On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. This condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range -- roughly speaking -- from being ``mildly infinite-type'' to very flat at the infinite-type points.Comment: Significant revisions made; simpler estimates; very mild strengthening of the hypotheses on Theorem 1.2 to get much stronger conclusions than in ver.1. To appear in Math. An

On the cohomology of pseudoeffective line bundles

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly positive, the prototype is the well known Nadel vanishing theorem, which is itself a generalized analytic version of the fundamental Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested here in the case where the curvature is merely semipositive in the sense of currents, and the base manifold is not necessarily projective. In this situation, one can still obtain interesting information on cohomology, e.g. a Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing theorem that depends on the concept of numerical dimension of a given pseudoeffective line bundle. The proof of these results depends in a crucial way on a general approximation result for closed (1,1)-currents, based on the use of Bergman kernels, and the related intersection theory of currents. Another important ingredient is the recent proof by Guan and Zhou of the strong openness conjecture. As an application, we discuss a structure theorem for compact K{\"a}hler threefolds without nontrivial subvarieties, following a joint work with F.Campana and M.Verbitsky. We hope that these notes will serve as a useful guide to the more detailed and more technical papers in the literature; in some cases, we provide here substantially simplified proofs and unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the Abel Symposium, Trondheim, July 201

Gunning-Narasimhan's theorem with a growth condition

Given a compact Riemann surface X and a point x_0 in X, we construct a holomorphic function without critical points on the punctured Riemann surface R = X - x_0 which is of finite order at the point x_0. This complements the result of Gunning and Narasimhan from 1967 who constructed a noncritical holomorphic function on every open Riemann surface, but without imposing any growth condition. On the other hand, if the genus of X is at least one, then we show that every algebraic function on R admits a critical point. Our proof also shows that every cohomology class in H^1(X;C) is represented as a de Rham class by a nowhere vanishing holomorphic one-form of finite order on the punctured surface X-x_0.Comment: J. Geom. Anal., in pres

Estimating the inelasticity with the information theory approach

Using the information theory approach, in both its extensive and nonextensive versions, we estimate the inelasticity parameter $K$ of hadronic reactions together with its distribution and energy dependence from $p\bar{p}$ and $pp$ data. We find that the inelasticity remains essentially constant in energy except for a variation around $K\sim 0.5$, as was originally expected.Comment: 14 pages, 8 figures. Misprints correcte

High mortality associated with tapeworm parasitism in geladas (Theropithecus gelada) in the Simien Mountains National Park, Ethiopia

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138266/1/ajp22684.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138266/2/ajp22684_am.pd

Complement in patients receiving maintenance hemodialysis: functional screening and quantitative analysis

<p>Abstract</p> <p>Background</p> <p>The complement system is vital for innate immunity and is implicated in the pathogenesis of inflammatory diseases and the mechanism of host defense. Complement deficiencies occasionally cause life-threatening diseases. In hemodialysis (HD) patients, profiles on complement functional activity and deficiency are still obscure. The objectives of the present study were to measure the functional complement activities of the classical pathway (CP), lectin pathway (LP) and alternative pathway (AP) using a novel method and consequently to elucidate the rates of deficiencies among HD patients.</p> <p>Methods</p> <p>In the present study, 244 HD patients at one dialysis center and 204 healthy controls were enrolled. Functional complement activities were measured simultaneously using the Wielisa^®-kit. The combination of the results of these three pathway activities allows us to speculate which candidate complement is deficient; subsequently, the deficient complement was determined.</p> <p>Results</p> <p>All three functional complement activities were significantly higher in the HD patients than in the control group (P < 0.01 for all cases). After identifying candidates in both groups with complement deficiencies using the Wielisa^®-kit, 16 sera (8.8%) with mannose-binding lectin (MBL) deficiency, 1 serum (0.4%) with C4 deficiency, 1 serum (0.4%) with C9 deficiency, and 1 serum (0.4%) with B deficiency were observed in the HD group, and 18 sera (8.8%) with MBL deficiency and 1 serum (0.5%) with B deficiency were observed in the control group. There were no significant differences in the 5-year mortality rate between each complement-deficient group and the complement-sufficient group among the HD patients.</p> <p>Conclusion</p> <p>This is the first report that profiles complement deficiencies by simultaneous measurement of functional activities of the three complement pathways in HD patients. Hemodialysis patients frequently suffer from infections or malignancies, but functional complement deficiencies do not confer additional risk of mortality.</p

Symmetries of Higher Dimensional Black Holes

We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension $n\geq 4$ contains a non-degenerate horizon with compact cross sections that are transverse to the stationarity generating Killing vector field then, for each connected component of the black hole's horizon, there is a Killing field which is tangent to the generators of the horizon. For the case of rotating black holes, the stationarity generating Killing field is not tangent to the horizon generators and therefore the isometry group of the spacetime is at least two dimensional. Our proof relies on significant extensions of our earlier work on the symmetries of spacetimes containing a compact Cauchy horizon, allowing now for non closed generators of the horizon.Comment: 57 page

Integrable Euler top and nonholonomic Chaplygin ball

We discuss the Poisson structures, Lax matrices, $r$-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio

Atomic-scale visualization of initial growth of homoepitaxial SrTiO3 thin film on an atomically ordered substrate

The initial homoepitaxial growth of SrTiO3 on a (\surd13\times\surd13) - R33.7{\deg}SrTiO3(001) substrate surface, which can be prepared under oxide growth conditions, is atomically resolved by scanning tunneling microscopy. The identical (\surd13\times\surd13) atomic structure is clearly visualized on the deposited SrTiO3 film surface as well as on the substrate. This result indicates the transfer of the topmost Ti-rich (\surd13\times\surd13) structure to the film surface and atomic-scale coherent epitaxy at the film/substrate interface. Such atomically ordered SrTiO3 substrates can be applied to the fabrication of atom-by-atom controlled oxide epitaxial films and heterostructures