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91.
The study of reductive group actions on a normal surface singularityX is facilitated by the fact that the group Aut X of automorphismsof X has a maximal reductive algebraic subgroup G which containsevery reductive algebraic subgroup of Aut X up to conjugation.If X is not weighted homogeneous then this maximal group G isfinite (Scheja, Wiebe). It has been determined for cusp singularitiesby Wall. On the other hand, if X is weighted homogeneous butnot a cyclic quotient singularity then the connected componentG1 of the unit coincides with the C* defining the weighted homogeneousstructure (Scheja, Wiebe, Wahl). Thus the main interest liesin the finite group G/G1. Not much is known about G/G1. Ganterhas given a bound on its order valid for Gorenstein singularitieswhich are not log-canonical. Aumann-Körber has determinedG/G1 for all quotient singularities. We propose to study G/G1 through the action of G on the minimalgood resolution of X. If X is weightedhomogeneous but not a cyclic quotient singularity, let E0 bethe central curve of the exceptional divisor of . We show that the natural homomorphism GAut E0 haskernel C* and finite image. In particular, this re-proves therest of Scheja, Wiebe and Wahl mentioned above. Moreover, itallows us to view G/G1 as a subgroup of Aut E0. For simple ellipticsingularities it equals (ZbxZb)Aut0 E0 where b is theself-intersection number of E0, ZbxZb is the group of b-torsionpoints of the elliptic curve E0 acting by translations, andAut0 E0 is the group of automorphisms fixing the zero elementof E0. If E0 is rational then G/G1 is the group of automorphismsof E0 which permute the intersection points with the branchesof the exceptional divisor while preserving the Seifert invariantsof these branches. When there are exactly three branches weconclude that G/G1 is isomorphic to the group of automorphismsof the weighted resolution graph. This applies to all non-cyclicquotient singularities as well as to triangle singularities.We also investigate whether the maximal reductive automorphismgroup is a direct product GG1xG/G1. This is the case, for instance,if the central curve E0 is rational of even self-intersectionnumber or if X is Gorenstein such that its nowhere-zero 2-form has degree ±1. In the latter case there is a naturalsection G/G1G of GG/G1 given by the group of automorphisms inG which fix . For a simple elliptic singularity one has GG1xG/G1if and only if E0 · E0 = 1. 相似文献
92.
93.
Multistage stochastic programs with interstage independent random parameters have recourse functions that do not depend on
the state of the system. Decomposition-based algorithms can exploit this structure by sharing cuts (outer-linearizations of
the recourse function) among different scenario subproblems at the same stage. The ability to share cuts is necessary in practical
implementations of algorithms that incorporate Monte Carlo sampling within the decomposition scheme. In this paper, we provide
methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency
models. These techniques enable sampling-based algorithms to handle a richer class of multistage problems, and may also be
used to accelerate the convergence of exact decomposition algorithms.
Research leading to this work was partially supported by the Department of Energy Contract DE-FG03-92ER25116-A002; the Office
of Naval Research Contract N00014-89-J-1659; the National Science Foundation Grants ECS-8906260, DMS-8913089; and the Electric
Power Research Institute Contract RP 8010-09, CSA-4O05335.
This author's work was supported in part by the National Research Council under a Research Associateship at the Naval Postgraduate
School, Monterey, California. 相似文献
94.
95.
Gerd Mitschke 《Archive for Mathematical Logic》1972,15(1-2):31-35
Ohne Zusammenfassung 相似文献
96.
97.
98.
Gerd Grubb 《Israel Journal of Mathematics》1971,10(1):32-95
The paper treats coerciveness inequalities (of the form Re(Au, u)≧c ‖u‖
s
2
−λ ‖u‖
0
2
,c>0,λ ∈ R) and semiboundedness inequalities (of the form Re (Au, u)≧−λ ‖u‖2) for the general boundary problems associated with an elliptic 2m-order differential operatorA in a compactn-dimensional manifold with boundary. In particular, we study the normal pseudo-differential boundary conditions, for which
we determine necessary and sufficient conditions for coerciveness withs=m, and for semiboundedness with ‖u‖ = ‖u‖m, in explicit form. 相似文献
99.
100.
The analysis of the influence of an intracavity absorbing dye cell on the spectral characteristics of a free running dye laser leads to the operation of two coupled dye lasers. A powerful flashlamp-pumped dye ring laser pumps a secondary intracavity dye laser with a conversion efficiency of 30 %. Both wavelengths are independently tunable and cover the spectral range from 580 nm to 652 nm in the case of the dye combination rhodamine 6G and cresyl violet. 相似文献