A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Stability of the curvature perturbation in dark sectors` mutual interacting models

We consider perturbations in a cosmological model with a small coupling between dark energy and dark matter. We prove that the stability of the curvature perturbation depends on the type of coupling between dark sectors. When the dark energy is of quintessence type, if the coupling is proportional to the dark matter energy density, it will drive the instability in the curvature perturbations: however if the coupling is proportional to the energy density of dark energy, there is room for the stability in the curvature perturbations. When the dark energy is of phantom type, the perturbations are always stable, no matter whether the coupling is proportional to the one or the other energy density. (C) 2008 Elsevier B.V. All rights reserved.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Quasinormal modes of semiclassical electrically charged black holes

We report the results concerning the influence of vacuum polarization due to quantum massive vector, scalar and spinor fields on the scalar sector of quasinormal modes in spherically symmetric charged black holes. The vacuum polarization from quantized fields produces a shift in the values of the quasinormal frequencies, and correspondingly the semiclassical system becomes a better oscillator with respect to the classical Reissner-Nordstrom black hole.

VACUUM POLARIZATION EFFECTS ON QUASINORMAL MODES IN ELECTRICALLY CHARGED BLACK HOLE SPACE-TIMES

We investigate the influence of vacuum polarization of quantum massive fields on the scalar sector of quasinormal modes in spherically symmetric black holes. We consider the evolution of a massless scalar field on the space-time corresponding to a charged semiclassical black hole, consisting of the quantum-corrected geometry of a Reissner-Nordstrom black hole dressed by a quantum massive scalar field in the large mass limit. Using a sixth order WKB approach we find a shift in the quasinormal mode frequencies due to vacuum polarization.

Predictions from an anisotropic inflationary era

This paper investigates the predictions of an inflationary phase starting from a homogeneous and anisotropic universe of the Bianchi I type. After discussing the evolution of the background spacetime, focusing on the number of e-folds and the isotropization, we solve the perturbation equations and predict the power spectra of the curvature perturbations and gravity waves at the end of inflation. The main features of the early anisotropic phase is (1) a dependence of the spectra on the direction of the modes, (2) a coupling between curvature perturbations and gravity waves and (3) the fact that the two gravity wave polarizations do not share the same spectrum on large scales. All these effects are significant only on large scales and die out on small scales where isotropy is recovered. They depend on a characteristic scale that can, but a priori must not, be tuned to some observable scale. To fix the initial conditions, we propose a procedure that generalizes the one standardly used in inflation but that takes into account the fact that the WKB regime is violated at early times when the shear dominates. We stress that there exist modes that do not satisfy the WKB condition during the shear-dominated regime and for which the amplitude at the end of inflation depends on unknown initial conditions. On such scales, inflation loses its predictability. This study paves the way for the determination of the cosmological signature of a primordial shear, whatever the Bianchi I spacetime. It thus stresses the importance of the WKB regime to draw inflationary predictions and demonstrates that, when the number of e-folds is large enough, the predictions converge toward those of inflation in a Friedmann-Lemaitre spacetime but that they are less robust in the case of an inflationary era with a small number of e-folds.

Quasinormal modes of black holes immersed in a strong magnetic field

We found quasinormal modes, both in time and frequency domains, of the Ernst black holes, that is neutral black holes immersed in an external magnetic field. The Ernst solution reduces to the Schwarzschild solution, when the magnetic field vanishes. It is found that the quasinormal spectrum for massless scalar field in the vicinity of the magnetized black holes acquires an effective ""mass"" mu = 2B vertical bar m vertical bar, where m is the azimuthal number and B is parameter describing the magnetic field. We shall show that in the presence of a magnetic field quasinormal modes are longer lived and have larger oscillation frequencies. The perturbations of higher-dimensional magnetized black holes by Ortaggio and of magnetized dilaton black holes by Radu are considered. (C) 2007 Elsevier B.V. All rights reserved.

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

Sensitivity of complex networks measurements

Complex networks obtained from real-world networks are often characterized by incompleteness and noise, consequences of imperfect sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality and completeness of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effects of the sampling on the network structure. One way to evaluate these effects is through an analysis of the sensitivity of complex network measurements to perturbations in the topology of the network. In this paper, measurement sensibility is quantified in terms of the relative entropy of the respective distributions. Three particularly important kinds of progressive perturbations to the network are considered, namely, edge suppression, addition and rewiring. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) are identified with respect to each type of perturbation. Such an analysis includes eight different measurements applied on six different complex networks models and three real-world networks. This approach allows one to choose the appropriate measurements in order to obtain accurate results for networks where sampling bias cannot be avoided-a very frequent situation in research on complex networks.

Generation of Vortices and Observation of Quantum Turbulence in an Oscillating Bose-Einstein Condensate

We report on the experimental observation of vortex formation and production of tangled vortex distribution in an atomic BEC of (87)Rb atoms submitted to an external oscillatory perturbation. The oscillatory perturbations start by exciting quadrupolar and scissors modes of the condensate. Then regular vortices are observed finally evolving to a vortex tangle configuration. The vortex tangle is a signature of the presence of a turbulent regime in the cloud. We also show that this turbulent cloud has suppression of the aspect ratio inversion typically observed in quantum degenerate bosonic gases during free expansion.

Novel Zn(2+)-binding Sites in Human Transthyretin IMPLICATIONS FOR AMYLOIDOGENESIS AND RETINOL-BINDING PROTEIN RECOGNITION

Human transthyretin (TTR) is a homotetrameric protein involved in several amyloidoses. Zn(2+) enhances TTR aggregation in vitro, and is a component of ex vivo TTR amyloid fibrils. We report the first crystal structure of human TTR in complex with Zn(2+) at pH 4.6-7.5. All four structures reveal three tetra-coordinated Zn(2+)-binding sites (ZBS 1-3) per monomer, plus a fourth site (ZBS 4) involving amino acid residues from a symmetry-related tetramer that is not visible in solution by NMR.Zn(2+) binding perturbs loop E-alpha-helix-loop F, the region involved in holo-retinol-binding protein (holo-RBP) recognition, mainly at acidic pH; TTR affinity for holo-RBP decreases similar to 5-fold in the presence of Zn(2+). Interestingly, this same region is disrupted in the crystal structure of the amyloidogenic intermediate of TTR formed at acidic pH in the absence of Zn(2+). HNCO and HNCA experiments performed in solution at pH 7.5 revealed that upon Zn(2+) binding, although the alpha-helix persists, there are perturbations in the resonances of the residues that flank this region, suggesting an increase in structural flexibility. While stability of the monomer of TTR decreases in the presence of Zn(2+), which is consistent with the tertiary structural perturbation provoked by Zn(2+) binding, tetramer stability is only marginally affected by Zn(2+). These data highlight structural and functional roles of Zn(2+) in TTR-related amyloidoses, as well as in holo-RBP recognition and vitamin A homeostasis.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

DIAGNOSTIC TECHNIQUES OF LOCAL INFLUENCE IN SPATIAL ANALYSIS OF SOYBEAN YIELD

Modeling of spatial dependence structure, concerning geoestatistics approach, is an indispensable tool for fixing parameters that define this structure, applied on interpolation of values in places that are not sampled, by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations on sampled data. Thus, this trial aimed at using diagnostics techniques of local influence in spatial linear Gaussians models, applied at geoestatistics in order to evaluate sensitivity of maximum likelihood estimators and restrict maximum likelihood to small perturbations in these data. So, studies with simulated and experimental data were performed. Those results, obtained from the study of real data, allowed us to conclude that the presence of atypical values among the sampled data can have a strong influence on thematic maps, changing, therefore, the spatial dependence. The application of diagnostics techniques of local influence should be part of any geoestatistic analysis, ensuring that the information from thematic maps has better quality and can be used with greater security by farmers.

Structure and Calcium-Binding Activity of LipL32, the Major Surface Antigen of Pathogenic Leptospira sp.

Leptospixosis, a spirochaetal zoonotic disease caused by Leptospira, has been recognized as an important emerging infectious disease. LipL32 is the major exposed outer membrane protein found exclusively in pathogenic leptospires, where it accounts for up to 75% of the total outer membrane proteins. It is highly immunogenic, and recent studies have implicated LipL32 as an extracellular matrix binding protein, interacting with collagens, fibronectin, and laminin. In order to better understand the biological role and the structural requirements for the function of this important lipoprotein, we have determined the 2.25-angstrom-resolution structure of recombinant LipL32 protein corresponding to residues 21-272 of the wild-type protein (LipL32(21-272)). The LipL32(21-272) monomer is made of a jelly-roll fold core from which several peripheral secondary structures protrude. LipL32(21-272) is structurally similar to several other jelly-roll proteins, some of which bind calcium ions and extracellular matrix proteins. Indeed, spectroscopic data (circular dichroism, intrinsic tryptophan fluorescence, and extrinsic 1-amino-2-naphthol-4-sulfonic acid fluorescence) confirmed the calcium-binding properties of LipL32(21-272). Ca(2+) binding resulted in a significant increase in the thermal stability of the protein, and binding was specific for Ca(2+) as no structural or stability perturbations were observed for Mg(2+), Zn(2+), or Cu(2+). Careful examination of the crystal lographic structure suggests the locations of putative regions that could mediate Ca(2+) binding as well as binding to other interacting host proteins, such as collagens, fibronectin, and lamixidn. (C) 2009 Elsevier Ltd. All rights reserved.

Mg(2+) Ions Bind at the C-Terminal Region of Skeletal Muscle alpha-Tropomyosin

Tropomyosin (Tm) is a dimeric coiled-coil protein that polymerizes through head-to-tail interactions. These polymers bind along actin filaments and play an important role in the regulation of muscle contraction. Analysis of its primary structure shows that Tm is rich in acidic residues, which are clustered along the molecule and may from sites for divalent cation binding. In a previous study, we showed that the Mg(2+)-induced increase in stability of the C-terminal half of Tin is sensitive to imitations near the C-terminus. In the present report, we study the interaction between Mg(2+) and full-length Tin and smaller fragments corresponding to the last 65 and 26 Tin residues. Although the smaller Tin peptide (Tm(259-284(W269))) is flexible and to large extent unstructured, the larger Tm(220-284(W269)) fragments forms a coiled coil in solution whose stability increases significantly in the presence of Mg(2+). NMR analysis shows thin Mg(2+) induces chemical shift perturbations in both Tm(220-284(W269)) and Tm(259-284(W269)) in the vicinity of His276, in which are located several negatively charged residues. (C) 2009 Wiley Periodicals, Inc. Biopolymers 91: 583-590, 2009.