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.     

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.     

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.     

A simple version of Karzanov's blocking flow algorithm

Dinic has shown that the classic maximum flow problem on a graph of n vertices and m edges can be reduced to a sequence of at most n ? 1 so-called ‘blocking flow’ problems on acyclic graphs. For dense graphs, the best time bound known for the blocking flow problems is O(n²). Karzanov devised the first O(n²)-time blocking flow algorithm, which unfortunately is rather complicated. Later Malhotra, Kumar and Maheshwari devise another O(n²)-time algorithm, which is conceptually very simple but has some other drawbacks. In this paper we propose a simplification of Karzanov's algorithm that is easier to implement than Malhotra, Kumar and Maheshwari's method.     

Oriented crystal growth model explains the formation of titania nanotubes

We discuss the formation mechanism of titania nanotubes synthesized by the hydrothermal method. On the basis of a comprehensive analysis of TEM, HRTEM, FT-Raman, and N(2) adsorption data, we point out some major shortcomings of the currently accepted trititanate sheet rollup mechanism. We suggest that a novel formation mechanism, oriented nanotube crystal growth from nanoloop seeds, can explain the experimental findings better than the ones proposed so far.