On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with $\gamma=0$. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as $s\to 1$. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with $\beta=0$.Comment: 38 pages, 5 figure

VLA observations of 6-cm excited OH

The VLA was used to determine precise positions for 4765-MHz OH maser emission sources toward star-forming regions which had been observed about seven months earlier with the Effelsberg 100-meter telescope. The observations were successful for K3-50, DR21EX, W75N, and W49A. No line was detected toward S255: this line had decreased to less than 5 per cent of the flux density observed only seven months earlier. The time-variability of the observed features during the past 30 years is summarised. In addition, to compare with the Effelsberg observations, the 4750-MHz and 4660-MHz lines were observed in W49A. These lines were found to originate primarily from an extended region which is distinguished as an exceptional collection of compact continuum components as well as by being the dynamical centre of the very powerful H_2 O outflow.Comment: 11 pages, will require MN style file to process. MNRAS, accepted Oct 15, 200

6D Muon Ionization Cooling with an Inverse Cyclotron

A large admittance sector cyclotron filled with LiH wedges surrounded by helium or hydrogen gas is explored. Muons are cooled as they spiral adiabatically into a central swarm. As momentum approaches zero, the momentum spread also approaches zero. Long bunch trains coalesce. Energy loss is used to inject the muons into the outer rim of the cyclotron. The density of material in the cyclotron decreases adiabatically with radius. The sector cyclotron magnetic fields are transformed into an azimuthally symmetric magnetic bottle in the center. Helium gas is used to inhibit muonium formation by positive muons. Deuterium gas is used to allow captured negative muons to escape via the muon catalyzed fusion process. The presence of ionized gas in the center may automatically neutralize space charge. When a bunch train has coalesced into a central swarm, it is ejected axially with an electric kicker pulse.Comment: Five pages. LaTeX, three postscript figure files. To appear in the AIP Conference Proceedings for COOL05: International Workshop on Beam Cooling, Galena, IL, 18-23 Sept. 200

Interdisciplinary (retail) research: The business of geography and the geography of business

NoAt the 2005 British Academy of Management conference several well-known economic geographers, including Neil Wrigley, Gordon Clark, and Susan Christopherson, called for management researchers to engage with economic geographers on interrelated geographical and managerial issues in the study of (retail) firms. In this commentary we reflect upon the present geography -management interface.We begin by considering the term `interdisciplinary research' and its relationship to any management - geography interface. This is followed by a context-specific discussion of international retailing and the role of research on the retail transnational corporation (TNC) in developing an interdisciplinary agenda. This commentary represents an initial more business and management focused response to the call from geography academics for more/better interdisciplinary research at the geography - management interface

Structures and Reactivity Patterns of Group 9 Metallocorroles

Group 9 metallocorroles 1-M(PPh_3) and 1-M(py)_2 [M = Co(III), Rh(III), Ir(III); 1 denotes the trianion of 5,10,15-tris-pentafluorophenylcorrole] have been fully characterized by structural, spectroscopic, and electrochemical methods. Crystal structure analyses reveal that average metal−N(pyrrole) bond lengths of the bis-pyridine metal(III) complexes increase from Co (1.886 Å) to Rh (1.957 Å)/Ir (1.963 Å); and the average metal−N(pyridine) bond lengths also increase from Co (1.995 Å) to Rh (2.065 Å)/Ir (2.059 Å). Ligand affinities for 1-M(PPh_3) axial coordination sites increase dramatically in the order 1-Co(PPh_3) < 1-Rh(PPh_3) < 1-Ir(PPh_3). There is a surprising invariance in the M(+/0) reduction potentials within the five- and six-coordinate corrole series, and even between them; the average M(+/0) potential of 1-M(PPh_3) is 0.78 V vs Ag/AgCl in CH_2Cl_2 solution, whereas that of 1-M(py)_2 is 0.70 V under the same conditions. Electronic structures of one-electron-oxidized 1-M(py)_2 complexes have been assigned by analysis of electron paramagnetic resonance spectroscopic measurements: oxidation is corrole-centered for 1-Co(py)_2 (g = 2.008) and 1-Rh(py)_2 (g = 2.003), and metal-centered for 1-Ir(tma)_2 (g_(zz) = 2.489, g_(yy) = 2.010, g_(xx) = 1.884, g_(av) = 2.128) and 1-Ir(py)_2 (g_(zz) = 2.401, g_(yy) = 2.000, g_(xx) = 1.937, g_(av) = 2.113)

SVOM pointing strategy: how to optimize the redshift measurements?

The Sino-French SVOM mission (Space-based multi-band astronomical Variable Objects Monitor) has been designed to detect all known types of gamma-ray bursts (GRBs) and to provide fast and reliable GRB positions. In this study we present the SVOM pointing strategy which should ensure the largest number of localized bursts allowing a redshift measurement. The redshift measurement can only be performed by large telescopes located on Earth. The best scientific return will be achieved if we are able to combine constraints from both space segment (platform and payload) and ground telescopes (visibility).Comment: Proceedings of Gamma-Ray Bursts 2007 conference, Santa Fe, USA, 5-9 November 2007. Published in AIP conf. proc. 1000, 585-588 (2008

Rigid collapsible dish structure

A collapsible dish structure composed of a plurality of rows of rigid radial petal assemblies concentric with the axis of the dish. The petal assemblies consist of a center petal and two side petals, the center petal hinged on an axis tangent to a circle concentric with the axis of the dish and the side petals hinged to the center petal at their mating edge. The center petal is foldable inwardly and the side petals rotate about their hinges such that the collapsed dish structure occupies a much smaller volume than the deployed dish. Means of controlling the shape of the dish to compensate for differential expansion of the deployed dish are also provided