The effects of algebra blocks on student achievement in algebra

This study examined the effects of Algebra Blocks on student understanding for the concepts of binomial expansion and trinomial factorisation. The purpose of the study was to illuminate the use and effectiveness of Algebra\u27 Blocks in the teaching-learning process. Two year nine classes with similar mathematics levels were taught binomial expansions and trinomial factorisations. The experimental class was taught using Algebra Blocks whilst the untreated class acted as the control group. After eight lessons of instruction, both classes were tested on their understanding of both concepts. To provide qualitative data, three randomly chosen students from each class were interviewed on their understanding of both concepts. The experimental results were statistically significant (

A Preliminary Investigation towards the Risk Stratification of Allogeneic Stem Cell Recipients with Respect to the Potential for Development of GVHD via Their Pre-Transplant Plasma Lipid and Metabolic Signature

The clinical outcome of allogeneic hematopoietic stem cell transplantation (SCT) may be influenced by the metabolic status of the recipient following conditioning, which in turn may enable risk stratification with respect to the development of transplant-associated complications such as graft vs. host disease (GVHD). To better understand the impact of the metabolic profile of transplant recipients on post-transplant alloreactivity, we investigated the metabolic signature of 14 patients undergoing myeloablative conditioning followed by either human leukocyte antigen (HLA)-matched related or unrelated donor SCT, or autologous SCT. Blood samples were taken following conditioning and prior to transplant on day 0 and the plasma was comprehensively characterized with respect to its lipidome and metabolome via liquid chromatography/mass spectrometry (LCMS) and gas chromatography/mass spectrometry (GCMS). A pro-inflammatory metabolic profile was observed in patients who eventually developed GVHD. Five potential pre-transplant biomarkers, 2-aminobutyric acid, 1-monopalmitin, diacylglycerols (DG 38:5, DG 38:6), and fatty acid FA 20:1 demonstrated high sensitivity and specificity towards predicting post-transplant GVHD. The resulting predictive model demonstrated an estimated predictive accuracy of risk stratification of 100%, with area under the curve of the ROC of 0.995. The likelihood ratio of 1-monopalmitin (infinity), DG 38:5 (6.0), and DG 38:6 (6.0) also demonstrated that a patient with a positive test result for these biomarkers following conditioning and prior to transplant will be at risk of developing GVHD. Collectively, the data suggest the possibility that pre-transplant metabolic signature may be used for risk stratification of SCT recipients with respect to development of alloreactivity

Squeezed gluon vacuum and the global colour model of QCD

We discuss how the vacuum model of Celenza and Shakin with a squeezed gluon condensate can explain the existence of an infrared singular gluon propagator frequently used in calculations within the global colour model. In particular, it reproduces a recently proposed QCD-motivated model where low energy chiral parameters were computed as a function of a dynamically generated gluon mass. We show how the strength of the confining interaction of this gluon propagator and the value of the physical gluon condensate may be connected.Comment: 13 pages, LaTe

Chirally symmetric quark description of low energy \pi-\pi scattering

Weinberg's theorem for \pi-\pi scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold \pi-\pi scattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.Comment: 10 pages, 7 figures, Revtex

Simple, but Not Branched, Plasmodesmata Allow the Nonspecific Trafficking of Proteins in Developing Tobacco Leaves

AbstractLeaves undergo a sink–source transition during which a physiological change occurs from carbon import to export. In sink leaves, biolistic bombardment of plasmids encoding GFP-fusion proteins demonstrated that proteins with an Mr up to 50 kDa could move freely through plasmodesmata. During the sink–source transition, the capacity to traffic proteins decreased substantially and was accompanied by a developmental switch from simple to branched forms of plasmodesmata. Inoculation of sink leaves with a movement protein-defective virus showed that virally expressed GFP, but not viral RNA, was capable of trafficking between sink cells during infection. Contrary to dogma that plasmodesmata have a size exclusion limit below 1 kDa, the data demonstrate that nonspecific “macromolecular trafficking” is a general feature of simple plasmodesmata in sink leaves

pi-pi scattering in a QCD based model field theory

A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyse the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking, asymptotic freedom and quark confinement, allows one to calculate $f_\pi$, $m_\pi$, $r_\pi$ and the partial wave amplitudes in $\pi$-$\pi$ scattering and obtain good agreement with the experimental data, with the latter being well described up to energies \mbox{$E\simeq 700$ MeV}.Comment: 23 Pages, 4 figures in PostScript format, PHY-7512-TH-93, REVTEX Available via anonymous ftp in /pub: login anonymou get pipi93.tex Fig1.ps Fig2.ps Fig3.ps Fig4.p

The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD

A solvable systematic truncation scheme for the Dyson-Schwinger equations of Euclidean QCD in Landau gauge is presented. It implements the Slavnov-Taylor identities for the three-gluon and ghost-gluon vertices, whereas irreducible four-gluon couplings as well as the gluon-ghost and ghost-ghost scattering kernels are neglected. The infrared behavior of gluon and ghost propagators is obtained analytically: The gluon propagator vanishes for small spacelike momenta whereas the ghost propagator diverges stronger than a massless particle pole. The numerical solutions are compared with recent lattice data for these propagators. The running coupling of the renormalization scheme approaches a fixed point, $\alpha_c \simeq 9.5$, in the infrared.Comment: 4 pages, 2 figures, Revtex; revised version accepted for publication in Physical Review Letter

Mesons as qbar-q Bound States from Euclidean 2-Point Correlators in the Bethe-Salpeter Approach

We investigate the 2-point correlation function for the vector current. The gluons provide dressings for both the quark self energy as well as the vector vertex function, which are described consistently by the rainbow Dyson-Schwinger equation and the inhomogeneous ladder Bethe-Salpeter equation. The form of the gluon propagator at low momenta is modeled by a 2-parameter ansatz fitting the weak pion decay constant. The quarks are confined in the sense that the quark propagator does not have a pole at timelike momenta. We determine the ground state mass in the vector channel from the Euclidean time Fourier transform of the correlator, which has an exponential falloff at large times. The ground state mass lies around 590 MeV and is almost independent of the model form for the gluon propagator. This method allows us to stay in Euclidean space and to avoid analytic continuation of the quark or gluon propagators into the timelike region.Comment: 21 pages (REVTEX), 8 Postscript figure

Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?

We study a model Dyson-Schwinger equation for the quark propagator closed using an {\it Ansatz} for the gluon propagator of the form \mbox{$D(q) \sim q^2/[(q^2)^2 + b^4]$} and two {\it Ans\"{a}tze} for the quark-gluon vertex: the minimal Ball-Chiu and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of $b=b_c$ such that the model does not support dynamical chiral symmetry breaking for $b>b_c$. We discuss and apply a confinement test which suggests that, for all values of $b$, the quark propagator in the model {\bf is not} confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behaviour of QCD.Comment: 21 Pages including 4 PostScript figures uuencoded at the end of the file. Replacement: slight changes of wording and emphasis. ADP-93-215/T133, ANL-PHY-7599-TH-93, FSU-SCRI-93-108, REVTEX 3.

Meson Condensation in Dense Matter Revisited

The results for meson condensation in the literature vary markedly depending on whether one uses chiral perturbation theory or the current-algebra-plus-PCAC approach. To elucidate the origin of this discrepancy, we re-examine the role of the sigma-term in meson condensation. We find that the resolution of the existing discrepancy requires a knowledge of terms in the Lagrangian that are higher order in density than hitherto considered.Comment: 10pages, USC(NT)-94-