The flavor problem and discrete symmetries

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A discrete finite-dimensional phase space approach for the description of Fe8 magnetic clusters: Wigner and Husimi functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stability of differential equations with piecewise constant argument via discrete equations

Lyapunov stability for a class of differential equation with piecewise constant argument (EPCA) is considered by means of the stability of a discrete equation. Applications to some nonlinear autonomous equations are given improving some linear known cases.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

ON DISCRETE SYSMMETRIES OF THE MULTI-BOSON KP HIERARCHIES

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce the concept of the square root lattice leading to a family of new pseudo-differential operators with covariance under additional Backlund transformations.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

On dichotomic maps for non autonomous discrete equations

A new procedure is given for the study of stability and asymptotic stability of the null solution of the non autonomous discrete equations by the method of dichotomic maps, which it includes Liapunov's Method asa special case. Examples are given to illustrate the application of the method.

Surgical Management of Impacted Teeth Using Three-Dimensional Computed Tomography

The surgical removal of impacted, supernumerary, or ectopic teeth is a routine procedure to the dental surgeon. Because any and all surgical interventions involve anatomic considerations that predispose the patient to a high risk of incidents or complications, it is absolutely necessary to precisely determine the location of the enclosed teeth, to better plan the procedure. Even though the conventional radiographic techniques are commonly used to detect the presence of such teeth, they can present deficiencies. In those situations, additional examinations can be requested. In this article, we are reporting the case of a 12-year-old patient, whose third superior molars appeared in a very atypical position. We chose to request a computed tomography and three-dimensional manipulation of the obtained images. This article, as its main goal, highlighted the importance of computed tomography and of three-dimensional reconstructions as a tool to precisely determine the location of enclosed teeth, thus allowing for a better planning of the surgery and a safer surgical intervention.

Importance of cone beam computed tomography for diagnosis of calcifying cystic odontogenic tumor associated to odontoma. Report of a case

The calcifying cystic odontogenic tumour (CCOT) is a rare benign cystic neoplasm not infrequently associated with odontoma. This report documents a case of CCOT associated with compound odontoma arising in the anterior maxilla in a 25-year-old woman. Conventional radiographs showed a large calcified mass with poorly visualized radiolucent margins. The extent and condition of the internal structure of the CCOT associated with odontoma was able to be determined based on radiographic findings from cone beam computed tomography. This advanced image technique proved to be extremely useful in the radiographic assessment of this particular neoplasm of the jawbones.