Non-unital Ore extensions

In this article, we study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings $R[x;\delta]$, under the hypothesis that $R$ is $s$-unital and $\ker(\delta)$ contains a nonzero idempotent. This result generalizes a result by \"Oinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings

Basic investigation into the electrical performance of solid electrolyte membranes

The electrical performance of solid electrolyte membranes was investigated analytically and the results were compared with experimental data. It is concluded that in devices that are used for pumping oxygen the major power losses have to be attributed to the thin film electrodes. Relations were developed by which the effectiveness of tubular solid electrolyte membranes can be determined and the optimum length evaluated. The observed failure of solid electrolyte tube membranes in very localized areas is explained by the highly non-uniform current distribution in the membranes. The analysis points to a possible contact resistance between the electrodes and the solid electrolyte material. This possible contact resistance remains to be investigated experimentally. It is concluded that film electrodes are not appropriate for devices which operate with current flow, i.e., pumps though they can be employed without reservation in devices that measure oxygen pressures if a limited increase in the response time can be tolerated

Adolph R. Krause and Augusta W. (Richter) Krause and their descendants (1860-2009)

This book has been split into several sections to allow for faster downloading."An electronic version of this document is posted on MOspace and with the Google Book Search Library Project. Printed copies are housed at the Center for Western Studies, Augustana College, Sioux Falls, South Dakota, and at the Ottertail Historical Society, Fergus Falls, Minnesota."This books summarizes the family history of Adolph R. and Augusta W. (Richter) Krause following their arrival in the United States

Low pressure arc electrode

Reducing the pressure in the vicinity of the arc attachment point by allowing the gas to flow through a supersonic nozzle minimizes local heating rates, prevents ablation, and increases the efficiency of coaxial gas-flow arcs

Scattering from Solutions of Star Polymers

We calculate the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced by Daoud and Cotton. In this model, a single star is regarded as a spherical region of a semi-dilute polymer solution with a local, position dependent screening length. For high enough concentrations, the outer sections of the arms overlap and build a semi-dilute solution (a sea of blobs) where the inner parts of the actual stars are embedded. The scattering function is evaluated following a method introduced by Auvray and de Gennes. In the dilute regime there are three regions in the scattering function: the Guinier region (low wave vectors, q R << 1) from where the radius of the star can be extracted; the intermediate region (1 << q R << f^(2/5)) that carries the signature of the form factor of a star with f arms: I(q) ~ q^(-10/3); and a high wavevector zone (q R >> f^(2/5)) where the local swollen structure of the polymers gives rise to the usual q^(-5/3) decay. In the semi-dilute regime the different stars interact strongly, and the scattered intensity acquires two new features: a liquid peak that develops at a reciprocal position corresponding to the star-star distances; and a new large wavevector contribution of the form q^(-5/3) originating from the sea of blobs.Comment: REVTeX, 12 pages, 4 eps figure

The Statistics of the Points Where Nodal Lines Intersect a Reference Curve

We study the intersection points of a fixed planar curve $\Gamma$ with the nodal set of a translationally invariant and isotropic Gaussian random field \Psi(\bi{r}) and the zeros of its normal derivative across the curve. The intersection points form a discrete random process which is the object of this study. The field probability distribution function is completely specified by the correlation G(|\bi{r}-\bi{r}'|) = . Given an arbitrary G(|\bi{r}-\bi{r}'|), we compute the two point correlation function of the point process on the line, and derive other statistical measures (repulsion, rigidity) which characterize the short and long range correlations of the intersection points. We use these statistical measures to quantitatively characterize the complex patterns displayed by various kinds of nodal networks. We apply these statistics in particular to nodal patterns of random waves and of eigenfunctions of chaotic billiards. Of special interest is the observation that for monochromatic random waves, the number variance of the intersections with long straight segments grows like $L \ln L$, as opposed to the linear growth predicted by the percolation model, which was successfully used to predict other long range nodal properties of that field.Comment: 33 pages, 13 figures, 1 tabl