Investigation of macrocyclisation routes to 1,4,7-triazacyclononanes : efficient syntheses from 1,2-ditosylamides

Two routes to the synthesis of a cyclohexyl-fused 1,4,7-triazacyclononane involving macrocyclisations of tosamides have been investigated. In the first approach, using a classic Richman-Atkins-type cyclisation of a cyclohexyl-substituted 1,4,7-tritosamide with ethylene glycol ditosylate, afforded the cyclohexyl-fused 1,4,7-triazacyclononane in 5.86% overall yield in four steps. The second, more concise, approach involving the macrocyclisation of trans-cyclohexane-1,2-ditosamide with the tritosyl derivative of diethanolamine initially gave poor yields (< 25%). The well-documented problems with efficiencies in macrocyclisations using 1,2-ditosamides led to the use of a wider range of 1,2-ditosamides including ethane-1,2-ditosamide and propane-1,2-ditosamide. These extended studies led to the development of an efficient macrocyclisation protocol using lithium hydride. This new method afforded 1,4,7-tritosyl-1,4,7-triazacyclononanes in good yield (57-90%) from 1,2-ditosamides in a single step. These efficient methods were then applied to the preparation of a chiral cyclohexyl-fused 1,4,7-tritosyl-1,4,7-triazacyclononane (65-70%). This key chiral intermediate was then converted into a copper(II) complex following detosylation and N-methylation. The resulting chiral copper(II) complex catalysed the aziridination of styrene but it did so in a racemic fashion

No Evidence Supporting Flare Driven High-Frequency Global Oscillations

The underlying physics that generates the excitations in the global low-frequency, < 5.3 mHz, solar acoustic power spectrum is a well known process that is attributed to solar convection; However, a definitive explanation as to what causes excitations in the high-frequency regime, > 5.3 mHz, has yet to be found. Karoff and Kjeldsen (Astrophys. J. 678, 73-76, 2008) concluded that there is a correlation between solar flares and the global high-frequency solar acoustic waves. We have used the Global Oscillations Network Group (GONG) helioseismic data in an attempt to verify Karoff and Kjeldsen (2008) results as well as compare the post-flare acoustic power spectrum to the pre-flare acoustic power spectrum for 31 solar flares. Among the 31 flares analyzed, we observe that a decrease in acoustic power after the solar flare is just as likely as an increase. Furthermore, while we do observe variations in acoustic power that are most likely associated with the usual p-modes associated with solar convection, these variations do not show any significant temporal association with flares. We find no evidence that consistently supports flare driven high-frequency waves.Comment: 20 pages, 9 figures, Accepted for publication in Solar Physic

Effective lattice actions for correlated electrons

We present an exact, unconstrained representation of the electron operators in terms of operators of opposite statistics. We propose a path--integral representation for the $t$-$J$ model and introduce a parameter controlling the semiclassical behaviour. We extend the functional approach to the Hubbard model and show that the mean--field theory is equivalent to considering, at Hamiltonian level, the Falikov--Kimball model. Connections with a bond-charge model are also discussed.Comment: 12 pages, REVTeX 3.0, no figure

Digital technology and governance in transition: The case of the British Library

Comment on the organizational consequences of the new information and communications technologies (ICTs) is pervaded by a powerful imagery of disaggregation and a tendency for ?virtual? forms of production to be seen as synonymous with the ?end? of bureaucracy. This paper questions the underlying assumptions of the ?virtual organization?, highlighting the historically enduring, diversified character of the bureaucratic form. The paper then presents case study findings on the web-based access to information resources now being provided by the British Library (BL). The case study evidence produces two main findings. First, radically decentralised virtual forms of service delivery are heavily dependent on new forms of capacity-building and information aggregation. Second, digital technology is embedded in an inherently contested and contradictory context of institutional change. Current developments in the management and control of digital rights are consistent with the commodification of the public sphere. However, the evidence also suggests that scholarly access to information resources is being significantly influenced by the ?information society? objectives of the BL and other institutional players within the network of UK research libraries

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

Shadowing in Inelastic Scattering of Muons on Carbon, Calcium and Lead at Low XBj

Nuclear shadowing is observed in the per-nucleon cross-sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.Comment: 22 pages, incl. 6 figures, to be published in Z. Phys.

Spectral and transport properties of doped Mott-Hubbard systems with incommensurate magnetic order

We present spectral and optical properties of the Hubbard model on a two-dimensional square lattice using a generalization of dynamical mean-field theory to magnetic states in finite dimension. The self-energy includes the effect of spin fluctuations and screening of the Coulomb interaction due to particle-particle scattering. At half-filling the quasiparticles reduce the width of the Mott-Hubbard `gap' and have dispersions and spectral weights that agree remarkably well with quantum Monte Carlo and exact diagonalization calculations. Away from half-filling we consider incommensurate magnetic order with a varying local spin direction, and derive the photoemission and optical spectra. The incommensurate magnetic order leads to a pseudogap which opens at the Fermi energy and coexists with a large Mott-Hubbard gap. The quasiparticle states survive in the doped systems, but their dispersion is modified with the doping and a rigid band picture does not apply. Spectral weight in the optical conductivity is transferred to lower energies and the Drude weight increases linearly with increasing doping. We show that incommensurate magnetic order leads also to mid-gap states in the optical spectra and to decreased scattering rates in the transport processes, in qualitative agreement with the experimental observations in doped systems. The gradual disappearence of the spiral magnetic order and the vanishing pseudogap with increasing temperature is found to be responsible for the linear resistivity. We discuss the possible reasons why these results may only partially explain the features observed in the optical spectra of high temperature superconductors.Comment: 22 pages, 18 figure

Z_2 Invariants of topological insulators as geometric obstructions

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to −1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones