scholarly journals Curvature, cones and characteristic numbers

2013 ◽  
Vol 155 (1) ◽  
pp. 13-37 ◽  
Author(s):  
MICHAEL ATIYAH ◽  
CLAUDE LEBRUN
Keyword(s):  
Einstein Metrics ◽  
Cone Angle ◽  
Gravitational Instantons ◽  
Characteristic Numbers ◽  
Cone Singularity ◽  
Integral Formulae ◽  
Do So

AbstractWe study Einstein metrics on smooth compact 4-manifolds with an edge-cone singularity of specified cone angle along an embedded 2-manifold. To do so, we first derive modified versions of the Gauss–Bonnet and signature theorems for arbitrary Riemannian 4-manifolds with edge-cone singularities, and then show that these yield non-trivial obstructions in the Einstein case. We then use these integral formulæ to obtain interesting information regarding gravitational instantons which arise as limits of such edge-cone manifolds.

scholarly journals INTEGRAL FORMULAE ON QUASI-EINSTEIN MANIFOLDS AND APPLICATIONS

2011 ◽  
Vol 54 (1) ◽  
pp. 213-223 ◽  
Author(s):  
A. BARROS ◽  
E. RIBEIRO
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Ricci Tensor ◽  
Einstein Metrics ◽  
Gradient Field ◽  
Ricci Solitons ◽  
Einstein Manifolds ◽  
De Rham ◽  
Integral Formulae

AbstractThe aim of this paper is to extend for the m-quasi-Einstein metrics some integral formulae obtained in [1] (C. Aquino, A. Barros and E. Ribeiro Jr., Some applications of the Hodge-de Rham decomposition to Ricci solitons, Results Math. 60 (2011), 245–254) for Ricci solitons and derive similar results achieved there. Moreover, we shall extend the m-Bakry-Emery Ricci tensor for a vector field X on a Riemannian manifold instead of a gradient field ∇f, in order to obtain some results concerning these manifolds that generalize their correspondents to a gradient field.

scholarly journals Positivity in Kähler–Einstein theory

2015 ◽  
Vol 159 (2) ◽  
pp. 321-338 ◽  
Author(s):  
GABRIELE DI CERBO ◽  
LUCA F. DI CERBO
Keyword(s):  
Scalar Curvature ◽  
Einstein Metrics ◽  
Cone Angle ◽  
Positive Scalar Curvature ◽  
Einstein Theory ◽  
Uniform Bounds ◽  
Projective Varieties ◽  
Edge Type ◽  
Negatively Curved ◽  
Kähler Einstein Metrics

AbstractTian initiated the study of incomplete Kähler–Einstein metrics on quasi–projective varieties with cone-edge type singularities along a divisor, described by the cone-angle 2π(1-α) for α∈ (0, 1). In this paper we study how the existence of such Kähler–Einstein metrics depends on α. We show that in the negative scalar curvature case, if such Kähler–Einstein metrics exist for all small cone-angles then they exist for every α∈((n+1)/(n+2), 1), wherenis the dimension. We also give a characterisation of the pairs that admit negatively curved cone-edge Kähler–Einstein metrics with cone angle close to 2π. Again if these metrics exist for all cone-angles close to 2π, then they exist in a uniform interval of angles depending on the dimension only. Finally, we show how in the positive scalar curvature case the existence of such uniform bounds is obstructed.

scholarly journals Kähler–Einstein metrics: From cones to cusps

2020 ◽  
Vol 2020 (759) ◽  
pp. 1-27
Author(s):  
Henri Guenancia
Keyword(s):  
Einstein Metrics ◽  
Boundary Behavior ◽  
Cone Angle ◽  
Kähler Manifold ◽  
Strong Sense ◽  
Kahler Manifold ◽  
Kähler Einstein Metrics ◽  
Compact Kähler Manifold

AbstractIn this note, we prove that on a compact Kähler manifold \hskip-0.569055pt{X}\hskip-0.569055pt carrying a smooth divisor D such that {K_{X}+D} is ample, the Kähler–Einstein cusp metric is the limit (in a strong sense) of the Kähler–Einstein conic metrics when the cone angle goes to 0. We further investigate the boundary behavior of those and prove that the rescaled metrics converge to a cylindrical metric on {\mathbb{C}^{*}\times\mathbb{C}^{n-1}}.

scholarly journals Diffraction by a quarter–plane. Analytical continuation of spectral functions

2018 ◽  
Vol 72 (1) ◽  
pp. 51-86 ◽  
Author(s):  
R C Assier ◽  
A V Shanin
Keyword(s):  
Complex Variables ◽  
Analytical Continuation ◽  
Hopf Equation ◽  
Spectral Functions ◽  
Riemann Manifold ◽  
3D Space ◽  
Quarter Plane ◽  
Integral Formulae ◽  
Do So

Summary The problem of diffraction by a Dirichlet quarter-plane (a flat cone) in a 3D space is studied. The Wiener–Hopf equation for this case is derived and involves two unknown (spectral) functions depending on two complex variables. The aim of the present work is to construct an analytical continuation of these functions onto a well-described Riemann manifold and to study their behaviour and singularities on this manifold. In order to do so, integral formulae for analytical continuation of the spectral functions are derived and used. It is shown that the Wiener–Hopf problem can be reformulated using the concept of additive crossing of branch lines introduced in the article. Both the integral formulae and the additive crossing reformulation are novel and represent the main results of this work.

Holding replication studies to mainstream standards of evidence

2018 ◽  
Vol 41 ◽  
Author(s):  
Duane T. Wegener ◽  
Leandre R. Fabrigar
Keyword(s):  
Replication Studies ◽  
Replication Research ◽  
Standards Of Evidence ◽  
Do So

AbstractReplications can make theoretical contributions, but are unlikely to do so if their findings are open to multiple interpretations (especially violations of psychometric invariance). Thus, just as studies demonstrating novel effects are often expected to empirically evaluate competing explanations, replications should be held to similar standards. Unfortunately, this is rarely done, thereby undermining the value of replication research.

Electron Microscopy of a Herpesvirus Isolated from Marek's Disease in Duck and Chicken Embryo Fibroblast Cultures

1968 ◽  
Vol 26 ◽  
pp. 222-223 ◽  
Author(s):  
Keyvan Nazerian
Keyword(s):  
Inclusion Bodies ◽  
Chicken Embryo Fibroblast ◽  
Marek's Disease ◽  
Marek’S Disease ◽  
Duck Embryo Fibroblast ◽  
Multinucleated Cells ◽  
Viral Particles ◽  
Infected Cells ◽  
And Control ◽  
Do So

A herpes-like virus has been isolated from duck embryo fibroblast (DEF) cultures inoculated with blood from Marek's disease (MD) infected birds. Cultures which contained this virus produced MD in susceptible chickens while virus negative cultures and control cultures failed to do so. This and other circumstantial evidence including similarities in properties of the virus and the MD agent implicate this virus in the etiology of MD.Histochemical studies demonstrated the presence of DNA-staining intranuclear inclusion bodies in polykarocytes in infected cultures. Distinct nucleo-plasmic aggregates were also seen in sections of similar multinucleated cells examined with the electron microscope. These aggregates are probably the same as the inclusion bodies seen with the light microscope. Naked viral particles were observed in the nucleus of infected cells within or on the edges of the nucleoplasmic aggregates. These particles measured 95-100mμ, in diameter and rarely escaped into the cytoplasm or nuclear vesicles by budding through the nuclear membrane (Fig. 1). The enveloped particles (Fig. 2) formed in this manner measured 150-170mμ in diameter and always had a densely stained nucleoid. The virus in supernatant fluids consisted of naked capsids with 162 hollow, cylindrical capsomeres (Fig. 3). Enveloped particles were not seen in such preparations.

Debates in Dysphagia Management: How Do You Use Evidence-Based Practice in Your Dysphagia Patient Care?

2011 ◽  
Vol 20 (4) ◽  
pp. 121-123
Author(s):  
Jeri A. Logemann
Keyword(s):  
Decision Making ◽  
Patient Care ◽  
Clinical Outcomes ◽  
Clinical Judgment ◽  
Clinical Decision Making ◽  
Evidence Based Practice ◽  
Clinical Decision ◽  
Evidence Based ◽  
Clinical Method ◽  
Do So

Evidence-based practice requires astute clinicians to blend our best clinical judgment with the best available external evidence and the patient's own values and expectations. Sometimes, we value one more than another during clinical decision-making, though it is never wise to do so, and sometimes other factors that we are unaware of produce unanticipated clinical outcomes. Sometimes, we feel very strongly about one clinical method or another, and hopefully that belief is founded in evidence. Some beliefs, however, are not founded in evidence. The sound use of evidence is the best way to navigate the debates within our field of practice.

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