L^p boundedness of the wave operator for the one dimensional Schroedinger operator

Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the wave operators are bounded operators on L^p for all 1<p<\infty, provided (1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a resonance. For p=\infty we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.Comment: 26 page

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo

Multidimensional Borg-Levinson Theorem

We consider the inverse problem of the reconstruction of a Schr\"odinger operator on a unknown Riemannian manifold or a domain of Euclidean space. The data used is a part of the boundary $\Gamma$ and the eigenvalues corresponding to a set of impedances in the Robin boundary condition which vary on $\Gamma$. The proof is based on the analysis of the behaviour of the eigenfunctions on the boundary as well as in perturbation theory of eigenvalues. This reduces the problem to an inverse boundary spectral problem solved by the boundary control method

Monetary policy and indeterminacy after the 2001 slump

Abstract not availableFirmin Doko Tchatoka, Nicolas Groshenny, Qazi Haque, Mark Wede

Associations between fruit and vegetable intake and quality of life

Abstract Dysregulation of the immune response to microbiota is associated with inflammatory bowel disease (IBD), which can trigger intestinal fibrosis. MyD88 is a key component of microbiota signalling but its influence on intestinal fibrosis has not been clarified. Small bowel resections from donor-mice were transplanted subcutaneously into the neck of recipients C57BL/6 B6-MyD88tm1 Aki (MyD88−/−) and C57BL/6-Tg(UBC-green fluorescence protein (GFP))30Scha/J (GFP-Tg). Grafts were explanted up to 21 days after transplantation. Collagen layer thickness was determined using Sirius Red stained slides. In the mouse model of fibrosis collagen deposition and transforming growth factor-beta 1 (TGF-β1) expression was equal in MyD88+/+ and MyD88−/−, indicating that MyD88 was not essential for fibrogenesis. Matrix metalloproteinase (Mmp)9 expression was significantly decreased in grafts transplanted into MyD88−/− recipients compared to MyD88+/+ recipients (0.2 ± 0.1 vs. 153.0 ± 23.1, respectively, p < 0.05), similarly recruitment of neutrophils was significantly reduced (16.3 ± 4.5 vs. 25.4 ± 3.1, respectively, p < 0.05). Development of intestinal fibrosis appears to be independent of MyD88 signalling indicating a minor role of bacterial wall compounds in the process which is in contrast to published concepts and theories. Development of fibrosis appears to be uncoupled from acute inflammation

The Boundary Conditions for Point Transformed Electromagnetic Invisibility Cloaks

In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several cloaks located in different points in space. Our results apply in particular to the first order invisibility cloaks introduced by Pendry et al. and to the high order invisibility cloaks introduced by Hendi et al. and by Cai et al.. We identify the appropriate {\it cloaking boundary conditions} that the solutions of Maxwell equations have to satisfy at the outside, $\partial K_+$, and at the inside, $\partial K_-$, of the boundary of the cloaked object $K$. Namely, that the tangential components of the electric and the magnetic fields have to vanish at $\partial K_+$ -what is always true- and that the normal components of the curl of the electric and the magnetic fields have to vanish at $\partial K_-$. These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified $K$ and a radial current at $\partial K$ we verify by an explicit calculation that our {\it cloaking boundary conditions} are satisfied and that cloaking of active devices holds even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with active and passive devices contained in general anisotropic media, in particular to objects with active and passive devices contained inside general crystals.Comment: This final, published, version has been edited, comments have been adde

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

Lack of association between a biallelic polymorphism in the adducin gene and blood pressure in whites and African Americans

Population-based candidate gene association analyses are becoming increasingly popular as a result of a greater number of genes and gene polymorphisms having been identified for which some functional information is available. Because many biochemical and physiologic systems impact blood pressure regulation and hypertension susceptibility, many of these identified genes and polymorphisms are candidates for population-level association studies involving blood pressure levels or hypertension status. Recent studies have suggested that the α-adducin gene may harbor polymorphisms that influence blood pressure level. Therefore, we embarked on a study to test one such polymorphism in two large US samples: one from an urban African American population (Maywood, IL) and another from a rural white population (Tecumseh, MI). We used both family-based association tests and tests that consider the impact of additional measured factors beyond adducin gene variation on blood pressure levels. We found no evidence for a significant effect of the chosen adducin polymorphism on blood pressure variation in either sample. We also found no association between Adducin genotypes and antihypertensive use. These facts, together with similar findings in companion studies, suggest that the α-adducin gene polymorphism does not have a pronounced effect on blood pressure variation in the populations studied. This does not suggest, however, that the α-adducin gene does not have a role in blood pressure regulation and hypertension susceptibility. © 2000 American Journal of Hypertension, Ltd

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru