Global solutions for abstract impulsive neutral differential equations

We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered. (C) 2010 Elsevier Ltd. All rights reserved.

C(alpha)-HOLDER CLASSICAL SOLUTIONS FOR NON-AUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of alpha-Holder classical solutions for non-autonomous abstract partial neutral functional differential equations. An application is considered.

Color Doppler imaging of the superior ophthalmic vein in different clinical forms of Graves` orbitopathy

To compare color Doppler imaging (CDI) parameters of the superior ophthalmic vein (SOV) in patients with Graves` orbitopathy (GO) and in normal controls. Forty-three GO patients and 14 normal controls underwent CDI of the SOV. Patients had either fibrotic (lipogenic or myogenic) or congestive orbitopathy. The findings for each group were compared. Fifty-eight orbits with fibrotic orbitopathy, 28 with congestive orbitopathy, and 28 from controls, were studied. In the congestive group, SOV flow was detected in 13, undetectable in 11, and reversed in four orbits; in the fibrotic group, it was present in 41 and undetectable in 17 orbits. In normal controls, SOV flow was detected in 25 and undetectable in three orbits. The differences among the three groups were significant. There was also a significant difference between controls and the congestive GO orbits but not between the fibrotic group and the other two groups. Fibrotic myogenic orbitopathy patients displayed a significantly smaller SOV flow than patients with lipogenic orbitopathy. SOV was significantly reduced in orbits with congestive GO or with myogenic fibrotic GO, but not in orbits with fibrotic lipogenic orbitopathy. SOV congestion may be a contributing pathogenic factor in both congestive and fibrotic myogenic Graves` orbitopathy.

Progressive bilateral enophthalmos associated with cerebrospinal shunting

A 22-year-old woman was examined for a complaint of bilateral progressive enophthalmos that had begun after the cerebrospinal fluid shunting procedure 9 years ago. Photographs and CT scans taken before surgery proved that the position of her eyes was normal before surgery. The enophthalmos was so severe that it induced a poor eyelid-globe apposition with trichiasis and superficial keratopathy. CT of the orbits showed that both orbital roofs were arched and displaced toward the anterior cranial fossa. The placement of porous polyethylene sheets on the orbital roofs through a coronal approach corrected the eye position. A literature review indicated that cerebrospinal shuntings are plagued by a variety of complications including bone changes and craniosynostosis. We believe that enophthalmos associated with cerebrospinal fluid shunting results from a rare acquired bony orbital anomaly.

Superior oblique muscle amyloidosis mimicking myositis

A 47-year-old man presented with complaints of progressive diplopia in downgaze and a painful firm mass on the left medial superior canthus. On examination, there was marked hyperemia of the superior bulbar conjunctiva of the left eye. Systemic examination revealed erythematous papules on his trunk and pulmonary infiltrates. CT of the orbits revealed a fusiform enlargement of the left superior oblique muscle and diffuse infiltration of the left temporal region. Biopsy of the left superior oblique muscle and temporal muscle disclosed Congo red deposits that show apple-green birefringence under polarized light. A comprehensive systemic investigation failed to show any disease that could explain the amyloid deposits. The patient was then diagnosed as having primary systemic amyloidosis. We think that this case highlights the necessity of a biopsy in any atypical extraocular muscle enlargement before a diagnosis of myositis.

Effects of Recession versus Tenotomy Surgery without Recession in Adult Rabbit Extraocular Muscle

PURPOSE. Surgical recession of an extraocular muscle (EOM) posterior to its original insertion is a common form of strabismus surgery, weakening the rotational force exerted by the muscle on the globe and improving eye alignment. The purpose of this study was to assess myosin heavy chain (MyHC) isoform expression and satellite cell activity as defined by Pax7 expression in recessed EOMs of adult rabbits compared with that in muscles tenotomized but not recessed and with that in normal control muscles. METHODS. The scleral insertion of the superior rectus muscle was detached and sutured either 7 mm posterior to its original insertion site (recession surgery) or at the same site (tenotomy). One day before euthanatization, the rabbits received bromodeoxyuridine (BrdU) injections. After 7 and 14 days, selected EOMs from both orbits were examined for changes in fast, slow, neonatal, and developmental MyHC isoform expression, Pax7 expression, and BrdU incorporation. RESULTS. Recession and tenotomy surgery resulted in similar changes in the surgical EOMs. These included a decreased proportion of fast MyHC myofibers, an increased proportion of slow MyHC myofibers, and increased BrdU-positive satellite cells. Similar changes were seen in the non-operated contralateral superior rectus muscles. The ipsilateral inferior rectus showed reciprocal changes to the surgical superior rectus muscles. CONCLUSIONS. The EOMs are extremely adaptive to changes induced by recession and tenotomy surgery, responding with modulations in fiber remodeling and myosin expression. These adaptive responses could be manipulated to improve surgical success rates. (Invest Ophthalmol Vis Sci. 2010;51:5646-5656) DOI:10.1167/iovs.10-5523

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

Transforming chaos to periodic oscillations

We demonstrate that the dynamics of an autonomous chaotic class C laser can be controlled to a periodic state via external modulation of the pump. In the absence of modulation, above the chaos threshold, the laser exhibits Lorenz-like chaotic pulsations. The average amplitude and frequency of these pulsations depend on the pump power. We find that there exist parameter windows where modulation of the pump power extinguishes the chaos in favor of simpler periodic behavior. Moreover we find a number of locking ratios between the pump and laser output follow the Farey sequence.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

Electrical transport properties of CuS single crystals

Electrical resistivity, transverse magnetoresistance and thermoelectric power measurements were performed on CuS high quality single crystals in the range 1.2-300 K and under fields of up to 16 T. The zero field resistivity data are well described below 55 K by a quasi-2D model, consistent with a carrier confinement at lower temperatures, before the transition to the superconducting state. The transverse magnetoresistance develops mainly below 30 K and attains values as large as 470% for a 16 T field at 5 K, this behaviour being ascribed to a band effect mechanism, with a possible magnetic field induced DOS change at the Fermi level. The transverse magnetoresistance shows no signs of saturation, following a power law with field Delta rho/rho(0) proportional to H(1.4), suggesting the existence of open orbits for carriers at the Fermi surface. The thermoelectric power shows an unusual temperature dependence, probably as a result of the complex band structure of CuS.

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

Sistema de localização de um veículo autónomo terrestre

Mestrado em Engenharia Electrotécnica e de Computadores.