AN ITERATION METHOD FOR INCOMPRESSIBLEVISCOUS/INVISCID COUPLED PROBLEM VIA A SPECTRALAPPROXIMATION

1.IntroductionDomaindecompositionmethodsareusefulapproximationtechniquestofacecomputationalfluiddynamicsproblems,especiallyincomplexphysicaldomainsandusingparallelcomputationalenvironments.Theyhavebeenfirstemployedinfinitedifferenceandfiniteelementme...     

A penalized Fischer-Burmeister NCP-function

We introduce a new NCP-function in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. This new NCP-function turns out to have stronger theoretical properties than the widely used Fischer-Burmeister function and other NCP-functions suggested previously. Moreover, numerical experience indicates that a semismooth Newton method based on this new NCP-function performs considerably better than the corresponding method based on the Fischer-Burmeister function. Received: March 10, 1997 / Accepted: February 15, 2000?Published online May 12, 2000     

Transitions to the Continuum: Three Different Approaches

We present three different derivations of the transition probabilities to the continuum. It is shown that calculations, performed as a direct application of the postulates of orthodox quantum mechanics (OQM), do not yield results consistent with experiments. Traditional treatments are summarized and criticized. The relation of the transitions to the continuum with the traditional quantum measurement problem is pointed out; we sum up and comment some contributions concerning this issue. It is shown that an approach based on the notion of spontaneous projections yields expressions of the transition probabilities similar to those obtained in the traditional way and new predictions which could be submitted to experimental tests.     

Laser secondary neutral mass spectrometry for copper detection in micro‐scale biopsies

Disease progression and clinical diagnostics of a number of hereditable metabolic diseases are determined by organ involvement in disturbed deposition of certain molecules. Current clinical imaging is unable to visualize this maldistribution with sufficient specificity and sensitivity, such as in Wilson's disease. The quest for understanding cellular Cu distribution in these patients requires element‐ and molecule‐specific images with nanometer‐scale spatial resolution. We have used a new cryo‐mass spectrometric instrument with an integrated cryosectioning chamber for preparation and analysis of frozen hydrated samples of Wilson's disease tissue. With laser post‐ionization secondary neutral mass spectrometry (laser‐SNMS), we were able to image Cu and other intrinsic elements and molecules in less than 1 mg of frozen hydrated liver tissue from a murine model of Wilson's disease. A 40–50 times higher Cu concentration was measured in the disease tissue as compared to the control mouse. Furthermore, major histomorphological changes were observed using this advanced nano‐science tool. The results showed that the combination of in‐vacuum cryosectioning and cryo‐laser‐SNMS technologies is particularly well suited for identifying specific cell structures and imaging trace element concentrations with subcellular resolution and upper‐parts‐per‐billion sensitivity in biological samples. This technology can provide a novel diagnostic tool for clinical applications in various diseases involving trace elements. Copyright © 2009 John Wiley & Sons, Ltd.     

Gauss-Green cubature and moment computation over arbitrary geometries

We have implemented in Matlab a Gauss-like cubature formula over arbitrary bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n−1 using N∼cmn² nodes, 1≤c≤p, m being the total number of points given on the boundary. It does not need any decomposition of the domain, but relies directly on univariate Gauss-Legendre quadrature via Green’s integral formula. Several numerical tests are presented, including computation of standard as well as orthogonal moments over a nonstandard planar region.     

2,2′-Biimidazole as an Efficient Ligand for Copper(I)-Catalyzed C‒N Coupling Reactions

An efficient copper(I)-catalyzed system using 2,2′-biimidazole as the ligand was applied to N-arylation of a broad spectrum of nitrogen nucleophiles with aryl halides. The reactions were carried out in relatively mild conditions with good to excellent yields.     

Brachistochrone with Coulomb friction as the solution of an isoperimetrical variational problem

The problem of finding the plane supporting curve (brachistochrone) along which a heavy particle released from rest at the given starting point slides with dry (Coulomb) friction and reaches the given destination point in least time, is stated as a variational isoperimetrical problem. The finite parametric equations of the extremal curve are obtained. This curve is the sought-for brachistochrone if the solution of the problem exists. Several numerical examples are given.     

On higher order Stickelberger-type theorems

We discuss an explicit refinement of Rubin?s integral version of Stark?s conjecture. We prove that this refinement is a consequence of the relevant case of the Equivariant Tamagawa Number Conjecture of Burns and Flach, hence obtaining a full proof in several important cases. We also derive several explicit consequences of this refinement concerning the annihilation as Galois modules of ideal class groups by explicit elements constructed from the values of higher order derivatives of Dirichlet L-functions. We finally describe the relation between our approach and those found in recent work of Emmons and Popescu and of Buckingham.