Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

ON AMINO ACID AND CODON ASSIGNMENT IN ALGEBRAIC MODELS FOR THE GENETIC CODE

We give a list of all possible schemes for performing amino acid and codon assignments in algebraic models for the genetic code, which are consistent with a few simple symmetry principles, in accordance with the spirit of the algebraic approach to the evolution of the genetic code proposed by Hornos and Hornos. Our results are complete in the sense of covering all the algebraic models that arise within this approach, whether based on Lie groups/Lie algebras, on Lie superalgebras or on finite groups.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

A characterisation of the Hoffman-Wohlgemuth surfaces in terms of their symmetries

For an embedded singly periodic minimal surface (M) over tilde with genus rho >= 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman-Wohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces.

Electronic Structure of the Ground and Low-Lying Electronic States of MoB and MoB(+)

Multiconfigurational second-order perturbation theory (CASSCF//CASPT2) and quadruple-zeta ANO-RCC basis sets were employed to investigate the ground and low-lying electronic states of MoB and MoB(+). Spectroscopic constants, potential energy curves, wavefunctions, Mulliken population analyses, and ionization energies are given. The ground state of MoB is of X(6)Pi symmetry (R(e) = 1.968 angstrom, omega(e) = 664 cm(-1), and mu = 2.7 D), giving rise to a Omega = 7/2 ground state after including spin-orbit coupling. For MoB(+), the ground state is computed to be of X(7)Sigma(+) symmetry (R(e) = 2.224 angstrom, omega(e) = 141 cm(-1), and mu = 1.2 D), with an adiabatic ionization energy of 7.19 eV and a vertical one of 7.53 eV. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3362-3370, 2011

Electronic Structure and Chemical Bonding in the Lowest Electronic States of TcN

Multiconfiguration second-order perturbation theory, with the inclusion of relativistic effects and spin-orbit Coupling, was employed to investigate the nature of the ground and low-lying Lambda-S and Omega states of the TcN molecule. Spectroscopic constants, effective bond order, and potential energy curves for 13 low-lying Lambda-S states and 5 Omega states are given, The computed ground state of TcN is of Omega = 3 symmetry (R(e) = 1.605 angstrom and omega(e) = 1085 cm(-1)), originating mainly from the (3)Delta Lambda-S ground state. This result is contrasted with the nature of the ground state for other VIIB transtion-metal mononitrides, including X(3)Sigma(-) symmetry for MnN and Omega = 0(+) symmetry for ReN, derived also from a X(3)Sigma(-) state.

Structural Investigation of MFe(2)O(4) (M = Fe, Co) Magnetic Fluids

Ferrites of the type M(II)Fe(2)O(4) (M = Fe and Co) have been prepared by the traditional coprecipitation method. These ferrites were modified by the adsorption of fatty acids derived from soybean and castor oil and were then dispersed in cyclohexane, providing very stable magnetic fluids, readily usable in nonpolar media. The structural properties of the ferrites and modified ferrites as well as the magnetic fluids were characterized by XRD (X-ray powder diffraction), TEM (transmission electron microscopy), DRIFTS (diffusion reflectance infrared Fourier transform spectroscopy), FTMR (Fourier transform near-infrared), UV-vis, normal Raman spectroscopy, and surface-enhanced Raman scattering (SERS). XRD and TEM analysis have shown that the magnetic nanoparticles (nonmodified and modified) present diameters in the range of 10-15 nm. DRIFTS measurements have shown that the carboxylate groups of soybean and castor oil fatty acids adsorb on the ferrite surface, forming three different structures: a bridging bidentate, a bridging monodentate, and a bidentate chelate structure. The FTIR and Raman spectra of nonmodified Fe(3)O(4) and CoFe(2)O(4) nanoparticles have shown that the number of observed phonons is not compatible with the expected O(h)(7) symmetry, since IR-only active phonons were observed. in the Raman spectra and vice versa. SERS measurements of a CoFe(2)O(4) thin film on a SERS-active gold electrode at different applied potentials made possible the assignment of the signals near 550 and 630 cm(-1) to Co-O motions and the signals near 470 and 680 cm(-1) to Fe-O motions.

SYNTHESIS, CHARACTERIZATION AND THERMAL ANALYSIS OF 1:1 AND 2:3 LANTHANIDE(III) CITRATES

The synthesis and characterization of lanthanide(III) citrates with stoichiometries 1:1 and 2:3; [LnL center dot xH(2)O] and [Ln(2)(LH)(3)center dot 2H(2)O], Ln=La, Ce, Pr, Nd, Sm and Eu are reported. L stands for (C6O7H5)(3-) and LH for (C6O7H6)(2-). Infrared absorption spectra of both series evidence coordination of carboxylate groups through symmetric bridges or chelation. X-ray powder patterns show the amorphous character of [LnL center dot xH(2)O]. The compounds [Ln(2)LH(3)center dot 2H(2)O] are crystalline and isomorphous. Emission spectra of Eu compounds suggest C-2v symmetry for the coordination polyhedron of [LnL center dot xH(2)O] and C-4v for [Ln(2)(LH)(3)center dot 2H(2)O]. Thermal analyses (TG-DTG-DTA) were carried out for both series. The thermal analysis patterns of the two series are quite different and both fit in a 4-step model of thermal decomposition, with lanthanide oxides as final products.

Evidences for charge-transfer complex formation in the benzene adsorption on sulfated TiO2-a resonance Raman spectroscopy investigation

Benzene adsorbed on highly acidic sulfated TiO2 (S-TiO2) shows an intriguing resonance Raman (RR) effect, with excitation in the blue-violet region. There are very interesting spectral features: the preferential enhancement of the e(2g) mode (1595 cm(-1)) in relation to the a(1g) mode (ring-breathing mode at 995 cm(-1)) and the appearance of bands at 1565 and 1514 cm(-1). The band at 1565 cm(-1) is probably one of the components of the e(2g) split band, originally a doubly degenerate mode (8a, 8b) in neat benzene, and the band at 1514 cm(-1) is assigned to the 19a mode, an inactive mode in neat benzene. These facts indicate a lowering of symmetry in adsorbed benzene, which may be caused by a strong interaction between S-TiO2 and the benzene molecule with formation of a benzene to Ti (IV) charge transfer (CT) complex or by the formation of a benzene radical cation species. However, the RR spectra of the adsorbed benzene cannot be assigned to the benzene radical cation because the observed wavenumber of the ring-breathing mode does not have the value expected for this species. Moreover, it was found by ESR measurements that the amount of radicals was very low, and so it was concluded that a CT complex is the species that originates the RR spectra. The most favorable intensification of the band at 1595 cm(-1) in the RR spectra of benzene/S-TiO2 at higher excitation energy corroborates this hypothesis, as an absorption band in this energy range, assigned to a CT transition, is observed. Copyright (C) 2008 John Wiley & Sons, Ltd.

Leakage current, ferroelectric and structural properties in Pb(1-x)Ba(x)TiO(3) thin films prepared by chemical route

Single-phase perovskite structure Pb(1-x)Ba(x)TiO(3) thin films (x = 0.30, 0.50 and 0.70) were deposited on Pt/Ti/SiO(2)/Si substrates by the spin-coating technique. The dielectric study reveals that the thin films undergo a diffuse type ferroelectric phase transition, which shows a broad peak. An increase of the diffusivity degree with the increasing Barium contents was observed, and it was associated to a grain decrease in the studied composition range. The temperature dependence of the phonon frequencies was used to characterize the phase transition temperatures. Raman modes persist above tetragonal to cubic phase transition temperature, although all optical modes should be Raman inactive. The origin of these modes was interpreted in terms of breakdown of the local cubic symmetry by chemical disorder. The absence of a well-defined transition temperature and the presence of broad bands in some interval temperature above FE-PE phase transition temperature Suggested a diffuse type phase transition. This result corroborates the dielectric constant versus temperature data, which showed a broad ferroelectric phase transition in these thin films. The leakage Current density of the PBT thin films was studied at different temperatures and the data follow the Schottky emission model. Through this analysis the Schottky barrier height values 0.75, 0.53 and 0.34 eV were obtained to the PBT70, PBT50 and PBT30 thin films, respectively. (C) 2008 Elsevier Ltd. All rights reserved.

Towards to the trans-bromination of 2-styrylpyridine with a palladacycle intermediary and structure analysis for trans-1,2-dibromo-2-styrylpyridine

The simple halogenation of alkynes in conventional organic reactions gives a blend of cis and trans isomers. It is proposed then, a synthesis of stereospecific halogenation of alkynes in trans position, using palladacycle as intermediaries. The recrystallization of the compound obtained by bromination of 2-Styrylpyridine, with cyclepalladium intermediary results in a single crystal, which is subjected to X-ray diffraction. The crystal packing is established through weak interactions of three types. The first one is of the type pi x pi interactions, from symmetry operation, between the centroids. The second one is of the type C-X center dot center dot center dot pi interactions. And the last type is an anomalous intermolecular interaction between halogens, C-X center dot center dot center dot X-C, with bond distances smaller than the sum of the van der Waals radii. The conformation on the C=C bond is trans and the dihedral angle between the aromatic rings is (with esd approximate) 18.1(3)degrees. (C) 2010 Elsevier B.V. All rights reserved.

Stock Markets and Household Wealth: Can a Stock Market Crash Cause a Recession in The U.S. Economy?

Stock market wealth effects on the level of consumption in the United States economy have been constantly debated; there is evidence for arguments for and against its prominence and its symmetry. This paper seeks to investigate the strength of its negative effect by creating models to analyze unexpected shocks to the Standard and Poor's 500 index. First, a transmission mechanism between the stock market and GDP is established through the use of second-order vector autoregressive models. Following which, theory from the life cycle model and adaptations of previous researchers' models are used to create a structural model. This paper finds that stock market wealth effects are small, but important to consider, especially if markets are overpriced; this claim is corroborated by evidence from simulation of 'alternative scenarios' and the historical experiences of 1987 and 2001.

Vector Theory of Spontaneous Lorentz Violation

Classical electromagnetism predicts two massless propagating modes, which are known as the two polarizations of the photon. On the other hand, if the Lorentz symmetry of classical electromagnetism is spontaneously broken, the new theory will still have two massless Nambu-Goldstone modes resembling the photon. If the Lorentz symmetry is broken by a bumblebee potential that allows for excitations out of the minimum, then massive modes arise. Furthermore, in curved spacetime, such massive modes will be created through a process other than the usual Higgs mechanism because of the dependence of the bumblebee potential on both the vector field and the metric tensor. Also, it is found that these massive modes do not propagate due to the extra constraints.