Codiameters of 3‐connected 3‐domination critical graphs

A graph G is 3‐domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3‐connected 3‐domination critical graph of order n. In this paper, we show that there is a path of length at least n?2 between any two distinct vertices in G and the lower bound is sharp. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76–85, 2002     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

Intercalated smectic-A structures in a new class of laterally branched substances

X-ray, DSC and optical studies of a new class of substances with aromatic rings in the lateral branches are reported. The thermal behaviour of the substances is discussed. The X-ray measurements lead to a structural model of the SA phases consisting of layer structures with intercalating molecules.     

Raman spectroscopic investigations of the structure and phase transitions of liquid crystalline lead(II) alkanoates

Lead(II) alkanoates with even chain lengths from octanoate to octadecanoate have been investigated by Raman spectroscopy. In the low frequency region, transverse and longitudinal acoustical modes (TAM, LAM) have been assigned. It was shown that LAM-1 is the vibration of the double chain with the node of the vibration in the Pb²⁺ layer. A fully extended conformation of the chains in the low temperature phase was confirmed. The frequencies and intensities of the LAMs as compared with those of the alkanes and the fatty acids led to an estimate of the force constant and polarizability of the Pb²⁺ -COO^- bond relative to the C-C bond. The defects at the chain ends were investigated in the ρ(CH₃) and v(CC) region. For the intermediate (CM) phase, both the Pb²⁺ layer distance reduction and the chain length independent enthalpy contributions can be attributed mainly to defects at the chain ends.     

Photoinduced electron transfer variables: rigidity or orientation?

The relatives photoreactives of bridged-ring systems 1, 3, 5-X and 6-X (X ≡ Cl or Br) have been studied at 254 nm in acetic acid. The formation of photosolvolysis product was rationalized in terms of photoinduced intramolecular electron transfer (ET) processes. The relative ease of ET in these donor—bridge—acceptor model system was analyzed in terms of known ET variables including free-energy changes, orientation effects and ridigity effects. The observed relative photoreactivities agreed better with the calculated free-energy changes when relative rigidities of the electron acceptor termini were evaluated. In general, the more rigid system were more photoreactive.     

Trace determination of Tl, Cu, Pb, Cd, and Zn in specimens of the limnic environment using isotope dilution mass spectrometry with thermal ionization

Within the framework of the German Environmental Specimen Bank program, Tl, Cu, Pb, Cd and Zn were determined in homogenized materials from the limnic environment using Isotope Dilution Mass Spectrometry (IDMS) with thermal ionization. The analytical procedures which were developed for the trace metal analysis of bioindicator and sediment samples are described in detail. Results obtained in bream, mussels (Dreissena polymorpha) and sediments of Lake Constance/Estuary of Constance in the sampling years 1981, 1985, 1988, 1990, 1992 and 1993 are discussed and compared with those of bream from the lakeland district of Born-hoeved/Lake Belau and from the River Saar as well as from reference materials.     

Model calculations of interface segregation in dilute systems

Using a discrete model for the segregation kinetics based on the Darken theory of diffusion and on the regular solution model (RSM), one and two dimensional simulations of interface segregation in binary and ternary systems have been performed. The aim of the calculations was to investigate the kinetics of segregation sequences in ternary systems, the segregation kinetics in discrete systems during the initial phase and finally the kinetics of surface segregation in the region of a grain boundary intersected by the surface.