Existence results for partial neutral functional differential equations with state-dependent delay

In this paper we study the existence of mild solutions for a class of first order abstract partial neutral differential equations with state-dependent delay. (C) 2008 Elsevier Ltd. All rights reserved.

Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system. (C) 2008 Elsevier Ltd. All rights reserved.

Existence of solutions for second order partial neutral functional differential equations

We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with unbounded delay in a Banach space.

Almost automorphic mild solutions to some partial neutral functional-differential equations and applications

The paper considers the existence and uniqueness of almost automorphic mild solutions to some classes of first-order partial neutral functional-differential equations. Sufficient conditions for the existence and uniqueness of almost automorphic mild solutions to the above-mentioned equations are obtained. As an application, a first-order boundary value problem arising in control systems is considered. (C) 2007 Elsevier Ltd. All fights reserved.

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

Dynamic portrait of the planetary 2/1 mean-motion resonance - I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (sigma-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (Delta pi-family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low-moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions. Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.

Measurement of the epicycle frequency in the Galactic disc and initial velocities of open clusters

A new method to measure the epicycle frequency kappa in the Galactic disc is presented. We make use of the large data base on open clusters completed by our group to derive the observed velocity vector (amplitude and direction) of the clusters in the Galactic plane. In the epicycle approximation, this velocity is equal to the circular velocity given by the rotation curve, plus a residual or perturbation velocity, of which the direction rotates as a function of time with the frequency kappa. Due to the non-random direction of the perturbation velocity at the birth time of the clusters, a plot of the present-day direction angle of this velocity as a function of the age of the clusters reveals systematic trends from which the epicycle frequency can be obtained. Our analysis considers that the Galactic potential is mainly axis-symmetric, or in other words, that the effect of the spiral arms on the Galactic orbits is small; in this sense, our results do not depend on any specific model of the spiral structure. The values of kappa that we obtain provide constraints on the rotation velocity of the in particular, V(0) is found to be 230 +/- 15 km s(-1) even if the scale (R(0) = 7.5 kpc) of the Galaxy is adopted. The measured kappa at the solar radius is 43 +/- 5 km s(-1) kpc(-1). The distribution of initial velocities of open clusters is discussed.

The spiral structure of the Galaxy revealed by CS sources and evidence for the 4:1 resonance

We present a map of the spiral structure of the Galaxy, as traced by molecular carbon monosulphide (CS) emission associated with IRAS sources which are believed to be compact H II regions. The CS line velocities are used to determine the kinematic distances of the sources in order to investigate their distribution in the galactic plane. This allows us to use 870 objects to trace the arms, a number larger than that of previous studies based on classical H II regions. The distance ambiguity of the kinematic distances, when it exists, is solved by different procedures, including the latitude distribution and an analysis of the longitude-velocity diagram. The study of the spiral structure is complemented with other tracers: open clusters, Cepheids, methanol masers and H II regions. The well-defined spiral arms are seen to be confined inside the corotation radius, as is often the case in spiral galaxies. We identify a square-shaped sub-structure in the CS map with that predicted by stellar orbits at the 4:1 resonance (four epicycle oscillations in one turn around the galactic centre). The sub-structure is found at the expected radius, based on the known pattern rotation speed and epicycle frequency curve. An inner arm presents an end with strong inwards curvature and intense star formation that we tentatively associate with the region where this arm surrounds the extremity of the bar, as seen in many barred galaxies. Finally, a new arm with concave curvature is found in the Sagitta to Cepheus region of the sky. The observed arms are interpreted in terms of perturbations similar to grooves in the gravitational potential of the disc, produced by crowding of stellar orbits.

A FOSSIL BULGE GLOBULAR CLUSTER REVEALED BY VERY LARGE TELESCOPE MULTI-CONJUGATE ADAPTIVE OPTICS

The globular cluster HP 1 is projected on the bulge, very close to the Galactic center. The Multi-Conjugate Adaptive Optics Demonstrator on the Very Large Telescope allowed us to acquire high-resolution deep images that, combined with first epoch New Technology Telescope data, enabled us to derive accurate proper motions. The cluster and bulge fields` stellar contents were disentangled through this process and produced an unprecedented definition in color-magnitude diagrams of this cluster. The metallicity of [Fe/H] approximate to -1.0 from previous spectroscopic analysis is confirmed, which together with an extended blue horizontal branch imply an age older than the halo average. Orbit reconstruction results suggest that HP 1 is spatially confined within the bulge.

Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analysed in more detail using a semi-analytical model. Apart from the well-known quasi-satellite orbits and the classical equilibrium Lagrangian points L(4) and L(5), we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at (delta lambda, delta pi) = (+/- 60 degrees, -/+ 120 degrees), where delta lambda is the difference in mean longitudes and delta pi is the difference in longitudes of pericentre. The position of these anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities and are found for eccentricities as high as similar to 0.7. Finally, we also applied a slow mass variation to one of the planets and analysed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.