8,047 research outputs found
Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension
In this article we prove an upper bound for the Lyapunov exponent
and a two-sided bound for the integrated density of states at an
arbitrary energy of random Schr\"odinger operators in one dimension.
These Schr\"odinger operators are given by potentials of identical shape
centered at every lattice site but with non-overlapping supports and with
randomly varying coupling constants. Both types of bounds only involve
scattering data for the single-site potential. They show in particular that
both and decay at infinity at least like
. As an example we consider the random Kronig-Penney model.Comment: 9 page
Cardiac arrest and COVID-19: inflammation, angiotensin-converting enzyme 2, and the destabilization of non-significant coronary artery disease-a case report.
The new β-coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) appears to exhibit cardiovascular pathogenicity through use of angiotensin-converting enzyme 2 (ACE2) for cell entry and the development of a major systemic inflammation. Furthermore, cardiovascular comorbidities increase susceptibility to SARS-CoV-2 infection and the development of a severe form of COronaVIrus Disease 2019 (COVID-19).
We describe the case of a COVID-19 patient whose inaugural presentation was a refractory cardiac arrest secondary to the destabilization of known, non-significant coronary artery disease. Patient was supported by venoarterial extracorporeal life support. After 12 h of support, cardiac function remained stable on low vasopressor support but the patient remained in a coma and brainstem death was diagnosed.
Myocardial injury is frequently seen among critically unwell COVID-19 patients and increases the risk of mortality. This case illustrates several potential mechanisms that are thought to drive the cardiac complications seen in COVID-19. We present the potential role of inflammation and ACE2 in the pathophysiology of COVID-19
Inverse Scattering for Gratings and Wave Guides
We consider the problem of unique identification of dielectric coefficients
for gratings and sound speeds for wave guides from scattering data. We prove
that the "propagating modes" given for all frequencies uniquely determine these
coefficients. The gratings may contain conductors as well as dielectrics and
the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page
Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum
Statistical -decay from highly excited states is determined by the
nuclear level density (NLD) and the -ray strength function
(SF). These average quantities have been measured for several nuclei
using the Oslo method. For the first time, we exploit the NLD and SF to
evaluate the -width in the energy region below the neutron binding
energy, often called the quasi-continuum region. The lifetimes of states in the
quasi-continuum are important benchmarks for a theoretical description of
nuclear structure and dynamics at high temperature. The lifetimes may also have
impact on reaction rates for the rapid neutron-capture process, now
demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure
Seismic tomography is locally ill-posed
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
The repulsion between localization centers in the Anderson model
In this note we show that, a simple combination of deep results in the theory
of random Schr\"odinger operators yields a quantitative estimate of the fact
that the localization centers become far apart, as corresponding energies are
close together
Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials
We study the spectral properties of discrete Schr\"odinger operators with
potentials given by primitive invertible substitution sequences (or by Sturmian
sequences whose rotation angle has an eventually periodic continued fraction
expansion, a strictly larger class than primitive invertible substitution
sequences). It is known that operators from this family have spectra which are
Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of
this set tends to as coupling constant tends to . Moreover, we
also show that at small coupling constant, all gaps allowed by the gap labeling
theorem are open and furthermore open linearly with respect to .
Additionally, we show that, in the small coupling regime, the density of states
measure for an operator in this family is exact dimensional. The dimension of
the density of states measure is strictly smaller than the Hausdorff dimension
of the spectrum and tends to as tends to
Molecular Cloning and Further Characterization of a Probable Plant Vacuolar Sorting Receptor
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