A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Dual descriptions of spin-two massive particles in D=2+1 via master actions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gleichmäßig dünne Basen zweiter Ordnung

Eine Menge B nicht negativer ganzer Zahlen heißt Basis h-ter Ordnung, wenn jede nicht negative ganze Zahl Summe von höchstens h Elementen von B ist. Eine der großen Fragen der additiven Zahlentheorie ist die nach der effektivsten Basis h-ter Ordnung für ein gegebenes h>=2. Im Fokus des Interesses steht dabei der immer noch offene Fall h=2. Bezeichnet B(x) die Anzahl der Elemente b aus B mit 0= af(x), wobei f die Wurzelfunktion bezeichne. Andererseits gibt es Basen B zweiter Ordnung mit B(x) <= cf(x). Daher kann man den Limes superior S(B), den Limes inferior s(B) sowie im Falle der Existenz den Limes d(B) des Quotienten B(x) / f(x) als Dichtefunktionen von Basen zweiter Ordnung betrachten. J. W. S. Cassels konstruierte 1957 eine Basis C zweiter Ordnung mit d(C)=5,196…. G. Hofmeister gab 2001 eine Basis H zweiter Ordnung mit asymptotischer Wurzeldichte d(H)=4,638… an. In der vorliegenden Arbeit wird eine Basis S zweiter Ordnung mit asymptotischer Wurzeldichte d(S)=3,464… konstruiert. Darüber hinaus wird für die von J. W. S. Cassels, für die von G. Hofmeister und für die in dieser Arbeit verwendete Klasse von Basen zweiter Ordnung gezeigt, dass die asymptotische Wurzeldichte innerhalb der jeweiligen Klasse nicht mehr zu verbessern ist. Bisher war die Frage nach möglichen Verbesserungen innerhalb der jeweiligen Konstruktionsprinzipien offen geblieben.

Resummation of infrared divergences in the free energy of spin-two fields

We derive a closed form expression for the sum of all the infrared divergent contributions to the free energy of a gas of gravitons. An important ingredient of our calculation is the use of a gauge fixing procedure such that the graviton propagator becomes both traceless and transverse. This has been shown to be possible, in a previous work, using a general gauge fixing procedure, in the context of the lowest order expansion of the Einstein-Hilbert action, describing noninteracting spin-two fields. In order to encompass the problems involving thermal loops, such as the resummation of the free energy, in the present work, we have extended this procedure to the situations when the interactions are taken into account.

Magnetic, thermal and spectral characterization of 2,6-dimethoxybenzoates of Co(II), Ni(II) and Cu(II)

The complexes of 2,6-dimethoxybenzoic acid anion with ions of Co(II), Ni(II), and Cu(II) have been synthesized as polycrystalline solids, and characterized by elemental analysis, spectroscopy, magnetic studies, and also by X-ray diffraction and thermogravimetric measurements. The analysed complexes have following colours: pink for Co(II), green for Ni(II), and blue for Cu(II) compounds. The carboxylate group binds as monodentate, and bidentate bridging and chelating ligands. On heating in air to 1173 K the complexes decompose in four, three or two steps. At first, they dehydrate in one or two steps to anhydrous salts, that next decompose to oxides of the respective metals. The solubility of the investigated dimethoxybenzoates in water at 293 K is of the order of 10-2 mol/dm3. Their magnetic moments were determined in the temperature range of 76-303 K. The results reveal the compounds of Co(II) and Ni(II) to be high-spin complexes and that of Cu(II) to form dimer.

Lag-1 sparing in the attentional blink: benefits and costs of integrating two events into a single episode

When people monitor a visual stream of rapidly presented stimuli for two targets (T1 and T2), they often miss T2 if it falls into a time window of about half a second after T1 onset-the attentional blink. However, if T2 immediately follows T1, performance is often reported being as good as that at long lags-the so-called Lag-1 sparing effect. Two experiments investigated the mechanisms underlying this effect. Experiment 1 showed that, at Lag 1, requiring subjects to correctly report both identity and temporal order of targets produces relatively good performance on T2 but relatively bad performance on T1. Experiment 2 confirmed that subjects often confuse target order at short lags, especially if the two targets are equally easy to discriminate. Results suggest that, if two targets appear in close succession, they compete for attentional resources. If the two competitors are of unequal strength the stronger one is more likely to win and be reported at the expense of the other. If the two are equally strong, however, they will often be integrated into the same attentional episode and thus get both access to attentional resources. But this comes with a cost, as it eliminates information about the targets' temporal order.

Configurational preferences of two 1,2-diamine adducts of bis(1-(2-thienyl)-4,4,4-trifluoro-1,3-butanedionato)cobalt(II)

The preparation, the IR and ligand field spectra and the structures of the mixed-ligand addition compounds [(N,N-dimethyl-1,2-diaminoethane)bis(1-(2-thienyl)-4,4,4-trifluoro-1,3-butanedionato)cobalt(II)], [Co(thtf)2me2en], and [(N,N,N′,N′-tetramethyl-1,2-diaminoethane)bis(1-(2-thienyl)-4,4,4-trifluoro-1,3-butanedionato)cobalt(II)], [Co(thtf)2me4en], are reported. The structures were determined by single crystal X-ray diffraction analysis (monoclinic, space group P21/c, Z=4 with a=10.708(6), b=19.531(6), c=13.352(6) Å, β=111.64(10)°, R1=0.0642 and wR2=0.1719 for [Co(thtf)2(me2en)] and a=12.033(6), b=15.565(6), c=15.339(6) Å, β=92.57(6)°, R1=0.0612 and wR2=0.1504 for [Co(thtf)2me4en]). The structures are distorted octahedral and the shortest cobalt–cobalt separation distances are 5.388(2) Å in [Co(thtf)2me2en] and 8.675(3) Å in [Co(thtf)2me4en]. In both compounds the diamine molecules attain the gauche conformation. The U(Z,Z) conformation of the β-dione leads to a semi-chair conformation of the β-dionato chelate rings. The relative orientation of the groups attached to the β-dionato moiety depends on the extent of stereoelectronic effects the N-substitution of the diamine entails. In [Co(thtf)2me2en] the intraligand distance separating the trifluoromethyl carbon atoms is 5.281(18) Å while in [Co(thtf)2me2en] it increases to 8.338(9) Å. The cobalt–cobalt separation distance, the orientation of the chelate rings and the extent of N-substitution seem to affect hydrogen bonding. While in [Co(thtf)2me2en] inter- and intraligand hydrogen bonding is implicated, it is totally absent in [Co(thtf)2me4en].

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

ON THE DOUBLE NATURED SOLUTIONS OF THE TWO-TEMPERATURE EXTERNAL SOFT PHOTON COMPTONIZED ACCRETION DISKS

We have analyzed pair production in the innermost region of a two-temperature external soft photon Comptonized accretion disk. We have shown that, if the viscosity parameter is greater than a critical value alpha(c), the solution to the disk equation is double valued: one, advection dominated, and the other, radiation dominated. When alpha <= alpha(c), the accretion rate has to satisfy (m) over dot(1) <= (m) over dot <= (m) over dot(c) in order to have two steady-state solutions. It is shown that these critical parameters (m) over dot(1), (m) over dot(c) are functions of r, alpha, and theta(e), and alpha(c) is a function of r and theta(e). Depending on the combination of the parameters, the advection-dominated solution may not be physically consistent. It is also shown that the electronic temperature is maximum at the onset of the thermal instability, from which results this inner region. These solutions are stable against perturbations in the electron temperature and in the density of pairs.

Chromosome polymorphism in Astyanax fasciatus (Teleostei, Characidae). 2-Chromosomal location of a satellite DNA

Studies about composition of repetitive sequences and their chromosomal location have been helpful to evolutionary studies in many distinct organisms. In order to keep on assessing the possible relationships among different cytotypes of Astyanax fasciatus (Teleostei, Characiformes) in the Mogi-Guacu River (Sao Paulo State, Brazil), C-banding, chromomycin A 3 staining, and fluorescent in situ hybridization with a repetitive DNA sequence (As51) isolated from Astyanax scabripinnis were performed in the present work. The constitutive heterochromatin was distributed in terminal regions on long arms of submetacentric, subtelocentric, and acrocentric chromosomes and in the terminal region on short arms of a pair of submetacentric chromosomes in both standard cytotypes. This latter heterochromatic site was also GC-rich, as revealed by chromomycin A(3) staining, corresponding to the nucleolar organizer region (NOR), as shown by previous studies. The sites of the satellite As51 DNA were located in terminal regions on long arms of several chromosomes. Some variant karyotypic forms, which diverge from the two standard cytotypes, also presented distinctive chromosomes carrying As51 satellite DNA. It is possible that the standard 2n = 46 cytotype represents an invader population in the Mogi-Guacu River able to interbreed with the resident standard 2n = 48 cytotype. Therefore, the variant karyotypes would be related to a possible viable offspring, where complementary chromosomal rearrangements could favor new locations of the satellite DNA analyzed. Copyright (C) 2008 S. Karger AG, Basel

Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

On the relationship between a 2 x 2 matrix and second-order scalar spectral problems for integrable equations

A simple proof is given that a 2 x 2 matrix scheme for an inverse scattering transform method for integrable equations can be converted into the standard form of the second-order scalar spectral problem associated with the same equations. Simple formulae relating these two kinds of representation of integrable equations are established.

Study of exclusive two-photon production of W+W- in pp collisions at √s=7 TeV and constraints on anomalous quartic gauge couplings

A search for exclusive or quasi-exclusive W+W- production by photon-photon interactions, pp → p(*)W +W-p(*), at √s=7 TeV is reported using data collected by the CMS detector with an integrated luminosity of 5.05 fb-1. Events are selected by requiring a μ ±e∓ vertex with no additional associated charged tracks and dilepton transverse momentum p T(μ ±e∓) > 30 GeV. Two events passing all selection requirements are observed in the data, compared to a standard model expectation of 2.2 ± 0.4 signal events with 0.84 ± 0.15 background. The tail of the dilepton p T distribution is studied for deviations from the standard model. No events are observed with p T > 100 GeV. Model-independent upper limits are computed and compared to predictions involving anomalous quartic gauge couplings. The limits on the parameters α0,C W/λ2 with a dipole form factor and an energy cutoff Λcutoff = 500 GeV are of the order of 10-4. © 2013 CERN for the benefit of the CMS collaboration.