On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

The Effect of the Federal Trade Commission Improvements Act of 1980 on the FTC\u27s Rulemaking and Enforcement Authority

A more detailed analysis of the Federal Trade Commission Improvements Act of 1980 follows

Small gaps and small spacings between zeta zeros

We show assuming RH that phenomena concerning pairs of zeros established $via$ pair correlations occur with positive density (with at most a slight adjustment of the constants). Also, while a double zero is commonly considered to be a close pair, we consider the difference between two $distinct$ zeros.Comment: 17 page

Exposure to Host Ligands Correlates with Colocalization of Gal/GalNAc Lectin Subunits in Lipid Rafts and Phosphatidylinositol (4,5)-Bisphosphate Signaling in Entamoeba histolytica

Entamoeba histolytica is an intestinal parasite that causes dysentery and liver abscess. Parasite cell surface receptors, such as the Gal/GalNAc lectin, facilitate attachment to host cells and extracellular matrix. The Gal/GalNAc lectin binds to galactose or N-acetylgalactosamine residues on host components and is composed of heavy (Hgl), intermediate (Igl), and light (Lgl) subunits. Although Igl is constitutively localized to lipid rafts (cholesterol-rich membrane domains), Hgl and Lgl transiently associate with this compartment in a cholesterol-dependent fashion. In this study, trophozoites were exposed to biologically relevant ligands to determine if ligand binding influences the submembrane distribution of the subunits. Exposure to human red blood cells (hRBCs) or collagen, which are bona fide Gal/GalNAc lectin ligands, was correlated with enrichment of Hgl and Lgl in rafts. This enrichment was abrogated in the presence of galactose, suggesting that direct lectin-ligand interactions are necessary to influence subunit location. Using a cell line that is able to attach to, but not phagocytose, hRBCs, it was shown that physical attachment to ligands was not sufficient to induce the enrichment of lectin subunits in rafts. Additionally, the mutant had lower levels of phosphatidylinositol (4,5)-bisphosphate (PIP2); PIP2 loading restored the ability of this mutant to respond to ligands with enrichment of subunits in rafts. Finally, intracellular calcium levels increased upon attachment to collagen; this increase was essential for the enrichment of lectin subunits in rafts. Together, these data provide evidence that ligand-induced enrichment of lectin subunits in rafts may be the first step in a signaling pathway that involves both PIP2 and calcium signaling

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.Comment: 15 pages, 9 figure

Low angular momentum flow model of Sgr A* activity

Sgr A* is the closest massive black hole and can be observed with the highest angular resolution. Nevertheless, our current understanding of the accretion process in this source is very poor. The inflow is almost certainly of low radiative efficiency and it is accompanied by a strong outflow and the flow is strongly variable but the details of the dynamics are unknown. Even the amount of angular momentum in the flow is an open question. Here we argue that low angular momentum scenario is better suited to explain the flow variability. We present a new hybrid model which describes such a flow and consists of an outer spherically symmetric Bondi flow and an inner axially symmetric flow described through MHD simulations. The assumed angular momentum of the matter is low, i.e. the corresponding circularization radius in the equatorial plane of the flow is just above the innermost stable circular orbit in pseudo-Newtonian potential. We compare the radiation spectrum from such a flow to the broad band observational data for Sgr A*.Comment: Proceedings of the AHAR 2008 Conference: The Universe under the Microscope; Astrophysics at High Angular Resolution, Bad Honef

Trait Anger, Anger Expression, and Suicide Attempts Among Adolescents and Young Adults: A Prospective Study

Previous studies of the relationship between anger, anger expression, and suicidal behavior have been largely cross-sectional and have yielded mixed findings. In a prospective, naturalistic study, we examined how trait anger and anger expression influenced the likelihood of suicide attempts among 180 adolescents followed for up to 13.3 years after discharge from an inpatient psychiatry unit. Results showed that higher trait anger and anger expressed outwardly over the follow-up was related to increased likelihood of suicide attempts among males. For girls, trait anger and both the inward and outward expression of anger moderated the risk for suicide attempts associated with major depression. These results are interpreted in light of theory regarding behavioral activation and behavioral inhibition systems

The Mikheyev-Smirnov-Wolfenstein Effect as a Probe of the Solar Interior

We relate the MSW effect to the efective absorption of the electronic collective motion energy by retaining the imaginary part of the index of refraction associated with the charged-current scattering and show that the small angle MSW solution to the solar neutrino anomaly can be used as a probe of the physical conditions of the solar interior if it is correct. We find that the constraint on the absorption imposed by the small angle MSW solution and the theoretical estimate of the absorption by the Boltzmann kinetic theory are consistent, which shows that a consistent theoretical picture can be developed when plasma absorption processes are taken into account.Comment: 4 pages, no figure, REVTeX, to appear in Phys. Rev.