Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 2: adjoint approximations and extensions

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] of discrete approximations to the linearized and adjoint equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. We consider a simple modified Lax–Friedrichs discretization on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It is proved that there is convergence in the discrete approximation of linearized output functionals even for Dirac initial perturbations and pointwise convergence almost everywhere for the solution of the adjoint discrete equations. In particular, the adjoint approximation converges to the correct uniform value in the region in which characteristics propagate into the discontinuity. Moreover, it is shown that the results of [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] and the present paper hold also for quite general nonlinear initial data which contain multiple shocks and for which shocks form at a later time and/or merge

Parastatistics of charged bosons partly localised by impurities

Coulomb repulsion is taken into account to derive the thermodynamics of charged bosons in a random external potential. A simple analytical form of the partition function is proposed for the case of non-overlapping localised states (i.e. a small amount of disorder). The density of localised bosons and the specific heat show a peculiar non-uniform temperature dependence below the Bose-Einstein condensation temperature. The superfluid - Bose-glass phase diagram is discussed. A new phase is predicted which is a Bose-glass at T=0 but a superfluid at finite T.Comment: 6 pages, Revtex, 6 figures (available on request from the authors

Gene-knockdown in the honey bee mite Varroa destructor by a non-invasive approach : studies on a glutathione S-transferase

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Transcriptome analysis of the synganglion from the honey bee mite, Varroa destructor and RNAi knockdown of neural peptide targets

Acknowledgements This work was funded by BBSRC-LINK grant # BB/J01009X/1 and Vita Europe Ltd. We are grateful to the Scottish Beekeepers Association, especially Mr Phil McAnespie in supporting this work at its inception. We acknowledge partial funding from a Genesis Faraday SPARK Award, part of a Scottish Government SEEKIT project for the early part of this work. We are grateful to Prof David Evans for his advice on Varroa destructor viruses.Peer reviewedPostprin

INCREASES IN COSTS AND RETURNS DUE TO INTENSIFYING RANGE FORAGE PRODUCTION SURVEYS: AN INFORMATION ECONOMIC ANALYSIS

The U.S. Congress and courts have directed federal natural resource agencies to use better information for management decisions than they have used in the past. It is also important for these agencies to improve the efficiency of resource use where possible. This information economics study estimates increased costs and revenues which can be directly imputed to improving the accuracy of range forage production surveys. It suggests that a high level of survey accuracy may often be justifiable.Crop Production/Industries, Research Methods/ Statistical Methods,

Program for computing partial pressures from residual gas analyzer data

A computer program for determining the partial pressures of various gases from residual-gas-analyzer data is given. The analysis of the ion currents of 18 m/e spectrometer peaks allows the determination of 12 gases simultaneously. Comparison is made to ion-gage readings along with certain other control information. The output data are presented in both tabular and graphical form