Extrinsic Killing spinors

 Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of non-negative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a flat disc. Received: 2 February 2002; in final form: 1 August 2002 / Published online: 1 April 2003 Mathematics Subject Classification (1991): 53C27, 53C40, 53C80, 58G25 The authors would like to thank Lars Andersson for helpful discussions and for bringing to our knowledge the information regarding Remark 4. We are also grateful to the referee for pointing out that Corollary 5 and Corollary 6 are only valid when the boundary is at least 2-dimensional. Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967     

Unsupported gold(I)-copper(I) interactions through eta1 Au-[Au(C6F5)2]- coordination to Cu+ Lewis acid sites

The reaction of the complex [Au2Ag2(C6F5)4)N[triple bond]CCH3)2]n (1) with 1 equiv of CuCl in the presence of 1 equiv of pyrimidine ligand leads to the formation of the heteronuclear Au(I)-Cu(I) organometallic polymer [Cu{Au(C6F5)2}(N[triple bond]CCH3)(mu2-C4H4N2)]n (2) through a transmetalation reaction. Complex 2 displays unprecedented unsupported Au(I)...Cu(I) interactions of [Au(C6F5)2]- units with the acid Cu(I) sites in a [Cu(N[triple bond]CCH3)(mu2-pyrimidine)]n+(n) polymeric chain. Complex 2 has a rich photophysics in solution and in the solid state.     

Comparison between isoelectric focusing methods for the detection of orosomucoid phenotypes

Orosomucoid (ORM) polymorphism was investigated by different methods including isoelectric focusing in acid pH ranges followed by silver staining, print immunofixation of desialyzed ORM, fixation using a lectin from the sea-weed Codium tomentosum, isoelectric focusing followed by immunofixation in miniaturized gels and isoelectric focusing in immobilized pH gradients. Population genetics studies were carried out in Galicia (NW Spain) and two new ORM variants were found.     

Influence of the metal loading on the electrocatalytic activity of carbon-supported (100) Pt nanoparticles

Journal of Solid State Electrochemistry - The influence of the metal loading (i.e. interparticle distance) of shape-controlled Pt nanoparticles on their electrocatalytic properties is evaluated for...     

Dirac Operators on Hypersurfaces of Manifolds with Negative Scalar Curvature

We give a sharp extrinsic lower bound for the first eigenvaluesof the intrinsic Dirac operator of certain hypersurfaces boundinga compact domain in a spin manifold of negative scalar curvature.Limiting-cases are characterized by the existence, on the domain,of imaginary Killing spinors. Some geometrical applications, as anAlexandrov type theorem, are given.     

Characterization of magnetic materials by low-field microwave absorption techniques

A low-field non-resonant microwave absorption has recently been observed in a variety of magnetically ordered materials at low DC fields (−1000 Oe H_DC+1000 Oe), which is known as low-field microwave absorption (LFA). It has been shown that LFA is essentially similar to giant magnetoimpedance (GMI), and clearly different from ferromagnetic resonance (FMR). LFA strongly depends on the anisotropy field of the sample. In contrast with FMR (which can be described as the homogeneous precession of spins in the saturated state), LFA can be thought as a spin rotation process occurring during the magnetic saturation. In this work, we present a detailed study of the basic features of LFA in several types of materials: ferrites and amorphous microwires and ribbons; in particular the effects sample shape, temperature up to the Curie transition, the influence of easy axis and the effects of annealings. These examples show that once LFA is fully understood, it can become a powerful characterization tool.     

Spectroscopic characterization of halogen- and cyano-substituted pyridinevinylenes synthesized without catalyst or solvent

An efficient Knoevenagel route using green chemistry conditions was applied for the synthesis of halogen- and cyano- substituted pyridinevinylene compounds. Absorption and fluorescence emission spectra of these conjugated compounds were recorded and compared in order to evaluate the effect of substituents on the electronic properties of pyridinevinylene compounds. The substituents studied were terminal Cl and F, two or three aromatic rings, as well as a cyano group attached to a C=C double bond. The compounds synthesized are: (E)-2-(4-fluorostyryl)pyridine, (E)-2-(4-chlorostyryl)pyridine, (E)-4-(4-chlorostyryl)pyridine, 2,3-diphenylacrylonitrile, 3-phenyl-2-(pyridin-2-yl)acrylonitrile, 3-phenyl-2-(pyridin-3-yl)acrylonitrile, 2-phenyl-3-(pyridin-2-yl)acrylonitrile, 3,3′-(1,4-phenylene)bis(2-phenylacrylonitrile), 3,3′-(1,4-phenylene)bis(2-(pyridin-2-yl)acrylonitrile), and 3,3′-(1,4-phenylene)bis(2-(pyridin-3-yl)acrylonitrile). The solvent-free method used in this work allows obtaining each compound by controlling the reaction temperature. The compounds were characterized by infrared spectroscopy and 1H-NMR spectroscopy.     

Efficient Total Synthesis of Racemic Bisabolane Sesquiterpenes Curcuphenol and Xanthorrhizol Starting from Substituted Acetophenones

A total synthesis of natural bisabolane sesquiterpenes curcuphenol ( 1 ) and xanthorrhizol ( 2 ) was developed by using the substituted acetophenones 4 and 5 , respectively, as starting materials. The acetyl group of the latter was activated through ethoxycarbonylation to carry out the prenylation, which was performed successfully to give their respective precursors 11a and 11b , and 21 that were converted into the corresponding natural sesquiterpenes 1 and 2 , respectively, over four steps and in high overall yields.     

A heuristic approach for the stochastic optimization of mine production schedules

Traditionally, mining engineers plan an open pit mine considering pre-established conditions of operation of the plant(s) derived from a previous plant optimization. By contrast, mineral processing engineers optimize the processing plants by considering a regular feed from the mine, with respect to quantity and quality of the materials. The methods implemented to optimize mine and metallurgical plans simultaneously are known in the mining industry as global or simultaneous optimizers. The development of these methods has been of major concern for the mining industry over the last decade. Some algorithms are available in commercial mining software packages however, these algorithms ignore the inherent geological uncertainty associated with the deposit being considered, which leads to shortfalls in production, quality, and expected cashflows. This paper presents a heuristic method to generate life-of-mine production schedules that consider operating alternatives for processing plants and incorporate geological uncertainty. The method uses iterative improvement by swapping periods and destinations of the mining blocks to generate the final solution. The implementation of the method at a copper deposit shows its ability to control mine and processing capacities while increasing the expected net present value by 30% when compared with a solution generated using a standard industry practice.