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.     

The Synthesis and Mechanistic Considerations of a Series of Ammonium Monosubstituted H-Phosphonate Salts

A series of ammonium monosubstituted H-phosphonate salts were synthesized by combining H-phosphonate diesters with amines in the absence of solvent at 80 °C. Variation of the ester substituent and amine produced a range of ionic liquids with low melting points. The products and by-products were analyzed by spectroscopic and spectrometric techniques in order to get a better mechanistic picture of the dealkylation and formal dearylation observed. For dialkyl H-phosphonate diesters, (RO)₂P(O)H (R=alkyl), the reaction proceeds via direct dealkylation with the reactivity increasing in the order R=iPr<Et<Me corresponding to DFT calculated activation enthalpies of 22.6, 20.8, and 17.9 kcal mol⁻¹. For the diphenyl H-phosphonate diesters, (PhO)₂P(O)H, the dearylation was found to proceed via phenol-assisted formation of a 5-coordinate intermediate, (PhO)₃PH(OH), from which P(OPh)₃ and water were eliminated. The presence of an equivalent of water then facilitated the formation of P(OH)₂OPh and the amine, R'NH₂, subsequently abstracted a proton from it to yield [(PhO)PH(O)O]^-[R'NH₃]⁺.     

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.     

Development of Magnesium Anode-Based Transient Primary Batteries

Biodegradable primary batteries, also known as transient batteries, are essential to realize autonomous biodegradable electronic devices with high performance and advanced functionality. In this work, magnesium, copper, iron, and zinc – metals that exist as trace elements in the human body – were tested as materials for biomedical transient electronic devices. Different full cell combinations of Mg and X (where X = Cu, Fe, and Zn and the anodized form of the metals) with phosphate buffered saline (PBS) as electrolyte were studied. To form the cathodes, metal foils were anodized galvanostatically at a current density of 2.0 mA cm⁻² for 30 mins. Electrochemical measurements were then conducted for each electrode combination to evaluate full cell battery performance. Results showed that the Mg−Cu_anodized chemistry has the highest power density at 0.99 mW/cm². Nominal operating voltages of 1.26 V for the first 0.50 h and 0.63 V for the next 3.7 h were observed for Mg−Cu_anodized which was discharged at a current density of 0.70 mA cm⁻². Among the materials tested, Mg−Cu_anodized exhibited the best discharge performance with an average specific capacity of 2.94 mAh cm⁻², which is comparable to previous reports on transient batteries.     

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     

An unexpected aminocyclopropane reductive rearrangement

A reductive rearrangement of aminocyclopropanes is described for the synthesis of cis- or trans-fused bicyclic 1,2-diaminocyclobutanes. Ionization of a cyclic aminal using BF₃·OEt₂ induces rearrangement to a cyclobutyl iminium ion, which is subsequently reduced by Et₃SiH. Substitution with allyltrimethylsilane allows carbon incorporation, giving a quaternary center. Silyloxy-substituted cyclopropanes rearrange rapidly to cyclobutanones which react with NaBH₄ to provide 1,2-aminohydroxycyclobutanes. These aminals were generated by the reduction of a Boc-imide with DIBAL-H or LiBH₄.     

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).