may be revealed as a low dimensional object in the phase space. We perform a numerical analysis of the time-resolved data recorded in that experiment to unveil any hypothetical low dimensional dynamics that may be present. We find no consistent indication of such dynamics except for one data file, the longest of all in the real time. The possible causes of these dynamics are discussed.      

Temperature dependence of electron properties of Sn doped nanobelts

This paper reports on the measurements of transport properties of high crystalline quality Sn doped In₂O₃ nanobelts. The samples presented metallic conduction in a large range of temperatures; however, at low temperatures, the resistivity showed a slight increase and the current–voltage curves showed a tendency to saturate even in the low-voltage range. From these observations, we discuss some arguments on the possibility of low dimensional conducting channels as the main responsible for the conduction at low temperatures. Additionally, we present an alternative technique for production of low resistance ohmic contacts, which can be further used in devices’ construction.