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11.
If M is an isoparametric hypersurface in a sphere S
n
with four distinct principal curvatures, then the principal curvatures κ1, . . . , κ4 can be ordered so that their multiplicities satisfy m
1 = m
2 and m
3 = m
4, and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible connected proper Dupin hypersurface in R
n
(or S
n
) with four distinct principal curvatures with multiplicities m
1 = m
2 ≥ 1 and m
3 = m
4 = 1, and constant Lie curvature r = −1, then M is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the
assumption of irreducibility is replaced by compactness and r is merely assumed to be constant.
相似文献
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T Christensen E B Jensen F Junker H Dalb?ge F Abildgaard J J Led 《Acta chemica Scandinavica (Copenhagen, Denmark : 1989)》1992,46(1):97-99
Biosynthetic human growth hormone specifically 13C-labelled in the carbonyl positions of all 26 leucine residues has been obtained by recombinant DNA techniques using 13C-labelled leucine and an E. coli strain that requires leucine. It is shown that, on the whole, the labelling is specific with no significant mislabelling as would have been the case had the 13C-labelled leucine been metabolized. 相似文献
15.
A 480 L evacuable reaction chamber, equipped with FT-IR spectroscopy on-line and ion chromatography off-line, has been used to study the gas phase reaction between the nitrate radical, NO3, and the reduced organic sulphur compounds CH3CH2SH, (CH3CH2)2S, (CH3CH2)2S2, and CH3CH2SCH3 in air. The products CH3CH2SO3H, SO2, H2SO4, CH3CHO, and CH3CH2ONO2 were identified and quantified in the reactions of the first three compounds, CH3CH2SH, (CH3CH2)2S, and (CH3CH2)2S2. The reaction products were CH3CH2SO3H, CH3SO3H, SO2, H2SO4, CH3CHO, and CH2O in the reaction of CH3CH2SCH3. On the basis of identified reaction products and intermediates observed in the infrared spectra, mechanisms are proposed for the reactions between the NO3 radical and the four reduced organic sulphur compounds. The results of this study, together with those from previous experiments performed in this laboratory on CH3SCH3, CH3SH, and CH3SSCH3 lead to the conclusion that all these species, in the reaction with the NO3 radical, follow a similar degradation mechanism producing SO2, H2SO4, R? SO3H, R? CHO, and R? CH2ONO2, as the main reaction products. The inital step of the reaction of NO3 with R? S? R and R? S? H type (R = CH3, CH2CH3) reduced organic sulphur compounds was found to be H-atom abstraction, probably after the formation of an initial adduct. For the reaction between NO3 and R? S? S? R type compounds, evidence for an addition-decomposition reaction, as the initial steps, was obtained. R? S·, R? S(O)·, and R? S(O)2· appear to be formed as intermediates in all the reactions. © John Wiley & Sons, Inc. 相似文献
16.
An adaptive pruning algorithm for the discrete L-curve criterion 总被引:1,自引:0,他引:1
Per Christian Hansen Toke Koldborg Jensen Giuseppe Rodriguez 《Journal of Computational and Applied Mathematics》2007
We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples. 相似文献
17.
Manil B. Anagnostopoulos D. F. Biri S. Borchert G. L. Breunlich W. Egger J. P. Gotta D. Gruber A. Hennebach M. Indelicato P. Jensen T. Liu Y. W. Markushin V. Nelms N. Simons L. M. Zmeskal H. 《Hyperfine Interactions》2003,146(1-4):343-347
Hyperfine Interactions - An experiment to measure the strong interaction width (Γ1s ) and shift (ε1s ) of the ground state of pionic hydrogen (π?p), in order to determine the... 相似文献
18.
19.
This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow. 相似文献
20.
The modified wave and scattering operators are shown to be bounded between weighted L
2-spaces for two-body Schrödinger operators with long range potentials. 相似文献