A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton-Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton-Kantorovich theorem.     

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.     

Representation formulae of general solutions in the theory of hemitropic elasticity

We consider the steady state oscillation equations of the theoryof elasticity of hemitropic materials. We derive general representationformulae for the displacement and microrotation vectors by meansof six scalar metaharmonic functions. These formulae are veryconvenient and useful in many particular problems for domainswith concrete geometry. Here we consider two canonical transmissionproblems for piecewise homogeneous bodies with spherical interfacesand with the help of the representation formulae construct explicitsolutions in the form of absolutely and uniformly convergentseries. The representations can also be applied to multi-layeredbodies with spherical and cylindrical interfaces.     

DFT-calculated structures based on 1H NMR chemical shifts in solution vs. structures solved by single-crystal X-ray and crystalline-sponge methods: Assessing specific sources of discrepancies

DFT calculations of ¹H NMR chemical shifts, using various functionals and basis sets, the conductor-like polarizable continuum model and discrete solute-solvent hydrogen bond interactions have been used to derive the solution structures of methyl salicylate and methyl 2,5-dihydroxybenzoate. We demonstrate that very good agreement between experimental and computed ¹H NMR chemical shifts can be obtained for various basis sets. The DFT structures in solution were compared with the recently reported X-ray structure, solved by the crystalline-sponge method, of the methyl salicylate and the single-crystal X-ray structure of methyl 2,5-dihydroxybenzoate. It is demonstrated that the information provided by ¹H NMR chemical shifts about the solution structure is significantly more precise than that obtained by the single-crystal X-ray and the crystalline-sponge methods.     

Design of a field flow system for the on-line spectrophotometric determination of phosphate, nitrite and nitrate in natural water and wastewater

This study describes the design and optimisation of a field flow system for the in-situ collection and on-line determination of phosphate, nitrate and nitrite by flow injection analysis-spectrophotometry. The method is based on the initial determination of phosphate as its phosphoantimonylmolybdenum blue complex which is then oxidized on-line by nitrite and the decrease in absorbance is monitored at 880 nm. Nitrate is determined as the difference between total and initial nitrite content in a separate flow after reduction to nitrite in a cadmium reductive column. The calibration curves were linear in the range 0–2.00 mg L⁻¹ P-phosphate, 0–10.00 mg L⁻¹ nitrite and 0–7.00 mg L⁻¹ nitrate with correlation coefficients of 0.9979, 0.9993 and 0.9995, respectively. The detection limits, calculated as 3S/N, were 0.15 mg L⁻¹ for P-phosphate, 0.17 mg L⁻¹ for nitrite and 0.09 mg L⁻¹ for nitrate. The reproducibility was below 3.0% (n = 7). Method validation in the analysis of natural water and wastewater samples revealed that it can efficiently be applied to the determination of the target analytes, with recoveries in the range of 92–108%. Correspondence: Athanasios G. Vlessidis, Laboratory of Analytical Chemistry, Department of Chemistry, University of Ioannina, Ioannina 45110, Greece     

Molecular dynamics simulations of pure methane and carbon dioxide hydrates: lattice constants and derivative properties

ABSTRACT

We report extensive molecular dynamics simulation results of pure methane and carbon dioxide hydrates at pressure and temperature conditions that are of interest to various practical applications. We focus on the calculation of the lattice constants of the two pure hydrates and their dependence on pressure and temperature. The calculated lattice constants are correlated using second order polynomials which are functions of either temperature or pressure. Finally, the obtained correlations are used in order to calculate two derivative properties, namely the isothermal compressibility and the isobaric thermal expansion coefficient. The current simulation results are also compared against reported experimental measurements and other simulation studies and good agreement is found for the case of isothermal compressibility. On the other hand, for the case of isobaric thermal expansion coefficient good agreement is found only with other simulation studies, while the simulation studies are in disagreement with experiments, particularly at low temperatures.     

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.     

A time domain analysis of wave motions in chiral materials

A time domain analysis of the equations governing wave propagation in an unbounded chiral medium is presented by a spectral family approach and by a direct eigenfunction expansion using Beltrami–Moses fields.