A dual graph-norm refinement indicator for finite volume approximations of the Euler equations

Summary. We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Süli and Warnecke in [15] and [16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement indicator into the DLR--Code which is based on a finite volume method of box type on an unstructured grid and present numerical results. Received May 15, 1995 / Revised version received April 17, 1996     

Enumerating disjunctions and conjunctions of paths and cuts in reliability theory

Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s₁ and s₂ to, respectively, a given vertex t₁, and each vertex of a given subset of vertices T₂.     

Studies on pyridazine derivatives. IV Mesylation reaction of pyridazinylpyrazoles

On mesylation, 1-pyridazinylpyrazoles ( 1 ), give, depending on the substituents and reaction conditions, O-mesylpyrazoles ( 2 ) and O-mesyl-4-N-mesyl-1,4-dihydro-4-pyridyl-pyrazole derivatives ( 3 ). The structures of these compounds were confirmed by ir and ¹H nmr spectral data.     

Preparation of new 2,3-diphenylpropenoic acid esters - good yields even for the more hindered Z isomers

The potassium salt of E- and Z-2,3-diphenylpropenoic acids prepared in situ could be esterified efficiently in DMSO with the appropriate alkyl halides at room temperature. In this way 10 previously undescribed esters of these acids were synthesised and characterised. Excellent yields were observed for most of the E isomers and the more hindered Z esters were also obtained in good yields, far better than those obtained applying the classical acid-catalysed esterification reaction.     

Stereocontrolled synthesis of cis-dibenzoquinolizine chlorofumarates: curare-like agents of ultrashort duration

The quaternizations of dibenzoquinolizines 9 and 14 with 3-halo-1-propanols are highly cis-selective (94-100% cis), results consistent with the N-methylation of O-methylcapaurine (7b), but in contrast to the proposed trans-stereochemistry of dibenzo[a,h]quinolizine methiodide 10 and the analogous quaternizations of 1-benzyl- and 1-phenylisoquinoline congeners 5b and 5c. In this report, we describe stereoselective preparation of the unique cis-dibenzoquinolizinium propanols 15 and 16and their transformation into bis- and mixed-onium chlorofumarates 19, 20ab, and 26. Dibenzo[a,g]quinolizinium propanol 15 was prepared enantioselectively in three steps from dihydroisoquinoline 11. Asymmetric transfer hydrogenation of 11 in the presence of triethylamine/formic acid and Noyori's chiral ruthenium catalyst 12 produced R-(-)-5',8-dimethoxynorlaudanosine (13) in 98% yield and 87% ee. Pictet-Spengler cyclization of 13 in formalin/formic acid afforded the dibenzo[a,g]quinolizine 14 in 65% yield. Quaternization of 14 with 3-chloro-1-propanol under Finkelstein conditions generated cis-dibenzoquinolizinium propanol 15 in 85% yield with >94% cis-selectivity. The cis-dibenzo[a,h]quinolizinium propanol 16 was obtained as a single stereoisomer by reaction of the known tetramethoxyquinolizine 9 with neat 3-iodo-1-propanol. Bis-onium chlorofumarates 18 and 19 and the mixed-onium derivative 20ab were prepared by a pool synthesis procedure from (1R)-trans-6a, 16, and chlorofumaryl chloride (17). Mixed-onium alpha-chlorofumarate 26 was synthesized from (1S)-trans-6d, 15 and (+/-)-trans-2,3-dichlorosuccinic anhydride (22), employing a recently disclosed chlorofumarate mixed-diester synthesis. The title compounds (19, 20ab, and 26) displayed curare-like effects of ultrashort duration in rhesus monkeys.     

Alkene oxidation by a platinum oxo complex and isolation of a platinaoxetane

Oxo complex [(1,5-COD)4Pt4(mu3-O)2Cl2](BF4)2 (1) reacts readily with ethylene and norbornylene. The ethylene reaction yields acetaldehyde and a 1:1 mixture of (1,5-COD)Pt(Cl)(CH2CH3) (2) and [(1,5-COD)Pt4(eta3-CH2CHCH(CH3))](BF4) (3), while the norbornylene reaction yields a platinaoxetane complex, the first metallaoxetane to be obtained from the reaction of an oxo complex and an alkene.     

Cyclocondensation reaction of a 1,5-diketone with 1,2-diamines

Reaction of 2-acetonyl-4,5-dimethoxy-3′-chlorobenzophenone (1) with ethylenediamine afforded the imidazo[2,1-a]isoquinoline 2, whereas 6-(3-chlorophenyl)-8,9-dimethoxybenzo[b]phenazine (3) and naphthol 4 were obtained with ortho-phenylenediamine.     

On the three-phase mass transfer with solid particles adhered to the gas-liquid interface

A heterogeneous, multi-layer mass transfer model is proposed for prediction of the effect of multi-layer packing of catalyst particles adhered to the gas-liquid interface. The behavior of the mass transfer rate with respect to the multi-layer packing, to the particle size and mass transfer coefficient without particles is discussed. It is shown that enhancement can be considerably increased by multi-layer packing compared to that of mono-layer packing, depending on the values of particle size and mass transfer coefficient. The predicted mass transfer rates using the proposed model was verified with experimental data taken from the literature. The model presented should be superior to that of published in the literature.     

Effect of pressure on retention factors in HPLC using a non-porous stationary phase

Summary Pressure and temperature have significant influence on retention in HPLC. This study investigates the effect of pressure and temperature on the retention behavior of aromatic hydrocarbons (toluene, ethyl benzene, butyl benzene, pentyl benzene) and polar, acidic and basic samples (phenol, acetophenone, N,N-dimethyl aniline, benzophenone) on a reversed phase column. The effect has been studied on non-porous, tetradecyl (C₁₄) coated silica particles. We found that the adsorption-induced decrease of the partial molar volume of the solutes investigated was between ΔV _m =5–15 cm³ mol⁻¹. The increment of the decrease of the partial molar volume due to the addition of one CH₂ group, for the homologous series of the aromatic hydrocarbons is approximately ΔV _CH2 =2.3 cm³mol⁻¹. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001.