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31.
New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament, non-filament, and ample, with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces. 相似文献
32.
Summary For the numerical solution of non-stiff semi-explicit differentialalgebraic equations (DAEs) of index 1 half-explicit Runge-Kutta methods (HERK) are considered that combine an explicit Runge-Kutta method for the differential part with a simplified Newton method for the (approximate) solution of the algebraic part of the DAE. Two principles for the choice of the initial guesses and the number of Newton steps at each stage are given that allow to construct HERK of the same order as the underlying explicit Runge-Kutta method. Numerical tests illustrate the efficiency of these methods. 相似文献
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Randolf Arnold 《Monatshefte für Mathematik》1989,108(4):277-293
LetK andL be convex bodies of then-dimensional Euclidean spaceE
n
. The -distance ofK andL is defined by
, whereh
k
andh
L
denote the support functions ofK andL restricted to the unit sphereS
n–1
E
n
. We consider the problem of best approximation ofL by the images k ofK under proper rigid motions :E
n
E
n
. A motion that minimizes 2(K
L) is called optimal for (K, L) in the sense of the metric 2. The results in the general case (n2 arbitrary) base on the fact that the Steiner points of K andL coincide if is optimal for (K, L). Forn=2 we obtain a relationship between convex convolution bodies and the underlying approximation problem. 相似文献
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A diastereoselective [4+2] annulation of vinyl carbodiimides with chiral N-alkyl imines has been developed to access the stereochemically rich tricyclic core of the batzelladine alkaloids. Its application to the asymmetric synthesis of batzelladine D permitted the use of long-range, directed hydrogenation and stereoselective intramolecular iodoamination as additional key steps to establish the remaining stereocenters within the natural product with excellent stereocontrol. 相似文献
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Malkinson JP Anim MK Zloh M Searcey M Hampshire AJ Fox KR 《The Journal of organic chemistry》2005,70(19):7654-7661
[reaction: see text] In this article, the first solid-phase-based total synthesis of TANDEM, a synthetic analogue of triostin A, is described. In initial studies, the synthesis incorporated depsipeptide formation, introduction of chromophores, and disulfide bond formation on the solid phase, prior to a final solution-phase macrolactamization, to give the target molecule. Although pure TANDEM was obtained in an overall yield comparable to those for all syntheses to date, the yield of the final cyclization was low (11%). A more efficient approach involved removal from the solid phase prior to disulfide bond formation. The resulting linear peptide underwent macrolactamization under mild conditions and high dilution. Final disulfide bond formation was essentially quantitative and gave the target molecule, TANDEM, in an overall yield of 18%. The final compound was assessed for its ability to bind to 5'-TpA sequences on DNA by DNase I footprinting. This efficient synthesis sets the stage for a study of the structure-activity relationship of TANDEM and the natural product triostin A, with analogues containing "point mutations" at every site within the cyclic compounds. 相似文献