Facets of the Graph Coloring Polytope

In this paper we present a study of the polytope associated to a classic linear integer programming formulation of the graph coloring problem. We determine some families of facets. This is the initial step for the development of a branch-and-cut algorithm to solve large instances of the graph coloring problem.     

On quantum operations as quantum states

We formalize Jamiolkowski’s correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in Choi’s proof of the operator sum representation of Completely Positive-preserving linear maps; we go further and show that all of the important theorems concerning quantum operations can be derived directly from those concerning quantum states. As we do so the discussion first provides an elegant and original review of the main features of quantum operations. Next (in the second half of the paper) we find more results stemming from our formulation of the correspondence. Thus, we provide a factorizability condition for quantum operations, and give two novel Schmidt-type decompositions of bipartite pure states. By translating the composition law of quantum operations, we define a group structure upon the set of totally entangled states. The question whether the correspondence is merely mathematical or can be given a physical interpretation is addressed throughout the text: we provide formulae which suggest quantum states inherently define a quantum operation between two of their subsystems, and which turn out to have applications in quantum cryptography.     

Continuous-flow extraction of organophosphorus pesticides coupled on-line with high-performance liquid chromatography

A continuous-flow extraction system coupled on-line with a high-performance liquid chromatograph with an ultraviolet detector is used to study the extraction of three organophosphorus pesticides (fenthion, azinphos methyl and diazinon) from aqueous samples with n-heptane as the organic solvent. Diazinon was not extracted significantly. The influence on the extraction of different parameters (coil length, flow rate and phase volume ratio) were studied. The calibration graphs are linear for 0.5–7 mg l^?1 and 8–20 mg l^?1 foor azinphos methyl where the percentage extraction (E%) is 90% and 70%, respectively, and up to 4 mg l^?1 for fenthion, where the E% is 33%. The detection limits and the relative standard deviations are 0.04 and 0.09 mg l^?1, and 3.4 and 5.3%, for azinphos methyl fenthion, respectively. Other pesticides and related compounds were found not to interfere. The sample throughput of this method was 15 h^?1.     

The numerical computation of compressed states of nonlinearly elastic anisotropic plates

Summary In this paper we study the numerical computation of the compressed states of nonlinearly elastic anisotropic circular plates. The singular boundary value problem giving the compressed states depend parametrically on the applied pressure at the edge of the plate. We give a finite difference approximation of this problem and derive bounds for the global error by using the techniques of Brezzi, Rappaz and Raviart for the finite dimensional approximation of nonlinear problems. Some numerical results are given for a class of materials whose constitutive functions reflect the standard Poisson ratio effects.     

General Behaviour of Bianchi VI0 Solutions with an Exponential-Potential Scalar Field

The solutions to the Einstein-Klein-Gordon equations without a cosmological constant are investigated for an exponential potential in a Bianchi VI₀ metric. There exists a two-parameter family of solutions which have a power-law inflationary behaviour when the exponent of the potential, k, satisfies k² < 2. In addition, there exists a two-parameter family of singular solutions for all k² values. A simple anisotropic exact solution is found to be stable when 2 < k².     

Simultaneous determination of iron and ruthenium by preconcentration on sulfopropyl sephadex cation exchanger

A new method for the simultaneous determination of iron and ruthenium at ultra-trace levels is proposed. The method is based on the formation of the iron and ruthenium complexes with 2,4,6-tri-(2-pyridil)-1,3,5-triazine (TPTZ) in the presence of hydroxylamine hydrochloride and buffer CH₂ClCOOH/CH₂ClCOONa (pH=3.0). The formation of the complexes and their retention on a cationic resin SP-Sephadex C25 were integrated in one step at 90 °C, with stirring for 90 min. Under these conditions a high preconcentration level was achieved for both analytes. The complexes retained on the solid phase were evaluated by second derivative spectrophotometry. The selected analytical wavelengths were 539.7 and 553.3 nm for the determination of ruthenium and iron, respectively, by using the zero crossing approach. The detection and quantification limits were 0.54 ng ml⁻¹ and 1.79 ng ml⁻¹ for ruthenium and 0.41 ng ml⁻¹ and 1.38 ng ml⁻¹ for iron. The proposed method was applied to the determination of both analytes in synthetic mixtures.