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Barycentric coordinates for convex polytopes 总被引:7,自引:0,他引:7
Joe Warren 《Advances in Computational Mathematics》1996,6(1):97-108
An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, theadjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. The barycentric coordinate functions for the polytope are rational combinations of adjoints of various dual cones associated with the polytope. 相似文献
105.
The commonly accepted linear stability analysis for the forward-time centred-space (FTCS) algorithm applied to the transport equation has led to the concept of a cell Reynolds number restriction on the spatial grid size. This paper shows where the commonly accepted original analysis is in error and presents the correct stability restrictions, which are restrictions on the time step, not the spatial grid size. There is no cell Reynolds number restriction. The results are confirmed by numerical computations for the two-dimensional driven cavity problem. 相似文献
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CdSe nanocrystals, also called quantum dots (Qdots) are a novel class of fluorophores, which have a diameter of a few nanometers and possess high quantum yield, tunable emission wavelength and photostability. They are an attractive alternative to conventional fluorescent dyes. Quantum dots can be silanized to be soluble in aqueous solution under biological conditions, and thus be used in bio-detection. In this study, we established a novel Qdot-based technology platform that can perform accurate and reproducible quantification of protein concentration in a crude cell lysate background. Protein lysates have been spiked with a target protein, and a dilution series of the cell lysate with a dynamic range of three orders of magnitude has been used for this proof-of-concept study. The dilution series has been spotted in microarray format, and protein detection has been achieved with a sensitivity that is at least comparable to standard commercial assays, which are based on horseradish peroxidase (HRP)-catalyzed diaminobenzidine (DAB) chromogenesis. The data obtained through the Qdot method has shown a close linear correlation between relative fluorescence unit and relative protein concentration. The Qdot results are in almost complete agreement with data we obtained with the well-established HRP-DAB colorimetric array (R2 = 0.986). This suggests that Qdots can be used for protein quantification in microarray format, using the platform presented here. 相似文献
107.
Jiang W Chen C Marinkovic D Tran JA Chen CW Arellano LM White NS Tucci FC 《The Journal of organic chemistry》2005,70(22):8924-8931
[reaction: see text] 2-[4-(tert-Butoxycarbonyl)piperazinyl]benzylidene-tert-butanesulfinamides underwent nucleophilic 1,2-addition with different organometallic reagents to give highly diastereomerically enriched adducts. X-ray crystallography of the resulting alpha-branched N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides confirms different mechanisms depending on the organometallic reagent used. Differential deprotection of the N-Boc and the tert-butanesulfinamides was investigated, and the dehydration byproducts have been identified and characterized. To avoid the formation of byproducts in the acidic deprotection step, the N-tert-butanesulfinamide group was converted to the corresponding N-tert-butanesulfonamide (Bus), which allowed for clean orthogonal deprotection. The efficient synthesis and deprotection of the N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides herein described constitutes an attractive method for extensive structure-activity studies in the search for novel ligands of the human melanocortin 4 receptor. 相似文献
108.
Joe G. Eisley 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1964,15(2):167-175
Zusammenfassung Der Einfluss von Vorspannungen auf die freien und erzwungenen nichtlinearen Schwingungen von Balken und rechteckigen Platten wird mittels einer einfachen Erweiterung der Lösungen für Fälle ohne Vorspannung untersucht. Es wird eine einzige Koordinatenfunktion benützt; es werden einfach aufgelegte und eingespannte Fälle betrachtet; und die Diskussion wird auch auf den überkritischen Bereich ausgedehnt. 相似文献
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An edge e in a 3-connected graph G is contractible if the contraction G/e is still 3-connected. The existence of contractible edges is a very useful induction tool. Let G be a simple 3-connected graph with at least five vertices. Wu [7] proved that G has at most vertices that are not incident to contractible edges. In this paper, we characterize all simple 3-connected graphs with exactly
vertices that are not incident to contractible edges. We show that all such graphs can be constructed from either a single
vertex or a 3-edge-connected graph (multiple edges are allowed, but loops are not allowed) by a simple graph operation.
Research partially supported by an ONR grant under grant number N00014-01-1-0917 相似文献