Abstract:
Este artigo tem o objetivo de apresentar a professores e demais interessados, uma proposta de abordagem de textos literários em prosa, para as 7a e 8a séries do Ensino Fundamental, através da aplica o das etapas do Método Recepcional associadas às concep es de transversalidade e de transdisciplinaridade.

Abstract:
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction method used in this article and its possible generalization to other maximally superintegrable systems.

Abstract:
We consider a $\pi$-mode solution of the Fermi-Pasta-Ulam $\beta$ system. By perturbing it, we study the system as a function of the energy density from a regime where the solution is stable to a regime, where is unstable, first weakly and then strongly chaotic. We introduce, as indicator of stochasticity, the ratio $\rho$ (when is defined) between the second and the first moment of a given probability distribution. We will show numerically that the transition between weak and strong chaos can be interpreted as the symmetry breaking of a set of suitable dynamical variables. Moreover, we show that in the region of weak chaos there is numerical evidence that the thermostatistic is governed by the Tsallis distribution.

Abstract:
We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional configuration space. These systems possess closed bounded orbits and integrals of motion which are polynomial in the momenta. They generalize known examples of superintegrable models in the Euclidean plane.

Abstract:
New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.

Abstract:
We present an algebraic formulation of the notion of integrability of dynamical systems, based on a nilpotency property of its flow: it can be explicitly described as a polynomial on its evolution parameter. Such a property is established in a purely geometric--algebraic language, in terms both of the algebra of all higher-order constants of the motion (named the nilpotent algebra of the dynamics), and of a maximal Abelian algebra of symmetries (called a Cartan subalgebra of the dynamics). It is shown that this notion of integrability amounts to the annihilator of the nilpotent algebra being contained in a Cartan subalgebra of the dynamics. Systems exhibiting this property will be said to be nilpotent integrable. Our notion of nilpotent integrability offers a new insight into the intrinsic dynamical properties of a system, which is independent of any auxiliary geometric structure defined on its phase space. At the same time, it extends in a natural way the classical concept of complete integrability for Hamiltonian systems. An algebraic reduction procedure valid for nilpotent integrable systems, generalizing the well-known reduction procedures for symplectic and/or Poisson systems on appropriate quotient spaces, is also discussed. In particular, it is shown that a large class of nilpotent integrable systems can be obtained by reduction of higher-order free systems. The case of the third-order free system is analyzed and a nontrivial set of third-order Calogero-Moser-like nilpotent integrable equations is obtained.

Abstract:
We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier-Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and throws light on the alignment mechanism between the vorticity and the vortex stretching vector. The symmetry algebra associated with the Navier-Stokes equations turns out to be infinite- dimensional. New vortical structures, generalizing in some cases well-known configurations such as, for example, the Burgers and Lundgren solutions, are obtained and discussed in relation to the value of the dynamic angle. A systematic treatment of the boundary conditions invariant under the symmetry group of the equations under study is also performed, and the corresponding invariant surfaces are recognized.

Abstract:
The Navier-Stokes-Fourier model for a 3D thermoconducting viscous fluid, where the evolution equation for the temperature T contains a term proportional to the rate of energy dissipation, is investigated analitically at the light of the rotational invariance property. Two cases are considered: the Couette flow and a flow with a radial velocity between two rotating impermeable and porous coaxial cylinders, respectively. In both cases, we show the existence of a maximum value of T, T_max, when the difference of temperature Delta T=T_2-T_1 on the surfaces of the cylinders is assigned. The role of T_max is discussed in the context of different physical situations.

Abstract:
We study the analytic properties of a matrix discrete system introduced in [7]. The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This paves the way to a generalization of Painleve analysis to discrete matrix models.

Abstract:
An algebraic method is devised to look for non-local symmetries of the pseudopotential type of nonlinear field equations. The method is based on the use of an infinite-dimensional subalgebra of the prolongation algebra $L$ associated with the equations under consideration. Our approach, which is applied by way of example to the Dym and the Korteweg-de Vries equations, allows us to obtain a general formula for the infinitesimal operator of the non-local symmetries expressed in terms of elements of $L$. The method could be exploited to investigate the symmetry properties of other nonlinear field equations possessing nontrivial prolongations.