Extension of a theorem of Cauchy and Jacobi

AbstractLet q and p be prime with q = a2 + b2 ≡ 1 (mod 4), a ≡ 1 (mod 4), and p = qf + 1. In the nineteenth century Cauchy (Mém. Inst. France 17 (1840), 249–768) and Jacobi (J. für Math. 30 (1846), 166–182) generalized the work of earlier authors, who had determined certain binomial coefficients (mod p) (see H. J. S. Smith, “Report on the Theory of Numbers,” Chelsea, 1964), by determining two products of factorials given by Πk kf! (mod p = qf + 1) where k runs through the quadratic residues and the quadratic non-residues (mod q), respectively. These determinations are given in terms of parameters in representations of ph or of 4ph by binary quadratic forms. A remarkable feature of these results is the fact that the exponent h coincides with the class number of the related quadratic field. In this paper C. R. Mathews' (Invent. Math. 54 (1979), 23–52) recent explicit evaluation of the quartic Gauss sum is used to determine four products of factorials (mod p = qf + 1, q ≡ 5 (mod 8) > 5), given by Πk kf! where k runs through the quartic residues (mod q) and the three cosets which may be formed with respect to this subgroup. These determinations appear to be considerably more difficult. They are given in terms of parameters in representations of 16ph by quaternary quadratic forms. Stickelberger's theorem is required to determine the exponent h which is shown to be closely related to the class number of the imaginary quartic field Q(i√2q + 2a√q), q = a2 + b2 ≡ 5 (mod 8), a odd

Development of a novel bi-specific monoclonal antibody approach for tumour targeting

To overcome the disadvantages of bi-specific antibody methodologies in vivo, a novel antibody approach has been designed to improve tumour targeting and effector to target ratio. The technique involves biotinylated anti-CD3 Fab fragments and streptavidinylated anti-tumour monoclonal antibodies (mAbs) that can spontaneously form cross-links. We describe here a method for the direct cross-linking of sulphydryl-conjugated HMFG1 (anti-MUC1 mucin mAb) to streptavidin by sulphosuccinimidyl-4-(N-maleimidomethyl) cyclohexane- 1-carboxylate. Fab fragments generated by papain digestion of the 1452C11 antibody (anti-CD3 mAb without Fc to avoid peripheral activation of T-cells) were biotinylated with NHS-Iminobiotin. MUC1-transfected BALB/c breast cancer cell lines 413BCR and 425CCR and the parental cell line (410.4) were labelled with streptavidinylated mouse anti-MUC1 mucin mAb. BALB/c effector T-cells were separately labelled with biotinylated anti-CD3 Fab fragments (1452C11) and mixed with tumour cells in different effector to target ratios. Percentage of killing was assessed using the 51Cr cytotoxicity assay. Seventy per cent lysis was measured in the case of 413BCR (high MUC1 mucin expressor) and 40% in the case of 425CCR (low expressor) cell line. No lysis was apparent in the MUC1 negative cell line. These results demonstrate that the novel T-cell redirecting approach we have developed can produce effective immune lysis of target cells in vitro. © 1999 Cancer Research Campaig

A laser based accelerator for ultracold atoms

We present first results on our implementation of a laser based accelerator for ultracold atoms. Atoms cooled to a temperature of 420 nK are confined and accelerated by means of laser tweezer beams and the atomic scattering is directly observed in laser absorption imaging. The optical collider has been characterized using Rb87 atoms in the |F=2,mF=2> state, but the scheme is not restricted to atoms in any particular magnetic substates and can readily be extended to other atomic species as well.Comment: (c) 2012 The Optical Society, 3 pages, 4 figures, 1 movie lin

An investigation of vocational progression pathways for young people and adults in building crafts and hospitality CoVEs: a London case study

This report was commissioned by the Learning and Skills Development Agency’s (LSDA’s) strategic programme of research and development, funded by the Learning and Skills Council (LSC). Project aims and objectives The principal aim of this project is to explore how vocational pathways have been developed and enhanced in two occupational areas – building crafts and hospitality – among 14–19 year olds and employed adults in London

River sediment geochemistry and provenance following the Mount Polley mine tailings spill, Canada:The role of hydraulic sorting and sediment dilution processes in contaminant dispersal and remediation

The failure of the Mount Polley tailings storage facility (TSF) in August 2014 was one of the largest magnitude failures on record, and released approximately 25 Mm3 of material, including c. 7.3 Mm3 of tailings into Hazeltine Creek, part of the Quesnel River watershed. This study evaluates the impact of the spill on the geochemistry of river channel and floodplain sediments and utilizes Pb isotope ratios and a multi-variate mixing model to establish sediment provenance. In comparison to sediment quality guidelines and background concentrations, Cu and V were found to be most elevated. Copper in river channel sediments ranged from 88-800 mg kg-1, with concentrations in sand-rich and clay/silt-rich sediments being statistically significantly different. Concentrations in river channel were believed to be influenced by hydraulic sorting during the rising and falling limbs of the flood wave caused by the tailings spill. Results highlight the importance of erosive processes, instigated by the failure, in incorporating soils and sediments into the sediment load transported and deposited within Hazeltine Creek. In this instance, these processes diluted tailings with relatively clean material that reduced metal concentrations away from the TSF failure. This does however, highlight environmental risks in similar catchments downstream of TSFs that contain metal-rich sediment within river channels and floodplain that have been contaminated by historical mining

Economies of space and the school geography curriculum

This paper is about the images of economic space that are found in school curricula. It suggests the importance for educators of evaluating these representations in terms of the messages they contain about how social processes operate. The paper uses school geography texts in Britain since the 1970s to illustrate the different ways in which economic space has been represented to students, before exploring some alternative resources that could be used to provide a wider range of representations of economic space. The paper highlights the continued importance of understanding the politics of school knowledge

Origin and Fate of Vanadium in the Hazeltine Creek Catchment following the 2014 Mount Polley Mine Tailings Spill in British Columbia, Canada

This is the final version. Available on open access from American Chemical Society via the DOI in this recordResults are presented from the analysis of aqueous and solid-phase V speciation within samples collected from the Hazeltine Creek catchment affected by the August 2014 Mount Polley mine tailings dam failure, Canada. Electron microprobe and XANES analysis found that V is present as V3+ substituted into magnetite, and V3+ and V4+ substituted into titanite, both of which occur in the spilled Mount Polley tailings. Secondary Fe oxyhydroxides forming in inflow waters and on creek beds have V K-edge XANES spectra exhibiting E½ positions and pre-edge features consistent with the presence of V5+ species, suggesting sorption of this species on these secondary phases. PHREEQC modelling suggests that the stream waters mostly contain V5+, and the inflow and pore waters contain a mixture of V3+ and V5+. These data, and stream, inflow and pore water chemical data, suggest that dissolution of V(III)-bearing magnetite, V(III,IV)-bearing titanite, V(V)-bearing Fe(-Al-Si-Mn) oxhydroxides, V-bearing Al(OH)3 and/or -clay minerals may have occurred. In the circumneutral pH environment of Hazeltine Creek elevated V concentrations are likely naturally attenuated by formation of V(V)-bearing secondary Fe oxyhydroxide, Al(OH)3 or clay mineral colloids, suggesting that the V is not bioavailable. A conceptual model is presented describing the origin and fate of V in Hazeltine Creek that is applicable to other river systems.Natural Environment Research Council (NERC

Cell trafficking through the choroid plexus

The choroid plexus is a multifunctional organ that sits at the interface between the blood and cerebrospinal fluid (CSF). It serves as a gateway for immune cell trafficking into the CSF and is in an excellent position to provide continuous immune surveillance by CD4+ T cells, macrophages and dendritic cells and to regulate immune cell trafficking in response to disease and trauma. However, little is known about the mechanisms that control trafficking through this structure. Three cell types within the choroid plexus, in particular, may play prominent roles in controlling the development of immune responses within the nervous system: the epithelial cells, which form the blood-CSF barrier, and resident macrophages and dendritic cells in the stromal matrix. Adhesion molecule and chemokine expression by the epithelial cells allows substantial control over the selection of cells that transmigrate. Macrophages and dendritic cells can present antigen within the choroid plexus and/or transmigrate into the cerebral ventricles to serve a variety of possible immune functions. Studies to better understand the diverse functions of these cells are likely to reveal new insights that foster the development of novel pharmacological and macrophage-based interventions for the control of CNS immune responses

Mitotic chromosomes are compacted laterally by KIF4 and condensin and axially by topoisomerase IIα

© 2012 Samejima et al. This article is distributed under the terms of an Attribution–Noncommercial–Share Alike–No Mirror Sites license for the first six months after the publication dateMitotic chromosome formation involves a relatively minor condensation of the chromatin volume coupled with a dramatic reorganization into the characteristic "X" shape. Here we report results of a detailed morphological analysis, which revealed that chromokinesin KIF4 cooperated in a parallel pathway with condensin complexes to promote the lateral compaction of chromatid arms. In this analysis, KIF4 and condensin were mutually dependent for their dynamic localization on the chromatid axes. Depletion of either caused sister chromatids to expand and compromised the "intrinsic structure" of the chromosomes (defined in an in vitro assay), with loss of condensin showing stronger effects. Simultaneous depletion of KIF4 and condensin caused complete loss of chromosome morphology. In these experiments, topoisomerase IIα contributed to shaping mitotic chromosomes by promoting the shortening of the chromatid axes and apparently acting in opposition to the actions of KIF4 and condensins. These three proteins are major determinants in shaping the characteristic mitotic chromosome morphology