95 research outputs found
The band spectrum of the periodic airy-schrodinger operator on the real line
We introduce the periodic Airy-Schr\"odinger operator and we study its band
spectrum. This is an example of an explicitly solvable model with a periodic
potential which is not differentiable at its minima and maxima. We define a
semiclassical regime in which the results are stated for a fixed value of the
semiclassical parameter and are thus estimates instead of asymptotic results.
We prove that there exists a sequence of explicit constants, which are zeroes
of classical functions, giving upper bounds of the semiclassical parameter for
which the spectral bands are in the semiclassical regime. We completely
determine the behaviour of the edges of the first spectral band with respect to
the semiclassical parameter. Then, we investigate the spectral bands and gaps
situated in the range of the potential. We prove precise estimates on the
widths of these spectral bands and these spectral gaps and we determine an
upper bound on the integrated spectral density in this range. Finally, in the
semiclassical regime, we get estimates of the edges of every spectral bands and
thus of the widths of every spectral bands and spectral gaps
A matrix-valued point interactions model
We study a matrix-valued Schr\"odinger operator with random point
interactions. We prove the absence of absolutely continuous spectrum for this
operator by proving that away from a discrete set its Lyapunov exponents do not
vanish. For this we use a criterion by Gol'dsheid and Margulis and we prove the
Zariski denseness, in the symplectic group, of the group generated by the
transfer matrices. Then we prove estimates on the transfer matrices which lead
to the H\"older continuity of the Lyapunov exponents. After proving the
existence of the integrated density of states of the operator, we also prove
its H\"older continuity by proving a Thouless formula which links the
integrated density of states to the sum of the positive Lyapunov exponents
Localization for a matrix-valued Anderson model
We study localization properties for a class of one-dimensional,
matrix-valued, continuous, random Schr\"odinger operators, acting on
L^2(\R)\otimes \C^N, for arbitrary . We prove that, under suitable
assumptions on the F\"urstenberg group of these operators, valid on an interval
, they exhibit localization properties on , both in the
spectral and dynamical sense. After looking at the regularity properties of the
Lyapunov exponents and of the integrated density of states, we prove a Wegner
estimate and apply a multiscale analysis scheme to prove localization for these
operators. We also study an example in this class of operators, for which we
can prove the required assumptions on the F\"urstenberg group. This group being
the one generated by the transfer matrices, we can use, to prove these
assumptions, an algebraic result on generating dense Lie subgroups in
semisimple real connected Lie groups, due to Breuillard and Gelander. The
algebraic methods used here allow us to handle with singular distributions of
the random parameters
H\"older continuity of the IDS for matrix-valued Anderson models
We study a class of continuous matrix-valued Anderson models acting on
L^{2}(\R^{d})\otimes \C^{N}. We prove the existence of their Integrated
Density of States for any and . Then for and for
arbitrary , we prove the H\"older continuity of the Integrated Density of
States under some assumption on the group generated by the
transfer matrices associated to our models. This regularity result is based
upon the analoguous regularity of the Lyapounov exponents associated to our
model, and a new Thouless formula which relates the sum of the positive
Lyapounov exponents to the Integrated Density of States. In the final section,
we present an example of matrix-valued Anderson model for which we have already
proved, in a previous article, that the assumption on the group
is verified. Therefore the general results developed here can be applied to
this model
Localization Properties of the Chalker-Coddington Model
The Chalker Coddington quantum network percolation model is numerically
pertinent to the understanding of the delocalization transition of the quantum
Hall effect. We study the model restricted to a cylinder of perimeter 2M. We
prove firstly that the Lyapunov exponents are simple and in particular that the
localization length is finite; secondly that this implies spectral
localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov
exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the
Lyapunov spectrum and finiteness of the localization length are proven. To
appear in Annales Henri Poincar
Fatigue Life Prediction of Welded Box Structures
The objective of this study is to predict fatigue
life of metal welded boxes. Experimental results
of fatigue life are satisfactory predicted using
an analytical scheme based on the
volumetric approach.Проведено прогнозирование усталостной долговечности сварных коробчатых конструкций.
Результаты расчета усталостной долговечности с использованием аналитической схемы,
базирующейся на объемном методе, хорошо согласуются с соответствующими экспериментальными
данными.Проведено прогнозування довговічності зварних коробчастих конструкцій
від утомленості. Результати розрахунку довговічності від утомленості з
використанням аналітичної схеми, що базується на об’ємному методі, добре
узгоджуються з відповідними експериментальними даними
Cystatin C: A Candidate Biomarker for Amyotrophic Lateral Sclerosis
Amyotrophic lateral sclerosis (ALS) is a fatal neurologic disease characterized by progressive motor neuron degeneration. Clinical disease management is hindered by both a lengthy diagnostic process and the absence of effective treatments. Reliable panels of diagnostic, surrogate, and prognostic biomarkers are needed to accelerate disease diagnosis and expedite drug development. The cysteine protease inhibitor cystatin C has recently gained interest as a candidate diagnostic biomarker for ALS, but further studies are required to fully characterize its biomarker utility. We used quantitative enzyme-linked immunosorbent assay (ELISA) to assess initial and longitudinal cerebrospinal fluid (CSF) and plasma cystatin C levels in 104 ALS patients and controls. Cystatin C levels in ALS patients were significantly elevated in plasma and reduced in CSF compared to healthy controls, but did not differ significantly from neurologic disease controls. In addition, the direction of longitudinal change in CSF cystatin C levels correlated to the rate of ALS disease progression, and initial CSF cystatin C levels were predictive of patient survival, suggesting that cystatin C may function as a surrogate marker of disease progression and survival. These data verify prior results for reduced cystatin C levels in the CSF of ALS patients, identify increased cystatin C levels in the plasma of ALS patients, and reveal correlations between CSF cystatin C levels to both ALS disease progression and patient survival
Congenic Mesenchymal Stem Cell Therapy Reverses Hyperglycemia in Experimental Type 1 Diabetes
OBJECTIVE - A number of clinical trials are underway to test whether mesenchymal stem cells (MSCs) are effective in treating various diseases, including type 1 diabetes. Although this cell therapy holds great promise, the optimal source of MSCs has yet to be determined with respect to major histocompatibility complex matching. Here, we examine this question by testing the ability of congenic MSCs, obtained from the NOR mouse strain, to reverse recent-onset type 1 diabetes in NOD mice, as well as determine the immunomodulatory effects of NOR MSCs in vivo. RESEARCH DESIGN AND METHODS - NOR MSCs were evaluated with regard to their in vitro immunomodulatory function in the context of autoreactive T-cell proliferation and dendritic cell (DC) generation. The in vivo effect of NOR MSC therapy on reversal of recent-onset hyperglycemia and on immunogenic cell subsets in NOD mice was also examined. RESULTS - NOR MSCs were shown to suppress diabetogenic T-cell proliferation via PD-L1 and to suppress generation of myeloid/inflammatory DCs predominantly through an IL-6-dependent mechanism. NOR MSC treatment of experimental type 1 diabetes resulted in long-term reversal of hyperglycemia, and therapy was shown to alter diabetogenic cytokine profile, to diminish T-cell effector frequency in the pancreatic lymph nodes, to alter antigen-presenting cell frequencies, and to augment the frequency of the plasmacytoid subset of DCs. CONCLUSIONS - These studies demonstrate the inimitable benefit of congenic MSC therapy in reversing experimental type 1 diabetes. These data should benefit future clinical trials using MSCs as treatment for type 1 diabetes
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