INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

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.

Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain 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 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. 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.

A thermoelastic system of memory type in noncylindrical domains

In this paper, we consider a hyperbolic thermoelastic system of memory type in domains with moving boundary. The problem models vibrations of an elastic bar under thermal effects according to the heat conduction law of Gurtin and Pipkin. Global existence is proved by using the penalty method of Lions. (c) 2007 Elsevier Inc. All rights reserved.

Infeasibility handling in genetic algorithm using nested domains for production planning

In this paper we present a genetic algorithm with new components to tackle capacitated lot sizing and scheduling problems with sequence dependent setups that appear in a wide range of industries, from soft drink bottling to food manufacturing. Finding a feasible solution to highly constrained problems is often a very difficult task. Various strategies have been applied to deal with infeasible solutions throughout the search. We propose a new scheme of classifying individuals based on nested domains to determine the solutions according to the level of infeasibility, which in our case represents bands of additional production hours (overtime). Within each band, individuals are just differentiated by their fitness function. As iterations are conducted, the widths of the bands are dynamically adjusted to improve the convergence of the individuals into the feasible domain. The numerical experiments on highly capacitated instances show the effectiveness of this computational tractable approach to guide the search toward the feasible domain. Our approach outperforms other state-of-the-art approaches and commercial solvers. (C) 2009 Elsevier Ltd. All rights reserved.

Structural Characterization of Photopolymerizable Binary Liposomes Containing Diacetylenic and Saturated Phospholipids

The use of liposomes to encapsulate materials has received widespread attention for drug delivery, transfection, diagnostic reagent, and as immunoadjuvants. Phospholipid polymers form a new class of biomaterials with many potential applications in medicine and research. Of interest are polymeric phospholipids containing a diacetylene moiety along their acyl chain since these kinds of lipids can be polymerized by Ultra-Violet (UV) irradiation to form chains of covalently linked lipids in the bilayer. In particular the diacetylenic phosphatidylcholine 1,2-bis(10,12-tricosadiynoyl)- sn-glycero-3-phosphocholine (DC8,9PC) can form intermolecular cross-linking through the diacetylenic group to produce a conjugated polymer within the hydrocarbon region of the bilayer. As knowledge of liposome structures is certainly fundamental for system design improvement for new and better applications, this work focuses on the structural properties of polymerized DC8,9PC:1,2-dimyristoyl-sn-glycero-3-phusphocholine (DMPC) liposomes. Liposomes containing mixtures of DC8,9PC and DMPC, at different molar ratios, and exposed to different polymerization cycles, were studied through the analysis of the electron spin resonance (ESR) spectra of a spin label incorporated into the bilayer, and the calorimetric data obtained from differential scanning calorimetry (DSC) studies. Upon irradiation, if all lipids had been polymerized, no gel-fluid transition would be expected. However, even samples that went through 20 cycles of UV irradiation presented a DSC band, showing that around 80% of the DC8,9PC molecules were not polymerized. Both DSC and ESR indicated that the two different lipids scarcely mix at low temperatures, however few molecules of DMPC are present in DC8,9PC rich domains and vice versa. UV irradiation was found to affect the gel fluid transition of both DMPC and DC8,9PC rich regions, indicating the presence of polymeric units of DC8,9PC in both areas, A model explaining lipids rearrangement is proposed for this partially polymerized system.

Electrical transport in disordered and ordered magnetic domains under pressures and magnetic fields

Magnetic M( T, H, P) and electrical transport.( T, H, P) measurements in a strong spin-lattice-charge coupled La(0.7)Ca(0.3)MnO(3) system have been conducted. The application of H and P leads to the formation of different magnetic domain structures in the vicinity and below the polaronic-to-ferromagnetic transition temperature. The charge mobility is more sensitive to the variation of the spatial wave function overlap between Mn(3+) eg and O(2-) 2p orbitals due to the applied compacting pressure rather than the relative spin orientation between neighbouring Mn ions when the magnetic field is applied. In spite of the presence of different magnetic domain structures due to the sample history, the effect of magnetic field and pressure is less pronounced at lower temperatures on electrical transport properties.

Vesicles with charged domains

This work summarizes results obtained on membranes composed of the ternary mixture dioleoylphosphatidylglycerol (DOPG), egg sphingomyelin (eSM) and cholesterol (Chol). The membrane phase state as a function of composition is characterized from data collected with fluorescence microscopy on giant unilamellar vesicles. The results suggest that the presence of the charged DOPG significantly decreases the composition region of coexistence of liquid ordered and liquid disordered phases as compared to that in the ternary mixture of dioleoylphosphatidycholine, sphingomyelin and cholesterol. The addition of calcium chloride to DOPG:eSM:Chol vesicles, and to a lesser extent the addition of sodium chloride, leads to the stabilization of the two-phase coexistence region, which is expressed in an increase in the miscibility temperature. On the other hand, addition of the chelating agent EDTA has the opposite effect, suggesting that impurities of divalent cations in preparations of giant vesicles contribute to the stabilization of charged domains. We also explore the behavior of these membranes in the presence of extruded unilamellar vesicles made of the positively charged lipid dioleoyltrimethylammoniumpropane (DOTAP). The latter can induce domain formation in DOPG:eSM:Chol vesicles with initial composition in the one-phase region. (C) 2010 Elsevier B.V. All rights reserved.

Reaction microtextures of monazite: Correlation between chemical and age domains in the Nazare Paulista migmatite, SE Brazil

Back-scattered imaging, X-ray element mapping and electron microprobe analyzer (EMPA) chemical dating reveal complex compositional and age zoning in monazite crystals from different layers and textural positions in a garnet-bearing migmatite in SE Brazil. Y-rich (variable Y(2)O(3), averaging 2.5 wt.%) relict cores are preserved in mesosome and melanosome monazite, and correspond to 793 +/- 6 Ma inherited crystals possibly generated in a previous metamorphic event. These cores are overgrown and widely replaced by two generations of monazite, which are present in all migmatite layers. The first, also Y-rich (average 2.5 wt.% Y(2)O(3)), was produced at similar to 635 Ma during prograde metamorphism under subsolidus conditions, while the second has an Y-poor (<1.5 wt.% Y(2)O(3)), low Th/U signature, and precipitated from low Y and HREE anatectic melts produced by reactions in which garnet was inert. Quartz-rich trondhjemitic leucosome represents lower temperature melt (bearing some subsolidus quartz and garnet with included monazite) formed at temperatures below muscovite breakdown; its Y-poor monazite indicates an age of 617 +/- 6 Ma. Granitic leucosomes formed close to peak metamorphic conditions (T>750 degrees C) above muscovite breakdown have their slightly younger character confirmed by a 609 +/- 7 Ma low-Y monazite age. A similar 606 +/- 5 Ma age was obtained for low-Y monazite rims and domains in mesosome and melanosome, and reflects the time of monazite saturation in interstitial granitic melt that was trapped in these layers. Our results confirm that inherited monazite crystals can be preserved during partial melting at temperatures above muscovite breakdown. Moreover, careful textural control aided by X-ray chemical mapping may allow monazite generated at different stages in a similar to 25 Myr prograde metamorphic path to be identified and dated using an electron microprobe. (C) 2008 Elsevier B.V. All rights reserved.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

On Polar Foliations and the Fundamental Group

In this work we investigate the relation between the fundamental group of a complete Riemannian manifold M and the quotient between the Weyl group and reflection group of a polar action on M, as well as the relation between the fundamental group of M and the quotient between the lifted Weyl group and lifted reflection group. As applications we give alternative proofs of two results. The first one, due to the author and Toben, implies that a polar action does not admit exceptional orbits, if M is simply connected. The second result, due to Lytchak, implies that the orbits are closed and embedded if M is simply connected. All results are proved in the more general case of polar foliations.

Skipping of exon 30 in C5 gene results in complete human C5 deficiency and demonstrates the importance of C5d and CUB domains for stability

The deficiency of complement C5 is rare and frequently associated with severe and recurrent infections, especially caused by Neisseria spp. We observed the absence of component C5 in the serum of 3 siblings from a Brazilian family with history of consanguinity. The patients had suffered from recurrent episodes of meningitis and other less severe infections. Sera from these patients were unable to mediate hemolytic activity either by the classical or alternative pathways and presented extremely low levels of C5 protein (13, 0.9 and 1.0 mu g/ml-normal range: 45-190 mu g/ml). Hemolytic activity could be restored by the addition of purified C5 to deficient serum. Sequencing of sibling C5 cDNA revealed a homozygous 153 bp deletion that corresponds precisely to exon 30. The parents carried the same deletion but only in one allele. Sequencing of the corresponding region in the genomic DNA revealed a C to C substitution within intron 30 and, most significantly, the substitution of GAG(4028) for GAA(4028) at the 3` end of exon 30 which is most likely responsible for skipping of exon 30. The resulting in-frame deletion in the C5 mRNA codes for a mutant C5 protein lacking residues 1289-1339. These residues map to the CUB and C5d domains of the C5 alpha chain. This deletion is expected to produce a non-functional and unstable C5 protein which is more susceptible to degradation. (C) 2009 Published by Elsevier Ltd.

AMIN domains have a predicted role in localization of diverse periplasmic protein complexes

We describe AMIN (Amidase N-terminal domain), a novel protein domain found specifically in bacterial periplasmic proteins. AMIN domains are widely distributed among peptidoglycan hydrolases and transporter protein families. Based on experimental data, contextual information and phyletic profiles, we suggest that AMIN domains mediate the targeting of periplasmic or extracellular proteins to specific regions of the bacterial envelope.