Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

Anomalous electron trapping by localized magnetic fields

We consider an electron with an anomalous magnetic moment g>2 confined to a plane and interacting with a nonzero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in the natural units is F\ge 0, the corresponding Pauli Hamiltonian has at least 1+[F] bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with B(r) = O(r^{-2-\delta}) correcting thus a recent result. Finally, we show that under mild regularity assumptions the existence can be proved for non-symmetric fields with tails as well.Comment: A LaTeX file, 12 pages; to appear in J. Phys. A: Math. Ge

Local erythropoietin and endothelial progenitor cells improve regional cardiac function in acute myocardial infarction

<p>Abstract</p> <p>Background</p> <p>Expanded endothelial progenitor cells (eEPC) improve global left ventricular function in experimental myocardial infarction (MI). Erythropoietin beta (EPO) applied together with eEPC may improve regional myocardial function even further by anti-apoptotic and cardioprotective effects. Aim of this study was to evaluate intramyocardial application of eEPCs and EPO as compared to eEPCs or EPO alone in experimental MI.</p> <p>Methods and Results</p> <p>In vitro experiments revealed that EPO dosed-dependently decreased eEPC and leukocyte apoptosis. Moreover, in the presence of EPO mRNA expression in eEPC of proangiogenic and proinflammatory mediators measured by TaqMan PCR was enhanced. Experimental MI was induced by ligation and reperfusion of the left anterior descending coronary artery of nude rats (n = 8-9). After myocardial transplantation of eEPC and EPO CD68+ leukocyte count and vessel density were enhanced in the border zone of the infarct area. Moreover, apoptosis of transplanted CD31 + TUNEL + eEPC was decreased as compared to transplantation of eEPCs alone. Regional wall motion of the left ventricle was measured using Magnetic Resonance Imaging. After injection of eEPC in the presence of EPO regional wall motion significantly improved as compared to injection of eEPCs or EPO alone.</p> <p>Conclusion</p> <p>Intramyocardial transplantation of eEPC in the presence of EPO during experimental MI improves regional wall motion. This was associated with an increased local inflammation, vasculogenesis and survival of the transplanted cells. Local application of EPO in addition to cell therapy may prove beneficial in myocardial remodeling.</p

Development of the self-modulation instability of a relativistic proton bunch in plasma

Self-modulation is a beam–plasma instability that is useful to drive large-amplitude wakefields with bunches much longer than the plasma skin depth. We present experimental results showing that, when increasing the ratio between the initial transverse size of the bunch and the plasma skin depth, the instability occurs later along the bunch, or not at all, over a fixed plasma length because the amplitude of the initial wakefields decreases. We show cases for which self-modulation does not develop, and we introduce a simple model discussing the conditions for which it would not occur after any plasma length. Changing bunch size and plasma electron density also changes the growth rate of the instability. We discuss the impact of these results on the design of a particle accelerator based on the self-modulation instability seeded by a relativistic ionization front, such as the future upgrade of the Advanced WAKefield Experiment

Edge Resonance in an Elastic Semi-Strip

. We study the elasticity operator in a semi-strip subject to free boundary conditions. In the case of zero Poisson ratio we prove the existence of a positive eigenvalue embedded in the essential spectrum. Physically, the eigenvalue corresponds to a &quot;trapped mode&quot;, that is, a harmonic oscillation of the semi-strip localized near the edge. This effect, known in mechanics as the &quot;edge resonance&quot;, has been extensively studied numerically and experimentally. Our result provides a mathematical justification. 1. Introduction In this paper we study a particular self-adjoint operator A with spectrum oe(A) = [0; +1) and prove the existence of a positive eigenvalue e . Our proof is based on the use of certain symmetries of A which allow us to identify suitable invariant subspaces. The crucial step is to choose an invariant subspace in such a way that the restriction of A to this subspace has essential spectrum separated from zero. Then the existence of an eigenvalue below this essential spectr..

Untersuchung des - und Teilchenzerfalls von Hochspinzustaenden im Al

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Molecuolar bridges between biochemistry and polymer chemistry

Abstract onl

Molecuolar bridges between biochemistry and polymer chemistry

Abstract onl