Crossed-products by finite index endomorphisms and KMS states

Given a unital -algebra A, an injective endomorphism preserving the unit, and a conditional expectation E from A to the range of α we consider the crossed-product of A by α relative to the transfer operator L=α⁻¹E. When E is of index-finite type we show that there exists a conditional expectation G from the crossed-product to A which is unique under certain hypothesis. We define a “gauge action” on the crossed-product algebra in terms of a central positive element h and study its KMS states. The main result is: if h>1 and E(ab)=E(ba) for all a,b∈A (e.g. when A is commutative) then the KMS_β states are precisely those of the form ψ=φ°G, where φ is a trace on A satisfying the identity

     

The Ribaucour transformation for flat Lagrangian submanifolds

We study the Ribaucour transformation for flat Lagrangian submanifolds in complex flat space and complex projective space. As a consequence, we obtain a process to generate a new family of such submanifolds from a given one. Analytically, this provides a method to construct new solutions of the corresponding systems of PDEs from a given one. We also show that such transformation always comes with a permutability formula.     

An Operative Electrostatic Slipping Mechanism along Macrocycle Flexibility Accelerates Guest Sliding during pseudo-Rotaxane Formation

A pseudo-rotaxane is a host−guest complex composed of a linear molecule encircled by a macrocyclic ring. These complexes can be assembled by sliding the host over the guest terminal groups. If there is a close match between the molecular volume of the flanking groups on the guest and the cavity size of the macrocycle, the slipping might occur slowly or even become completely hindered. We have previously shown that it is possible to overcome the restraints imposed by steric effects on the sliding process by integrating electrostatic attractive interactions during the slipping step. In this work, we extend our electrostatically assisted slipping approach (EASA) to a new host−guest system featuring a flexible macrocyclic ring and a series of asymmetric guests containing a cyclic tertiary ammonium group. Compelling evidence for pseudo-rotaxane formation is presented, along with thermodynamic and kinetic data. Experimental results suggests that the higher conformational flexibility of 24-crown-8 significantly increases the sliding rate, compared with the more rigid dibenzo-24-crown-8, without affecting complex stability. Furthermore, by combining the EASA and macrocycle flexibility, we were capable to slip a large eight-membered cyclic group across the 24-crown-8 annulus, setting a new limit on the ring molecular size that can pass through a 24-membered crown ether.     

An Approach to the Use of Glycol Alkoxysilane–Polysaccharide Hybrids in the Conservation of Historical Building Stones

Stone consolidants have been widely used to protect historical monuments. Consolidants and hydrophobic formulations based on the use of tetraethoxysilane (TEOS) and alkylalkoxysilanes as precursors have been widely applied, despite their lack of solubility in water and requirement to be applied in organic media. In the search for a “greener” alternative based on silicon that has potential use in this field, the use of tetrakis(2-hydroxyethyl)silane (THEOS) and tris(2-hydroxyethyl)methyl silane (MeTHEOS) as precursors, due their high water solubility and stability, is proposed in this paper. It is already known that THEOS and MeTHEOS possess remarkable compatibility with different natural polysaccharides. The investigated approach uses the water-soluble silanes THEOS–chitosan and MeTHEOS–chitosan as a basis for obtaining hybrid consolidants and hydrophobic formulations for the conservation of siliceous and calcareous stones. In the case of calcareous systems, their incompatibility with alkoxysilanes is known and is expected to be solved by the developed hybrid consolidant. Their application in the conservation of building stones from historical and archeological sites from Guanajuato, México was studied. The evaluation of the consolidant and hydrophobic formulation treatment was mainly conducted by determining the mechanical properties and contact angle measurements with satisfactory results in terms of the performance and compatibility with the studied stones.     

Measurement of transverse single-spin asymmetries for Dijet production in proton-proton collisions at sqrt[s]=200 GeV

We report the first measurement of the opening angle distribution between pairs of jets produced in high-energy collisions of transversely polarized protons. The measurement probes (Sivers) correlations between the transverse spin orientation of a proton and the transverse momentum directions of its partons. With both beams polarized, the wide pseudorapidity (-1< or = eta < or = +2) coverage for jets permits separation of Sivers functions for the valence and sea regions. The resulting asymmetries are all consistent with zero and considerably smaller than Sivers effects observed in semi-inclusive deep inelastic scattering. We discuss theoretical attempts to reconcile the new results with the sizable transverse spin effects seen in semi-inclusive deep inelastic scattering and forward hadron production in pp collisions.     

The Crossed Product by a Partial Endomorphism

Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I , a *-homomorphism α : A → M(I ) and a map L : J → A with some properties, based on earlier works of Pimsner and Katsura, we define a C*-algebra which we call the Crossed Product by a Partial Endomorphism. We introduce the Crossed Product by a Partial Endomorphism induced by a local homeomorphism σ : U → X where X is a compact Hausdorff space and U is an open subset of X. A bijection between the gauge invariant ideals of and the σ, σ^-1- invariant open subsets of X is showed. If (X, σ) has the property that is topologically free for each closed σ, σ^-1-invariant subset X′ of X then we obtain a bijection between the ideals of and the open σ, σ^-1-invariant subsets of X. *Partially supported by CNPq. **Supported by CNPq.     

Microwave-assisted synthesis and luminescent activity of imidazo[1,2-a]pyridine derivatives

In this work, a series of phenacyl bromide derivatives was synthesized and employed as key intermediate for the synthesis of substituted imidazo[1,2-a]pyridines. First, phenacyl bromide molecules were obtained from the bromination reaction of acetophenones assisted by microwave irradiation, obtaining the products 4a-v in a 15 minutes reaction with yields in the range of 50% to 99%. Subsequently, the conjugation of these molecules with 2-aminopyridine conduced to the production of imidazo[1,2-a]pyridine derivatives ( 7a-v ) in a 60-second reaction with yields of 24% to 99%. Improved yields were determined with respect to those obtained with more tedious methodologies like thermally and mechanically assisted routes. Intense luminescence emissions in the purple and blue regions of the electromagnetic spectra were observed under UV excitation according to the nature of the substituents. This environmentally friendly methodology is expected to constitute an important class of organic compounds for the development of biomarkers, photochemical sensors, and medicinal applications.     

Identified hadron compositions in p+p and Au+Au collisions at high transverse momenta at √S(NN)=200 GeV

We report transverse momentum (p(T)≤15 GeV/c) spectra of π(±), K(±), p, p[over ˉ], K(S)(0), and ρ(0) at midrapidity in p+p and Au+Au collisions at √S(NN)=200 GeV. Perturbative QCD calculations are consistent with π(±) spectra in p+p collisions but do not reproduce K and p(p[over ˉ]) spectra. The observed decreasing antiparticle-to-particle ratios with increasing p(T) provide experimental evidence for varying quark and gluon jet contributions to high-p(T) hadron yields. The relative hadron abundances in Au+Au at p(T)?8 GeV/c are measured to be similar to the p+p results, despite the expected Casimir effect for parton energy loss.     

Inverse semigroup actions as groupoid actions

To an inverse semigroup, we associate an étale groupoid such that its actions on topological spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow space of this groupoid are non-Hausdorff. We show that this construction provides an adjoint functor to the functor that maps a groupoid to its inverse semigroup of bisections, where we turn étale groupoids into a category using algebraic morphisms. We also discuss how to recover a groupoid from this inverse semigroup.     

Measurement of the bottom quark contribution to nonphotonic electron production in p + p collisions at √s=200 GeV

The contribution of B meson decays to nonphotonic electrons, which are mainly produced by the semileptonic decays of heavy-flavor mesons, in p + p collisions at √s=200 GeV has been measured using azimuthal correlations between nonphotonic electrons and hadrons. The extracted B decay contribution is approximately 50% at a transverse momentum of pT≥5 GeV/c. These measurements constrain the nuclear modification factor for electrons from B and D meson decays. The result indicates that B meson production in heavy ion collisions is also suppressed at high pT.