Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.

Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

Identification of the sharks of the genus Etmopterus Rafinesque, 1810 (Elasmobranchii: Etmopteridae) from the upper slope of southern Brazil, with comparison between the species E. bigelowi Shirai & Tachikawa, 1993 and E. pusillus Lowe, 1839

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new species of Baurusuchus (Crocodyliformes, Mesoeucrocodylia) from the Upper Cretaceous of Brazil, with the first complete postcranial skeleton described for the family Baurusuchidae

The present work describes a new species of Baurusuchidae from Upper Cretaceous sediments of the Bauru Basin, and provides the first complete postcranial description for the family. Many postcranial features observed in the new species are also present in other notosuchian taxa, and are thus considered plesiomorphic for the genus. These are: long cervical neural spines; robust deltopectoral crest of the humerus; large proximal portion in the radiale that contacts the ulna; ulnare anterior distal projection; supra-acetabular crest well developed laterally; post-acetabular process posterodorsally deflected; presence of an anteromedial crest in the femur; fourth trocanter of femur posteriorly positioned; tibia with a laterally curved shaft; calcaneum tuber posteroventrally oriented; osteoderms ornamented with grooves and imbricated in the tail. On the other hand, we found the following sacral and carpal features to be unique among all mesoeucrocodylians analyzed: transverse processes of sacral vertebrae dorsolaterally deflected; presence of a longitudinal crest in the lateral surface of sacral vertebrae; pisiform carpal with a condyle-like surface. The majority of these cited features corroborates a cursorial locomotion for the new species described in the present study, suggesting that members of the family Baurusuchidae were also cursorial species.

Cranial anatomy of a new genus of hyperodapedontine rhynchosaur (Diapsida, Archosauromorpha) from the Upper Triassic of southern Brazil

Detailed description of the cranial anatomy of the rhynchosaur previously known as Scaphonyx sulcognathus allows its assignment to a new genus Teyumbaita. Two nearly complete skulls and a partial skull have been referred to the taxon, all of which come from the lower part of the Caturrita Formation, Upper Triassic of Rio Grande do Sul, southern Brazil. Cranial autapomorphies of Teyumbaita sulcognathus include anterior margin of nasal concave at midline, prefrontal separated from the ascending process of the maxilla, palatal ramus of pterygoid expanded laterally within palatines, dorsal surface of exoccipital markedly depressed, a single tooth lingually displaced from the main medial tooth-bearing area of the maxilla, and a number of other characters (such as skull broader than long; a protruding orbital anterior margin; anguli oils extending to anterior ramus of the jugal; bar between the orbit and the lower temporal fenestra wider than 0.4 of the total orbital opening; mandibular depth reaching more than 25% of the total length) support its inclusion in Hyperodapedontinae. T. sulcognathus is the only potential Norian rhynchosaur, suggesting that the group survived the end-Carnian extinction event.

Fascicular Topography of the Suprascapular Nerve in the C5 Root and Upper Trunk of the Brachial Plexus: A Microanatomic Study From a Nerve Surgeon`s Perspective

BACKGROUND: In patients with supraclavicular injuries of the brachial plexus, the suprascapular nerve (SSN) is frequently reconstructed with a sural nerve graft coapted to C5. As the C5 cross-sectional diameter exceeds the graft diameter, inadequate positioning of the graft is possible. OBJECTIVE: To identify a specific area within the C5 proximal stump that contains the SSN axons and to determine how this area could be localized by the nerve surgeon, we conducted a microanatomic study of the intraplexal topography of the SSN. METHODS: The right-sided C5 and C6 roots, the upper trunk with its divisions, and the SSN of 20 adult nonfixed cadavers were removed and fixed. The position and area occupied by the SSN fibers inside C5 were assessed and registered under magnification. RESULTS: The SSN was monofascicular in all specimens and derived its fibers mainly from C5. Small contributions from C6 were found in 12 specimens (60%). The mean transverse area of C5 occupied by SSN fibers was 28.23%. In 16 specimens (80%), the SSN fibers were localized in the ventral (mainly the rostroventral) quadrants of C5, a cross-sectional area between 9 o`clock and 3 o`clock from the surgeon`s intraoperative perspective. CONCLUSION: In reconstruction of the SSN with a sural nerve graft, coaptation should be performed in the rostroventral quadrant of C5 cross-sectional area (between 9 and 12 o`clock from the nerve surgeon`s point of view in a right-sided brachial plexus exploration). This will minimize axonal misrouting and may improve outcome.

TRANSFER OF A FASCICLE FROM THE POSTERIOR CORD TO THE SUPRASCAPULAR NERVE AFTER INJURY OF THE UPPER ROOTS OF THE BRACHIAL PLEXUS: TECHNICAL CASE REPORT

OBJECTIVE: A new nerve transfer technique using a healthy fascicle of the posterior cord for suprascapular nerve reconstruction is presented. This technique was used in a patient with posttraumatic brachial plexopathy resulting in upper trunk injury with proximal root stumps that were unavailable for grafting associated with multiple nerve dysfunction. CLINICAL PRESENTATION: A 45-year-old man sustained a right brachial plexus injury after a bicycle accident. Clinical evaluation and electromyography indicated upper trunk involvement. Trapezius muscle function and triceps strength were normal on physical examination. INTERVENTION: The patient underwent a combined supra- and infraclavicular approach to the brachial plexus. A neuroma-in-continuity of the upper trunk and fibrotic C5 and C6 roots were identified. Electrical stimulation of the phrenic and spinal accessory nerves produced no response. The suprascapular nerve was dissected from the upper trunk, transected, and rerouted to the infraclavicular fossa. A healthy fascicle of the posterior cord to the triceps muscle was transferred to the suprascapular nerve. At the time of the 1-year follow-up evaluation, arm abduction against gravity and external rotation reached 40 and 34 degrees, respectively. CONCLUSION: The posterior cord can be used as a source of donor fascicle to the suprascapular nerve after its infraclavicular relocation. This new intraplexal nerve transfer could be applied in patients with isolated injury of the upper trunk and concomitant lesion of the extraplexal nerve donors usually used for reinnervation of the suprascapular nerve.

Long-term effects of pharyngeal flaps on the upper airways of subjects with velopharyngeal insufficiency

Objectives: To investigate the long-term effects of pharyngeal flap surgery (PFS) on nasal and nasopharyngeal dimensions of patients with velopharyngeal insufficiency (VPI) and to correlate the findings with the onset of respiratory complaints after surgery. Design/Participants: Prospective study in 58 nonsyndromic patients with repaired cleft palate and VPI, evaluated 2 days before and 5 months (POST1) and 1 year (POST2) after PFS, on average. Patients were divided into two groups: one consisting of patients with postoperative respiratory complaints (RC group) and the other without complaints (NRC group). Interventions: Superiorly based PFS. Main Outcome Measures: Respiratory complaints (self reports of mouth breathing, snoring, and other sleep obstructive events) assessed at POST1 and POST2, and minimum nasal (NCSA) and nasopharyngeal (NPA) cross-sectional areas assessed by rhinomanometry at POST2. Results: Respiratory complaints were reported by 55% and 36% of the patients evaluated at POST1 and POST2, respectively. Posterior rhinomanometry showed a significant postoperative reduction of mean NCSA in the RC and NRC groups (p < .05), to subnormal levels in some of them. The decrease was more pronounced in the RC group. No significant changes in NCSA were observed by anterior rhinomanometry. Similar results were obtained when NPA was assessed by modified anterior rhinomanometry. Conclusion: In the long-term, PFS yielded a significant reduction in upper airways dimensions beyond what should be expected and associated with persistent respiratory complaints in some cases.

On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Multicusped crocodyliform teeth from the Upper Cretaceous (Sao Jose do Rio Preto Formation, Bauru Group) of Sao Paulo, Brazil

The six peculiar multicusped teeth described here were collected from sediments of the Upper Cretaceous of Sao Jose do Rio Preto Formation, near Ibira (northeastern Sao Paulo, Brazil). Their bulbous crowns are slightly labio-lingual compressed, and bear a main plus two accessory cusps, which conceal a well developed cingulum. Wear facets are seen on the main and distal accessory cusps. Comparison to the known Crocodyliformes with multicusped teeth show that the new material is not referable to ""protosuchians"" or eusuchians, nor related to two unnamed forms from Morocco and ""notosuchians"" such as Uruguaysuchus, Chiamaerasuchus, and Simosuchus. On the other hand, possible affinities with Candidodon and Malawisuchus were maintained based on shared traits. This includes teeth with the main cusp and some accessory cusps arranged in more than one axis, a previously defined unambiguous apomorphy of the putative clade composed of Candidodon plus Malawisuchus. The term Candidodontidae can be applied to this group, and defined as all taxa closer to Candidodon itapecuruensis than to Notosuchus terrestris, Uruguaysuchus aznarezi, Comahuesuchus brachybuccalis, Sphagesaurus huenei, Baurusuchus pachecoi, and Crocodylus niloticus. (C) 2009 Elsevier Ltd. All rights reserved.

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations. (C) 2011 Elsevier Ltd. All rights reserved.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.