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.

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.

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.

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.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 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.

Is a lower dose of vitamin D supplementation enough to increase 25(OH)D status in a sunny country?

Calcium and vitamin D are essential nutrients for bone metabolism Vitamin D can either be obtained from dietary sources or cutaneous synthesis. The study was conducted in subtropic weather; therefore, some might believe that the levels of solar radiation would be sufficient in this area. To evaluate calcium and vitamin D supplementation in postmenopausal women with osteoporosis living in a sunny country. A 3-month controlled clinical trial with 64 postmenopausal women with osteoporosis, mean age 62 +/- A 8 years. They were randomly assigned to either the supplement group, who received 1,200 mg of calcium carbonate and 400 IU (10 mu g) of vitamin D(3,) or the control group. Dietary intake assessment was performed, bone mineral density and body composition were measured, and biochemical markers of bone metabolism were analyzed. Considering all participants at baseline, serum vitamin D was under 75 nmol/l in 91.4% of the participants. The concentration of serum 25(OH)D increased significantly (p = 0.023) after 3 months of supplementation from 46.67 +/- A 13.97 to 59.47 +/- A 17.50 nmol/l. However, the dose given was limited in effect, and 86.2% of the supplement group did not reach optimal levels of 25(OH)D. Parathyroid hormone was elevated in 22.4% of the study group. After the intervention period, mean parathyroid hormone tended to decrease in the supplement group (p = 0.063). The dose given (400 IU/day) was not enough to achieve 25(OH)D concentration, considered optimal for bone health.

Mandibulofacial Dysostosis, Severe Lower Eyelid Coloboma, Cleft Palate, and Alopecia: A New Distinct Form of Mandibulofacial Dysostosis or a Severe Form of Johnson-McMillin Syndrome?

We describe a patient with a phenotype characterized by mandibulofacial dysostosis with severe lower eyelid coloboma, cleft palate, abnormal ears, alopecia, delayed eruption and crowded teeth, and sensorioneural hearing loss. The karyotype and the screening for mutations in the coding region of TCOF1 gene were normal. The clinical signs of our case overlap the new mandibulofacial dysostosis described by Stevenson et al. [2007] and the case with Johnson-McMillin syndrome described by Cushman et al. [2005]. The similar clinical signs, mainly, the severe facial involvement observed in these cases suggest that they can represent a new distinct form of mandibulofacial dysostosis or the end of the spectrum of Johnson McMillin syndrome. (C) 2010 Wiley-Liss, Inc.

Karyotypes of a Cryptic Diploid Form of the Unisexual Leposoma percarinatum (Squamata, Gymnophthalmidae) and the Bisexual Leposoma ferreirai from the Lower Rio Negro, Amazonian Brazil

Karyotypes of Leposoma show a clear differentiation between species of the scincoides group from Brazilian Atlantic Forest (2n = 52, without distinctive size groups of chromosomes) and those of the parietale group from the Amazon (2n = 44, with 20M + 24m). In a previous study, we found that in the parietale group the parthenoform Leposoma percarinatum from the state of Mato Grosso, Brazil, exhibited a triploid karyotype (3n = 66) with 30 macrochromosomes and 36 microchromosomes. It was suggested that this karyotype arose after hybridization between a bisexual species with N = 22 (10M + 12m) and a hypothetical unisexual cryptic diploid form of the L. percarinatum complex. Herein, we describe the karyotypes for two species of the parietale group occurring sympatrically in the Arquipelago das Anavilhanas, lower Rio Negro, in Amazonian Brazil. The first represents a distinctive diploid parthenogenetic clone of the L. percarinatum complex, and the other is the recently described Leposoma ferreirai. Both species have 44 biarmed chromosomes clearly represented by 20 macrochromosomes and 24 microchromosomes and present Ag-NORs in one pair of the smallest sized microchromosomes; heteromorphism of size for these regions was detected in L. percarinatum. C-banding revealed blocks of constitutive heterochromatin on the telomeric and pericentromeric regions of macrochromosomes and some microchromosomes. The description of a diploid karyotype (2n = 44, 20M + 24m) for the L. percarinatum complex and its sympatric congener L. ferreirai provides new insight for a better understanding of the origin of parthenogenesis in the L. percarinatum complex.

Lower serum IgA levels in horses kept under intensive sanitary management and physical training

Quantity and variety of environmental antigens, age, diet, vaccine protocols, exercising practice and mucosal cytokine microenvironment are factors that influence serum immunoglobulin (Ig) levels. IgA, IgG, IgG(T) and IgM were quantified in 60 horses, which were classified into two groups, `intensive` or `relaxed`, according to sanitary standards of the facilities and physical exercise to which animals were subjected to. The `intensive` group presented lower means for all isotypes, but only IgA presented a significant (P < 0.0064) difference when compared to the `relaxed` group. This suggests that mucosal immunity found in the `intensive` group is lower when compared to the `relaxed` group. Our data suggest that athlete horses may be less poised to mount an effective mucosal immunity response to environmental challenges and should not be considered by the same perspectives as a free-ranging horse.

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.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Lower and Upper Neoproterozoic magmatic records in Itaiacoca Belt (Parana-Brazil): Zircon ages and lithostratigraphy studies

The Itaiacoca Belt is a sequence of metavolcanic and metasedimentary rocks that crop out east of Parana and southeast of Sao Paulo states, in southern Brazil. This geologic-geochronologic study supports division of the Itaiacoca Belt into two major lithologic sequences. The older is a carbonate platform sequence (dolomitic meta-limestones/metamarls/calc-phyllites/ carbonate phyllites) with minimum deposition ages related to the end of the Mesoproterozoic/beginning of the Neoproterozoic (1030-908 Ma:U-Pb, zircon of metabasic rocks). The younger sequence contains mainly clastics deposits (meta-arkoses/metavolcanics/metaconglomerates/metapelites) with deposition ages related to the Neoproterozoic (645-628 Ma:U-Pb,zircon of metavolcanic rocks). These ages are quite close to K-Ar ages (fine fraction) of the 628-610 Ma interval, associated with metamorphism and cooling of the Itaiacoca Belt. The contact between the dolomitic meta-limestones and meta-arkoses is marked by intense stretching and high-angle foliation, suggesting that the discontinuity between these associations resulted from shearing. It is proposed here that the term Itaiacoca Sequence, should represent the dolomitic meta-limestones, and the term Abapa Sequence represents the meta-arkoses/metavolcanics/phyllites. in a major tectonic context, these periods are related to the break-up of Rodinia Supercontinent (1030-908 Ma) and the amalgamation of the Gondwana Supercontinent (645-628 Ma). (C) 2008 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.