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.

Hemigrammus arua, a new species of characid (Characiformes: Characidae) from the lower Amazon, Brazil

A new Hemigrammus species is described from tributaries of the igarapé Juruti Grande and rio Arapiuns, lower rio Amazonas, Pará State, Brazil. The new species can be easily diagnosed from all its congeners, except from Hemigrammus stictus (Durbin), by possessing a single, large humeral spot which extends longitudinally from the fifth or sixth to the posterior margin of eighth to tenth, lateral line scales. It can be distinguished from Hemigrammus stictus by possessing a pronounced upper, anteriorly-oriented extension in the humeral blotch, conferring an inverted-comma shape to it, and by displaying a distinct life color pattern.

Relationship Between Eccentric Hip Torque and Lower-Limb Kinematics: Gender Differences

The purposes of this study were to compare lower-limb kinematics between genders, and determine the relationships among eccentric hip abductor and lateral rotator torques and lower-limb kinematics. The movements of the pelvis, femur, and knee were calculated for 16 women and 16 men during the single-leg squat. Eccentric hip abductor and lateral rotator torques were measured using an isokinetic dynamometer. The results showed that women had greater contralateral pelvic depression, femur adduction, and knee abduction than men. The eccentric hip abductor and lateral rotator torques were correlated with coronal plane femur and knee movements in the overall sample. When the genders were analyzed separately, it was observed that women with greater eccentric hip abductor torque exhibited less femur adduction and femur medial rotation, and greater knee adduction excursion. No significant relationship was observed between the isokinetic and kinematic variables in the male group. The differences between the genders help to explain the greater rate of knee disorders observed in women. Moreover, the eccentric hip abduction action seemed to be more important in women to control the lower-limb movements.

A comparison of lower limb EMG and ground reaction forces between barefoot and shod gait in participants with diabetic neuropathic and healthy controls

Background: It is known that when barefoot, gait biomechanics of diabetic neuropathic patients differ from nondiabetic individuals. However, it is still unknown whether these biomechanical changes are also present during shod gait which is clinically advised for these patients. This study investigated the effect of the participants own shoes on gait biomechanics in diabetic neuropathic individuals compared to barefoot gait patterns and healthy controls. Methods: Ground reaction forces and lower limb EMG activities were analyzed in 21 non-diabetic adults (50.9 +/- 7.3 yr, 24.3 +/- 2.6 kg/m(2)) and 24 diabetic neuropathic participants (55.2 +/- 7.9 yr, 27.0 +/- 4.4 kg/m(2)). EMG patterns of vastus lateralis, lateral gastrocnemius and tibialis anterior, along with the vertical and antero-posterior ground reaction forces were studied during shod and barefoot gait. Results: Regardless of the disease, walking with shoes promoted an increase in the first peak vertical force and the peak horizontal propulsive force. Diabetic individuals had a delay in the lateral gastrocnemius EMG activity with no delay in the vastus lateralis. They also demonstrated a higher peak horizontal braking force walking with shoes compared to barefoot. Diabetic participants also had a smaller second peak vertical force in shod gait and a delay in the vastus lateralis EMG activity in barefoot gait compared to controls. Conclusions: The change in plantar sensory information that occurs when wearing shoes revealed a different motor strategy in diabetic individuals. Walking with shoes did not attenuate vertical forces in either group. Though changes in motor strategy were apparent, the biomechanical did not support the argument that the use of shoes contributes to altered motor responses during gait.

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

VARIATION IN STOMATAL NUMBERS OF GLOSSOPTERIS LEAVES FROM THE LOWER PERMIAN OF PARANA BASIN, BRAZIL

The stomatal density and index in compressed leaves of Glossopteris communis from two different roof shales from the Lower Permian in Parana Basin, Brazil (Western Gondwana) have been investigated to test the possible relationship with modeled global changes in atmospheric CO(2) during the Phanerozoic. The obtained parameters show that the genus Glossopteris from the Cool Temperate biome can be used as CO(2) -proxy, despite the impossibility of being compared with living relatives or equivalents. When confronted with already published data for the Tropical Summer Wet biome, the present results confirm the detection of low levels of atmospheric CO(2) during the Early Permian, as predicted by the modeled curve. Nevertheless, the lower stomatal numbers detected at the climax of the coal interval (Faxinal Coalfield, Sakmarian) when compared to the higher ones obtained in leaves from a younger interval (Figueira Coalfield, Artinskian) could be attributed to temporarily high levels of atmospheric CO(2). Therefore, the occurrence of an extensive peat generating event at the southern part of the basin and subsequent greenhouse gases emissions from this environment may have been enough to reverse regionally and temporarily the reduction trend in atmospheric CO(2). Additionally, the Faxinal flora is preserved in a tonstein layer, which is a record of volcanic activity that could also cause a rise in atmospheric CO(2). During the Artinskian, the scarce generation of peat mires, as revealed by the occurrence of thin and discontinuous coal layers, and the lack of volcanism evidence would be insufficient to affect the general low CO(2) trend.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Comparison of three-dimensional lower extremity running kinematics of young adult and elderly runners

The objective of this study was to compare the three-dimensional lower extremity running kinematics of young adult runners and elderly runners. Seventeen elderly adults (age 67-73 years) and 17 young adults (age 26-36 years) ran at 3.1ms-1 on a treadmill while the movements of the lower extremity during the stance phase were recorded at 120Hz using three-dimensional video. The three-dimensional kinematics of the lower limb segments and of the ankle and knee joints were determined, and selected variables were calculated to describe the movement. Our results suggest that elderly runners have a different movement pattern of the lower extremity from that of young adults during the stance phase of running. Compared with the young adults, the elderly runners had a substantial decrease in stride length (1.97 vs. 2.23m; P=0.01), an increase in stride frequency (1.58 vs. 1.37Hz; P=0.002), less knee flexion/extension range of motion (26 vs. 33; P=0.002), less tibial internal/external rotation range of motion (9 vs. 12; P0.001), larger external rotation angle of the foot segment (toe-out angle) at the heel strike (-5.8 vs. -1.0; P=0.009), and greater asynchronies between the ankle and knee movements during running. These results may help to explain why elderly individuals could be more susceptible to running-related injuries.

Treatment of vitamin D deficiency increases lower limb muscle strength in institutionalized older people independently of regular physical activity: a randomized double-blind controlled trial

Aims: To investigate the effects of a 6-month supplementation with calcium and cholecalciferol on biochemical parameters and muscle strength of institutionalized elderly. Methods: This prospective, double-blind, placebo-controlled, randomized trial included Brazilian institutionalized people 6 60 years of age receiving a 6-month supplementation ( December to May) of daily calcium plus monthly placebo (calcium/placebo group) or daily calcium plus oral cholecalciferol (150,000 IU once a month during the first 2 months, followed by 90,000 IU once a month for the last 4 months; calcium/vitamin D group). Fasting blood samples for 25-(OH) D, PTH and calcium determination were collected (n = 56) and muscle tests were performed ( n = 46) to measure the strength of hip flexors (SHF) and knee extensors (SKE) before ( baseline) and after the 6-month intervention ( 6 months). Results: Due to seasonal variations, serum 25( OH) D significantly enhanced in both groups after treatment, but the calcium/vitamin D group had significantly higher 25-(OH) D levels than the calcium/placebo group (84 vs. 33%, respectively; p < 0.0001). No cases of hypercalcemia were observed. While the calcium/placebo group showed no improvement in SHF and SKE at 6 months (p = 0.93 and p = 0.61, respectively), SHF was increased in the calcium/vitamin D group by 16.4% (p = 0.0001) and SKE by 24.6% (p = 0.0007). Conclusions: The suggested cholecalciferol supplementation was safe and efficient in enhancing 25(OH)D levels and lower limb muscle strength in the elderly, in the absence of any regular physical exercise practice. Copyright (C) 2009 S. Karger AG, Basel

Incidence of injuries to the lower limbs joints in kung fu athletes

Background and Study Aim: This study evaluated the influence of competitive practice and training aspects on incidence of injuries to the lower limbs joints in formalized (taolu) and combat (sanshou) kung fu athletes. Material/Methods: One hundred and twenty-seven kung fu athletes (taolu, n=82; sanshou, n=45) were interviewed about kung fu practice (practice time, competition time and competition level), training volume (days of training per week and hours per training session) and injury profiles (incidence and type). Continuous variables were compared by non-parametric Kolmogorov-Smirnov test (disciplines and competition levels as grouping variables). The effects of categorical variables (kung fu practice) on injury profiles were analyzed using the Pearson`s chi-square test. The level of significance was set at p<0.05. Results: Our data exhibited large frequency of injury reports (70.1%) and significantly differences on injury profiles between disciplines and competition levels. Taolu athletes, despite the lower practice/competition time (-51.5 and -41.8%, respectively), presented frequency of injury reports twofold greater, longer daily training volume (23.3%) and higher incidence of lower limbs joints injuries than sanshou athletes (35.4% and 11.8%, respectively). Conclusions: Our results suggest a link between injury profiles (incidence and type) and specific characteristics of kung fu disciplines.