On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parametrize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holmand Dym-type equations. The two-component generalizations of Camassa-Holm- and Dym-type equations can be obtained from the negative-order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive-order Hamiltonians, which follow froth the Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm- and two-component Dym-type equations.

Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S-2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S-2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.

DERIVATION OF THE ENERGY-TIME UNCERTAINTY RELATION

A derivation from first principles is given of the energy-time uncertainty relation in quantum mechanics. A canonical transformation is made in classical mechanics to a new canonical momentum, which is energy E, and a new canonical coordinate T, which is called tempus, conjugate to the energy. Tempus T, the canonical coordinate conjugate to the energy, is conceptually different from the time t in which the system evolves. The Poisson bracket is a canonical invariant, so that energy and tempus satisfy the same Poisson bracket as do p and q. When the system is quantized, we find the energy-time uncertainty relation DELTAEDELTAT greater-than-or-equal-to HBAR/2. For a conservative system the average of the tempus operator T is the time t plus a constant. For a free particle and a particle acted on by a constant force, the tempus operators are constructed explicitly, and the energy-time uncertainty relation is explicitly verified.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

THE CONSERVED CHARGES AND INTEGRABILITY OF THE CONFORMAL AFFINE TODA MODELS

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges, all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.

Hamiltonian reduction and the construction of q-deformed extensions of the Virasoro algebra

In this paper we employ the construction of the Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-Wess-Zumino-Witten model and the Liouville theory are imposed to show that it satisfies the q-Virasoro algebra proposed by Frenkel and Reshetikhin The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

Integrable deformations of strings on symmetric spaces

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

Canonically Conjugate Variables for the μCH Equation

2010 Mathematics Subject Classification: 35Q35, 37K10.

Gyrokinetic modelling of plasma transport and investigation on test particle dynamics

Turbulent plasmas inside tokamaks are modeled and studied using guiding center theory, applied to charged test particles, in a Hamiltonian framework. The equations of motion for the guiding center dynamics, under the conditions of a constant and uniform magnetic field and turbulent electrostatic field are derived by averaging over the fast gyroangle, for the first and second order in the guiding center potential, using invertible changes of coordinates such as Lie transforms. The equations of motion are then made dimensionless, exploiting temporal and spatial periodicities of the model chosen for the electrostatic potential. They are implemented numerically in Python. Fast Fourier Transform and its inverse are used. Improvements to the original Python scripts are made, notably the introduction of a power-law curve fitting to account for anomalous diffusion, the possibility to integrate the equations in two steps to save computational time by removing trapped trajectories, and the implementation of multicolored stroboscopic plots to distinguish between trapped and untrapped guiding centers. The post-processing of the results is made in MATLAB. The values and ranges of the parameters chosen for the simulations are selected based on numerous simulations used as feedback tools. In particular, a recurring value for the threshold to detect trapped trajectories is evidenced. Effects of the Larmor radius, the amplitude of the guiding center potential and the intensity of its second order term are studied by analyzing their diffusive regimes, their stroboscopic plots and the shape of guiding center potentials. The main result is the identification of cases anomalous diffusion depending on the values of the parameters (mostly the Larmor radius). The transitions between diffusive regimes are identified. The presence of highways for the super-diffusive trajectories are unveiled. The influence of the charge on these transitions from diffusive to ballistic behaviors is analyzed.

Spectrophotometric Evaluation Of Dental Bleaching Under Orthodontic Bracket In Enamel And Dentin.

Aware of the diffusion capacity of bleaching in the dental tissues, many orthodontists are subjecting their patients to dental bleaching during orthodontic treatment for esthetic purposes or to anticipate the exchange of esthetic restorations after the orthodontic treatment. For this purpose specific products have been developed in pre-loaded whitening trays designed to fit over and around brackets and wires, with clinical efficacy proven. The objective of this study was to evaluate, through spectrophotometric reflectance, the effectiveness of dental bleaching under orthodontic bracket. Thirty-two bovine incisors crown blocks of 8 mm x 8 mm height lengths were used. Staining of tooth blocks with black tea was performed for six days. They were distributed randomly into 4 groups (1-home bleaching with bracket, 2- home bleaching without bracket, 3- office bleaching with bracket, 4 office bleaching without bracket). The color evaluation was performed (CIE L * a * b *) using color reflectance spectrophotometer. Metal brackets were bonded in groups 1 and 3. The groups 1 and 2 samples were subjected to the carbamide peroxide at 15%, 4 hours daily for 21 days. Groups 3 and 4 were subjected to 3 in-office bleaching treatment sessions, hydrogen peroxide 38%. After removal of the brackets, the second color evaluation was performed in tooth block, difference between the area under the bracket and around it, and after 7 days to verified color stability. Data analysis was performed using the paired t-test and two-way variance analysis and Tukey's. The home bleaching technique proved to be more effective compared to the office bleaching. There was a significant difference between the margin and center color values of the specimens that were subjected to bracket bonding. The bracket bond presence affected the effectiveness of both the home and office bleaching treatments. Key words:Tooth bleaching, spectrophotometry, orthodontics.

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Hysterectomy fractions in New South Wales, 1971-2006

Hysterectomy fractions by age group for particular periods are of interest for: estimating proper population denominators for calculation of disease and procedure rates affecting the cervix and uterus; estimating the target population for Pap test programs, and response rates; and as a way of displaying the cumulative consequences of hysterectomies in a population. Hysterectomy fractions for populations can be determined by direct inquiry via a representative sample survey, or, as in this study, from prior hysterectomy rates of the cohorts of women which compose each age bracket. Hysterectomy data 1979-93 were obtained from the hospital In-patients Statistics Collection (ISC) which covers both public and private hospitals in NSW. Annual population denominators of women were obtained from Census data. Data were modelled by Poisson regression, using five.-year age group (15-greater than or equal to 85 years), annual period, and five-year birth cohort (APC model). Forward- and back-projection of the period effects were undertaken. The resultant NSW hysterectomy fractions by age and period are consistent with fractions obtained from modelled hysterectomy rates for Western Australia (1980-84), and fractions from national representative sample surveys (1989/90 and 1995) for younger women, but not for women aged greater than or equal to 70 years in 1995, which revealed higher hysterectomy fractions than modelled hysterectomy data would suggest. Hysterectomy fractions for NSW women by five-year age group for quinquennia centred on 1971 to 2006 are provided.

POISSON DISTRIBUTION TO ANALYZE NEAR-THRESHOLD MOTOR EVOKED POTENTIALS

Motor unit action potentials (MUAPs) evoked by repetitive, low-intensity transcranial magnetic stimulation can be modeled as a Poisson process. A mathematical consequence of such a model is that the ratio of the variance to the mean of the amplitudes of motor evoked potentials (MEPs) should provide an estimate of the mean size of the individual MUAPs that summate to generate each MEP. We found that this is, in fact, the case. Our finding thus supports the use of the Poisson distribution to model MEP generation and indicates that this model enables characterization of the motor unit population that contributes to near-threshold MEPs. Muscle Nerve 42: 825-828, 2010