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.     

Synthesis,properties, and crystal structure of a novel 3-hydroxy-(4<Emphasis Type="Italic">H</Emphasis>)-benzopyran-4-one containing copper(II) complex,and its oxygenation and relevance to quercetinase

The preparation, spectroscopic properties, and crystal structure of [Cu(ind)(mco)] [ind is the anion of 1,3-bis(2-pyridylimino)isoindoline and mco is the anion of 3-hydroxy-(4H)-benzopyran-4-one] are reported. The complex exhibits a distorted square pyramidal geometry. The oxygenation of the title compound results in oxidative cleavage of the heterocyclic ring to give the (acetylsalicylato)copper(II) complex [Cu(asp)(ind)] (asp is the anion of acetylsalicylic acid) and CO as primary products, which reaction resembles the enzymatic reaction of quercetinase.     

Asymptotic behaviour of the least squares estimator of the mean of AR(1) models

The aim of the paper is to investigate the limit behaviour of the least squares estimator of the shift parameter of nearly unstable, nearly stable, and nearly explosive AR(1) models. Both zero start and stationary cases are treated. Connection with the maximum likelihood estimator of the shift parameter of continuous time AR(1) processes is also discussed.     

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.     

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.     

Bemerkungen zu bromatometrischen Messungen. III

Zusammenfassung Ascorbinsäure kann in 1 n salzsaurer Lösung mit Kaliumbromatmaßlösung bei Anwesenheit von Kaliumjodid und Stärke titriert werden.Teil II: diese Z. 161, 38 (1958).     

Strong cooperativeness in the mononuclear iron(II) derivative exhibiting an abrupt spin transition above 400 K

The spin crossover system, [Fe(bzimpy)(2)](ClO(4))(2).0.25H(2)O, was reinvestigated above room temperature (bzimpy = 2,6-bis(benzimidazol-2-yl)pyridine). The system exhibits an abrupt low-spin to high-spin transition at T(c) = 403 K. Liberation of a fractional amount of water does not affect the spin crossover: the system is perfectly reversible with a hysteresis width of DeltaT = 12 K. The existence of the hysteresis at such high temperature determines that the lowest limit of the solid-state cooperativity parameter is J/k > 403 K despite long iron(II) separations (10 A). The high cooperativeness has been assigned to a perfect pi-stacking of the benzimidazole rings in the crystal lattice at a distance as short as 3.6 A. Variable-temperature IR data and the heat capacity measurements match well the magnetic data. The thermodynamic properties are DeltaH = 17 kJ mol(-)(1), DeltaS = 43 J K(-)(1) mol(-)(1), so that the entropy of the spin transition shows a considerable contribution from the molecular vibrations. A theoretical model has been applied in fitting the magnetic data along the whole hysteresis path. A statistical distribution of the cooperativity parameter led to the feature that angled walls of the hysteresis loop are well reproduced.     

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.