Theory of linear G-difference equations

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other equations,symmetries of an equation are module endomorphisms and conserved structures are invariants in the tensor algebra of the given equation. We show that the equations and their solutions can be described through representations of the isotropy group of the symmetry group of the underluing set. We relate our notion of difference equations and solutions to systems of classical difference equations and their solutions and show that our notions include these as a special case.Comment: 34 page

Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

Investigating CXOU J163802.6-471358: a new pulsar wind nebula in the Norma region?

We present the first analysis of the extended source CXOU J163802.6--471358, which was discovered serendipitously during the {\em Chandra} X-ray survey of the Norma region of the Galactic spiral arms. The X-ray source exhibits a cometary appearance with a point source and an extended tail region. The complete source spectrum is fitted well with an absorbed power law model and jointly fitting the {\em Chandra} spectrum of the full source with one obtained from an archived {\em XMM-Newton} observation results in best fit parameters $N_{\rm H}$ $=1.5^{+0.7}_{-0.5}\times10^{23} \text{cm}{^{-2}}$ and $\Gamma=1.1^{+0.7}_{-0.6}$ (90$$ confidence uncertainties). The unabsorbed luminosity of the full source is then $L_X\sim 4.8\times10^{33}d_{10}^2$ergs s$^{-1}$ with $d_{10}=d/10$kpc, where a distance of 10 kpc is a lower bound inferred from the large column density. The radio counterpart found for the source using data from the Molonglo Galactic Plane Survey epoch-2 (MGPS-2) shows an elongated tail offset from the X-ray emission. No infrared counterpart was found. The results are consistent with the source being a previously unknown pulsar driving a bow shock through the ambient medium

Investigations of lubricant rheology as applied to elastohydrodynamic lubrication

The pressure viscometer was modified to permit the measurement of viscosity at elevated pressures and shear stresses up to 5 x 10 to the 6th power N/sq m (720 psi). This shear stress is within a factor of three of the shear stress occurring in a sliding ehd point contact such as occurs in the ehd simulator. Viscosity data were taken on five lubricant samples, and it was found that viscous heating effects on the viscosity were predominant and not non-Newtonian behavior at the high shear stresses. The development of the infrared temperature measuring technique for the ehd simulator was completed, and temperature data for a set of operating conditions and one lubricant are reported. The numerical analysis of the behavior of nonlinear lubricants in the lubrication of rollers is reported

Using self-monitoring to increase the academic responsibility of eighth grade mainstreamed students

The purpose of this study was to investigate the impact of a self-monitoring program on the academic performance of eighth grade mainstreamed learning disabled students ages 13-14. Ten subjects underwent an intervention involving private conferencing on academic responsibility and use of self-monitoring using assignment books. Data was collected on frequency of using assignment books and homework completion for pre-intervention and post-intervention. Data was analyzed for increases in use of assignment books, homework completion, and correlations between self-recorded assignments and assignment completion. The major finding of this investigation was that there was a significant increase in completing assignments on time when self-monitoring was used