Witten's conjecture and Property P

Let K be a non-trivial knot in the 3-sphere and let Y be the 3-manifold obtained by surgery on K with surgery-coefficient 1. Using tools from gauge theory and symplectic topology, it is shown that the fundamental group of Y admits a non-trivial homomorphism to the group SO(3). In particular, Y cannot be a homotopy-sphere.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper7.abs.html Version 5: links correcte

Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of transformations: congruence transformations (which shuffle components of the multi-component wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray

ACE inhibition and glomerular repair: restructuring or regeneration?

In this issue of Kidney International, Andrea Remuzzi et al. convincingly demonstrate glomerular repair in spontaneous renal disease by ACE inhibition. These findings provoke questions about how ACE inhibition (or AT1R blockade) can on the one hand actually repair some diseased kidneys while on the other interfering with normal renal development or the recovery of other diseased kidneys

A q-analog of the ADHMN construction and axisymmetric multi-instantons

In the preceding paper (Phys. Lett. B463 (1999) 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.Comment: 11pages, Latex2e, to appear in Journal of Physics A: Mathematical and General as a `Special Issue/Difference Equations

Vortices on Hyperbolic Surfaces

It is shown that abelian Higgs vortices on a hyperbolic surface $M$ can be constructed geometrically from holomorphic maps $f:M \to N$, where $N$ is also a hyperbolic surface. The fields depend on $f$ and on the metrics of $M$ and $N$. The vortex centres are the ramification points, where the derivative of $f$ vanishes. The magnitude of the Higgs field measures the extent to which $f$ is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang--Mills fields on $\R^4$ is also given.Comment: Revised version: new section on four-dimensional interpretation of hyperbolic vortices added

Исследование закономерностей развития структурно-химической неоднородности в разнородном сварном соединении трубопроводного переходника

Данная работа посвящена исследованию структурно-химической неоднородности (СХН) трубопроводного переходника из разнородных сталей, выполненного аргонодуговой сваркой (АрДС). При помощи оптического микроскопа получены фотографии СХН и ее размеры. СХН выражается в появлении прослоек (карбидной и ферритной) с разным химическим составом. Приведены графики роста ширин прослоек от времени выдержки и температуры.This paper is devoted to the comparison of the structural and chemical inhomogeneity (SCI) of adapters made of dissimilar steels, made by tungsten insert gas (TIG). By means of optical microscope, photographs of the SCI and its dimensions were obtained. SCI is expressed in the appearance of interlayers (carbide and ferritic) with different chemical composition. Graphs of the growth of the widths of the interlayers from the time of exposure and temperature are given

Recognition of cognitive impairment and depressive symptoms in older patients with heart failure

INTRODUCTION: Cognitive impairment and depression in patients with heart failure (HF) are common comorbidities and are associated with increased morbidity, readmissions and mortality. Timely recognition of cognitive impairment and depression is important for providing optimal care. The aim of our study was to determine if these disorders were recognised by clinicians and, secondly, if they were associated with hospital admissions and mortality within 6 months’ follow-up. METHODS: Patients (aged ≥65 years) diagnosed with HF were included from the cardiology outpatient clinic of Gelre Hospitals. Cognitive status was evaluated with the Montreal Cognitive Assessment test (score ≤22). Depressive symptoms were assessed with the Geriatric Depression Scale (score >5). Patient characteristics were collected from electronic patient files. The clinician was blinded to the tests and asked to assess cognitive status and mood. RESULTS: We included 157 patients. Their median age was 79 years (65–92); 98 (62%) were male. The majority had New York Heart Association functional class II. Cognitive impairment was present in 56 (36%) patients. Depressive symptoms were present in 21 (13%) patients. In 27 of 56 patients (48%) cognitive impairment was not recognised by clinicians. Depressive symptoms were not recognised in 11 of 21 patients (52%). During 6 months’ follow-up 24 (15%) patients were readmitted for HF-related reasons and 18 (11%) patients died. There was no difference in readmission and mortality rate between patients with or without cognitive impairment and patients with or without depressive symptoms. CONCLUSION: Cognitive impairment and depressive symptoms were infrequently recognised during outpatient clinic visits

Khovanov homology is an unknot-detector

We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.Comment: 124 pages, 13 figure

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part