Refined inequalities on graded Lie groups

We construct a Littlewood–Paley decomposition associated to a Rockland operator on graded Lie groups, which allows us to deduce refined Gagliardo–Nirenberg, Sobolev and Hardy inequalities.     

Approaches to Modeling Bed Drag in Pine Forest Litter for Wildland Fire Applications

Transport in Porous Media - Modeling flow in vegetative fuel beds is a key component in any detailed physics-based tool for simulating wildland fire dynamics. Current approaches for drag modeling,...     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Synthesis of 8-(S)-methoxy-11-desmethyl laulimalide: a novel laulimalide analogue

A strategy is outlined which enables preparation of novel laulimalide analogues at C.8 and C.11. A representative analogue, 8-(S)-methoxy-11-desmethyl laulimalide, was synthesized via this route.     

Deformation und Stabilität windbeanspruchter Kühlturmschalen

Übersicht Nach der Formulierung des Deformations- und des Stabilitätsproblems auf der Grundlage ursprünglich nicht-konformer, dreiecksförmiger, gekrümmter finiter Elemente wird zunächst das Deformationsproblem für eine ausgeführte Kühlturmschale numerisch gelöst. Die nachfolgende Stabilitätsanalyse dieser Kühlturmschale zeigt gute Übereinstimmung der mittels der Methode der finiten Elemente errechneten Beulsicherheit mit dem aufgrund des Munganschen Beulkriteriums erhaltenen Kleinstwert der Beulsicherheit.

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Summary Following the formulation of the deformation and stability problem on the basis of originally non-conforming triangular curved finite elements with the help of a variational principle with subsidiary conditions, the deformation problem is solved numerically for an existing cooling tower shell. The subsequent stability analysis of this cooling tower shell shows relatively good agreement of the buckling safety computed by means of the finite element method and the minimum of buckling safety obtained with the help of Mungan's stability criterion.

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Diese Arbeit wurde mit Unterstützung der Cooling Tower Division von Zurn Industries, Tampa, Florida, USA, begonnen und mit Unterstützung Seitens des Fonds zur Förderung der wissenschaftlichen Forschung, Wien, zu Ende geführt. Beiden Sponsoren Sei an dieser Stelle aufrichtig gedankt. Der erstgenannte Autor ist darüber hinaus der Max Kade Foundation, New York, N. Y., für die Finanzierung Seines Studienaufenthaltes an der Cornell University, Ithaca, N. Y., im Rahmen dessen er mit der Thematik dieses Aufsatzes konfrontiert wurde, zu Dank verpflichtet. Aus demselben Grund sagt der dritte Autor für ein NATO Fellowship Dank.     

Synthesis of molybdenum nitrido complexes for triple-bond metathesis of alkynes and nitriles

Complexes of the type N≡Mo(OR)(3) (R = tertiary alkyl, tertiary silyl, bulky aryl) have been synthesized in the search for molybdenum-based nitrile-alkyne cross-metathesis (NACM) catalysts. Protonolysis of known N≡Mo(NMe(2))(3) led to the formation of N≡Mo(O-2,6-(i)Pr(2)C(6)H(3))(3)(NHMe(2)) (12), N≡Mo(OSiPh(3))(3)(NHMe(2)) (5-NHMe(2)), and N≡Mo(OCPh(2)Me)(3)(NHMe(2)) (17-NHMe(2)). The X-ray structure of 12 revealed an NHMe(2) ligand bound cis to the nitrido ligand, while 5-NHMe(2) possessed an NHMe(2) bound trans to the nitride ligand. Consequently, 17-NHMe(2) readily lost its amine ligand to form N≡Mo(OCPh(2)Me)(3) (17), while 12 and 5-NHMe(2) retained their amine ligands in solution. Starting from bulkier tris-anilide complexes, N≡Mo(N[R]Ar)(3) (R = isopropyl, tert-butyl; Ar = 3,5-dimethylphenyl) allowed for the formation of base-free complexes N≡Mo(OSiPh(3))(3) (5) and N≡Mo(OSiPh(2)(t)Bu)(3) (16). Achievement of a NACM cycle requires the nitride complex to react with alkynes to form alkylidyne complexes; therefore the alkyne cross-metathesis (ACM) activity of the complexes was tested. Complex 5 was found to be an efficient catalyst for the ACM of 1-phenyl-1-butyne at room temperature. Complexes 12 and 5-NHMe(2) were also active for ACM at 75 °C, while 17-NHMe(2) and 16 did not show ACM activity. Only 5 proved to be active for the NACM of anisonitrile, which is a reactive substrate in NACM catalyzed by tungsten. NACM with 5 required a reaction temperature of 180 °C in order to initiate the requisite alkylidyne-to-nitride conversion, with slightly more than two turnovers achieved prior to catalyst deactivation. Known molybdenum nitrido complexes were screened for NACM activity under similar conditions, and only N≡Mo(OSiPh(3))(3)(py) (5-py) displayed any trace of NACM activity.