Über eine Erweiterung des kleinen Fermatschen Satzes

Ohne Zusammenfassung     

Über die Verteilung der Potenzreste

Ohne Zusammenfassung     

Crystallinity of pure silica glass studied by positron annihilation

The crystallinity of silica glass fused from Brasilian quartz is demonstrated by positron annihilation lineshape measurements using a high resolution Ge(Li)-detector as well as by positron lifetime measurement.     

Fluoroborates by Cleavage of Trimethylamine‐bis(trifluoromethyl)boranes with NEt3 × 3 HF. Structures of C6F5(CF3)2B · NMe3, K[C6H5CH2(CF3)2BF], and K[C6H5(CF3)2BF]

Trimethylamine‐bis(trifluoromethyl)boranes R(CF₃)₂B · NMe₃ (R = cis/trans‐CF₃CF=CF ( 1/2 ), HC≡C ( 3 ), H₂C=CH ( 4 ), C₂H₅ ( 5 ), C₆H₅CH₂ ( 6 ), C₆F₅ ( 7 ), C₆H₅ ( 8 )) react with NEt₃ × 3 HF depending on the nature of R at 155–200 °C under replacement of the trimethylamine ligand to form the corresponding fluoro‐bis(trifluoromethyl)borates [R(CF₃)₂BF]^– ( 1 a/2 a – 8 a ). The structures of 7 , K[C₆H₅CH₂(CF₃)₂BF] ( K‐6 a ), and K[C₆H₅(CF₃)₂BF] ( K‐8 a ) have been investigated by single‐crystal X‐ray diffraction. In 7 the CF₃ groups make short repulsive contacts with NMe₃ and C₆F₅ entities – the B–CF₃ bonds being unusually long. The B–F bond lengths of K‐6 a and K‐8 a (1.446(3) and 1.452(2) Å, respectively) are long for a fluoroborate.     

Defects in nanocrystalline Nb films: Effect of sputtering temperature

Thin niobium (Nb) films (thickness 350-400 nm) were prepared on (1 0 0)Si substrate in a UHV chamber using the cathode beam sputtering. The sputtering temperature T_s was varied from 40 up to 500 °C and the influence of the sputtering temperature on the microstructure of thin Nb films was investigated. Defect studies of the thin Nb films sputtered at various temperatures were performed by slow positron implantation spectroscopy (SPIS) with measurement of the Doppler broadening of the annihilation line. SPIS was combined with transmission electron microscopy (TEM) and X-ray diffraction (XRD). We have found that the films sputtered at T_s = 40 °C exhibit elongated, column-like nanocrystalline grains. No significant increase of grain size with T_s (up to 500 °C) was observed by TEM. The thin Nb films sputtered at T_s = 40 °C contain a high density of defects. It is demonstrated by shortened positron diffusion length and a high value of the S parameter for Nb layer compared to the well-annealed (defect-free) bulk Nb reference sample. A drastic decrease of defect density was found in the films sputtered at T_s ≥ 300 °C. It is reflected by a significant increase of the positron diffusion length and a decrease of the S parameter for the Nb layer. The defect density in the Nb layer is, however, still substantially higher than in the well-annealed reference bulk Nb sample. Moreover, there is a layer at the interface between the Nb film and the substrate with very high density of defects comparable to that in the films sputtered at T_s < 300 °C. All the Nb films studied exhibit a strong (1 1 0) texture. The films sputtered at T_s < 300 °C are characterized by a compressive macroscopic in-plane stress due to lattice mismatch between the film and the substrate. Relaxation of the in-plane stress was observed in the films sputtered at T_s ≥ 300 °C. The width of the XRD profiles of the films sputtered at T_s ≥ 300 °C is significantly smaller compared to the films sputtered at lower temperatures. This is most probably due to a lower defect density which results in reduced microstrains in the films sputtered at higher temperatures.     

Instationärer Wärmetransport durch die Grenzfläche von Kugeln

Zusammenfassung In einer theoretisch-numerischen Studie wurde der instationäre Wärmeaustausch zwischen einer Kugel und seiner Umgebung untersucht. Es wurde angenommen, daß entweder in beiden Phasen Wärmewiderstände vorhanden sind oder nur in der umgebenden Phase 2. Von den erzielten Ergebnissen wurden Beispiele für die Temperaturprofile in beiden Phasen, für die mittlere Temperatur der Kugel und für die mittlere Nußelt-Zahl dargestellt. Die Einflüsse der wichtigsten Parameter wurden ausführlich diskutiert. Abschließend wurden die analogen Kennzahlen für den Wärme- und den Stofftransport angegeben. Damit ist es möglich, bereits bekannte Ergebnisse für den Stofftransport auch für den Wärmetransport zu nutzen.

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Unsteady state heat transfer through the interface of spherical particles

Unsteady state heat exchange between a spherical particle and a surrounding fluid has been investigated by means of theoretical-numerical methods. It has been assumed that there is a heat transfer resistance either in both phases or in one of the two phases only. Some of the results obtained are thoroughly discussed. The examples selected include temperature profiles in both phases, mean temperature of the sphere and the mean Nußelt number. Finally the analogy between unsteady state heat and mass transfer is discussed. On the basis of the established analogy relations available mass transfer results may be used for the solution of heat transfer problems.

     

Templated Generation of a Bcl-xL Inhibitor by Isomer-Free SPAAC Based on Azacyclonon-5-yne

High-affinity inhibitors of large protein–protein interactions often have a high molecular weight, which compromises their cell permeability and oral bioavailability. We recently presented isomer-free, strain-promoted azide-alkyne cycloaddition (iSPAAC) as a method by which to generate large, chemically uniform bioactive molecules inside living cells from two smaller components with higher cell permeability. Here, we present the synthesis of Fmoc-protected azacyclonon-5-yne (Fmoc-ACN) as the first cyclononyne suitable for iSPAAC. ACN facilitated the structure-guided development of a single-digit micromolar triazole inhibitor of the protein–protein interaction domain of the antiapoptotic protein Bcl-x_L. Inhibitor formation in aqueous buffer at 37 °C, templated by the target protein Bcl-x_L, proceeded 2800 times faster than the reaction between Fmoc-ACN and benzyl azide under standard conditions in acetonitrile. Our data demonstrate the utility of cyclononynes for iSPAAC and their potential for achieving vastly accelerated templated reactions in aqueous environments.     

Fluiddynamik bei quer angeströmten Zylindern

Zusammenfassung Die vorliegende Untersuchung befa\t sich mit der stationÄren Umströmung eines einzelnen Kreiszylinders. Die vollstÄndige Navier-Stokessche Gleichung wurde für den Bereich der Reynolds-Zahl von Re=10^–4 bis Re=1,2·10² numerisch intergriert. — Die das Strömungsfeld kennzeichnenden Merkmale sind der Strömungswiderstand, die Grö\en für die Ablösung der Strömung sowie die kritische Reynolds-Zahl. Sie sind abhÄngig von der Ausdehnung des umgebenden Fluids. Zur Berechnung dieser Grö\en werden Gleichungen mit praktisch bedeutsamen Gültigkeitsbereich mitgeteilt. Diese Berechnungsgleichungen sind durch theoretisch-numerische Daten sowie durch zahlreiche Me\daten gestützt. — Insbesondere wird ein Widerstandsgesetz erörtert, dessen Gültigkeit im Bereich der Reynolds-Zahl von Re=10^–4 bis zur kritischen Reynolds-Zahl theoretisch und experimentell einwandfrei gesichert ist. Es ist das bisher umfassendste Widerstandsgesetz für Kreiszylinder. Für kleinere Werte der Reynolds-Zahl als Re=10^–4 wird ein analytisches NÄherungsgesetz für den Widerstandsbeiwert mitgeteilt.

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Investigation of the flow around transverse cylinders

The steady incompressible flow around a circular cylinder has been investigated. Numerical solutions of the full Navier-Stokes equation have been obtained for a range of Reynolds numbers from Re=10^–4 to Re=1,2·10². The calculated velocity distributions allowed to determine the values of the drag coefficient, the angles of separation, and the wake lengths. They depend on the extend of the numerical field. These quantities can be predicted now by means of correlations, which are in good agreement with all available experimental and theoretical data. Especially it is presented a drag equation for the range of Reynolds numbers from Re=10^–4 up to Re=Re_kr. The critical Reynolds number, Re_kr, is a function of the turbulence intensity. This function is known. For very low Reynolds numbers, Re < 10^–4, there is an analytical drag equation, that based on Oseen type linearization of the Navier-Stokes equation.

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Formelzeichen d Zylinderdurchmesser - F SchattenflÄche des Zylinders - l^* bezogene LÄnge des Rückströmungsgebietes - p,p^* örtlicher, bezogener örtlicher Druck - R Zylinderradius - r,r^* radiale, bezogene radiale Koordinate - W Strömungswiderstand des Zylinders - w Anströmgeschwindigkeit des Fluids - w_r,w _r ^* örtliche, bezogene örtliche Geschwindigkeitskomponente in radialer Richtung - w,w ^* örtliche, bezogene örtliche Geschwindigkeitskomponente in Umfangsrichtung - w zeitliche Schwankungsgeschwindigkeit - Widerstandsbeiwert des Zylinders - _D,_R Druck- und Reibungsanteil des Widerstandsbeiwerts - Umfangswinkel vom vorderen Staupunkt gemessen - _A Ablösewinkel vom hinteren Staupunkt gemessen - kinematische ViskositÄt des Fluids - Massendichte des Fluids - ,^* örtliche, bezogene örtliche WirbelstÄrke - ,^* örtliche, bezogene örtliche Stromfunktion - Reynolds-Zahl - Re_kr kritischer Wert der Reynolds-Zahl - Turbulenzgrad Indices r in radialer Richtung - b Umfangsrichtung