Forest diagrams for elements of Thompson's group F

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.Comment: 44 pages, 70 figure

An inverse source problem for the heat equation and the enclosure method

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given.Comment: 23page

The Age Dependent Luminosities of the Red Giant Branch Bump, Asymptotic Giant Branch Bump, and Horizontal Branch Red Clump

Color-magnitude diagrams of globular clusters often exhibit a prominent horizontal branch (HB) and may also show features such as the red giant branch (RGB) bump and the asymptotic giant branch (AGB) bump. Stellar evolution theory predicts that the luminosities of these features will depend on the metallicity and age of the cluster. We calculate theoretical lines of 2 to 12 Gyr constant age RGB-bumps and AGB-bumps in the V(HB-Bump)--[Fe/H] diagram, which shows the brightness difference between the bump and the HB as a function of metallicity. In order to test the predictions, we identify giant branch bumps in new Hubble Space Telescope color-magnitude diagrams for 8 SMC clusters. First, we conclude that the SMC cluster bumps are RGB-bumps. The data for clusters younger than ~6 Gyr are in fair agreement the relative age dependent luminosities of the HB and RGB-bump. The V(HB-Bump)--[Fe/H] data for clusters older then ~6 Gyr demonstrate a less satisfactory agreement with our calculations. We conclude that ~6 Gyr is a lower bound to the age of clusters for which the Galactic globular cluster, age independent V(HB-Bump)--[Fe/H] calibration is valid. Application of the V(HB-bump)--[Fe/H] diagram to stellar population studies is discussed.Comment: Accepted for publication in the Astrophysical Journal, 30 pages, Latex aaspp4.sty, including 7 postscript figure

Elementary amenable subgroups of R. Thompson's group F

The subgroup structure of Thompson's group F is not yet fully understood. The group F is a subgroup of the group PL(I) of orientation preserving, piecewise linear self homeomorphisms of the unit interval and this larger group thus also has a poorly understood subgroup structure. It is reasonable to guess that F is the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we explore the complexity of the elementary amenable subgroups of F in an attempt to understand the boundary between the elementary amenable subgroups and the non-elementary amenable. We construct an example of an elementary amenable subgroup up to class (height) omega squared, where omega is the first infinite ordinal.Comment: 20 page

Nitrogen-grafted activated carbon for removing nitrate from water

Nitrate (NO3~) and nitrite (NO2~) ions are ubiquitous in the environment and considered hazardous to humans. The primary health hazard from drinking water containing NO3~ occurs when it is transformed to NO2~ in the digestive system (Robillard et al., 2006). Currently nitrate is removed from water using polymer anion exchangers. However, this process is expensive and requires a lot of brine (NaCl) for the exchanger regeneration. Alternative physicochemical methods such as reverse osmosis are expensive and inefficient. The proposed research aims to develop anion-selective nitrogen-containing activated carbon, NGAC that can be regenerated electrochemically and does not require concentrated brine for regeneration. The key to the selectivity of the NGAC is achieved by the deposition of N-bearing conductive polymers or other species such as polypyrrole, polyaniline, pyridinium, quaternary ammonium, etc. onto the AC surface. Our preliminary results indicate that the polypyrrole charge can remain stable through multiple redox cycles (at least 50)

Phase Diagram of One-Dimensional Extended Hubbard Model at Half Filling

We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the g-ology to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge density wave (CDW) and spin density wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.Comment: 4 pages, 3 figure

A review of breeding objectives, genomic resources, and marker-assisted methods in common bean (Phaseolus vulgaris L.)

Common bean (Phaseolus vulgaris L.), one of the most important grain legume crops for direct human consumption, faces many challenges as a crop. Domesticated from wild relatives that inhabit a relatively narrow ecological niche, common bean faces a wide range of biotic and abiotic constraints within its diverse agroecological settings. Biotic stresses impacting common bean include numerous bacterial, fungal, and viral diseases and various insect and nematode pests, and abiotic stresses include drought, heat, cold, and soil nutrient deficiencies or toxicities. Breeding is often local, focusing on improvements in responses to biotic and abiotic stresses that are particular challenges in certain locations and needing to respond to conditions such as day-length regimes. This review describes the major breeding objectives for common bean, followed by a description of major genetic and genomic resources, and an overview of current and prospective marker-assisted methods in common bean breeding. Improvements over traditional breeding methods in CB can result from the use of different approaches. Several important germplasm collections have been densely genotyped, and relatively inexpensive SNP genotyping platforms enable implementation of genomic selection and related marker-assisted breeding approaches. Also important are sociological insights related to demand-led breeding, which considers local value chains, from farmers to traders to retailers and consumers

Cohesion, team mental models, and collective efficacy: Towards an integrated framework of team dynamics in sport

A nomological network on team dynamics in sports consisting of a multi-framework perspective is introduced and tested. The aim was to explore the interrelationship among cohesion, team mental models (TMM), collective-efficacy (CE), and perceived performance potential (PPP). Three hundred and forty college-aged soccer players representing 17 different teams (8 female and 9 male) participated in the study. They responded to surveys on team cohesion, TMM, CE and PPP. Results are congruent with the theoretical conceptualization of a parsimonious view of team dynamics in sports. Specifically, cohesion was found to be an exogenous variable predicting both TMM and CE beliefs. TMM and CE were correlated and predicted PPP, which in turn accounted for 59% of the variance of objective performance scores as measured by teams’ season record. From a theoretical standpoint, findings resulted in a parsimonious view of team dynamics, which may represent an initial step towards clarifying the epistemological roots and nomological network of various team-level properties. From an applied standpoint, results suggest that team expertise starts with the establishment of team cohesion. Following the establishment of cohesiveness, teammates are able to advance team-related schemas and a collective sense of confidence. Limitations and key directions for future research are outlined

Use of Non-Steroidal Anti-Inflammatory Drugs That Elevate Cardiovascular Risk: An Examination of Sales and Essential Medicines Lists in Low-, Middle-, and High-Income Countries

PMCID: PMC3570554This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited