A framework and algorithms for circular drawings of graphs

In this paper, we present a framework and two linear time algorithms for obtaining circular drawings of graphs. The first technique produces circular drawings of biconnected graphs and finds a zero crossing circular drawing if one exists. The second technique finds multiple embedding circle drawings. Techniques for the reduction of edge crossings are also discussed. Results of experimental studies are included.     

Improving the order and rates of convergence for the Super-Halley method in Banach spaces

In this study we are concerned with the problem of approximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4], [5], [8]. These results were not given in affine invariant form, and made use of a real quadratic majorizing polynomial. Here, we provide our results in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.     

Encapsulation of the corrosion inhibitor 8-hydroxyquinoline into ceria nanocontainers

Ceria nanocontainers were synthesized through a two-step process and then loaded with 8-hydroxyquinoline (8-HQ). The size of the containers was 110 nm as determined by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). X-ray diffraction analysis (XRD) showed that the ceria nanocontainers were of the cerianite crystalline phase. The presence of 8-HQ in the nanocontainers was confirmed with Fourier-transform infrared spectroscopy (FT-IR). The loading of the inhibitor in the nanocontainers was estimated with differential thermal analysis (DTA) and thermogravimetric analysis (TGA). The loading amount of 8-HQ was 4.28% w/w. Based on the size of the nanocontainers and the assumption that they are not broken, we deduced that there were approximately 6.0 × 10⁵ molecules of 8-HQ per container. Furthermore, release of 8-HQ in a corrosive environment was studied by potentiodynamic measurements, showing that the inhibitor is released from the nanocontainers, suppressing the corrosion activities by a strong barrier effect. SEM and dynamic light scattering (DLS) measurements confirmed that the nanocontainers are not significantly agglomerated and maintain their shape after suspension in 0.5 M NaCl solution for more than 72 h.     

Acquisition times,relaxation rates and solvent and temperature effects as sensitivity parameters for quadrupolar nuclei

The relationship between the signal-to-noise ration and T₂ and, hence, the line width of a resonance for quadrupolar nuclei, with particular reference to ¹⁷O at natural abundance, is discussed. Emphasis is placed on the importance of choosing appropriate FID acquisition times related to the T₂ values or resonance widths of the quadrupolar nuclei. When this is feasible (i.e. when the principal resonances in a spectrum have similar widths) the signal-to-noise ratio attainable against a flat base line in a given time of spectral accumulation is independent of resonance line width. Although resolution improvements can be made by using appropriate solvents or elevated sample temperatures, the sensitivity has been to be strongly dependent on the acquisition parameters used.     

Relativistic internal time operator

We construct a self-adjoint time operator for massless relativistic systems in terms of the generators of the Poincaré group. The Lie algebra generated by the time operator and the generators of the Poincaré group turns out to be an infinitedimensional extension of the Poincaré algebra. The internal time operator generates two new entities, namely the velocity operator and the internal position operator. The transformation properties of the internal time and position operator under Lorentz boosts are different from what one would expect from relativity theory. This difference reflects the fact that the time concept associated with the internal time operator is radically different from the time coordinate of Minkowski space, due to the nonlocality of the time operator. The spectral projections of the time operator allow us to construct incoming subspaces for the wave equation without invoking Huygens' principle, as in two and one spatial dimensions where Huygens' principle does not hold.     

Probabilistic aspects of finite-fuel,reflected follower problems

The issue is that of following the path of a Brownian particle by a process of bounded total variation and subject to a reflecting barrier at the origin, in such a way as to minimize expected total cost over a finite horizon. We establish the existence of optimal processes and the dynamic programming equations for this question, and show (by purely probabilistic arguments) its relation to an appropriatefamily of optimal stopping problems with absorption at the origin.Work carried out during a visit by the second author at the University Pierre et Marie Curie (Paris VI), and at INRIA (Institut National de Recherche en Informatique et en Automatique). The hospitality of these institutions is gratefully acknowledged.Research supported in part by the U.S. Air Force Office of Scientific Research, under grant AFOSR-86-0203.     

17O nuclear magnetic resonance studies of some enriched amino acids

The ¹⁷O NMR chemical shifts of five enriched amino acids have been measured under strictly controlled conditions of concentration, ionic strength, pH and temperature. The α, β and α, γ carboxyl resonances of aspartic and glutamic acid, respectively, have been resolved. Line widths were examined as a function of solution viscosity.     

Deuterium kinetic isotope effects in homogeneous decatungstate catalyzed photooxygenation of 1,1-diphenylethane and 9-methyl-9H-fluorene: evidence for a hydrogen abstraction mechanism

The homogeneous decatungstate catalyzed photooxygenation of 1,1-diphenylethane and 9-methyl-9H-fluorene has been studied mechanistically. The primary and β-secondary kinetic isotope effects provide strong evidence for a stepwise mechanism, with a hydrogen atom abstraction in the rate-determining step.