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

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

Duality and differential operators for harmonic Maass forms

Due to the graded ring nature of classical modular forms, there are many interesting relations between the coefficients of different modular forms. We discuss additional relations arising from Duality, Borcherds products, theta lifts. Using the explicit description of a lift for weakly holomorphic forms, we realize the differential operator ${D}^{k-1} := {( \frac{1} {2\pi \mathrm{i}} \frac{\partial } {\partial z})}^{k-1}$ acting on a harmonic Maass form for integers k > 2 in terms of ${\xi }_{2-k} := 2\mathrm{i}{y}^{2-k}\overline{ \frac{\partial } {\partial \overline{z}}}$ acting on a different form. Using this interpretation, we compute the image of D k − 1. We also answer a question arising in recent work on the p-adic properties of mock modular forms. Additionally, since such lifts are defined up to a weakly holomorphic form, we demonstrate how to construct a canonical lift from holomorphic modular forms to harmonic Maass forms.postprin

Introduction to The Special Issue: Advances in Methods and Measurement in Family Psychology

This special issue presents a collection of reports that highlight recent advances in methods and measurement and also shed light on the complexity of family psychology. The importance of theory in guiding solid family science is evident throughout these reports. The reports include guides for researchers who incorporate direct observation into their research protocols and the ever-expanding field of tele-health interventions. Advanced analytic approaches are offered in the areas of grid sequence analysis, latent fixed-effects models, and the Factors of Curves Model (FOCUS). These sophisticated analytic approaches may be applied to advance systemic thinking in family psychology. The last set of articles illustrate how complex and innovative methodologies are applied to address important societal issues. Work experiences and marital relationships in African American couples address the importance of spillover effects in contemporary families. The creation of biobehavioral plasticity index has the potential to inform gene x environment contributions to family functioning. Finally, the unique methodological issues that are particularly germane to the diverse nature of stepfamilies and nonresident fathers are addressed. We hope that readers of this special issue will return to these reports as resources and examples of theory-driven methods and measurements

An intelligent, free-flying robot

The ground based demonstration of the extensive extravehicular activity (EVA) Retriever, a voice-supervised, intelligent, free flying robot, is designed to evaluate the capability to retrieve objects (astronauts, equipment, and tools) which have accidentally separated from the Space Station. The major objective of the EVA Retriever Project is to design, develop, and evaluate an integrated robotic hardware and on-board software system which autonomously: (1) performs system activation and check-out; (2) searches for and acquires the target; (3) plans and executes a rendezvous while continuously tracking the target; (4) avoids stationary and moving obstacles; (5) reaches for and grapples the target; (6) returns to transfer the object; and (7) returns to base

Multiple electromagnetic electron positron pair production in relativistic heavy ion collisions

We calculate the cross sections for the production of one and more electron-positron pairs due to the strong electromagnetic fields in relativistic heavy ion collisions. Using the generating functional of fermions in an external field we derive the N-pair amplitude. Neglecting the antisymmetrisation in the final state we find that the total probability to produce N pairs is a Poisson distribution. We calculate total cross sections for the production of one pair in lowest order and also include higher-order corrections from the Poisson distribution up to third order. Furthermore we calculate cross sections for the production of up to five pairs including corrections from the Poisson distribution.Comment: 13 pages REVTeX, 4 Postscript figures, This and related papers may also be obtained from http://www.phys.washington.edu/~hencken

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

Asymptotic normalization coefficients for 8B->7Be+p from a study of 8Li->7Li+n

Asymptotic normalization coefficients (ANCs) for 8Li->7Li+n have been extracted from the neutron transfer reaction 13C(7Li,8Li)12C at 63 MeV. These are related to the ANCs in 8B->7Be+p using charge symmetry. We extract ANCs for 8B that are in very good agreement with those inferred from proton transfer and breakup experiments. We have also separated the contributions from the p_1/2 and p_3/2 components in the transfer. We find the astrophysical factor for the 7Be(p,gamma)8B reaction to be S_17(0)=17.6+/-1.7 eVb. This is the first time that the rate of a direct capture reaction of astrophysical interest has been determined through a measurement of the ANCs in the mirror system.Comment: 5 pages, 3 figures, 2 table

On several families of elliptic curves with arbitrary large Selmer groups

In this paper, we calculate the $\phi (\hat{\phi})-$Selmer groups S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic curves $y^{2} = x (x + \epsilon p D) (x + \epsilon q D)$ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.Comment: 22 page