Time evolution of the Wigner function in discrete quantum phase space for a soluble quasi-spin model

The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wi:ner function is written for some chosen states associated to discrete angle and angular momentum variables, and the rime evolution is numerically calculated using the discrete von Neumnnn-Liouville equation. Direct evidences in the lime evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU(2)-based semiclassical continuous approach to the Lipkin model is also presented.

Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies

In this paper, we present relations between Camassa-Holm (CH), Harry-Dym (HD) and modified Korteweg-de Vries (mKdV) hierarchies, which are given by the hodograph type transformation. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

Physical activity and postural control in the elderly: Coupling between visual information and body sway

Background: Aging is characterized by a decline in the postural control performance, which is based on a coherent and stable coupling between sensory information and motor action. Therefore, changes in postural control in elderlies can be related to changes in this coupling. In addition, it has been observed that physical activity seems to improve postural control performance in elderlies. These improvements can be due to changes in the coupling between sensory information and motor action related to postural control. Objective: the purpose of this study was to verify the coupling between visual information and body sway in active and sedentary elderlies. Methods: Sixteen sedentary elderlies ( SE), 16 active elderlies ( AE) and 16 young adults ( YA) were asked to stand upright inside a moving room in two experimental conditions: ( 1) discrete movement and ( 2) continuous movement of the room. Results: In the continuous condition, the results showed that the coupling between the movement of the room and body sway was stronger and more stable for SE and AE compared to YA. In the discrete condition, SE showed larger body displacement compared to AE and YA. Conclusions: SE have more difficulty to discriminate and to integrate sensory information than AE and YA indicating that physical activity may improve sensory integration. Copyright (C) 2005 S. Karger AG, Basel.

Synthesis, spectroscopic characterization and X-ray crystallographic studies of trans-[PtCl2(PEt3)(PySOR)] complexes, where PySOR=(2-methylsulphinyl)-pyridine and (2-n-propylsulphinyl)pyridine

Alkylsulphinylpyridine ligands containing three potential donor centres: N, S and O atoms and two complexes of general formula trans-[PtCl2(PEt3)PySOR)] (R = Me and Pr-n) were prepared and characterized by elemental analysis, i.r. spectroscopy, H-1- and P-31-n.m.r. and X-ray crystallography. The ambidentate ligands act in both situations as monodentate ligands, bonded to the metal exclusively through the nitrogen atom. The crystal structures revealed the occurrence of discrete molecules and, in both complexes, the Pt atoms are coordinated in square planar arrangements by two chloride ions, in a trans configuration, by the pyridine nitrogen atom, and by the phosphine P atom. The oxygen atoms do not take part in the complexation scheme.

Using transient and steady state considerations to investigate the mechanism of loss of stability of a dynamical system

This work presents the complete set of features for solutions of a particular non-ideal mechanical system near the fundamental and near to a secondary resonance region. The system comprises a pendulum with a horizontally moving suspension point. Its motion is the result of a non-ideal rotating power source (limited power supply), acting oil the Suspension point through a crank mechanism. Main emphasis is given to the loss of stability, which occurs by a sequence of events, including intermittence and crisis, when the system reaches a chaotic attractor. The system also undergoes a boundary-crisis, which presents a different aspect in the bifurcation diagram due to the non-ideal supposition. (c) 2004 Published by Elsevier B.V.

A case study of convective organization into precipitating lines in the Southwest Amazon during the WETAMC and TRMM-LBA

A case study of convective development in the Southwest Amazon region during the Wet Season Atmospheric Mesoscale Campaign (WETAMC) and Tropical Rainfall Measuring Mission (TRMM)/Large-Scale Biosphere-Atmosphere (LBA) Experiment in Amazonia is presented. The convective development during 7 February 1999 is shown to occur during a period of very weak large-scale forcing in the presence of topography and deforestation. The available data include dual Doppler radar analysis, radiosonde launches, and surface and boundary layer observations. The observational analysis is complemented with a series of model simulations using the RAMS with 2-km resolution over a 300 km 300 km area forced by a morning radiosonde profile. A comparison of the observed and simulated thermodynamic transformation of the boundary layer and of the formation of convective lines, and of their kinematic and microphysical properties is presented. It is shown that only a few very deep and intense convective cells are necessary to explain the overall precipitating line formation and that discrete propagation and coupling with upper atmosphere circulations may explain the appearance of several lines. The numerical simulation indicates that topography may be the cause of initial convective development, although later on the convective line is parallel to the midlevel shear. There are indications that small-scale deforestation may have an effect on increasing rainfall in the wet season when the large-scale forcing is very weak.

Symbolic power, robotting, and surveilling

Symbolic power is discussed with reference to mathematics and formal languages. Two distinctions are crucial for establishing mechanical and formal perspectives: one between appearance and reality, and one between sense and reference. These distinctions include a nomination of what to consider primary and secondary. They establish the grammatical format of a mechanical and a formal world view. Such views become imposed on the domains addressed by means of mathematics and formal languages. Through such impositions symbolic power of mathematics becomes exercised. The idea that mathematics describes as it prioritises is discussed with reference to robotting and surveillance. In general, the symbolic power of mathematics and formal languages is summarised through the observations: that mathematics treats parts and properties as autonomous, that it dismembers what it addresses and destroys the organic unity around things, and that it simplifies things and reduces them to a single feature. But, whatever forms the symbolic power may take, it cannot be evaluated along a single good-bad axis.

On the Optimality of Finite Constellations from Algebraic Lattices

A construction technique of finite point constellations in n-dimensional spaces from ideals in rings of algebraic integers is described. An algorithm is presented to find constellations with minimum average energy from a given lattice. For comparison, a numerical table of lattice constellations and group codes is computed for spaces of dimension two, three, and four. © 2001.

On the construction and labelling of geometrically uniform signal sets in ℤ2 matched to additive quotient groups

We establish the conditions under which it is possible to construct signal sets satisfying the properties of being geometrically uniform and matched to additive quotient groups. Such signal sets consist of subsets of signal spaces identified to integers rings ℤ[i] and ℤ[ω] in ℤ2. © 2008 KSCAM and Springer-Verlag.

Pesquisa em Resolução de Problemas: caminhos, avanços e novas perspectivas

We discuss the knowledge that has been constructed regarding Problem Solving in Math Education as a result of research developed by GTERP - Work and Study Group in Problem Solving, UNESP-Rio Claro/SP. The research is guided by the following general questions: How do students construct mathematical knowledge and how do teachers implement the methodology of Math Teaching-Learning-Evaluation through Problem Solving? Historical aspects of Problem Solving are very important in the configuration of the current trends for Problem Solving. One of them is the Methodology of Math Teaching-Learning- Evaluation through Problem Solving, based on clear foundations and an approach of renewal. In addition to that methodology, two aspects have been developed by the group: The conception of Math as a science of pattern and order and Discrete Mathematics. The knowledge constructed and the scientific production of GTERP prove its relevant contribution to intensifying dialogues between research and educational practice, students and teachers, and to increasing the possibilities of that practice particularly in Math work.

A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action

A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.

Análise combinatória no ensino médio apoiada na metodologia de ensino-aprendizagem-avaliação de matemática através da resolução de problemas

Pós-graduação em Educação Matemática - IGCE

Matemática financeira contextualizada em sistemas de amortização e impostos de renda

Pós-graduação em Matemática em Rede Nacional - IBILCE

Perspectives on the use of lakes and ponds as model systems for macroecological research

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)