Über Effekte zweiter Ordnung bei Biegung und Torsion dünnwandiger Rohre elliptischen Querschnitts

Zusammenfassung Mittels einfacher Gleichgewichtsbetrachtungen wird gezeigt, daÜ bei der Biegung eines dünnwandigen Rohres von elliptischem Querschnitt neben den Längsspannungen der elementaren Biegungstheorie auch Biegungsspannungen auftreten, deren EinfluÜ bei geringer Wandstärke im Vergleich zu den Ellipsenachsen nicht zu vernachlässigen ist, vor allem wegen der Verformung des Querschnitts, den sie zur Folge haben. Diese Abplattung der Ellipse wird mit Hilfe des Castiglianoschen Satzes berechnet. Bei den zusätzlichen Biegungsspannungen und der zugeordneten Deformation handelt es sich um Effekte zweiter Ordnung, die eine Verminderung der Sicherheit gegen Einbeulen der Rohre verursachen. Entsprechende Betrachtungen werden für die Torsion angestellt, wobei gleichartige Ergebnisse erzielt werden. Die Aussage über die Herabsetzung der Instabilitätsgrenze ist nur qualitativer Art. Es wird eine einfache Anwendung auf das Bourdonsche Manometer gebracht und dabei die Erklärung der Tatsache gegeben, daÜ eine Röhrenfeder in den Endpunkten der groÜen Achse ihres Querschnittes zuerst aufreiÜt.Der Verfasser dankt Herrn Prof.L. Föppl für die Anregung dieser Arbeit, sowie für die überlassung der Gleichungen (25), (27), (36) aus unveröffentlichten Arbeiten.     

Tetraphenylantimony carboxylates in the cascade Pd-catalyzed C-phenylation reaction of methyl acrylate in the presence of peroxide

Tetraphenylantimony(V) carboxylates have been used in the palladium-catalyzed C-phenylation reaction of methyl acrylate in the presence of (PhCO₂)₂ or t-BuOOH under mild conditions (50 °C). The peroxides promote a cascade participation of the organoantimony compound and result in the transfer of three phenyl groups. Organoantimony intermediates have been isolated from the reaction.     

Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Vorticity-velocity-pressure formulation for Stokes problem

We propose a three-field formulation for efficiently solving a two-dimensional Stokes problem in the case of nonstandard boundary conditions. More specifically, we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary. The proposed computational methodology consists in reformulating the considered boundary value problem via a mixed-type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the Lagrange multiplier. The obtained formulation is then discretized and a convergence analysis is performed. A priori error estimates are established, and some numerical results are presented to highlight the perfomance of the proposed computational methodology.

     

Application of enzyme-field effect transistor sensor arrays as detectors in a flow-injection analysis system for simultaneous monitoring of medium components. Part II. Monitoring of cultivation processes

Glucose, maltose, sucrose, lactose, ethanol and urea concentrations were monitored simultaneously during the cultivation of Escherichia coli and Saccharomyces cerevisiae by means of enzyme field effect transistors (EnFETs) applying glucose dehydrogenase (GDH), maltase (MAL)/GDH, invertase (INV)/GDH, β-galactosidase (β-GAL)/galactosedehydrogenase (GALDH), alcoholdehydrogenase (ADH)/aldehydedehydrogenase (ALDH), and urease. These enzymes were (co)immobilized on the pH sensitive gates of an eight-FET array. The FET array was integrated in a commercial FIA system.     

Character formulas for some classes of atypical gl(m+nε)- and p(m)-modules

If p is an arbitrary parabolic subsuperalgebra of g = gl(m + n), p(m), a character formula for the generic finite-dimensional irreducible g-module, such that p is the stabilizer of its lowest weight space, is announced. Furthermore, an estimate for the character of any finite-dimensional irreducible g-module in terms of its highest weight with respect to a distinguished Borel subsuperalgebra is presented (inequality (4)) and a sufficient condition for this to be an equality is found. In this way, two generalizations of the Kac character formula for typical modules are obtained: a formula concerning an arbitrary Borel subsuperalgebra ((1)) and a more effective formula ((3)) for the special case of a distinguished Borel subsuperalgebra. The complete proofs will appear in [14].Partially supported by Contract 911/11.04.88 with the Bulgarian Ministry of Culture, Science, and Education.     

Total synthesis of a conformationally constrained didemnin B analog

The total synthesis of a didemnin B analogue containing a conformationally constrained replacement for the isostatine moiety is reported. Synthetic highlights include an improved preparation of 2-hydroxy-3-cyclohexenecarboxylic acid and a new strategy for accessing the macrocycle.     

Supramolecular structures of macromolecules containing bipyridine–copper(I) complexes as revealed from transmission electron microscopy studies

Transmission electron microscopy (TEM) studies on bipyridine (bpy) containing block copolymer systems showed the formation of nanoscopic polymer–ion complexes through complexation with copper(I) ions which segregated to highly ordered columnar domains of mesoscopic dimensions. The domains, i.e. stacks of [(bpy)₂Cu(I)] complex moieties could be visualized by complementary TEM techniques. First, electron energy loss spectra (EELS) showed the absorption edges of copper and nitrogen, which are specific for the bipyridine copper complexes. The element spectroscopic imaging (ESI) technique allowed the imaging of the net copper and net nitrogen distribution, and the coinciding pictures exhibited a microphase separated system in the case of a 3-block copolymer with complexed end segments. High resolution elastic bright field images showed interference lines with a line to line distance of about 8 A which could be related to the Cu–Cu distance in staggered Cu(I)–bipyridine complexes. Received: 6 August 1997 Accepted: 28 April 1998