Efficiently Hex-Meshing Things with Topology

A topological quadrilateral mesh \(Q\) of a connected surface in \(\mathbb {R}^3\) can be extended to a topological hexahedral mesh of the interior domain \(\varOmega \) if and only if \(Q\) has an even number of quadrilaterals and no odd cycle in \(Q\) bounds a surface inside \(\varOmega \) . Moreover, if such a mesh exists, the required number of hexahedra is within a constant factor of the minimum number of tetrahedra in a triangulation of \(\varOmega \) that respects \(Q\) . Finally, if \(Q\) is given as a polyhedron in \(\mathbb {R}^3\) with quadrilateral facets, a topological hexahedral mesh of the polyhedron can be constructed in polynomial time if such a mesh exists. All our results extend to domains with disconnected boundaries. Our results naturally generalize results of Thurston, Mitchell, and Eppstein for genus-zero and bipartite meshes, for which the odd-cycle criterion is trivial.     

Development and validation of a dried blood spot–HPLC assay for the determination of metronidazole in neonatal whole blood samples

A selective and sensitive high-performance liquid chromatography method with UV detection for the determination of metronidazole in dried blood spots (DBS) has been developed and validated. DBS samples [spiked or patient samples] were prepared by applying blood (30 µL) to Guthrie cards. Discs (6 mm diameter) were punched from the cards and extracted using water containing the internal standard, tinidazole. The extracted sample was chromatographed without further treatment using a reversed phase system involving a Symmetry® C18 (5 µm, 3.9?×?150 mm) preceded by a Symmetry® guard column of matching chemistry and a detection wavelength of 317 nm. The mobile phase comprised acetonitrile/0.01?M phosphate solution (KH₂PO₄), pH 4.7, 15:85, v/v, with a flow rate of 1 mL/min. The calibration was linear over the range 2.5–50 mg/mL. The limits of detection and quantification were 0.6 and 1.8 µg/mL, respectively. The method has been applied to the determination of 203 DBS samples from neonatal patients for a phamacokinetic/pharmacodynamic study.     

统计学者的工作及风范:灵感、抱负、雄心

1985年5月我第一次到中国来,距离这次我被邀请已经隔了25年.这次我该讲什么呢?我是这么想的,假如20年前的中国像个穷人,现在的中国就像个富人,或者快变成富人.那么对富人讲话应该跟对穷人不一样,所以今天我想讲的题目是怎么看待学术成就和学术风范.为什么呢?各位从历史上看,一个国家要变成大国,变成真正受人尊敬的大国,或者一个科学界,要衡量它的成熟以及它本身的品质,其中一个很重要的衡量标准是它怎么对待学术成就和学术风范.     

A Homological Approach to Two Problems on Finite Sets

We propose a homological approach to two conjectures descended from the Erdös-Ko-Rado Theorem, one due to Chvátal and the other to Frankl and Füredi. We apply the method to reprove, and in one case improve, results of these authors related to their conjectures.     

A law of large numbers result for a bifurcating process with an infinite moving average representation

This paper derives a law of large numbers theorem for bifurcating processes defined on a perfect binary tree. This theorem can be viewed as a generalization of some results that have already appeared in the literature. For instance, all that is required of the bifurcating process is an infinite moving average representation with geometrically decaying coefficients and a finite moment assumption. In addition, the summands are assumed to belong to a flexible class of functions that satisfy a generalized Lipschitz type condition. These two criteria allow for an expansive range of applicability. Two examples are given as corollaries to the theorem.     

On the analytic model of a class of semi-hyponormal operators

The analytic model of a class of semi-hyponormal operators is derived using three kernal functions. In addition, explicit forms of the kernal functions are given and the Pincus principal functions of the operators are calculated.     

An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.