Elliptic integrals and the Schwarz-Christoffel transformation

AbstractThe real elliptic integrals of the first and second kind in Jacobi's normal form are computed efficiently, using the convolution number in conjunction with the method of Frobenius. For this purpose certain treatments of the Laurent series are included. Different regions of convergence on the real axis are determined, and for each one a different series is developed. The real elliptic integral of the third kind is solved within a limited parameter plane by the same method.The integral of the Schwarz-Christoffel transformation is solved in the complex variable by complex convolution number algebra, using the unit disk as mapping region. Different regions of convergence of Frobenius, Laurent, and Taylor series are determined to cover the whole disk. The complex evaluation of the elliptic integral of the third kind is included. A Schwarz-Christoffel formula for an infinite periodic mapping is given. The solutions for exterior, interior, periodic, and cyclic polygons are separately treated. Examples of several polygon mappings are presented graphically, and compared with previous numerically integrated solutions.The parameter problem is solved by the Newton-Raphson method, using a quotient matrix as approximation for the Jacobian matrix. The coordinate relations are simplified by using an overdetermined system. An exact analytical Jacobian matrix is computed, solving Leibniz' derivative of the Schwarz-Christoffel integral, and results are compared with the approximate quotient matrix method

Local Bacteriological Survey: Isolation and Characterization of Bacteria in Two Lynchburg Parks

Water samples were collected from the bodies of water at Peaks View Park and Percival’s Isle Park in Lynchburg, Virginia in two separate trials per collection site. The samples were filtered to isolate bacteria present in the water. The filters were placed on Trypticase Soy Agar (TSA) and Eosin Methylene Blue (EMB) plates and incubated to obtain colony counts of the bacteria. Subsequently, distinct colonies were selected from the filtration plates and streaked for isolation. Isolates were subjected to a variety of analytical methods and thereby identified by genus and species. Fifteen different species were identified from twenty-three different samples. The samples included an alarming number of E. coli colonies, as well as other enterobacteria and human pathogens

Development of a miniaturized, sterilizable, gamma-backscatter atmosphere density sensor

Design, development, and characteristics of gamma backscatter atmosphere density senso

Variance of wind estimates using spaced antenna techniques with the MU radar

International audienceVariance of horizontal wind estimates in conditions of anisotropic scattering are obtained for the Spaced Antenna (SA) Full Correlation Analysis (FCA) method of Holloway et al. (1997b) and Doviak et al. (1996), but are equally applicable to the Briggs method of FCA. Variance and covariance of cross-correlation magnitudes are theoretically estimated, and the standard theory of error propagation is used to estimate the variance of the wind components for the infinite SNR case. The effect of baseline orientation is investigated, and experimental data from the MU radar in Japan is presented

Comparisons of refractive index gradient and stability profiles measured by balloons and the MU radar at a high vertical resolution in the lower stratosphere

Many experimental studies have demonstrated that VHF Stratosphere-Troposphere (ST) radar echo power is proportional to the generalized refractive index gradient squared <I>M</I><sup>2</sup> when using a vertically oriented beam. Because humidity is generally negligible above the tropopause, VHF ST radars can thus provide information on the static stability (quantified by the squared Brunt-Väisälä frequency <I>N</I><sup>2</sup>) at stratospheric heights and this capability is useful for many scientific applications. Most studies have been performed until now at a vertical resolution of 150 m or more. In the present paper, results of comparisons between radar- and (balloon borne) radiosonde-derived <I>M</I><sup>2</sup> and <I>N</I><sup>2</sup> are shown at a better vertical resolution of 50 m with the MU radar (34.85° N, 136.15° E; Japan) by benefiting from the range resolution improvement provided by the multi-frequency range imaging technique, using the Capon processing method. Owing to favorable winds in the troposphere, the radiosondes did not drift horizontally more than about 30 km from the MU radar site by the time they reached an altitude of 20 km. The measurements were thus simultaneous and almost collocated. Very good agreements have been obtained between both high resolution profiles of <i>M</i><sup>2</sup>, as well as profiles of <i>N</i><sup>2</sup>. It is also shown that this agreement can still be improved by taking into account a frozen-in advection of the air parcels by a horizontally uniform wind. Therefore, it can be concluded that 1) the range imaging technique with the Capon method really provides substantial range resolution improvement, despite the relatively weak Signal-to-Noise Ratios (SNR) over the analyzed region of the lower stratosphere, 2) the proportionality of the radar echo power to <I>M</I><sup>2</sup> at a vertical scale down to 50 m in the lower stratosphere is experimentally demonstrated, 3) the MU radar can provide stability profiles with a vertical resolution of 50 m at heights where humidity is negligible, 4) stable stratospheric layers as thin as 50 m or less have at least a horizontal extent of a few km to several tens of kilometers and can be considered as frozenly advected over scales of a few tens of minutes

Marxismus und Industriekritik: Otto Ullrichs 'Weltniveau' und der marx'sche Begriff der Industriekritik

Sein Buch 'Technik und Herrschaft', erschienen 1977 bei Suhrkamp, machte auf Otto Ullrich aufmerksam. Einer breiteren Öffentlichkeit bekannt wurde er freilich durch seine populär verfaßte Schrift 'Weltniveau - in der Sackgasse des Industriesystems', Rotbuch Verlag, Berlin 1979. Der vielgelesene Autor gilt mancherorts als ein Theoretiker einer postmarxistischen, ökologischen bzw. industriekritischen 'Linken'. Ullrich entwickelt seine industriekritische Position in prononcierter und breit angelegter Auseinandersetzung mit dem 'Marxismus'. Diesen hält er für zutiefst industrieborniert, affirmativ gegenüber der wissenschaftlichen Technologie der großen Industrie. Ullrichs zentrale These ist, daß der 'Marxismus'(und damit das vorherrschende linke Bewußtsein) zwar eine Kritik der Produktionsverhältnisse, nicht aber eine Kritik der Produktivkräfte vorweisen könne. Er habe, einer geschichtsmetaphysischen Tradition folgend, die komplexe große Industrie und deren technischen Fortschritt zum Maßstab der Emanzipation der Menschheit genommen. Da jedoch die große Industrie in Wahrheit durch und durch herrschaftsförmig strukturiert sei, verzichte der 'Marxismus' bereits im Ansatz auf die Einlösung seiner emanzipatorischen Ansprüche. Ullrichs Konsequenz: Der Prozeß der Veränderung sozialer Beziehungen muß gestützt werden durch eine überschaubare, dezentrale, kleinere Technik, die unterhalb einer 'sozialkritischen Grenze' (der Terminus stammt von Ivan Illich) verbleibt

Die Theatralisierung des öffentlichen Raumes

Wissenschaftliches Kolloquium vom 14. bis 16. Oktober 1999 in Weimar an der Bauhaus-Universität zum Thema: ‚global village - Perspektiven der Architektur

High-resolution vertical imaging of the troposphere and lower stratosphere using the new MU radar system

International audienceIn the present paper, a new application of the range imaging technique called Frequency Interferometry Imaging (FII) or Range Imaging (RIM), performed in April 2005, is shown using the new 46.5-MHz Middle and Upper (MU) atmosphere radar system (Shigaraki, Japan). Height-time images of brightness distribution have been computed at the highest resolution ever obtained for imaging with VHF radars in the troposphere and, for the very first time, in the lower stratosphere, up to about 22 km. The images were produced by processing signals obtained with an initial range-resolution of ?r=150 m and five equally-spaced frequencies within ?f=1.0 MHz, with the adaptive Capon method. These values represent an improvement of a factor 2 over all the previous published experiments at VHF, which were performed with ?r=300 m and ?f=0.5 MHz. The Capon images present realistic and self-consistent features, and reveal many more organized structures than the height-time SNR plots at the initial range-resolution. For example, the Capon images show persistent enhanced brightness layers significantly thinner than 150 m in the stratosphere, which are impossible to track with the standard single-frequency mode owing to a lack of range resolution. These observations thus support the idea of strong stratification even at vertical scales much smaller than 100 m, as suggested by recent high-resolution temperature observations by balloons (Dalaudier et al., 1994). We also present comparisons of Capon images with patterns obtained from the dual-FDI technique and two parametric methods (the MUSIC algorithm and the newly-introduced Maximum Entropy Method based on an auto-regressive (AR) model). The comparisons confirm the insufficiencies of the dual-FDI technique and indicate that parametric methods such as MEM and the MUSIC algorithm can help to validate the Capon images when the parametric methods provide similar patterns