On the solution of Falkner-Skan equations

New existence and uniqueness proofs are given for the solutions of the equations governing the self-similar compressible boundary layer (Falkner-Skan equations). The properties of the solutions are studied and some bounds on important quantities are concluded. The paper is restricted to favourable pressure gradients and to wall cooling.     

Decomposition results for stochastic storage processes and queues with alternating Lévy inputs

In this paper we generalize known workload decomposition results for Lévy queues with secondary jump inputs and queues with server vacations or service interruptions. Special cases are polling systems with either compound Poisson or more general Lévy inputs. Our main tools are new martingale results, which have been derived in a companion paper.     

On Lévy-driven vacation models with correlated busy periods and service interruptions

This paper considers queues with server vacations, but departs from the traditional setting in two ways: (i) the queueing model is driven by Lévy processes rather than just compound Poisson processes; (ii) the vacation lengths depend on the length of the server’s preceding busy period. Regarding the former point: the Lévy process active during the busy period is assumed to have no negative jumps, whereas the Lévy process active during the vacation is a subordinator. Regarding the latter point: where in a previous study (Boxma et al. in Probab. Eng. Inf. Sci. 22:537–555, 2008) the durations of the vacations were positively correlated with the length of the preceding busy period, we now introduce a dependence structure that may give rise to both positive and negative correlations. We analyze the steady-state workload of the resulting queueing (or: storage) system, by first considering the queue at embedded epochs (viz. the beginnings of busy periods). We show that this embedded process does not always have a proper stationary distribution, due to the fact that there may occur an infinite number of busy-vacation cycles in a finite time interval; we specify conditions under which the embedded process is recurrent. Fortunately, irrespective of whether the embedded process has a stationary distribution, the steady-state workload of the continuous-time storage process can be determined. In addition, a number of ramifications are presented. The theory is illustrated by several examples.     

Nachweis und Bestimmung von Kohlehydraten

Ohne Zusammenfassung     

Tetrapterosides A and B,two new oleanane‐type saponins from Tetrapleura tetraptera

From the stem bark of Tetrapleura tetraptera, two new oleanane‐type saponins, tetrapteroside A 3‐O‐{6‐O‐[(2E,6S)‐2,6‐dimethyl‐6‐hydroxyocta‐2,7‐dienoyl]‐β‐D ‐glucopyranosyl‐(1 → 2)‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐(1 → 4)‐[β‐D ‐glucopyranosyl‐(1 → 2)]‐β‐D ‐glucopyranosyl}‐3,27‐dihydroxyoleanolic acid (1), and tetrapteroside B 3‐O‐{ β‐D ‐glucopyranosyl‐(1 → 2)‐6‐O‐[(E)‐feruloyl]‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐(1 → 4)‐[β‐D ‐glucopyranosyl‐(1 → 2)]‐β‐D ‐glucopyranosyl}‐3,27‐dihydroxyoleanolic acid (2), were isolated. Further extractions from the roots led to the isolation of four known oleanane‐type saponins. Their structures were elucidated by the combination of mass spectrometry (MS), one and two‐dimensional NMR experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

Presenegenin Glycosides from Securidaca welwitschii

The five new presenegenin glycosides 1 – 5 were isolated from Securidaca welwitschii, together with one known sucrose diester. Compounds 1 – 4 were obtained as pairs of inseparable (E)/(Z)‐isomers of a 3,4‐dimethoxycinnamoyl derivative, i.e., 1 / 2 and 3 / 4 . Their structures were elucidated mainly by 2D‐NMR techniques and mass spectrometry as 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐β‐D ‐xylopyranosyl‐(1→4)‐O‐α‐L ‐rhamnopyranosyl‐(1→2)‐O‐[β‐D ‐glucopyranosyl‐(1→3)]‐4‐O‐[(E)‐3,4‐dimethoxycinnamoyl]‐β‐D ‐fucopyranosyl} ester ( 1 ) and its (Z)‐isomer 2 , 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐β‐D ‐galactopyranosyl‐(1→4)‐O‐β‐D ‐xylopyranosyl‐(1→4)‐O‐3‐O‐acetyl‐α‐L ‐rhamnopyranosyl‐(1→2)‐O‐[β‐D ‐glucopyranosyl‐(1→3)]‐4‐O‐[(E)‐3,4‐dimethoxycinnamoyl]‐β‐D ‐fucopyranosyl} ester ( 3 ) and its (Z)‐isomer 4 , and 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐[O‐β‐D ‐galactopyranosyl‐(1→3)‐O‐β‐D ‐xylopyranosyl‐(1→4)‐O‐α‐L ‐rhamnopyranosyl‐(1→2)‐β‐D ‐fucopyranosyl] ester ( 5 ) (presenegenin=(2β,3β,4α)‐2,3,27‐trihydroxyolean‐12‐ene‐23,28‐dioic acid).     

On the nonexistence of certain Hughes generalized quadrangles

In this paper, we prove that the Hermitian quadrangle is the unique generalized quadrangle Γ of order (q ², q ³) containing some subquadrangle of order (q ², q) isomorphic to such that every central elation of the subquadrangle is induced by a collineation of Γ. Dedicated to Dan Hughes on the occasion of his 80th birthday.     

Two New Triterpene Saponins from Acanthophyllum laxiusculum

Two new triterpene glycosides, 1 and 2 , together with three known ones, were isolated from roots of Acanthophyllum laxiusculum Schiman ‐Czeika . The structures of the new compounds were established by extensive 1D‐ and 2D‐NMR spectroscopic experiments and MS analyses as 23‐O‐β‐D ‐galactopyranosylgypsogenic acid 28‐O‐{β‐D ‐glucopyranosyl‐(1→2)‐6‐O‐[4‐carboxy‐3‐hydroxy‐3‐methyl‐1‐oxobutyl]‐β‐D ‐glucopyranosyl‐(1→6)}‐[β‐D ‐glucopyranosyl‐(1→3)]‐β‐D ‐galactopyranosyl ester ( 1 ) and gypsogenic acid 28‐O‐{β‐D ‐glucopyranosyl‐(1→2)‐6‐O‐[4‐carboxy‐3‐hydroxy‐3‐methyl‐1‐oxobutyl]‐β‐D ‐glucopyranosyl‐(1→6)}‐[β‐D ‐glucopyranosyl‐(1→3)]‐β‐D ‐galactopyranosyl ester ( 2 ).     

Polyoxometalate-Engineered Building Blocks with Gold Cores for the Self-Assembly of Responsive Water-Soluble Nanostructures

The controlled assembly of gold nanoparticles (AuNPs) with the size of quantum dots into predictable structures is extremely challenging as it requires the quantitatively and topologically precise placement of anisotropic domains on their small, approximately spherical surfaces. We herein address this problem by using polyoxometalate leaving groups to transform 2 nm diameter gold cores into reactive building blocks with hydrophilic and hydrophobic surface domains whose relative sizes can be precisely tuned to give dimers, clusters, and larger micelle-like organizations. Using cryo-TEM imaging and ¹H DOSY NMR spectroscopy, we then provide an unprecedented “solution-state” picture of how the micelle-like structures respond to hydrophobic guests by encapsulating them within 250 nm diameter vesicles whose walls are comprised of amphiphilic AuNP membranes. These findings provide a versatile new option for transforming very small AuNPs into precisely tailored building blocks for the rational design of functional water-soluble assemblies.