Para‐hydrogen induced polarization of Si‐29 NMR resonances as a potentially useful tool for analytical applications

Para‐hydrogen–induced polarization effects have been observed in the ²⁹Si NMR spectra of trimethylsilyl para‐hydrogenated molecules. The high signal enhancements and the long T₁ values observed for the ²⁹Si hyperpolarized resonances point toward the possibility of using ²⁹Si for hyperpolarization applications. A method for the discrimination of multiple compounds and/or complex mixtures of hydroxylic compounds (such as steroids), consisting of the silylization of alcoholic functionalities with an unsaturated silylalkyl moiety and subsequent reaction with para‐H₂, is proposed. Copyright © 2012 John Wiley & Sons, Ltd.     

Syntheses and characterization of a new class of mono‐ and heterodinuclear derivatives of boron derived from Schiff bases

Reactions of 2‐isopropoxy‐1, 3, 2‐ benzodioxaborole with equivalent amounts of Schiff base ligands having two hydroxyl groups ( 1a–3a ) yield mononuclear derivatives with one residual hydroxy group. The reactions of these mononuclear derivatives with hexamethyldisilazane in a 2:1 ratio yield heterodinuclear derivatives. All these newly synthesized derivatives have been characterized by elemental analyses and molecular weight measurements. Tentative structures have been proposed on the basis of IR and NMR (¹H, ¹³C, ¹¹B,²⁹Si)spectral data and Fab‐mass studies. Schiff bases and their corresponding mono‐ and heterodinuclear derivatives of boron have also been screened for antifungal activities. Copyright © 2010 John Wiley & Sons, Ltd.     

Topological structure of complete Riemannian manifolds with cyclic holonomy groups

Let M be a complete m-dimensional Riemannian manifold with cyclic holonomy group, let X be a closed flat manifold homotopy equivalent to M, and let L→X be a nontrivial line bundle over X whose total space is a flat manifold with cyclic holonomy group. We prove that either M is diffeomorphic to X×Rm-dimX or M is diffeomorphic to L×Rm-dimX−1.     

Class groups of quadratic fields of 3-rank at least 2: Effective bounds

In this paper, we give parametric families of both real and complex quadratic number fields whose class group has 3-rank at least 2. As a consequence, we obtain that for all large positive real numbers x, the number of both real and complex quadratic fields whose class group has 3-rank at least 2 and absolute value of the discriminant ?x is >cx1/3, where c is some positive constant.     

Regularized fast multiple-image deconvolution for LBT

In this paper we study a fast deconvolution technique for the image restoration problem of the Large Binocular Telescope (LBT) interferometer. Since LBT provides several blurred and noisy images of the same object, it requires the use of multiple-image deconvolution methods in order to produce a unique image with high resolution. Hence the restoration process is basically a linear ill-posed problem, with overdetermined system and data corrupted by several components of noise.     

Square classes of totally positive units

In this article, we investigate some conditions for a real cyclic extension K over Q to satisfy the property that every totally positive unit of K is a square. As an application, we give a partial answer to Taussky's conjecture. We then extend our result to real abelian extensions of certain type.     

Sussmann's orbit theorem and maps

A map between manifolds which matches up families of complete vector fields is a fiber bundle mapping on each orbit of those vector fields.     

Revised Iterative Solution for Groundstate of Schrodinger Equation

A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schrodinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.     

Structural stability of (C, A)-marked subspaces

Given an observable pair of matrices (C, A) we consider the manifold of (C, A)-invariant subspaces having a fixed Brunovsky-Kronecker structure. Using Arnold techniques we obtain the explicit form of a miniversal deformation of a marked (C, A)-invariant subspace with respect to the usual equivalence relation. As an application, we obtain the dimension of the orbit and we characterize the structurally stable subspaces (those with open orbit).