Bounds for the points of spectral concentration of sturm-liouville problems

§1. Introduction. We consider the spectral function ρα(λ) associated with the Sturm–Liouville equation with the boundary conditio

The spectral function for Sturm-Liouville problems where the potential is of Wigner-von Neumann type or slowly decaying

We consider the linear, second-order, differential equation (∗) with the boundary condition (∗∗) We suppose that q(x) is real-valued, continuously differentiable and that q(x)→0 as x→∞ with q∉L1[0,∞). Our main object of study is the spectral function ρα(λ) associated with () and (). We derive a series expansion for this function, valid for λ⩾Λ0 where Λ0 is computable and establish a Λ1, also computable, such that () and () with α=0, have no points of spectral concentration for λ⩾Λ1. We illustrate our results with examples. In particular we consider the case of the Wigner–von Neumann potential

Higher derivatives of spectral functions associated with one-dimensional schrodinger operators

We investigate the existence and asymptotic behaviour of higher derivatives of the spectral function in the context of one-dimensional Schr¨odinger operators on the half-line with integrable potentials. In particular, we identify sufficient conditions on the potential for the existence and continuity of the n-th derivative, and outline a systematic procedure for estimating numerical upper bounds for the turning points of such derivatives. Explicit worked examples illustrate the development and application of the theory

Large-scale Bright Fronts in the Solar Corona: A Review of "EIT waves"

``EIT waves" are large-scale coronal bright fronts (CBFs) that were first observed in 195 \AA\ images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the \emph{Solar and Heliospheric Observatory (SOHO)}. Commonly called ``EIT waves", CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100--700 km s$^{-1}$ with front widths of 50-100 Mm. As their speed is greater than the quiet coronal sound speed ($c_s\leq$200 km s$^{-1}$) and comparable to the local Alfv\'{e}n speed ($v_A\leq$1000 km s$^{-1}$), they were initially interpreted as fast-mode magnetoacoustic waves ($v_{f}=(c_s^2 + v_A^2)^{1/2}$). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.Comment: 34 pages, 19 figure

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations

Aharonov-Bohm Physics with Spin II: Spin-Flip Effects in Two-dimensional Ballistic Systems

We study spin effects in the magneto-conductance of ballistic mesoscopic systems subject to inhomogeneous magnetic fields. We present a numerical approach to the spin-dependent Landauer conductance which generalizes recursive Green function techniques to the case with spin. Based on this method we address spin-flip effects in quantum transport of spin-polarized and -unpolarized electrons through quantum wires and various two-dimensional Aharonov-Bohm geometries. In particular, we investigate the range of validity of a spin switch mechanism recently found which allows for controlling spins indirectly via Aharonov-Bohm fluxes. Our numerical results are compared to a transfer-matrix model for one-dimensional ring structures presented in the first paper (Hentschel et al., submitted to Phys. Rev. B) of this series.Comment: 29 pages, 15 figures. Second part of a series of two article

On the Nature and Genesis of EUV Waves: A Synthesis of Observations from SOHO, STEREO, SDO, and Hinode

A major, albeit serendipitous, discovery of the SOlar and Heliospheric Observatory mission was the observation by the Extreme Ultraviolet Telescope (EIT) of large-scale Extreme Ultraviolet (EUV) intensity fronts propagating over a significant fraction of the Sun's surface. These so-called EIT or EUV waves are associated with eruptive phenomena and have been studied intensely. However, their wave nature has been challenged by non-wave (or pseudo-wave) interpretations and the subject remains under debate. A string of recent solar missions has provided a wealth of detailed EUV observations of these waves bringing us closer to resolving their nature. With this review, we gather the current state-of-art knowledge in the field and synthesize it into a picture of an EUV wave driven by the lateral expansion of the CME. This picture can account for both wave and pseudo-wave interpretations of the observations, thus resolving the controversy over the nature of EUV waves to a large degree but not completely. We close with a discussion of several remaining open questions in the field of EUV waves research.Comment: Solar Physics, Special Issue "The Sun in 360",2012, accepted for publicatio

Global epidemiology of avian influenza A H5N1 virus infection in humans, 1997–2015: a systematic review of individual case data

Avian influenza A H5N1 viruses have caused many, typically severe, human infections since the first human case was reported in 1997. However, no comprehensive epidemiological analysis of global human cases of H5N1 from 1997 to 2015 exists. Moreover, few studies have examined in detail the changing epidemiology of human H5N1 cases in Egypt, especially given the outbreaks since November, 2014, which have the highest number of cases ever reported worldwide in a similar period. Data on individual patients were collated from different sources using a systematic approach to describe the global epidemiology of 907 human H5N1 cases between May, 1997, and April, 2015. The number of affected countries rose between 2003 and 2008, with expansion from east and southeast Asia, then to west Asia and Africa. Most cases (67·2%) occurred from December to March, and the overall case-fatality risk was 483 (53·5%) of 903 cases which varied across geographical regions. Although the incidence in Egypt has increased dramatically since November, 2014, compared with the cases beforehand, there were no significant differences in the fatality risk, history of exposure to poultry, history of patient contact, and time from onset to hospital admission in the recent cases

What is the Nature of EUV Waves? First STEREO 3D Observations and Comparison with Theoretical Models

One of the major discoveries of the Extreme ultraviolet Imaging Telescope (EIT) on SOHO were intensity enhancements propagating over a large fraction of the solar surface. The physical origin(s) of the so-called `EIT' waves is still strongly debated. They are considered to be either wave (primarily fast-mode MHD waves) or non-wave (pseudo-wave) interpretations. The difficulty in understanding the nature of EUV waves lies with the limitations of the EIT observations which have been used almost exclusively for their study. Their limitations are largely overcome by the SECCHI/EUVI observations on-board the STEREO mission. The EUVI telescopes provide high cadence, simultaneous multi-temperature coverage, and two well-separated viewpoints. We present here the first detailed analysis of an EUV wave observed by the EUVI disk imagers on December 07, 2007 when the STEREO spacecraft separation was $\approx 45^\circ$. Both a small flare and a CME were associated with the wave cadence, and single temperature and viewpoint coverage. These limitations are largely overcome by the SECCHI/EUVI observations on-board the STEREO mission. The EUVI telescopes provide high cadence, simultaneous multi-temperature coverage, and two well-separated viewpoints. Our findings give significant support for a fast-mode interpretation of EUV waves and indicate that they are probably triggered by the rapid expansion of the loops associated with the CME.Comment: Solar Physics, 2009, Special STEREO Issue, in pres

Dystrophin expression in muscle following gene transfer with a fully deleted ("Gutted") adenovirus is markedly improved by Trans-acting adenoviral gene products

Helper-dependent adenoviruses (HDAd) are Ad vectors lacking all or most viral genes. They hold great promise for gene therapy of diseases such as Duchenne muscular dystrophy (DMD), because they are less immunogenic than E1/E3-deleted Ad (first-generation Ad or FGAd) and can carry the full-length (Fl) dystrophin (dys) cDNA (12 kb). We have compared the transgene expression of a HDAd (HDAdCMVDysFl) and a FGAd (FGAdCMV-dys) in cell culture (HeLa, C2C12 myotubes) and in the muscle of mdx mice (the mouse model for DMD). Both vectors encoded dystrophin regulated by the same cytomegalovirus (CMV) promoter. We demonstrate that the amount of dystrophin expressed was significantly higher after gene transfer with FGAdCMV-dys compared to HDAdCMVDysFl both in vitro and in vivo. However, gene transfer with HDAdCMVDysFl in the presence of a FGAd resulted in a significant increase of dystrophin expression indicating that gene products synthesized by the FGAd increase, in trans, the amount of dystrophin produced. This enhancement occurred in cell culture and after gene transfer in the muscle of mdx mice and dystrophic golden retriever (GRMD) dogs, another animal model for DMD. The E4 region of Ad is required for the enhancement, because no increase of dystrophin expression from HDAdCMVDysFl was observed in the presence of an E1/E4-deleted Ad in vitro and in vivo. The characterization of these enhancing gene products followed by their inclusion into an HDAd may be required to produce sufficient dystrophin to mitigate the pathology of DMD by HDAd-mediated gene transfer