Natural neighbor coordinates of points on a surface

Natural neighbor coordinates and natural neighbor interpolation have been introduced by Sibson for interpolating multivariate scattered data. In this paper, we consider the case where the data points belong to a smooth surface , i.e., a (d−1)-manifold of . We show that the natural neighbor coordinates of a point X belonging to tends to behave as a local system of coordinates on the surface when the density of points increases. Our result does not assume any knowledge about the ordering, connectivity or topology of the data points or of the surface. An important ingredient in our proof is the fact that a subset of the vertices of the Voronoi diagram of the data points converges towards the medial axis of when the sampling density increases.     

Delaunay Triangulation of Manifolds

We present an algorithm for producing Delaunay triangulations of manifolds. The algorithm can accommodate abstract manifolds that are not presented as submanifolds of Euclidean space. Given a set of sample points and an atlas on a compact manifold, a manifold Delaunay complex is produced for a perturbed point set provided the transition functions are bi-Lipschitz with a constant close to 1, and the original sample points meet a local density requirement; no smoothness assumptions are required. If the transition functions are smooth, the output is a triangulation of the manifold. The output complex is naturally endowed with a piecewise-flat metric which, when the original manifold is Riemannian, is a close approximation of the original Riemannian metric. In this case the output complex is also a Delaunay triangulation of its vertices with respect to this piecewise-flat metric.     

Synthesis and biological evaluation of the first example of an eight-membered iminoalditol

The synthesis of the first examples of eight-membered iminoalditols has been achieved from 2,3,4,6-tetra-O-benzyl-d-glucopyranose by way of a ring-closing metathesis. The (2R,3R,4R,5S)-2-hydroxymethyl-azocane-3,4,5-triol (3a), which has the d-gluco configuration for C-2-C-5 and appears to exist predominantly in a boat-chair conformation, is a weak inhibitor of glycosidases.     

Platinum oxide catalyzed hydrosilylation of unsymmetrical internal aryl alkynes under ortho-substituent regiocontrol

[chemical reaction: see text]. PtO2- and H2PtCl6-catalyzed hydrosilylation of internal aryl alkynes having a para or an ortho substituent with triethylsilane are discussed and compared. The regioselectivity of the H-Si bond addition was found to be controlled by the ortho substituent rather than the nature of the platinum catalyst. Arylalkynes with an ortho substituent, regardless of its electronic nature, directed the silyl substituent mainly to the alpha-position. PtO2 proved to be a versatile and powerful catalyst compared to H2PtCl6 since it prevents the alkyne reduction.     

Investigating the Influence of (Deoxy)fluorination on the Lipophilicity of Non‐UV‐Active Fluorinated Alkanols and Carbohydrates by a New log P Determination Method

Property tuning by fluorination is very effective for a number of purposes, and currently increasingly investigated for aliphatic compounds. An important application is lipophilicity (log P) modulation. However, the determination of log P is cumbersome for non‐UV‐active compounds. A new variation of the shake‐flask log P determination method is presented, enabling the measurement of log P for fluorinated compounds with or without UV activity regardless of whether they are hydrophilic or lipophilic. No calibration curves or measurements of compound masses/aliquot volumes are required. With this method, the influence of fluorination on the lipophilicity of fluorinated aliphatic alcohols was determined, and the log P values of fluorinated carbohydrates were measured. Interesting trends and changes, for example, for the dependence on relative stereochemistry, are reported.     

Tandem amine propargylation-Sonogashira reactions: new three-component coupling leading to functionalized substituted propargylic amines

Three-component coupling reactions of propargyl halides, amines, and organic halides in the presence of palladium-copper catalysis produced efficiently highly functionalized propargylic amines in good to excellent yields at room temperature. Extension to the synthesis of 2-(dialkylaminomethyl)benzo[b]furan or indole derivatives is described.     

O-ethyl thiocarbamates. A convenient route to 2-aryliminoimidazolidines

The reaction of N-aryl thionocarbamates and ethylenediamine lead to the corresponding 2-arylimino-imidazolidines, whose structure in pharmacology is well known. But, the behaviour of the N-alkyl thionocarbamates is quite different under operative conditions and these compounds afford with ethylenediamine, to 2-(2′-aminoethylamino)-Δ²-imidazoline, according to a mechanism which is discussed.     

Palladium-catalyzed stereoselective synthesis of E- and Z-1,1-diaryl or triarylolefins

A stereoselective and flexible synthesis of various E- and Z-1,1-diaryl and triarylolefins 3 was achieved from readily available vinylstannanes 1 via stereospecific iodo-destannylation and subsequent palladium-catalyzed Negishi-type cross-coupling reaction with arylzinc reagents under mild conditions.