Search results for "Type I"
showing 10 items of 966 documents
The equality case in a Poincaré–Wirtinger type inequality
2016
It is known that, for any convex planar set W, the first non-trivial Neumann eigenvalue μ1 (Ω) of the Hermite operator is greater than or equal to 1. Under the additional assumption that Ω is contained in a strip, we show that β1 (Ω) = 1 if and only if Ω is any strip. The study of the equality case requires, among other things, an asymptotic analysis of the eigenvalues of the Hermite operator in thin domains.
Comparison results for Hessian equations via symmetrization
2007
where the λ’s are the eigenvalues of the Hessian matrix D2u of u and Sk is the kth elementary symmetric function. For example, for k = 1, S1(Du) = 1u, while, for k = n, Sn(D 2u) = detD2u. Equations involving these operators, and some more general equations of the form F(λ1, . . . , λn) = f in , (1.2) have been widely studied by many authors, who restrict their considerations to convenient cones of solutions with respect to which the operator in (1.2) is elliptic. Following [25] we define the cone 0k of ellipticity for (1.1) to be the connected component containing the positive cone 0 = {λ ∈ R : λi > 0 ∀i = 1, . . . , n} of the set where Sk is positive. Thus 0k is an open, convex, symmetric…
Relationship between the comma theory and Witten’s string field theory
1998
The comma representation of interacting string field theory is further elucidated. The proof that Witten's vertex solves the comma overlap equations is established. In this representation, the associativity of the star algebra is seen to hold. The relationship of the symmetry K in the standard formulation of Witten's string field theory to that in the comma theory is discussed.
Quasisymmetric maps and string theory
1994
Association Between Exercise and Pubertal BMD Is Modulated by Estrogen Receptor α Genotype
2003
Genetic and environmental factors contribute to bone mass, but the ways they interact remain poorly understood. This study of 245 pre- and early pubertal girls found that the PvuII polymorphism in the ER- gene modulates the effect of exercise on BMD at loaded bone sites. Introduction: Impaired achievement of bone mass at puberty is an important risk factor for the development of osteoporosis in later life. Genetic, as well as environmental, factors contribute to bone mass, but the ways they interact with each other remain poorly understood. Materials and Methods: We investigated the interaction between a PvuII polymorphism at the ER- gene and physical activity (PA) on the modulation of bone…
Prevalence, risk factor burden, and severity of coronary artery disease in patients with heterozygous familial hypercholesterolemia hospitalized for …
2019
Individuals with heterozygous familial hypercholesterolemia (FH) are at high risk of early myocardial infarction (MI). However, coronary artery disease (CAD) burden of FH remains not well described, especially for French patients.The objective of this study was to assess the prevalence of FH and severity of CAD from a large database of a French regional registry of acute MI.All consecutive patients hospitalized for an acute MI in a multicenter database from 2001 to 2017 were considered. FH was diagnosed using an algorithm adapted from the Dutch Lipid Clinic Network criteria. The prevalence and clinical features of FH and the severity of CAD were assessed.Among the 11,624 patients included i…
Core-collapse supernova simulations in one and two dimensions: comparison of codes and approximations
2018
We present spherically symmetric (1D) and axisymmetric (2D) supernova simulations for a convection-dominated 9 Msun and a 20 Msun progenitor that develops violent activity by the standing-accretion-shock instability (SASI). We compare in detail the Aenus-Alcar code, which uses fully multidimensional two-moment neutrino transport with an M1 closure, with a ray-by-ray-plus (RbR+) version of this code and with the Prometheus-Vertex code that employs RbR+ two-moment transport with a Boltzmann closure. Besides testing consequences of ignored non-radial neutrino-flux components in the RbR+ approximation, we also discuss the influence of various transport ingredients applied or not applied in rece…
Dark gamma-ray bursts
2016
Many theories of dark matter (DM) predict that DM particles can be captured by stars via scattering on ordinary matter. They subsequently condense into a DM core close to the center of the star and eventually annihilate. In this work, we trace DM capture and annihilation rates throughout the life of a massive star and show that this evolution culminates in an intense annihilation burst coincident with the death of the star in a core collapse supernova. The reason is that, along with the stellar interior, also its DM core heats up and contracts, so that the DM density increases rapidly during the final stages of stellar evolution. We argue that, counterintuitively, the annihilation burst is …
Non-supersymmetric AdS6 and the swampland
2021
We discuss infinite families of non-supersymmetric AdS$_6$ solutions in Type IIB string theory. They are siblings of supersymmetric solutions which are associated with $(p,q)$ 5-brane webs and holographically dual to 5d SCFTs engineered by those brane webs. The non-supersymmetric backgrounds carry identical 5-brane charges and are connected to the supersymmetric ones by RG flows. We study the stability of the non-supersymmetric solutions, identifying perturbative and non-perturbative decay channels for all the backgrounds explicitly available. We also identify likely decay mechanisms for solutions that have not been constructed explicitly but may be expected to exist based on brane web cons…
Oh, wait, O8 de Sitter may be unstable!
2021
We analyze the stability of four-dimensional de Sitter vacua constructed by compactifying massive Type IIA supergravity in the presence of two O8 sources [1]. When embedded in String Theory the first source has a clear interpretation as an O8$_-$ plane, but the second one could correspond to either an O8$_+$ plane or to an O8$_-$ plane with 16 D8-branes on top. We find that this latter solution has a tachyonic instability, corresponding to the D8-branes moving away from the O8$_-$ plane. We comment on the possible ways of distinguishing between these sources.