Speciation of Zn‐aminopolycarboxylic complexes by electrospray ionization mass spectrometry and ion chromatography with inductively coupled plasma mass spectrometry

The speciation of Zn‐aminopolycarboxylic complexes was investigated using both electrospray ionization mass spectrometry (ESI‐MS) and ion chromatography (IC) with inductively coupled plasma mass spectrometry (ICP‐MS). The resulting ESI mass spectra indicated that [Zn(HEDTA)]^1?, [Zn(NTA)]^1?, [Zn(EDTA)]^2? and [Zn(DTPA)]^3? were all simultaneously detected in solution; [Zn(NTA)]^1? exhibited the weakest intensity of all these Zn‐aminopolycarboxylic complexes. IC/ICP‐MS was also successfully used to separate Zn complexes by anion‐exchange chromatography using a mobile phase containing 30 mM (NH₄)₂HPO₄ at pH 7.5 giving reasonable resolution within 15 min. A weak peak attributable to the poor stability [Zn(NTA)]^1? ion was also observed using IC/ICP‐MS. With the exception of [Zn(NTA)]^1?, detection limits ranging from 0.5 to 1.0 µg/L were obtained and the proposed method was used for the determination of Zn aminopolycarboxylic complexes in soil solution. Copyright © 2009 John Wiley & Sons, Ltd.     

Index of refraction engineering in five-level dressed interacting ground states atoms

We present a five-level atomic system in which the index of refraction of a probe laser can be enhanced or reduced below unity with vanishing absorption in the region between pairs of absorption and gain lines formed by dressing of the atoms with a control laser and rf/microwave fields. By weak incoherent pumping of the population into a single metastable state, one can create several narrow amplifying resonances. At frequencies between these gain lines and additional absorption lines, there exist regions of vanishing absorption but resonantly enhanced index of refraction. In Rb vapors with density N in units of cm(-3), we predict an index of refraction up to n≈√(1+1.2×10(-14)N) for the D1 line, which is more than an order of magnitude larger than other proposals for index of refraction enhancement. Furthermore, the index can be readily reduced below 1 by simply changing the sign of the probe or rf field detunings. This enhancement is robust with respect to homogeneous and inhomogeneous broadening.     

Degenerations to unobstructed Fano Stanley–Reisner schemes

We construct degenerations of Mukai varieties and linear sections thereof to special unobstructed Fano Stanley–Reisner schemes corresponding to convex deltahedra. This can be used to find toric degenerations of rank one index one Fano threefolds. Furthermore, we show that the Stanley–Reisner ring of the boundary complex of the dual polytope of the associahedron has trivial \(T^2\) . This can be used to find new toric degenerations of linear sections of \(G(2,n)\) .     

Solution of goal programming models using a basic taboo search algorithm

Goal programming is a very powerful technique for solving multiple objective optimisation problems. It has been successfully applied to numerous diverse real life problems. In this paper a Taboo search based method is developed to solve preemptive goal programming problems. The method can easily be applied to any kind of preemptive goal programming problems.     

The Bethe-Salpeter equation for spin-1 particles

We develop here the general treatment of the Bethe—Salpeter equation for the bound state of two spin-l particles interacting through an electromagnetic interaction. The treatment here, which can be generalized to strong interactions, combines the two-component approach utilized previously by the author in conjunction with spontaneous symmetry breaking. This is done by using a Lagrangian having SU(2)×U(1) symmetry (without fermions) and then choosing the ′t Hooft gauge. In this way, a renormalizable theory for the interaction of two spin-l particles via an electromagnetic interaction is ensured.     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

Indirect control of corporations

We consider situations in which shares ofn firms are held by the samen firms as well as by individual investors. The probelm is to determine the actual control of the firms by the individual investors.In part 1, we develop the mathematical model, and explain the basic notions of clutter and of effective reduction. In part 2 we introduce the idea of a consistent reduction, prove existence of such, and show the relation between consistent and effective reductions. In part 3 we introduce multilinear extensions and show how these can be used to calculate the effective and consistent reductions. Several examples are worked out in detail.     

Automorphisms and weighted values

The notion of automorphism is an essential tool to capture the meaning of any mathematical structure. We apply this idea to cooperative games and obtain two interesting characterizations of the automorphisms of such a game: the one, in the complete case, as the permutations of players which preserve the (classical) Shapley value; the other, for the general case, as the permutations preservingall weighted Shapley values.Carreras' research supported by project UPV 036321-HA186/92 of the Basque Country University. Owen's research supported by the National Science Foundation, Grant DMS-9116416. This collaboration was made possible by the Polytechnic University of Catalonia, which sponsored Owen's visit to Terrassa.