Discovery of a Kiloparsec Scale X-ray/Radio Jet in the z=4.72 Quasar GB 1428+4217

We report the discovery of a one-sided 3.6" (24 kpc, projected) long jet in the high-redshift, z=4.72, quasar GB 1428+4217 in new Chandra X-ray and VLA radio observations. This is the highest redshift kiloparsec-scale X-ray/radio jet known. Analysis of archival VLBI 2.3 and 8.6 GHz data reveal a faint one-sided jet extending out to ~200 parsecs and aligned to within ~30 deg of the Chandra/VLA emission. The 3.6" distant knot is not detected in an archival HST image, and its broad-band spectral energy distribution is consistent with an origin from inverse Compton scattering of cosmic microwave background photons for the X-rays. Assuming also equipartition between the radiating particles and magnetic field, the implied jet Lorentz factor is ~5. This is similar to the other two known z ~ 4 kpc-scale X-ray jet cases and smaller than typically inferred in lower-redshift cases. Although there are still but a few such very high-redshift quasar X-ray jets known, for an inverse Compton origin, the present data suggest that they are less relativistic on large-scales than their lower-redshift counterparts.Comment: ApJL, accepted, 5 pages, 3 figure

Chiral differential operators on supermanifolds

The first part of this paper provides a new formulation of chiral differential operators (CDOs) in terms of global geometric quantities. The main result is a recipe to define all sheaves of CDOs on a smooth cs-manifold; its ingredients consist of an affine connection and an even 3-form that trivializes the first Pontrjagin form. With the connection fixed, two suitable 3-forms define isomorphic sheaves of CDOs if and only if their difference is exact. Moreover, conformal structures are in one-to-one correspondence with even 1-forms that trivialize the first Chern form. Applying our work in the first part, we construct what may be called "chiral Dolbeault complexes" of a complex manifold M, and analyze conditions under which these differential vertex superalgebras admit compatible conformal structures or extra gradings (fermion numbers). When M is compact, their cohomology computes (in various cases) the Witten genus, the two-variable elliptic genus and a spin-c version of the Witten genus. This part contains some new results as well as provides a geometric formulation of certain known facts from the study of holomorphic CDOs and sigma models.Comment: much simplified calculations in section 3, making full use of the formulation from section 2; improved notation

A note on Charmed and Bottomed Pentaquark Production by Fragmentation

H1 Collaboration recently observed the charmed pentaquark. In this short note, we point out that the dominant production mechanism for pentaquark consisting of a heavy quark is heavy quark fragmentation. We obtain a crude estimate on the fragmentation probability for charm quark into Theta_c^0, based on the known fragmentation probabilities of charm quark into mesons and baryons: f(c-bar --> Theta_c^0) =~ (2-7) x 10^{-3}. Similarly, we also obtain the fragmentation probability for bottom quark into Theta_b^+: f(b-bar --> Theta_b^+) =~ (5-20) x 10^{-3}. We also estimate the prospect of observing Theta_c^0 and Theta_b^+ at HERA, LEP, and Tevatron.Comment: RevTex, 4 pages, no figures, references adde

Culturally responsive teacher actions to support Pāsifika students in mathematical discourse : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education at Massey University, Palmerston North, New Zealand

This study examines culturally responsive teaching to support a group of Pāsifika students aged 11-13 years old in mathematical discourse. It builds on previous work which has advocated culturally responsive practices where students learn mathematics through collaborative interaction that fosters greater student participation, engagement, and potentially better achievement in mathematics. In this study, the teacher’s actions drew on Pāsifika cultural practices and the value of the family, respect, and collectivism. This was significant in the establishment of social and mathematical behaviours which were important in supporting the development of productive mathematical discourse. In addition, the communicative and participation structures within the classroom that lead to mathematics learning are also considered. This study was situated in an inquiry classroom. A socio-cultural perspective provided the framework for analysing the classroom context. A case study approach drawing on a qualitative design was implemented. Data was collected through teacher and student interviews, classroom audio and video-recorded observations, and students’ written work. Detailed retrospective analysis of the data was undertaken to develop the findings of this classroom case study. Significant changes were revealed in the shifts of student discourse from long silences and hesitation to asking valid questions and developing mathematical justification with appropriate language and specific terms. The explicit instructional practices developed and implemented by the teacher fostered greater collaborative communication and interaction between group members and this was important in how they made mathematical meaning. The findings provide insights into the multi-dimensional ways that teachers can draw on students’ cultural strengths, values, and practices as invaluable resources which potentially will make a difference in students’ mathematical learning