A general treatment of geometric phases and dynamical invariants

Based only on the parallel-transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee`s non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non- Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature. Copyright (c) EPLA, 2008.

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

A large-scale synthesis of enantiomerically pure gamma-hydroxy-organochalcogenides

Enantiomerically pure (R)- and (S)-gamma-hydroxy-organochalcogenides are prepared using poly-[R]-3-hydroxybutanoate (PHB) as the starting material. (C) 2009 Elsevier Ltd. All rights reserved.

Solvation in Pure Liquids: What Can Be Learned from the Use of Pairs of Indicators?

The solvation of six solvatochromic probes in a large number of solvents (33-68) was examined at 25 degrees C. The probes employed were the following: 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenyl pyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), respectively. Of these, MePMBr is a novel compound. They can be grouped in three pairs, each with similar pK(a) in water but with different molecular properties, for example, lipophilicity and dipole moment. These pairs are formed by RB and MePM; QB and MePMBr; WB and MePMBr(2), respectively. Theoretical calculations were carried out in order to calculate their physicochemical properties including bond lengths, dihedral angles, dipole moments, and wavelength of absorption of the intramolecular charge-transfer band in four solvents, water, methanol, acetone, and DMSO, respectively. The data calculated were in excellent agreement with available experimental data, for example, bond length and dihedral angles. This gives credence to the use of the calculated properties in explaining the solvatochromic behaviors observed. The dependence of an empirical solvent polarity scale E(T)(probe) in kcal/mol on the physicochemical properties of the solvent (acidity, basicity, and dipolarity/polarizability) and those of the probes (pK(a), and dipole moment) was analyzed by using known multiparameter solvation equations. For each pair of probes, values of E(T)(probe) (for example, E(T)(MePM) versus E(T)(RB)) were found to be linearly correlated with correlation coefficients, r, between 0.9548 and 0.9860. For the mercyanine series, the values of E(T)(probe) also correlated linearly, with (r) of 0.9772 (MePMBr versus MePM) and 0.9919 (MePMBr(2) versus MePM). The response of each pair of probes (of similar pK(a)) to solvent acidity is the same, provided that solute-solvent hydrogen-bonding is not seriously affected by steric crowding (as in case of RB). We show, for the first time, that the response to solvent dipolarity/polarizability is linearly correlated to the dipole moment of the probes. The successive introduction of bromine atoms in MePM (to give MePMBr, then MePMBr(2)) leads to the following linear decrease: pK(a) in water, length of the phenolate oxygen-carbon bond, length of the central ethylenic bond, susceptibility to solvent acidity, and susceptibility to solvent dipolarity/polarizability. Thus studying the solvation of probes whose molecular structures are varied systematically produces a wealth of information on the effect of solute structure on its solvation. The results of solvation of the present probes were employed in order to test the goodness of fit of two independent sets of solvent solvatochromic parameters.

Pure strategy equilibria of multidimensional and non-monotonic auctions

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials

The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential in the Sturm-Liouville problem, exact bounded solutions are found in closed form. The case of a pure scalar potential with their isolated zero-energy solutions, already analyzed in a previous work, is obtained as a particular case. The behavior of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2004 Elsevier B.V. All rights reserved.

Vacuum effects on massive spinor fields: S-1 x R-3 topology

The aim of this work was to investigate the role played by an external field on the Casimir energy density for massive fermions under S-1 x R-3 topology. Both twisted- and untwisted-spin connections are considered and the calculation in a closed form is performed using an alternative approach based on the combination of the analytic regularization method and the Euler-Maclaurin summation formula. It is shown that no mass scale appears in the final result and, therefore, Casimir effect arises only from the boundary conditions and vacuum fluctuations induced by the coupling with the external field.

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method. (C) 2007 Elsevier B.V. All rights reserved.

Exotic dark spinor fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Evaluation of the fretting fatigue behaviour of commercially pure titanium

Fretting fatigue occurs when the contact surfaces of two components undergo small oscillatory movement while they are subjected to a clamping force. A cyclic external load gives rise to the early initiation of fatigue cracks, thus reducing their service life. In this paper, the fretting fatigue behaviour of commercially pure titanium flat samples (1.5 mm thick) is evaluated. A fretting device composed of a frame, load cell, and two screw-mounted cylindrical fretting pads with convex extremities was built and set to a servo-hydraulic testing machine. The fatigue tests were conducted under load control at a frequency of 10 Hz and stress ratio R = 0.1, with various contact load values applied to the fretting pads. Additional tests under inert environment allowed assessing the role of oxidation on the wear debris formation. The fracture surfaces and fretting scars were analysed via scanning electron microscopy in order to evaluate the surface damage evolution and its effect on the fatigue crack features. The effect of the fretting condition on the S-N curve of the material in the range of 10(4)-10(6) cycles is described. Fatigue crack growth calculations allowed estimating the crack initiation and propagation lives under fretting conditions. The effect of the fretting condition in fatigue life is stronger for the lower values of cyclic stress and does not seem to depend on the contact loading value.

Detection of Leptospira spp. from pure cultures and from experimentally contaminated bovine semen by polymerase chain reaction

Considerando a importância do sêmen na transmissão da leptospira bovina, foi realizado o presente estudo que teve como objetivo aplicar a reação em cadeia pela polimerase (PCR) para a detecção de leptospiras em sêmen bovino experimentalmente contaminado. A reação de PCR foi capaz de amplificar um fragmento de DNA específico de 330 pares de bases a partir de cultivos puros de 26 sorovares de Leptospira spp. A contaminação experimental de sêmen com Leptospira interrogans serovar hardjo revelou que a técnica de PCR conseguiu detectar 10 bactérias/ml, concentração sensivelmente mais baixa que as 1.000 bactérias/ml detectadas através do cultivo microbiológico. Os resultados observados revelam o grande potencial da reação de PCR para a detecção de Leptospira spp. em sêmen bovino, notadamente em centrais de inseminação artificial.

Analysis of failed commercially pure titanium dental implants: A scanning electron microscopy and energy-dispersive spectrometer X-ray study

Background: the failure of osseointegration in oral rehabilitation has gained importance in current literature and in clinical practice. The integration of titanium dental implants in alveolar bone has been partly ascribed to the biocompatibility of the implant surface oxide layer. The aim of this investigation was to analyze the surface topography and composition of failed titanium dental implants in order to determine possible causes of failure.Methods: Twenty-one commercially pure titanium (cpTi) implants were retrieved from 16 patients (mean age of 50.33 +/- 11.81 years). Fourteen implants were retrieved before loading (early failures), six after loading (late failures), and one because of mandibular canal damage. The failure criterion was lack of osseointegration characterized as dental implant mobility. Two unused implants were used as a control group. All implant surfaces were examined by scanning electron microscopy (SEM) and energy-dispersive spectrometer x-ray (EDS) to element analysis. Evaluations were performed on several locations of the same implant.Results: SEM showed that the surface of all retrieved implants consisted of different degrees of organic residues, appearing mainly as dark stains. The surface topography presented as grooves and ridges along the machined surface similar to control group. Overall, foreign elements such as carbon, oxygen, sodium, calcium, silicon, and aluminum were detected in failed implants. The implants from control group presented no macroscopic contamination and clear signs of titanium.Conclusion: These preliminary results do not suggest any material-related cause for implant failures, although different element composition was assessed between failed implants and control implants.

Influence of a Fluoridated Medium with Different pHs on Commercially Pure Titanium-Based Implants

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)