Arithmetic Properties of Overpartition Pairs

Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of $\bar{pp}(n)$, the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for the number $\bar{pp}(n)$. In this paper, we shall derive two Ramanujan-type identities and some explicit congruences for $\bar{pp}(n)$. Moreover, we find three ranks as combinatorial interpretations of the fact that $\bar{pp}(n)$ is divisible by three for any n. We also construct infinite families of congruences for $\bar{pp}(n)$ modulo 3, 5, and 9.Comment: 19 page

Short Gamma-Ray Bursts with Extended Emission Observed with Swift/BAT and Fermi/GBM

Some short GRBs are followed by longer extended emission, lasting anywhere from ~10 to ~100 s. These short GRBs with extended emission (EE) can possess observational characteristics of both short and long GRBs (as represented by GRB 060614), and the traditional classification based on the observed duration places some of them in the long GRB class. While GRBs with EE pose a challenge to the compact binary merger scenario, they may therefore provide an important link between short and long duration events. To identify the population of GRBs with EE regardless of their initial classifications, we performed a systematic search of short GRBs with EE using all available data (up to February 2013) of both Swift/BAT and Fermi/GBM. The search identified 16 BAT and 14 GBM detected GRBs with EE, several of which are common events observed with both detectors. We investigated their spectral and temporal properties for both the spikes and the EE, and examined correlations among these parameters. Here we present the results of the systematic search as well as the properties of the identified events. Finally, their properties are also compared with short GRBs with EE observed with BATSE, identified through our previous search effort. We found several strong correlations among parameters, especially when all of the samples were combined. Based on our results, a possible progenitor scenario of two-component jet is discussed.Comment: Published in MNRAS; matched to the published versio

DLC2 modulates angiogenic responses in vascular endothelial cells by regulating cell attachment and migration.

Deleted in liver cancer 1 (DLC1) is a RhoGTPase activation protein-containing tumor suppressor that associates with various types of cancer. Although DLC2 shares a similar domain structure with that of DLC1, the function of DLC2 is not well characterized. Here, we describe the expression and ablation of DLC2 in mice using a reporter-knockout approach. DLC2 is expressed in several tissues and in endothelial cells (ECs) of blood vessels. Although ECs and blood vessels show no histological abnormalities and mice appear overall healthy, DLC2-mutant mice display enhanced angiogenic responses induced by matrigel and by tumor cells. Silencing of DLC2 in human ECs has reduced cell attachment, increased migration, and tube formation. These changes are rescued by silencing of RhoA, suggesting that the process is RhoA pathway dependent. These results indicate that DLC2 is not required for mouse development and normal vessel formation, but may protect mouse from unwanted angiogenesis induced by, for example, tumor cells

Tooth profile analysiis of circular-cut, spiral-bevel gears

An analysis of tooth profile changes in the transverse plane of circular-cut, spiral-bevel crown gears is presented. The analysis assumes a straight-line profile in the mid-transverse plane. The profile variation along the centerline is determined by using expressions for the variation of the spiral angle along the tooth centerline, together with the profile description at the mid-transverse plane. It is shown that the tooth surface is a hyperboloid and that significant variations in the pressure angle are possible