PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier B.V. All rights reserved.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Stability results for impulsive functional differential equations with infinite delay

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

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences

In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.

Integrability and conformal symmetry in higher dimensions: A model with exact hopfion solutions

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two-dimensional target space. Requiring the existence of lagrangean and the stability of static solutions singles out a class of models which have an additional conformal symmetry. That is used to explain the existence of an ansatz leading to solutions with non-trivial Hopf charges. © SISSA/ISAS 2002.

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Migration of diethylhexyl phthalate from PVC bags into intravenous cyclosporine solutions

The migration of diethylhexyl phthalate (DEHP) from PVC bags into LVPS (0.9% NaCl) and LVPS with cyclosporine at concentrations of 2.5 and 0.5 mg/ml was studied. PVC bags were placed in contact with these solutions and stored at 25 1 degrees C. They were taken for analysis each 30 min during 6 h and after this period at each 1 h until 12 h of contact. Water was used as reference, and exposed and analyzed under the same conditions. After contact, the solutions were submitted to extraction with hexane and analyzed by GC-FID. The results showed that DEHP did not migrate into water and LVPS during all the time. Also, no measurable amount of DEHP was detected during the first 3 h of contact between the PVC bag and the diluted cyclosporine solution. However, the amount of released DEHP reached a detectable level after 4 It of contact, increased until 6 h, stabilized, and increased again after 9-10 h. The 12 h of contact showed the highest DEHP levels for both cyclosporine concentrations. The DEHP migrated was 0.02-0.08% of that present in the bag. (c) 2005 Elsevier B.V. All rights reserved.

Raman and photoluminescence of Er3+-doped SnO2 obtained via the sol-gel technique from solutions with distinct pH

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials

The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential in the Sturm-Liouville problem, exact bounded solutions are found in closed form. The case of a pure scalar potential with their isolated zero-energy solutions, already analyzed in a previous work, is obtained as a particular case. The behavior of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2004 Elsevier B.V. All rights reserved.