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.

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)

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

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.

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.

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.

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.

Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

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