First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

Gastric Torsion from an Intestinal Hernia Through a Rent in the Gastrosplenic Ligament in a Horse

The present report describes an 8-year-old gelding presenting with signs of severe abdominal pain. After performing a thorough physical examination, including rectal palpation and additional diagnostic tests, an exploratory laparotomy was recommended. The jejunum was found herniated through the gastrosplenic ligament, and the stomach was severely distended with gas. Given a poor prognosis, the horse was euthanized on the table. At necropsy, the stomach appeared dilated, with an 180 horizontal gastric torsion, from left (lateral) to right (medial), dividing the organ into dorsal and ventral compartments. We believe that the chronic traction exerted by an incarcerated and distended loop of jejunum, in the dorsal aspect of the gastrosplenic ligament, associated with trauma during episodes of intense rolling, enlarged the rent until it ruptured. Because of this rupture, the lateral dorsal aspect of the stomach became unattached, predisposing it to the torsion. (C) 2012 Elsevier B.V. All rights reserved.

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1 + 1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen-Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.

PT-symmetric kinks

Some kinks for non-Hermitian quantum field theories in 1+1 dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under PT transformations.

On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Mass generation for Abelian spin-1 particles via a symmetric tensor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Study of the dimensions of double-torsion test specimens

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

Microstructural Evolution of Ti-6Al-7Nb Alloy During High Pressure Torsion

Ti-6Al-7Nb alloys are being evaluated for biomedical applications, in substitution of the more conventional Ti-6Al-7V. Both types of alloys present a microstructure containing the alpha and the beta phases, which result in good compromise for mechanical applications. In the present work Ti-6Al-7Nb alloys were processed by High Pressure Torsion (HPT), varying the number of revolutions and thus the total imposed strain. X-Ray Diffraction (XRD) results revealed the formation of different crystallographic textures in samples subjected to HPT. Microhardness distribution, across the diameters of the disks, is rather homogeneous for all samples, with higher values for those subjected to 03 and 05 turns. Transmission electron microscopy (TEM) micrographs have showed that an ultra-fine grained microstructure was obtained in all the samples.

Torsion and gravitation: A new view

According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Though equivalent, they act differently: curvature yields a geometric description, in which the concept of gravitational force is absent whereas torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the teleparallel case. This means that the gravitational coupling prescription can be minimal only in the geometric case. Relying on this property, a new gravitational coupling prescription in the presence of curvature and torsion is proposed. It is constructed in such a way to preserve the equivalence between curvature and torsion, and its basic property is to be equivalent to the usual coupling prescription of general relativity. According to this view, no new physics is connected with torsion, which is just an alternative to curvature in the description of gravitation. An application of this formulation to the equations of motion of both a spinless and a spinning particle is discussed.

The quadratic spinor Lagrangian, axial torsion current and generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field-Weyl, Majorana, flagpole, or flag-dipole spinor fields-yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

Lessons of spin and torsion: Reply to Consistent coupling to Dirac fields in teleparallelism

In reply to the criticism made by Mielke in the preceding Comment on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for all sources with spin and is by no means restricted to the Dirac field. In this sense the SL(4,R)-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.