Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices

This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation frequency. The development of the solutions to this periodic differential equation can be described by a discrete map, where the matrix elements are given by the principal solutions for each cycle. Variations in the forcing strength and oscillation frequency lead to matrix elements that vary from cycle to cycle. This paper presents an analysis of the growth rates including cases where all of the cycles are highly unstable, where some cycles are near the stability border, and where the map would be stable in the absence of fluctuations. For all of these regimes, we provide expressions for the growth rates of the matrices that describe the solutions.Comment: 22 pages, 3 figure

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

We study the influence of ferromagnetic and antiferromagnetic bond defects on the ground-state energy of antiferromagnetic spin chains. In the absence of translational invariance, the energy spectrum of the full Hamiltonian is obtained numerically, by an iterative modification of the power algorithm. In parallel, approximate analytical energies are obtained from a local-bond approximation, proposed here. This approximation results in significant improvement upon the mean-field approximation, at negligible extra computational effort.Comment: 3 pages, 2 figures. Manuscript accepted by Journal of Magnetism and Magnetic Materials, special issue for LAWMMM 2007 conferenc

Light induced electron spin resonance in a-Ge:H

We report the observation of light-induced electron spin resonance (LESR) in amorphous hydrogenated germanium. Two new lines with zero crossings near g=2.01 and g=2.03 were detected and ascribed to electrons and holes in the conduction- and valence-band-tail states, respectively. The ratio between the LESR spin densities of both lines is approximately one, suggesting the absence of spin pairing, charge defect creation, or LESR of dangling bonds. The growth and decay spectra exhibit dispersive behavior with a dispersion parameter ∼0.5. The decay spectrum is best fit assuming bimolecular recombination. The LESR spin density depends weakly on the photogeneration rate as a sublinear power law

Neurology training around the world

Lancet Neurol. 2003 Sep;2(9):572-9. Neurology training around the world. Hooker J, Eccher M, Lakshminarayan K, Souza-Lima FC, Rejdak K, Kwiecinski H, Corea F, Lima JM. The National Hospital for Neurology and Neurosurgery, Queen Square, WC1N 3BG, London, UK. Comment in: Lancet Neurol. 2003 Oct;2(10):594; discussion 594

Thermodynamics of Chaplygin gas

We clarify thermodynamics of the Chaplygin gas by introducing the integrability condition. All thermal quantities are derived as functions of either volume or temperature. Importantly, we find a new general equation of state, describing the Chaplygin gas completely. We confirm that the Chaplygin gas could show a unified picture of dark matter and energy which cools down through the universe expansion without any critical point (phase transition).Comment: 5 pages, 4 figures, version "Accepted for publication in Astrophysics & Space Science

Bayesian Analysis and Constraints on Kinematic Models from Union SNIa

The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter (constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter (constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with the flat $\Lambda$CDM model. Analytical expressions and estimates for the deceleration and cosmic jerk parameters today ($q_0$ and $j_0$) and for the transition redshift ($z_t$) between a past phase of cosmic deceleration to a current phase of acceleration are given. All models characterize an accelerated expansion for the universe today and largely indicate that it was decelerating in the past, having a transition redshift around 0.5. The cosmic jerk is not strongly constrained by the present supernovae data. For the most realistic kinematic models the $1\sigma$ confidence limits imply the following ranges of values: $q_0\in[-0.96,-0.46]$, $j_0\in[-3.2,-0.3]$ and $z_t\in[0.36,0.84]$, which are compatible with the $\Lambda$CDM predictions, $q_0=-0.57\pm0.04$, $j_0=-1$ and $z_t=0.71\pm0.08$. We find that even very simple kinematic models are equally good to describe the data compared to the concordance $\Lambda$CDM model, and that the current observations are not powerful enough to discriminate among all of them.Comment: 13 pages. Matches published versio

Inflationary cosmology in the central region of String/M-theory moduli space

The "central" region of moduli space of M- and string theories is where the string coupling is about unity and the volume of compact dimensions is about the string volume. Here we argue that in this region the non-perturbative potential which is suggested by membrane instanton effects has the correct scaling and shape to allow for enough slow-roll inflation, and to produce the correct amplitude of CMB anisotropies. Thus, the well known theoretical obstacles for achieving viable slow-roll inflation in the framework of perturbative string theory are overcome. Limited knowledge of some generic properties of the induced potential is sufficient to determine the simplest type of consistent inflationary model and its predictions about the spectrum of cosmic microwave background anisotropies: a red spectrum of scalar perturbations, and negligible amount of tensor perturbations.Comment: 9 pages, 1 figur

1-[2-(4-methyl-7-coumarinyloxy)ethyl]-4-(5-{1-[2-(4-methyl-7-coumarinyloxy)ethyl]-1h-1, 2, 3-triazol-4-yl}pentyl)-1h-1, 2, 3-triazole

Nature often produces compounds with a high degree of symmetry to reduce structural information and complexity. Synthesis of identical twin drugs, through the linkage of two identical pharmacophoric entities, is a classical strategy to produce more potent and/or selective drugs. Herein, two units of the privileged core of the coumarin hymecromone were linked together using “click chemistry”. Synthesis of 1-[2-(4-Methyl-7-coumarinyloxy)ethyl]-4-(5-{1-[2-(4-methyl- 7-coumarinyloxy)ethyl]-1H-1, 2, 3-triazol-4-yl}pentyl)-1H-1, 2, 3-triazole was achieved by coupling of two identical units of an azido coumarin with a symmetrical alkine using copper(I)-catalyzed alkyne-azide cycloaddition reaction, in good yields and with complete regioselectivity. © 2016 by the authors; licensee MDPI, Basel, Switzerland.2016