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41.
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Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy $ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $ is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i)—this is readily done because (i) has a large family of Ljapunov functionals. 相似文献
43.
Walter Fischer Cyril A. Grob Reinhard Hanreich Georg von Sprecher Adrian Waldner 《Helvetica chimica acta》1981,64(7):2298-2311
The solvolysis rates and products of the 6-exo-substituted 2-exo- 1a - 1u , and 2-endo-norbornyl p-toluenesulfonates 2a - 2u , have been determined. In general, the rate constants for 1 and 2 (log k) correlate well with the inductive constants σ of the substitutents at C(6); however, their sensitivity to σ is much larger in the 2-exo-series 1 than in the 2-endo-series 2 . This differential transmission of polar effects is the cause of decreasing 2-exo/2-endo rate ratios from 2388 for R = t-C4H9 to 0.37 for R = Br, i. e. with increasing electron attraction by the substituent. The high sensitivity of the rate constants for the 2-exo-p-toluenesulfonates 1 to σ indicates an unusually strong inductive interaction between C(6) and the incipient cationic center at C(2). This interaction is ascribed to the participation of the pentacoordinate C(6)-atom, i. e. to 1,3-bridging, a consequence of steric hindrance of nucleophilic solvent participation in norbornanes. Donor substituents enhance 1,3-bridging, lead to faster reactions and to the formation of 2-exo substitution products. Conversely, acceptor substituents reduce 1,3-bridging, decrease rates and facilitate the formation of 2-endo substitution products. Graded 1,3-bridging is discussed in the light of Winstein's nonclassical ion concept. 相似文献
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Novel Inorganic Ring Systems. 34. Derivatives of the Cyclo-1-thiaIV- and of the Cyclo-1-thia VI-3,4-disila-2,5-diazane Variations of fivemembered “hetero” cyclosilazanes of the type Si2N2El could be enlarged to the systems with El = SO and SO2. They are obtained by the formation principles 4 + 1 and 2 + 3 respectively, according to the equation (1), (4) and (5). The prepared compound are described in their properties and confirmed in their structure (Tables 1–2). 相似文献
48.
The synthetically interesting processes available for indolization reactions are discussed and illustrated in tabular form and particular emphasis is placed on the more recent methods. 相似文献
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Ti7Cl16 and Ti7Br16 and Further Investigations with Titanium Halides. Al2X6 as a Complex Forming Agent TiCl3,s can be transported with Al2Cl6 via TiAlCl6,g in a temperature gradient. The equilibrium of this reaction was studied by mass spectroscopy. There is no indication of the existence of a TiAl2Cl9 molecule as assumed in the literature. β-TiBr3 was prepared from the elements in the presence of the transporting agent Al2Br6,g. The transport of TiCl2 with Al2Cl6,g involves, as an important step, the disproportionation which is favoured by the reaction of Ti with the glass wall. If the disproportionation is made impossible by addition of Ti the novel compound Ti7Cl16 is obtained. Independent of Ti7Cl16, a phase TiCl(2 + x) with a broad range of homogeneity exists. The compound Ti7Br16, being isostructural with Ti7Cl16, was also prepared. Results of magnetic measurements and observations on the thermal decomposition of the compounds are reported. 相似文献
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