A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Psychological Health, Well-Being, and the Mind-Heart-Body Connection A Scientific Statement From the American Heart Association

As clinicians delivering health care, we are very good at treating disease but often not as good at treating the person. The focus of our attention has been on the specific physical condition rather than the patient as a whole. Less attention has been given to psychological health and how that can contribute to physical health and disease. However, there is now an increasing appreciation of how psychological health can contribute not only in a negative way to cardiovascular disease (CVD) but also in a positive way to better cardiovascular health and reduced cardiovascular risk. This American Heart Association scientific statement was commissioned to evaluate, synthesize, and summarize for the health care community knowledge to date on the relationship between psychological health and cardiovascular health and disease and to suggest simple steps to screen for, and ultimately improve, the psychological health of patients with and at risk for CVD. Based on current study data, the following statements can be made: There are good data showing clear associations between psychological health and CVD and risk; there is increasing evidence that psychological health may be causally linked to biological processes and behaviors that contribute to and cause CVD; the preponderance of data suggest that interventions to improve psychological health can have a beneficial impact on cardiovascular health; simple screening measures can be used by health care providers for patients with or at risk for CVD to assess psychological health status; and consideration of psychological health is advisable in the evaluation and management of patients with or at risk for CVD

Measurements of differential production cross sections for a Z boson in association with jets in pp collisions at root s=8 TeV

Peer reviewe

Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

Peer reviewe

Search for black holes and other new phenomena in high-multiplicity final states in proton-proton collisions at root s=13 TeV

Peer reviewe

Search for heavy resonances decaying into a vector boson and a Higgs boson in final states with charged leptons, neutrinos, and b quarks

Peer reviewe

Search for high-mass diphoton resonances in proton-proton collisions at 13 TeV and combination with 8 TeV search

Peer reviewe

Search for the associated production of the Higgs boson with a top-quark pair

A search for the standard model Higgs boson produced in association with a top-quark pair t t ¯ H (tt¯H) is presented, using data samples corresponding to integrated luminosities of up to 5.1 fb −1 and 19.7 fb −1 collected in pp collisions at center-of-mass energies of 7 TeV and 8 TeV respectively. The search is based on the following signatures of the Higgs boson decay: H → hadrons, H → photons, and H → leptons. The results are characterized by an observed t t ¯ H tt¯H signal strength relative to the standard model cross section, μ = σ/σ SM ,under the assumption that the Higgs boson decays as expected in the standard model. The best fit value is μ = 2.8 ± 1.0 for a Higgs boson mass of 125.6 GeV

Measurement of prompt Jψ\psi pair production in pp collisions at \sqrt s = 7 Tev

Production of prompt J/ ψ meson pairs in proton-proton collisions at s s√ = 7 TeV is measured with the CMS experiment at the LHC in a data sample corresponding to an integrated luminosity of about 4.7 fb −1 . The two J/ ψ mesons are fully reconstructed via their decays into μ + μ − pairs. This observation provides for the first time access to the high-transverse-momentum region of J/ ψ pair production where model predictions are not yet established. The total and differential cross sections are measured in a phase space defined by the individual J/ ψ transverse momentum ( p T J/ ψ ) and rapidity (| y J/ ψ |): | y J/ ψ | 6.5 GeV/ c ; 1.2 4.5 GeV/ c . The total cross section, assuming unpolarized prompt J/ ψ pair production is 1.49 ± 0.07 (stat) ±0.13 (syst) nb. Different assumptions about the J/ ψ polarization imply modifications to the cross section ranging from −31% to +27%