Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On some extension of optimal control theory

Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature.

Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system

In this paper, by using the Poincare compactification in R(3) we make a global analysis of the Lorenz system, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameter value b = 0 the system presents an infinite set of singularly degenerate heteroclinic cycles, which consist of invariant sets formed by a line of equilibria together with heteroclinic orbits connecting two of the equilibria. The dynamical consequences related to the existence of such cycles are discussed. In particular a possibly new mechanism behind the creation of Lorenz-like chaotic attractors, consisting of the change in the stability index of the saddle at the origin as the parameter b crosses the null value, is proposed. Based on the knowledge of this mechanism we have numerically found chaotic attractors for the Lorenz system in the case of small b > 0, so nearby the singularly degenerate heteroclinic cycles.

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.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.

Electronic spectra, ESR and crystal structure of tetrahedral halocuprates(II). The existence of cations (2tbpo·H+) with a very short hydrogen bond

Two compounds [2tbpo·H+)2[CuCl4]= (yellow) and (2tbpo·H+)2[CuBr4]= (dark purple) (tbpo = tribenzylphosphine oxide) have been prepared and investigated by means of crystal structure, electronic, vibrational and ESR spectra. The crystal structure of the (2tbpo·H+)2[CuCl4]= complex was determined by three-dimensional X-ray diffraction. The compound crystallizes in the space group P42/n with unit-cell dimensions a = 19.585(2), c = 9.883(1)Å, V = 3790 (1)Å3, Z = 2, Dm = 1.303 (flotation) Dx = 1.302 Mg m-3. The structure was solved by direct methods and refined by blocked full-matrix least-squares to R = 0.053 for 2583 observed reflections. Cu(II) is coordinated to four chlorides in a tetrahedral arrangement. Tribenzylphosphine oxide molecules, related by a centre of inversion, are connected by a short hydrogen bridge. Chemical analysis, electronic and vibrational spectra showed that the bromide compound is similar to the chloride one and can be formulated as (2tbpo·H+)2[CuBr4]=. The position of the dd transition bands, the charge transfer bands, the ESR and the vibrational spectra of both complexes are discussed. The results are compared with analogous complexes cited in the literature. © 1983.

Existence of Lagrangians for the Yang-Mills equations

The Yang-Mills equations only admit a Lagrangian for gauge groups which are either semisimple or Abelian, or a direct product of groups of both kinds. © 1988.

Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect

A theoretic-oriented strategy was taken to address the weak decay of uniformly accelerated protons. The decay of uniformly accelerated p+'s was analyzed using standard quantum field theory (QFT). It was shown that the FDU effect is essential to reproduce the proper decay rate in the uniformly accelerated frame.

On the existence of ordered phases of encapsulated diamondoids into carbon nanotubes

We have investigated some diamondoids encapsulation into single walled carbon nanotubes (with diameters ranging from1.0 up to 2.2 nm) using fully atomistic molecular dynamics simulations. Diamondoids are the smallest hydrogen-terminated nanosized diamond-like molecules. Diamondois have been investigated for a large class of applications, ranging from oil industry to pharmaceuticals. Molecular ordered phases were observed for the encapsulation of adamantane, diamantane, and dihydroxy diamantanes. Chiral ordered phases, such as; double, triple, 4- and 5-stranded helices were also observed for those diamondoids. Our results also indicate that the modification of diamondoids through chemical functionalization with hydroxyl groups can lead to an enhancement of the molecular packing inside the carbon nanotubes in comparison to non-functionalized molecules. For larger diamondoids (such as, adamantane tetramers), we have not observed long-range ordering, but only a tendency of incomplete helical structural formation. © 2012 Materials Research Society.

Absolute continuity and existence of solutions to dynamic inclusions in time scales

We provide some properties for absolutely continuous functions in time scales. Then we consider a class of dynamical inclusions in time scales and extend to this class a convergence result of a sequence of almost inclusion trajectories to a limit which is actually a trajectory of the inclusion in question. We also introduce the so called Euler solution to dynamical systems in time scales and prove its existence. A combination of the existence of Euler solutions with the compactness type result described above ensures the existence of an actual trajectory for the dynamical inclusion when the setvalued vector field is nonempty, compact, convex and has closed graph. © 2012 Springer-Verlag.

Existence of solutions for the 3D-micropolar fluid system with initial data in Besov-Morrey spaces

In this paper, we show a local-in-time existence result for the 3D micropolar fluid system in the framework of Besov-Morrey spaces. The initial data class is larger than the previous ones and contains strongly singular functions and measures. © 2013 Springer Basel.

Molecular and morphological data support the existence of a sexual cycle in species of the genus Paracoccidioides

The genus Paracoccidioides includes the thermodimorphic species Paracoccidioides brasiliensis and P. lutzii, both of which are etiologic agents of paracoccidioidomycosis, a systemic mycosis that affects humans in Latin America. Despite the common occurrence of a sexual stage among closely related fungi, this has not been observed with Paracoccidioides species, which have thus been considered asexual. Molecular evolutionary studies revealed recombination events within isolated populations of the genus Paracoccidioides, suggesting the possible existence of a sexual cycle. Comparative genomic analysis of all dimorphic fungi and Saccharomyces cerevisiae demonstrated the presence of conserved genes involved in sexual reproduction, including those encoding mating regulators such as MAT, pheromone receptors, pheromone-processing enzymes, and mating signaling regulators. The expression of sex-related genes in the yeast and mycelial phases of both Paracoccidioides species was also detected by realtime PCR, with nearly all of these genes being expressed preferentially in the filamentous form of the pathogens. In addition, the expression of sex-related genes was responsive to the putative presence of pheromone in the supernatants obtained from previous cocultures of strains of two different mating types. In vitro crossing of isolates of different mating types, discriminated by phylogenetic analysis of the α-box (MAT1-1) and the high-mobility-group (HMG) domain (MAT1-2), led to the identification of the formation of young ascocarps with constricted coiled hyphae related to the initial stage of mating. These genomic and morphological analyses strongly support the existence of a sexual cycle in species of the genus Paracoccidioides. © 2013, American Society for Microbiology.

Multilocus molecular phylogeny of Gasteropelecidae (Ostariophysi: Characiformes) reveals the existence of an unsuspected diversity

The characiform family Gasteropelecidae, the so-called freshwater hatchetfishes, is comprised of three genera and nine species found in Panama and all South American countries except Chile. Our goal was to investigate the molecular characteristics, phylogenetic relationships among the species and genera of Gasteropelecidae and phylogenetic relationships between the Gasteropelecidae family with other Characiformes. DNA fragments from two mitochondrial (16S rRNA and Cytochrome B) and three nuclear genes (Rag1, Rag2 and Myh6) were sequenced. Our results corroborate the morphology-based hypothesized monophyly of the Gasteropelecidae family and most of the relationships among its genera. However, the genus Gasteropelecus is polyphyletic because G. maculatus is placed as the sister group to all other gasteropelecids, whereas G. sternicla is more closely related to species of Carnegiella. Similarly, the species Carnegiella strigata is not monophyletic, which suggests that the family needs a taxonomic review. Moreover, the species Thoracocharax stellatus was composed by four distinct lineages suggesting the this species may represents a species complex. © 2013 Elsevier Inc.

Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Controle Ótimo Aplicado em um Modelo de Câncer

Pós-graduação em Matematica Aplicada e Computacional - FCT