38 research outputs found
Total Synthesis of Zoanthamine Alkaloids, Part 2. Construction of the C1-C5, C6-C10, and C11-C24 Fragments of Zoanthamine.
Geometry of River Networks I: Scaling, Fluctuations, and Deviations
This article is the first in a series of three papers investigating the
detailed geometry of river networks. Large-scale river networks mark an
important class of two-dimensional branching networks, being not only of
intrinsic interest but also a pervasive natural phenomenon. In the description
of river network structure, scaling laws are uniformly observed. Reported
values of scaling exponents vary suggesting that no unique set of scaling
exponents exists. To improve this current understanding of scaling in river
networks and to provide a fuller description of branching network structure, we
report here a theoretical and empirical study of fluctuations about and
deviations from scaling. We examine data for continent-scale river networks
such as the Mississippi and the Amazon and draw inspiration from a simple model
of directed, random networks. We center our investigations on the scaling of
the length of sub-basin's dominant stream with its area, a characterization of
basin shape known as Hack's law. We generalize this relationship to a joint
probability density and show that fluctuations about scaling are substantial.
We find strong deviations from scaling at small scales which can be explained
by the existence of linear network structure. At intermediate scales, we find
slow drifts in exponent values indicating that scaling is only approximately
obeyed and that universality remains indeterminate. At large scales, we observe
a breakdown in scaling due to decreasing sample space and correlations with
overall basin shape. The extent of approximate scaling is significantly
restricted by these deviations and will not be improved by increases in network
resolution.Comment: 16 pages, 13 figures, Revtex4, submitted to PR
Unified View of Scaling Laws for River Networks
Scaling laws that describe the structure of river networks are shown to
follow from three simple assumptions. These assumptions are: (1) river networks
are structurally self-similar, (2) single channels are self-affine, and (3)
overland flow into channels occurs over a characteristic distance (drainage
density is uniform). We obtain a complete set of scaling relations connecting
the exponents of these scaling laws and find that only two of these exponents
are independent. We further demonstrate that the two predominant descriptions
of network structure (Tokunaga's law and Horton's laws) are equivalent in the
case of landscapes with uniform drainage density. The results are tested with
data from both real landscapes and a special class of random networks.Comment: 14 pages, 9 figures, 4 tables (converted to Revtex4, PRE ref added
Regio- and Enantioselective Formal Hydroamination of Enamines for the Synthesis of 1,2-Diamines
The asymmetric formal hydroamination of enamines using a CuH catalyst is reported. The method provides a straightforward and efficient approach to the synthesis of chiral 1,2-dialkyl amines in good yields with high levels of enantioselectivities for a broad range of substrates, and should have significant value for the preparation of molecules bearing a 1,2-diamine motif
Determination of the relative configuration of vic-amino alcohols
A large set of syn- and anti-1,2-amino alcs. has been synthesized. Upon comparison of the CHO and CHN 1H NMR shifts a general trend has been obsd., making it possible to det. the relative configuration of 1,2-amino alcs. without derivatization or shift reagents
Synthesis of Imidates : TFA-Mediated Regioselective Amide Alkylation Using Meerwein's Reagent
Regioselective O-alkylation of an amide to form the corresponding imidate is a common synthetic problem, often resulting in varying amounts of N-alkylation. Screening existing methods for converting amides to imidates gave inconsistent or irreproducible results, sometimes affording N-alkylamide as the major product. A simple and reliable protocol for amide O-alkylation with complete regioselectivity has been designed, and its scope and efficiency demonstrated on a number of substrates
Enantioselective synthesis of anti-beta-amido-alpha-hydroxy esters via asymmetric transfer hydrogenation coupled with dynamic kinetic resolution
The asymmetric transfer hydrogenation of beta-amido-alpha-keto esters providing the corresponding anti-beta-amido-alpha-hydroxy esters via dynamic kinetic resolution is reported. The use of a commercially available, or simply prepared, chiral ruthenium catalyst results in good yields as well as high diastereoselectivities and enantioselectivities. (C) 2013 Elsevier Ltd. All rights reserved