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991.
Gebhard Böckle 《Compositio Mathematica》2000,121(2):109-154
We determine the universal deformation ring, in the sense of Mazur, of a residual representation
, where k is a finite field of characteristic p and K is a local field of residue characteristic p. As one might hope for, but is not proven in the global case, the deformation ring is a complete intersection, flat over W(k), with the exact number of equations given by the dimension of
. We then go on to determine the ordinary locus inside the deformation space and, using ideas of Mazur, apply this to compare the universal and the universal ordinary deformation spaces. Provided that the universal ring for ordinary deformations with fixed determinant is finite flat over W(k), as was shown in many cases by Diamond, Fujiwara, Taylor–Wiles and Wiles, we show that the corresponding universal deformation ring – with no restriction of ordinariness or fixed determinant – is a complete intersection, finite flat over W(k) of the dimension conjectured by Mazur, provided that the restriction of
to the inertia subgroup is different from the inverse cyclotomic character. 相似文献
992.
This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category:
and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of
and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give
a sufficient and necessary condition for the braid of,
Hℳ to induce the braid of
, or equivalently, the braid of
, whereA is a quantum commutativeH-module algebra 相似文献
993.
Wen-ling Huang 《Proceedings of the American Mathematical Society》2000,128(8):2451-2455
In the space of invariant -dimensional subspaces of a null system in -dimensional projective space, W.L. Chow characterized the basic group of transformations as all the bijections , for which both and preserve adjacency. In the present paper we show that the two conditions is a surjection and preserves adjacency are sufficient to characterize the basic group. At the end of this paper we give an application to Lie geometry.
994.
Given the Sobolev bilinear form (f, g)
S
=>u
0, f
g< + >u
1, f " g "<, with u
0 and u
1 linear functionals, a characterization of the linear second–order differential operators with polynomial coefficients, symmetric with respect to (, )
S
in terms of u
0 and u
1 is obtained. In particular, several interesting functionals u
0 and u
1 are considered, recovering as particular cases of our study, results already known in the literature. 相似文献
995.
色散吸收非对称介质光腔中光场的量子理论 总被引:7,自引:2,他引:5
利用格林函数方法对色散吸收介质中的电磁场量子化,研究了由色散吸收介质构成的非对称介质光腔中光场的量子理论,并分析了非对称性对光腔量子性质、工作性能等的影响. 相似文献
996.
Masahide Kuwada 《Annals of the Institute of Statistical Mathematics》1987,39(1):649-659
Summary By use of the algebraic structure, we obtain a simplified expression for the outlier-insensitivity factor for balanced fractional
2m factorial (2m-BFF) designs of resolution 2l+1 derived from simple arrays (S-arrays), whose measure has been introduced by Ghosh and Kipnegeno (1985,J. Statist. Plann. Inference,11, 119–129). It is defined by use of the measure suggested by Box and Draper (1975,Biometrika, 62 (2), 347–352). As examples, we study the sensitivity ofA-optimal 2m-BFF designs of resolution VII (i.e.,l=3) given by Shirakura (1976,Ann. Statist.,4, 515–531; 1977,Hiroshima Math. J.,7, 217–285). We observe that these designs are robust in the sense that they have low sensitivities.
Research supported in part by Grant 59530012 (C) and 60530014 (C), Japan. 相似文献
997.
A Steiner quadruple system of order 2n is Semi‐Boolean (SBQS(2n) in short) if all its derived triple systems are isomorphic to the point‐line design associated with the projective geometry PG(n?1, 2). We prove by means of explicit constructions that for any n, up to isomorphism, there exist at least 2? 3(n?4)/2? regular and resolvable SBQS(2n). © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 229–239, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10050 相似文献
998.
Stephen James Wolfe 《Journal of multivariate analysis》1975,5(2):236-242
Several theorems are obtained concerning the unimodality of spherically symmetric distribution functions. These theorems are used to show that a class of spherically symmetric infinitely divisible distribution functions that contains the class of spherically symmetric stable distribution functions is unimodal. 相似文献
999.
Explicit equations are given for the elliptic curves (in characteristic ) with mod representation isomorphic to that of a given one.
1000.
David Eisenbud Craig Huneke Bernd Ulrich 《Proceedings of the American Mathematical Society》2001,129(9):2535-2540
Using symmetric algebras we simplify and slightly strengthen the Bruns-Eisenbud-Evans ``generalized principal ideal theorem' on the height of order ideals of nonminimal generators in a module. We also obtain a simple proof and an extension of a result by Kwiecinski, which estimates the height of certain Fitting ideals of modules having an equidimensional symmetric algebra.