Splittings of generalized Baumslag-Solitar groups

We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (`fully reduced' decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the isomorphism problem for generalized Baumslag-Solitar groups with no non-trivial integral moduli.Comment: 20 pages; hyperlinked latex. Version 2: minor change

An explicit KO-degree map and applications

The goal of this note is to study the analog in unstable ${{\mathbb A}^1}$-homotopy theory of the unit map from the motivic sphere spectrum to the Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We show that "Suslin matrices", which are explicit maps from odd dimensional split smooth affine quadrics to geometric models of the spaces appearing in Bott periodicity in Hermitian K-theory, stabilize in a suitable sense to the unit map. As applications, we deduce that $K^{MW}_i(F) = GW^i_i(F)$ for $i \leq 3$, which can be thought of as an extension of Matsumoto's celebrated theorem describing $K_2$ of a field. These results provide the first step in a program aimed at computing the sheaf $\pi_{n}^{{\mathbb A}^1}({\mathbb A}^n \setminus 0)$ for $n \geq 4$.Comment: 36 Pages, Final version, to appear Journal of Topolog

Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices

Evidence for nonhadronic degrees of freedom in the transverse mass spectra of kaons from relativistic nucleus-nucleus collisions?

We investigate transverse hadron spectra from relativistic nucleus-nucleus collisions which reflect important aspects of the dynamics - such as the generation of pressure - in the hot and dense zone formed in the early phase of the reaction. Our analysis is performed within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. Both transport models show their reliability for elementary $pp$ as well as light-ion (C+C, Si+Si) reactions. However, for central Au+Au (Pb+Pb) collisions at bombarding energies above $\sim$ 5 A$\cdot$GeV the measured $K^{\pm}$ transverse mass spectra have a larger inverse slope parameter than expected from the calculation. Thus the pressure generated by hadronic interactions in the transport models above $\sim$ 5 A$\cdot$GeV is lower than observed in the experimental data. This finding shows that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - is generated by strong partonic interactions in the early phase of central Au+Au (Pb+Pb) collisions.Comment: 4 pages, 3 figures,discussions extended, references added, to be published in Phys. Rev. Let

A Multi-Phase Transport model for nuclear collisions at RHIC

To study heavy ion collisions at energies available from the Relativistic Heavy Ion Collider, we have developed a multi-phase transport model that includes both initial partonic and final hadronic interactions. Specifically, the parton cascade model ZPC, which uses as input the parton distribution from the HIJING model, is extended to include the quark-gluon to hadronic matter transition and also final-state hadronic interactions based on the ART model. Predictions of the model for central Au on Au collisions at RHIC are reported.Comment: 7 pages, 4 figure

Animal, Plant, Collagen and Blended Dietary Proteins: Effects on Musculoskeletal Outcomes

This is the final version. Available from MDPI via the DOI in this record.Dietary protein is critical for the maintenance of musculoskeletal health, whereappropriate intake (i.e., source, dose, timing) can mitigate declines in muscle and bone mass and/orfunction. Animal-derived protein is a potent anabolic source due to rapid digestion and absorptionkinetics stimulating robust increases in muscle protein synthesis and promoting bone accretion andmaintenance. However, global concerns surrounding environmental sustainability has led to anincreasing interest in plant- and collagen-derived protein as alternative or adjunct dietary sources.This is despite the lower anabolic profile of plant and collagen protein due to the inferior essentialamino acid profile (e.g., lower leucine content) and subordinate digestibility (versus animal). Thisreview evaluates the efficacy of animal-, plant- and collagen-derived proteins in isolation, and asprotein blends, for augmenting muscle and bone metabolism and health in the context of ageing,exercise and energy restriction.Medical Research Council (MRC)National Institute for Health Researc

Applications of aerospace technology in biology and medicine

Utilization of National Aeronautics and Space Administration (NASA) technology in medicine is discussed. The objective is best obtained by stimulation of the introduction of new or improved commercially available medical products incorporating aerospace technology. A bipolar donor/recipient model of medical technology transfer is presented to provide a basis for the team's methodology. That methodology is designed to: (1) identify medical problems and NASA technology that, in combination, constitute opportunities for successful medical products; (2) obtain the early participation of industry in the transfer process; and (3) obtain acceptance by the medical community of new medical products based on NASA technology. Two commercial transfers were completed: the Stowaway, a lightweight wheelchair that provides mobility for the disabled and elderly in the cabin of commercial aircraft, and Micromed, a portable medication infusion pump for the reliable, continuous infusion of medications such as heparin or insulin. The marketing and manufacturing factors critical to the commercialization of the lightweight walker incorporating composite materials were studied. Progress was made in the development and commercialization of each of the 18 currently active projects

Ho3+ To Yb3+ Back Transfer And Thermal Quenching Of Up-Conversion Green Emission In Fluoride-Crystals

Energy transfer from Ho3+ to Yb3+ has been demonstrated in fluoride crystals such as KYF4, BaY2F8, and LiYF4. This transfer was found to occur above a certain temperature and its efficiency increases with temperature. It accounts for the thermal quenching of green emission from upconverted Ho3+ and partly explains the failure, to date, to obtain room temperature, Yb3+ sensitized Ho3+ upconversion lasers in these three hosts. Low Yb3+ concentration is suggested for future attempts to achieve room temperature Yb3+, Ho3+ upconversion green laser operation of these crystals

Using tasks to explore teacher knowledge in situation-specific contexts

This article was published in the journal, Journal of Mathematics Teacher Education [© Springer] and the original publication is available at www.springerlink.comResearch often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of x+x−1=0 of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore