Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order

The spectral theory for linear autonomous neutral functional differential equations (FDE) yields explicit formulas for the large time behaviour of solutions. Our results are based on resolvent computations and Dunford calculus, applied to establish explicit formulas for the large time behaviour of solutions of FDE. We investigate in detail a class of two-dimensional systems of FDE. (C) 2009 Elsevier Inc. All rights reserved.

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our system remains oscillatory. (C) 2009 Elsevier Inc. All rights reserved.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

Shot Noise in a Spin-Diode Geometry

We apply the master equation technique to calculate shot noise in a system composed of single level quantum dot attached to a normal metal lead and to a ferromagnetic lead (NM-QD-FM). It is known that this system operates as a spin-diode, giving unpolarized currents for forward bias and polarized current for reverse bias. This effect is observed when only one electron can tunnel at a time through the dot, due to the strong intradot Coulomb interaction. We find that the shot noise also presents a signature of this spin-diode effect, with a super-Poissonian shot noise for forward and a sub-Poissonian shot noise for reverse bias voltages. The shot noise thus can provide further experimental evidence of the spin-rectification in the NM-QD-FM geometry.

Differential effects of TR ligands on hormone dissociation rates: Evidence for multiple ligand entry/exit pathways

Some nuclear receptor (NR) ligands promote dissociation of radiolabeled bound hormone from the buried ligand binding cavity (LBC) more rapidly than excess unlabeled hormone itself This result was interpreted to mean that challenger ligands bind allosteric sites on the LBD to induce hormone dissociation, and recent findings indicate that ligands bind weakly to multiple sites on the LBD surface. Here we show, that a large fraction of thyroid hormone receptor (TR) ligands promote rapid dissociation (T(1/2) < 2 h) of , radiolabeled T(3) vs. T(3) (T(1/2), approximate to 5-7 h). We cannot discern relationships between this effect and ligand size, activity or affinity for TR beta. One ligand, GC-24, binds the TR LBC and (weakly) to the TR beta-LBD surface that mediates dimer/heterodimer interaction, but we cannot link this interaction to rapid T(3) dissociation. Instead, several lines of evidence suggest that the challenger ligand must interact with the buried LBC to promote rapid T(3) release. Since previous molecular dynamics simulations suggest that TR ligands leave the LBC by several routes, we propose that a subset of challenger ligands binds and stabilizes a partially unfolded intermediate state of TR that arises during T(3) release and that this effect enhances hormone dissociation. (C) 2009 Elsevier Ltd. All rights reserved.

An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet, together with learning management systems. These tools are implemented using the dynamic geometry software, iGeom, which has been used in a geometry course since 2004 and has a successful track record in the classroom. Empowered with these new features, iGeom simplifies teachers` tasks, solves non-trivial problems in student solutions and helps to increase student motivation by providing feedback in real time. (c) 2008 Elsevier Ltd. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Prediction of the economic activity from the short and long-term interest rate differential: new evidences in Chile and the United States of America cases

The purpose of this work is to verify the stability of the relationship between real activity and interest rate spread. The test is based on Chen (1988) and Osorio and Galea (2006). The analysis is applied to Chile and the United States, from 1980 to 1999. In general, in both cases the relationship was statistically significant in early 80s, but a break point is found in both countries during that decades, suggesting that the relationship depends on the monetary rule follow by the Central Bank.

Protein variation in blood-dwelling schistosome worms generated by differential splicing of micro-exon gene transcripts

Schistosoma mansoni is a well-adapted blood-dwelling parasitic helminth, persisting for decades in its human host despite being continually exposed to potential immune attack. Here, we describe in detail micro-exon genes (MEG) in S. mansoni, some present in multiple copies, which represent a novel molecular system for creating protein variation through the alternate splicing of short (<= 36 bp) symmetric exons organized in tandem. Analysis of three closely related copies of one MEG family allowed us to trace several evolutionary events and propose a mechanism for micro-exon generation and diversification. Microarray experiments show that the majority of MEGs are up-regulated in life cycle stages associated with establishment in the mammalian host after skin penetration. Sequencing of RT-PCR products allowed the description of several alternate splice forms of micro-exon genes, highlighting the potential use of these transcripts to generate a complex pool of protein variants. We obtained direct evidence for the existence of such pools by proteomic analysis of secretions from migrating schistosomula and mature eggs. Whole-mount in situ hybridization and immunolocalization showed that MEG transcripts and proteins were restricted to glands or epithelia exposed to the external environment. The ability of schistosomes to produce a complex pool of variant proteins aligns them with the other major groups of blood parasites, but using a completely different mechanism. We believe that our data open a new chapter in the study of immune evasion by schistosomes, and their ability to generate variant proteins could represent a significant obstacle to vaccine development.

Differential Acetyl Cholinesterase Inhibition by Volatile Oils from two Specimens of Marlierea racemosa (Myrtaceae) Collected from Different Areas of the Atlantic Rain Forest

The volatile oil composition and anti-acetyl cholinesterase activity were analyzed in two specimens of Marlierea racemosa growing in different areas of the Atlantic Rain Forest (Cananeia and Caraguatatuba, SP, Brazil). Component identifications were performed by GUMS and their acetyl cholinesterase inhibitory activity was measured through colorimetric analysis. The major constituent in both specimens was spathulenol (25.1 % in Cananeia and 31.9% in Caraguatatuba). However, the first one also presented monoterpenes (41.2%), while in the Carguatatuba plants, this class was not detected. The oils from the plants collected in Cananeia were able to inhibit the acetyl cholinesterase activity by LIP to 75%, but for oils from the other locality the maximal inhibition achieved was 35%. These results suggested that the monoterpenes are more effective in the inhibition of acetyl cholinesterase activity than sesquiterpenes as these compounds are present in higher amounts in the M. racemosa plants collected in Cananeia.

Understanding the Effect of Adsorption Geometry over Substrate Selectivity in the Surface-Enhanced Raman Scattering Spectra of Simazine and Atrazine

This paper studies the selectivity of Well-defined Au and Ag nanostructures as substrates for the SERS, (surface-enhanced Raman scattering) detection of simazine (6-chloro-N,N`-diethyl-1,3,5-triazine-2,4-diamine) and atrazine (6-chloro-N-ethyl-N`-isopropyl-1,3,5-triazine-2,4-diamine). Our data showed that simazine and atrazine displayed similar SERS spectra when the Au was employed as substrate. Conversely, distinct SERS signatures were obtained upon the utilization of Ag substrates. Density functional theory (DFT) calculations and vibrational assignments suggested that, while simazine and atrazine adsorbed on Au via the N3 position of the triazine ring, simazine adsorbed on Ag via N3 and atrazine via N5. The results presented herein demonstrated that the adsorption geometry of analyte molecules can play a central role over substrate selectivity in SERS, which is particularly important in applications involving ultrasensitive analysis of mixtures containing structurally similar molecules.