Curvature and finite domination

Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in --spaces dominating such manifolds.

     

Eclipsed Isopropyl Conformations of Two Dimeric Hydrazines

The X-ray structures of 4,10-di-tert-butyl-5,9-diisopropyl-4,5,9,10-tetraazatetracyclo[6.2.2.2(3,6)]tetradecane (s4iPr) and its 4,9-di-tert-butyl-5,10-diisopropyl isomer (a4iPr) are reported. Both compounds are in conformations having their in-N-alkyl groups (directed toward the central CH-CH bond of the molecule) anti to each other, as expected from previous work. The principal feature of interest is that one in-isopropyl group in each compound is in an eclipsed conformation, NN,C(alpha)Me twist angle -0.5(5) degrees for s4iPr and -6.4(4) degrees for a4iPr. Low energy (somewhat less) eclipsed in-isopropyl conformations are predicted by both molecular mechanics (MM2) and semiempirical quantum mechanical (AM1) calculations. The asymmetry of the potentially C(2) symmetric a4iPr because the two in-isopropyl groups are in different rotamers is apparently not a result of crystal packing forces, because a conformation with different isopropyl rotamers is the more stable one by at least 1.0 kcal/mol in solution, determined by (13)C-NMR spectroscopy. This result is not predicted by either calculation method. The "monomer", 2-tert-butyl-3-isopropyl-2,3-diazabicyclo[2.2.2]octane (3), proves to be a poor model for the conformations of 4iPr.     

On two methods of determining the ellipses and ellipsoids of positioning accuracy of robot manipulators

Summary When analysing the problem of the positioning accuracy of robot manipulators it is important to know how far random deviations of the hand may be from the desired position if the joint positioning errors possess a normal distribution. Two methods of determining the ellipses and ellipsoids of probability concentration are compared. The first of them is based on the standard procedure of the probability calculus. The second approximate method consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid with principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. Examples of application demonstrate that these two methods give very close results.

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Zwei Methoden zur Bestimmung der Ellipsen und Ellipsoide der Positioniergenauigkeit von Handhabungsrobotern

Übersicht Bei der Untersuchung der Positioniergenauigkeit von Handhabungsrobotern ist es wichtig, die Größe zufälliger Abweichungen des Greifers von der erstrebten Position zu kennen, wenn die Lagefehler der Verbindungen eine Normalverteilung besitzen. Es werden zwei Methoden zur Bestimmung der Ellipsen bzw. Ellipsoide der Wahrscheinlichkeitsdichte verglichen. Die erste beruht auf dem Standardverfahren der Wahrscheinlichkeitsrechnung. Die zweite Näherungsmethode besteht darin, daß zunächst das Polygon bzw. Polyeder der Positioniergenauigkeit bestimmt wird und danach die Ellipse bzw. das Ellipsoid mit den Hauptachsen und Momenten zweiter Ordnung wie das Polygon oder Polyeder. Beispiele zeigen, daß beide Methoden zu sehr ähnlichen Ergebnissen führen.

     

The effects of temperature and pressure on the lifetime of benzophenone emission

The variation in the lifetime of flash-excited gaseous benzophenone with pressure and temperature indicates that (1) self-quenching is a relatively inefficient process for the long-lived emission, k_sq = 9 × 10⁵ M^?1 s^?1 (estimated from solution data) at 25°C and 1.2 × 10⁷ M^?1 s^?1 at 170°C and (2) the lifetime decreases with increasing temperature as a result of photochemical and photophysical decay pathways which have significant activation energies. The importance of diffusion to the walls on lifetime measurements is discussed.