Asymptotics for rank and crank moments

Moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves a conjecture due to Bringmann and Mahlburg that refined a conjecture of Garvan. Garvan's conjecture states that the moments of the crank function are always larger than the moments of the rank function, even though the moments have the same main asymptotic term. The proof uses the Hardy-Ramanujan method to provide precise asymptotic estimates for rank and crank moments and their differences.Comment: 11 page

Sticky physics of joy: On the dissolution of spherical candies

Assuming a constant mass-decrease per unit-surface and -time we provide a very simplistic model for the dissolution process of spherical candies. The aim is to investigate the quantitative behavior of the dissolution process throughout the act of eating the candy. In our model we do not take any microscopic mechanism of the dissolution process into account, but rather provide an estimate which is based on easy-to-follow calculations. Having obtained a description based on this calculation, we confirm the assumed behavior by providing experimental data of the dissolution process. Besides a deviation from our prediction caused by the production process of the candies below a diameter of 2 mm, we find good agreement with our model-based expectations. Serious questions on the optimal strategy of enjoying a candy will be addressed, like whether it is wise to split the candy by breaking it with the teeth or not

Genetic analysis of the human tumor necrosis factor alpha/cachectin promoter region in a macrophage cell line.

The 615-bp 5' flanking region of the human TNF-alpha/cachectin gene was isolated and ligated to the luciferase reporter gene. In addition, a series of truncated promoter constructs was generated by exonuclease III digestion. The promoter activity of these constructs was studied in a transient transfection system using the TNF-alpha-producing U937 cell line. Full-length and truncated TNF promoter constructions extending from -615 to -95 bp relative to the transcription start site (TSS) could be induced by phorbol esters. A construct truncated to within 36 bp of the TSS (and within 11 bp of the TATAA box) was inactive. Therefore, the phorbol ester responsive is localized in the TNF/cachectin promoter to a relatively short region proximal to the TATAA box

The native bee fauna of the Palouse Prairie (Hymenoptera: Apoidea)

While synoptic collections provide data on the range and general composition of the North American bee fauna, bee communities associated with specific habitats are largely uncharacterized.  This report describes the community of native bees currently found in remnant fragments of the Palouse Prairie of northern Idaho and southeastern Washington State.  Native bees were collected using standardized collection techniques including blue vane traps, colored pan traps and aerial netting.  More than 13,000 individuals were collected, representing at least 174 species and 36 morphospecies in 29 genera.  These data provide the most thorough characterization of the bee fauna of this vulnerable ecosystem, as well as community level information on bee species of unknown conservation status.  These results are relevant to regional conservation efforts and, more broadly, are representative of conditions in fragmented grasslands surrounded by intense agriculture, a common global land use pattern of conservation concern

Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive-like operators

In this paper we use the general class of contractive-like operators introduced by Bosede and Rhoades (J. Adv. Math. Stud. 3(2):1-3, 2010) to prove strong convergence and stability results for Picard-Mann hybrid iterative schemes considered in a real normed linear space. We establish the strong convergence and stability of the Picard iterative scheme as a corollary. Our results generalize and improve a multitude of results in the literature, including the recent results of Chidume (Fixed Point Theory Appl. 2014:233, 2014)

Observational constraints on the neutron star mass distribution

Radio observations of neutron star binary pulsar systems have constrained strongly the masses of eight neutron stars. Assuming neutron star masses are uniformly distributed between lower and upper bounds $m_l$ and $m_u$, the observations determine with 95\% confidence that $1.01 < m_l/\text{M}_\odot < 1.34$ and $1.43 < m_u/\text{M}_\odot < 1.64$. These limits give observational support to neutron star formation scenarios that suggest that masses should fall predominantly in the range $1.3<m/\text{M}_\odot<1.6$, and will also be important in the interpretation of binary inspiral observations by the Laser Interferometer Gravitational-wave Observatory.Comment: Postscript, 4 pages, NU-GR-

Tests of Transfer Reaction Determinations of Astrophysical S-Factors

The ${}^{16}O ({}^{3}He,d) {}^{17}F$ reaction has been used to determine asymptotic normalization coefficients for transitions to the ground and first excited states of ${}^{17}F$. The coefficients provide the normalization for the tails of the overlap functions for ${}^{17}F \to{}^{16}O + p$ and allow us to calculate the S-factors for ${}^{16}O (p,\gamma){}^{17}F$ at astrophysical energies. The calculated S-factors are compared to measurements and found to be in very good agreement. This provides the first test of this indirect method to determine astrophysical direct capture rates using transfer reactions. In addition, our results yield S(0) for capture to the ground and first excited states in $^{17}F$, without the uncertainty associated with extrapolation from higher energies.Comment: 6 pages, 2 figure

Expanding the parameters of academia

This paper draws on qualitative data gathered from two studies funded by the UK Leadership Foundation for Higher Education to examine the expansion of academic identities in higher education. It builds on Whitchurch’s earlier work, which focused primarily on professional staff, to suggest that the emergence of broadly based projects such as widening participation, learning support and community partnership is also impacting on academic identities. Thus, academic as well as professional staff are increasingly likely to work in multi-professional teams across a variety of constituencies, as well as with external partners, and the binary distinction between ‘academic’ and ‘non-academic’ roles and activities is no longer clear-cut. Moreover, there is evidence from the studies of an intentionality about deviations from mainstream academic career routes among respondents who could have gone either way. Consideration is therefore given to factors that influence individuals to work in more project-oriented areas, as well as to variables that affect ways in which these roles and identities develop. Finally, three models of academically oriented project activity are identified, and the implications of an expansion of academic identities are reviewed