A Duality Exact Sequence for Legendrian Contact Homology

We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact homology CH_* which maps to singular homology. In particular, the sequence implies a duality between the kernel of the map (CH_*\to H_*) and the cokernel of the map (H_* \to CH^*). Furthermore, this duality is compatible with Poincare duality in L in the following sense: the Poincare dual of a singular class which is the image of a in CH_* maps to a class \alpha in CH^* such that \alpha(a)=1. The exact sequence generalizes the duality for Legendrian knots in Euclidean 3-space [24] and leads to a refinement of the Arnold Conjecture for double points of an exact Lagrangian admitting a Legendrian lift with linearizable contact homology, first proved in [6].Comment: 57 pages, 10 figures. Improved exposition and expanded analytic detai

The Minimal Length of a Lagrangian Cobordism between Legendrians

To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian Contact Homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee comments. More general statement in Proposition 3.3 and some reorganization at the end of Section

Stability of the magnetic Schr\"odinger operator in a waveguide

The spectrum of the Schr\"odinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also if the waveguide is bent eigenvalues will arise below the continuous spectrum. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schr\"odinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own

On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator in non-simply connected domains

We consider the Dirichlet Pauli operator in bounded connected domains in the plane, with a semi-classical parameter. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semi-classical parameter tends to zero and estimate this decay rate. This extends our results, discussing the results of a recent paper by Ekholm--Kova\v{r}\'ik--Portmann, to include also non-simply connected domains.Comment: 15 pages, 4 figure

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page

Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube

We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.Comment: 11 page

A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

Importance of correlation effects in hcp iron revealed by a pressure-induced electronic topological transition

We discover that hcp phases of Fe and Fe0.9Ni0.1 undergo an electronic topological transition at pressures of about 40 GPa. This topological change of the Fermi surface manifests itself through anomalous behavior of the Debye sound velocity, c/a lattice parameter ratio and M\"ossbauer center shift observed in our experiments. First-principles simulations within the dynamic mean field approach demonstrate that the transition is induced by many-electron effects. It is absent in one-electron calculations and represents a clear signature of correlation effects in hcp Fe

Effect of a reduction in glomerular filtration rate after nephrectomy on arterial stiffness and central hemodynamics: rationale and design of the EARNEST study

Background: There is strong evidence of an association between chronic kidney disease (CKD) and cardiovascular disease. To date, however, proof that a reduction in glomerular filtration rate (GFR) is a causative factor in cardiovascular disease is lacking. Kidney donors comprise a highly screened population without risk factors such as diabetes and inflammation, which invariably confound the association between CKD and cardiovascular disease. There is strong evidence that increased arterial stiffness and left ventricular hypertrophy and fibrosis, rather than atherosclerotic disease, mediate the adverse cardiovascular effects of CKD. The expanding practice of live kidney donation provides a unique opportunity to study the cardiovascular effects of an isolated reduction in GFR in a prospective fashion. At the same time, the proposed study will address ongoing safety concerns that persist because most longitudinal outcome studies have been undertaken at single centers and compared donor cohorts with an inappropriately selected control group.<p></p> Hypotheses: The reduction in GFR accompanying uninephrectomy causes (1) a pressure-independent increase in aortic stiffness (aortic pulse wave velocity) and (2) an increase in peripheral and central blood pressure.<p></p> Methods: This is a prospective, multicenter, longitudinal, parallel group study of 440 living kidney donors and 440 healthy controls. All controls will be eligible for living kidney donation using current UK transplant criteria. Investigations will be performed at baseline and repeated at 12 months in the first instance. These include measurement of arterial stiffness using applanation tonometry to determine pulse wave velocity and pulse wave analysis, office blood pressure, 24-hour ambulatory blood pressure monitoring, and a series of biomarkers for cardiovascular and bone mineral disease.<p></p> Conclusions: These data will prove valuable by characterizing the direction of causality between cardiovascular and renal disease. This should help inform whether targeting reduced GFR alongside more traditional cardiovascular risk factors is warranted. In addition, this study will contribute important safety data on living kidney donors by providing a longitudinal assessment of well-validated surrogate markers of cardiovascular disease, namely, blood pressure and arterial stiffness. If any adverse effects are detected, these may be potentially reversed with the early introduction of targeted therapy. This should ensure that kidney donors do not come to long-term harm and thereby preserve the ongoing expansion of the living donor transplant program.<p></p&gt