Integrating over Higgs Branches

We develop some useful techniques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperk?hler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperk?hler periods. We also reduce these volumes for a large class of hyperk?hler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on ℝ⁴ and ALE manifolds, Hitchin spaces, and moduli spaces of (parabolic) Higgs bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of the volume reduces to a summation over solutions of Bethe Ansatz equations for the non-linear Schr?dinger system. We discuss some applications of our results. Received: 2 May 1999/ Accepted: 16 July 1999     

Influence of Fe(III) on the Fluorescence of Lysozyme: a Facile and Direct Method for Sensitive and Selective Sensing of Fe(III)

Lysozyme is widely used for the synthesis of nanomaterials (e.g., gold nanoparticle) to fluorescently sense metal ions. However, the effect of metal ions on the fluorescence of lysozyme is not studied yet. Herein, we have explored the interactions of lysozyme with different metal ions to develop a direct sensing platform for Fe(III). It has been observed that the fluorescence of lysozyme was slightly decreased in the presence of Cu(II), Hg(II), As(V), Co(II), Cd(II), Cr(II), Fe(II), Mn(II), Pb(II), and Zn(II), while a significant decrease in the lysozyme fluorescence was observed for Fe(III). The effect of thermal stability on the fluorescence quenching was also studied from 25 to 60 °C. In the present study, the lysozyme sensing probe was able to selectively and accurately detect 0.5–50 ppm of Fe(III) with a LOD of 0.1 ppm (1.8 µM) at 25 °C.

     

Supramolecular chirogenesis in zinc porphyrins: mechanism, role of guest structure, and application for the absolute configuration determination.

The achiral syn folded (face-to-face conformation) host molecule of the ethane-bridged bis(zinc porphyrin) transforms into the corresponding chiral extended anti bis-ligated species in the presence of enantiopure amine guests. The mechanism of the supramolecular chirogenesis is based upon the screw formation in bis(zinc porphyrin), arising from steric interactions between the largest substituent at the ligand's asymmetric carbon and peripheral alkyl groups of the neighboring porphyrin ring pointing toward the covalent bridge. The screw direction is determined by the guest's (amines) absolute configuration resulting in a positive chirality induced by (S)-enantiomers due to formation of the right-handed screw, and a negative chirality produced by the left-handed screw of (R)-enantiomers. The screw magnitude is strongly dependent upon the structure of the chiral guests. The amines with bulkier substituents result in stronger CD signals and larger (1)H NMR resonance splittings of enantiotopic protons. This system possesses a high degree of chiroptical activity, which allows the differentiation of one of the smallest homologous elements of organic chemistry, that is, the methyl and ethyl groups attached to the asymmetric carbon, and additionally, which senses a remote chiral center at a position beta to the amine binding group.     

MgFe2O4@SiO2–SO3H: an efficient,reusable catalyst for the microwave-assisted synthesis of benzoxazinone and benzthioxazinone via multicomponent reaction under solvent free condition

Research on Chemical Intermediates - We report the synthesis of sulfuric acid-functionalized silica-coated magnetic nanoparticles (MgFe2O4@SiO2–SO3H) as a catalyst for the microwave-assisted...     

Perovskites with the Framework‐Forming Xenon

The Group 18 elements (noble gases) were the last ones in the periodic system to have not been encountered in perovskite structures. We herein report the synthesis of a new group of double perovskites KM(XeNaO₆) (M=Ca, Sr, Ba) containing framework‐forming xenon. The structures of the new compounds, like other double perovskites, are built up of the alternating sequence of corner‐sharing (XeO₆) and (NaO₆) octahedra arranged in a three‐dimensional rocksalt order. The fact that xenon can be incorporated into the perovskite structure provides new insights into the problem of Xe depletion in the atmosphere. Since octahedrally coordinated Xe^VIII and Si^IV exhibit close values of ionic radii (0.48 and 0.40 Å, respectively), one could assume that Xe^VIII can be incorporated into hyperbaric frameworks such as MgSiO₃ perovskite. The ability of Xe to form stable inorganic frameworks can further extend the rich and still enigmatic chemistry of this noble gas.     

Piecewise linear processes with Poisson‐modulated exponential switching times

We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.