Sample preparation procedure for the determination of sulphur and trace metals in oil products by the ICP with a minitorch using emulsions

A quick sample preparation method was used for the determination of sulphur and trace metals in oil and oily products by the ICP with a minitorch. Stable aqueous emulsions of oils and oil products were made by using two kinds of emulsifiers (one with low sulphur content, the other sulfonated). Aqueous standard solutions can be used for the preparation of calibration solutions. The contents of S, Al, Cr, Cu, Fe, Mg, Ni and Pb in aqueous emulsions were determined and the results were in good agreement with the composition of oil standard solutions used for control analysis procedure.     

Ab initio potential energy surface and pressure broadening coefficients for the He-CH3F complex

Symmetry-adapted perturbation theory has been applied to compute the He-CH<sub>3</sub>F potential with the CH<sub>3</sub>F molecule assumed rigid. The potential has a global minimum of −48.9 cm<sup>−1</sup> at the center of mass separation of 7.2 bohr with the helium atom lying along the C-F bond on the hydrogen’s side. The computed points were fitted to an analytic energy surface with a correct asymptotic behaviour. This potential has been used to compute the pressure broadening (PB) coefficients for the (<em>j</em>, <em>k</em>) = (0, 0) → (1, 0) and (1, 0) → (2, 0) rotational transitions of CH<sub>3</sub>F perturbed by helium for a wide range of temperatures. Close-coupling results are compared with the experimental data of Willey et al. [J. Chem. Phys. 97 (1992) 4723], Beaky et al. [J. Mol. Struct. 352/353 (1995) 245] and infinite order sudden results are compared with those of Grigoriev et al. [J. Mol. Struct. 186 (1997) 48] for the <em>ν</em><sub>6</sub> band of CH<sub>3</sub>F perturbed by helium at room temperature. To our knowledge, present work is the first attempt of making fully ab initio calculations of collisional cross-sections and pressure broadening coefficients for this simple symmetric top system at low and room temperature.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale <em>n</em> <sup>1/4</sup>, where <em>n</em> is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale <em>n</em> <sup>1/4</sup> and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH<sub>2</sub>)<sub>2</sub>C<sub>6</sub>H<sub>3</sub>OH (LH) revealed compounds L<sub>3</sub>Al ( 1 ) and L<sub>2</sub>AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe<sub>2</sub> ( 3 ), rather 2 together with Me<sub>3</sub>Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, <sup>1</sup>H and <sup>13</sup>C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph<sub>3</sub>SnOH, giving LSnPh<sub>3</sub> ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, <sup>1</sup>H, <sup>13</sup>C and <sup>119</sup>Sn NMR spectroscopy and <sup>1</sup>H, <sup>119</sup>Sn HMBC experiments. The system 2 and B(C<sub>6</sub>F<sub>5</sub>)<sub>3</sub> in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Coloring mixed hypertrees

A mixed hypergraph is a triple (<em>V</em>,<em>C</em>,<em>D</em>) where <em>V</em> is its vertex set and <em>C</em> and <em>D</em> are families of subsets of <em>V</em>, called <em>C</em>-edges and <em>D</em>-edges, respectively. For a proper coloring, we require that each <em>C</em>-edge contains two vertices with the same color and each <em>D</em>-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all <em>k</em>'s for which there exists a proper coloring using exactly <em>k</em> colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by <em>k</em> colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

Crystal structure of m-nitrobenzoic anhydride

The title compound (C<sub>14</sub>H<sub>8</sub>N<sub>2</sub>O<sub>7</sub>,<i>M</i> <sub> <i>r</i> </sub>=306.2) crystallizes in the orthorhombic space group Pbca with<i>a</i>=6.962(1).<i>b</i>=24.688(1), and<i>c</i>=15.890(1)Å,<i>V</i>=2731.0 Å<sup>3</sup>,<i>D</i> <sub> <i>x</i> </sub>=1.489 g·cm<sup>–3</sup> for<i>Z</i>=8,<i><img src="/content/un636365g4634w20/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0"></i>=0.98 mm<sup>–1</sup>,<i>F</i>(000)=1296,<i>T</i>=293 K. Final<i>R</i>=0.053 for 1873 observed reflections. The structure was solved by direct methods. Approximately planar molecules lie perpendicular to the [100] direction and show partial stacking. The structure is the first example of a symmetric anhydride which does not retain the symmetry in the crystal state. The two independent nitro groups twist out of the ring planes by 10.5 and 14.8°, respectively.     

On two mean value properties and functional equations associated with them

Summary Motivated by different mean value properties, the functional equations<i>f(x) – f(y)/x–y=<img src="/content/j17t6586453x3684/xxlarge966.gif" alt="phgr" align="MIDDLE" BORDER="0">[<img src="/content/j17t6586453x3684/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">(x, y)]</i>, (i)<i>xf(y) – yf(x)/x–y=<img src="/content/j17t6586453x3684/xxlarge966.gif" alt="phgr" align="MIDDLE" BORDER="0">[<img src="/content/j17t6586453x3684/xxlarge950.gif" alt="zeta" align="MIDDLE" BORDER="0">(x, y)]</i> (ii) (<i>x <img src="/content/j17t6586453x3684/xxlarge8800.gif" alt="ne" align="MIDDLE" BORDER="0"> y</i>) are completely solved when<i><img src="/content/j17t6586453x3684/xxlarge950.gif" alt="zeta" align="MIDDLE" BORDER="0">, <img src="/content/j17t6586453x3684/xxlarge331.gif" alt="eng" align="MIDDLE" BORDER="0"></i> are arithmetic, geometric or harmonic means and<i>x, y</i> elements of proper real intervals. In view of a duality between (i) and (ii), three of the results are consequences of other three.The equation (ii) is also solved when<i><img src="/content/j17t6586453x3684/xxlarge950.gif" alt="zeta" align="MIDDLE" BORDER="0"></i> is a (strictly monotonic) quasiarithmetic mean while the real interval contains 0 and when<i><img src="/content/j17t6586453x3684/xxlarge950.gif" alt="zeta" align="MIDDLE" BORDER="0"></i> is the arithmetic mean while the domain is a field of characteristic different from 2 and 3. (A result similar to the latter has been proved previously for (i).)