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991.
We study the structure of the most common type of Riemannian submersions, namely those whose fibers are given by the orbits
of an isometric group action on a Riemannian manifold. Special emphasis is given to the case where the ambient space has nonnegative
curvature.
The first author was supported by research grant MTM2004-04794-MEC. Most of this work was done during a visit of the second
author to Madrid, financed in part by funds of the aforementioned grant. 相似文献
992.
Karin Melnick 《Geometriae Dedicata》2007,126(1):131-154
We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general
construction, leading to a new example, of codimension-one actions – those for which the dimension of the Heisenberg group
is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the
assumption they are real-analytic. 相似文献
993.
Patrick Dehornoy 《Journal of Combinatorial Theory, Series A》2007,114(3):389-409
Many natural counting problems arise in connection with the normal form of braids—and seem to have not been much considered so far. Here we solve some of them. One of the noteworthy points is that a number of different induction schemes appear. The key technical ingredient is an analysis of the normality condition in terms of permutations and their descents, in the vein of the Solomon algebra. As was perfectly summarized by a referee, the main result asserts that the size of the automaton involved in the automatic structure of Bn associated with the normal form can be lowered from n! to p(n), the number of partitions of n. 相似文献
994.
A. Montinaro 《Journal of Combinatorial Theory, Series A》2007,114(6):993-1023
The projective planes of order n with a collineation group acting 2-transitively on an arc of length v, with n>v?n/2, are investigated and several new examples are provided. 相似文献
995.
Jonas Sjöstrand 《Journal of Combinatorial Theory, Series A》2007,114(7):1182-1198
We characterise the permutations π such that the elements in the closed lower Bruhat interval [id,π] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations π such that [id,π] corresponds to a flag manifold defined by inclusions, studied by Gasharov and Reiner.Our characterisation connects the Poincaré polynomials (rank-generating function) of Bruhat intervals with q-rook polynomials, and we are able to compute the Poincaré polynomial of some particularly interesting intervals in the finite Weyl groups An and Bn. The expressions involve q-Stirling numbers of the second kind, and for the group An putting q=1 yields the poly-Bernoulli numbers defined by Kaneko. 相似文献
996.
Volker Runde 《Journal of Mathematical Analysis and Applications》2007,329(1):736-751
Let G be a locally compact group, and let R(G) denote the ring of subsets of G generated by the left cosets of open subsets of G. The Cohen-Host idempotent theorem asserts that a set lies in R(G) if and only if its indicator function is a coefficient function of a unitary representation of G on some Hilbert space. We prove related results for representations of G on certain Banach spaces. We apply our Cohen-Host type theorems to the study of the Figà-Talamanca-Herz algebras Ap(G) with p∈(1,∞). For arbitrary G, we characterize those closed ideals of Ap(G) that have an approximate identity bounded by 1 in terms of their hulls. Furthermore, we characterize those G such that Ap(G) is 1-amenable for some—and, equivalently, for all—p∈(1,∞): these are precisely the abelian groups. 相似文献
997.
We apply functional separation of variables within the approach of the group foliation method to the nonlinear wave equation with variable speed and external force: utt=A(x)(Dx(u)ux)+B(x)Q(u), Ax≠0. A classification of these equations admitting functionally separable solutions is performed and the resulting solutions are obtained in explicit form in many cases. 相似文献
998.
P.A. Kuzmin 《Journal of Mathematical Analysis and Applications》2007,330(1):744-750
This note is devoted to construction of the domain of the regular representation of Diff+(S1). We consider a subgroup of diffeomorphism group such that the Malliavin-Shavgulidze measure is quasi-invariant with respect to the left action of the subgroup. The measure appears to be quasi-invariant with respect to the left action of diffeomorphisms with discontinuous second derivative. We derive an expression for quasi-invariance density and obtain an additional PSL(2,R) symmetry breaking term. 相似文献
999.
Chein-Shan Liu 《Journal of Mathematical Analysis and Applications》2007,331(1):547-566
In this paper we study a circular differential equation under a discontinuous periodic input, developing a quadratic differential equations system on S1 and a linear differential equations system in the Minkowski space M3. The symmetry groups of these two systems are, respectively, PSOo(2,1) and SOo(2,1). The Poincaré circle map is constructed exactly, and a critical value αc of the parameter is identified. Depending on α of the input amplitude the equation may exhibit periodic, subharmonic or quasiperiodic motions. When α varies from α>αc to α<αc, there undergoes an inverse tangent bifurcation; consequently, the resultant Poincaré circle map offers one route to the quasiperiodicity via a type I intermittency. In the parameter range of α<αc the orbit generated by the Poincaré circle map is either m-periodic or quasiperiodic when n/m is a rational or an irrational number. 相似文献
1000.
We prove the existence of infinite subgroups with nontrivial locally finite radicals and of infinite locally finite subgroups in the groups with almost finite almost solvable elements of order 2 and 4 and in the groups with almost finite elements. 相似文献