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On sait associer à certaines structures de Poisson surRn, de 1-jet nul en 0, des actions de R2 sur Rn, donnéespar le rotationnel de leur partie quadratiqueet un autre champ de vecteurs. Lorsque ces actions sont nonrésonantes et hyperboliques, onmontre que ces structures sont quadratisables,en ce sens qu'il existe des coordonnées dans lesquelles,elles sont quadratiques. Dans le cas de la dimension 3, nosrésultats mènent à la non-dégénérescencegénérique des structures de Poisson quadratiquesà rotationnels inversibles. We can associate with some Poisson structures defined on Rnwith a zero 1-jet at zero, actions from R2 on Rn, given by thecurl of their quadratic part and another vectorfield. Assuming that those actions are hyperbolicsand without resonances, we give a normal formfor those structures. On R3, we prove that every quadratic Poissonstructure with invertible curl, is generically non degenerate. 相似文献
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Two convex bodies K and K' in Euclidean space En can be saidto be in exceptional relative position if they have a commonboundary point at which the linear hulls of their normal coneshave a non-trivial intersection. It is proved that the set ofrigid motions g for which K and gK' are in exceptional relativeposition is of Haar measure zero. A similar result holds trueif exceptional relative position is defined viacommon supporting hyperplanes. Both results were conjecturedby S. Glasauer; they have applications in integral geometry. 相似文献
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Let M be a Hamiltonian K-space with proper moment map µ.The symplectic quotient X = µ1(0)/K is a singularstratified space with a symplectic structure on the strata.In this paper we generalise the Kirwan map, which maps the Kequivariant cohomology of µ1(0) to the middle perversityintersection cohomology of X, to this symplectic setting. The key technical results which allow us to do this are Meinrenken'sand Sjamaar's partial desingularisation of singular symplecticquotients and a decomposition theorem, proved in Section 2 ofthis paper, exhibiting the intersection cohomology of a symplecticblowup of the singular quotient X along a maximal depthstratum as a direct sum of terms including the intersectioncohomology of X. 相似文献
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Zero-Sets of Quaternionic and Octonionic Analytic Functions with Central Coefficients 总被引:1,自引:0,他引:1
We prove that the zero set of any quaternionic (or octonionic)analytic function f with central (that is, real) coefficientsis the disjoint union of codimension two spheres in R4 or R8(respectively) and certain purely real points. In particular,for polynomials with real coefficients, the complete root-setis geometrically characterisable from the lay-out of the rootsin the complex plane. The root-set becomes the union of a finitenumber of codimension 2 Euclidean spheres together with a finitenumber of real points. We also find the preimages f1for any quaternion (or octonion) A. We demonstrate that this surprising phenomenon of complete spheresbeing part of the solution set is very markedly a special realphenomenon. For example, the quaternionic or octonionic Nthroots of any non-real quaternion (respectively octonion) turnout to be precisely N distinct points. All this allows us todo some interesting topology for self-maps of spheres. 相似文献
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Ordered C*-Modules 总被引:1,自引:0,他引:1
In this first part of a study of ordered operator spaces, wedevelop the basic theory of ordered C*-bimodules.A crucial role is played by open tripotents, aJB*-triple variant of Akemann's notion of open projection. 2000Mathematics Subject Classification 46L08, 47L07 (primary), 46L07,47B60, 47L05 (secondary). 相似文献
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Farouki Rida T.; Manni Carla; Sestini Alessandra 《IMA Journal of Numerical Analysis》2003,23(2):175-195
The interpolation of a planar sequence of points p0, ..., pNby shape-preserving G1 or G2 PH quintic splines with specifiedend conditions is considered. The shape-preservation propertyis secured by adjusting tension parameters thatarise upon relaxing parametric continuity to geometric continuity.In the G2 case, the PH spline construction is based on applyingNewtonRaphson iterations to a global system of equations,commencing with a suitable initialization strategythisgeneralizes the construction described previously in NumericalAlgorithms 27, 3560 (2001). As a simpler and cheaperalternative, a shape-preserving G1 PH quintic spline schemeis also introduced. Although the order of continuity is lower,this has the advantage of allowing construction through purelylocal equations. 相似文献
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Products of Consecutive Integers 总被引:3,自引:0,他引:3
In this paper, a number of results are deduced on the arithmeticstructure of products of integers in short intervals. By wayof an example, work of Saradha and Hanrot, and of Saradha andShorey, is completed by the provision of an answer to the questionof when the product of k out of k + 1 consecutive positive integerscan be an almost perfect power. The main new ingredientin these proofs is what might be termed a practical method forresolving high-degree binomial Thue equations of the form axnbyn= ±1, based upon results from the theory of Galois representationsand modular forms. 2000 Mathematics Subject Classification 11D41,11D61. 相似文献
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Nearly four hundred years ago, the cubic close-packing of equalspheres in R3 was discovered by Kepler [21], in which each spheretouches 12 others. In 1694, Gregory and Newton discussed thefollowing thirteen spheres problem. Can a rigid material spherebe brought into contact with 13 other such spheres of the samesize? Gregory believed yes, while Newton thoughtno. 1991 Mathematics Subject Classication 11H31,52C17. 相似文献
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** Email: rovas{at}uiuc.edu*** Email: luc_machiels{at}mckinsey.com**** Corresponding author. Email: maday{at}ann.jussieu.fr In this paper, we extend reduced-basis output bound methodsdeveloped earlier for elliptic problems, to problems describedby parameterized parabolic partial differentialequations. The essential new ingredient and the novelty of thispaper consist in the presence of time in the formulation andsolution of the problem. First, without assuming a time discretization,a reduced-basis procedure is presented to efficientlycompute accurate approximations to the solution of the parabolicproblem and relevant outputs of interest. In addition,we develop an error estimation procedure to a posteriorivalidate the accuracy of our output predictions. Second,using the discontinuous Galerkin method for the temporal discretization,the reduced-basis method and the output bound procedure areanalysed for the semi-discrete case. In both cases the reduced-basisis constructed by taking snapshots of the solutionboth in time and in the parameters: in that sense the methodis close to Proper Orthogonal Decomposition (POD). 相似文献
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The paper contains a final identification theorem for the genericK*-groups of finite Morley rank. 相似文献
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Let X and Y be reflexive Banach spaces with strictly convexduals, and let T be a compact linear map from X to Y. It isshown that a certain nonlinear equation, involving T and itsadjoint, has a normalised solution (an eigenvector)corresponding to an eigenvalue, and that the sameis true for each member of a countable family of similar equationsinvolving the restrictions of T to certain subspaces of X. Theaction of T can be described in terms of these eigenvectors.There are applications to the p-Laplacian, the p-biharmonicoperator and integral operators of Hardy type. 相似文献
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Under very general conditions, a proof is given, via Morse theory,of the existence of solutions for asymptotically linearp-Laplacian equations, where the asymptotic limit may be greaterthan the second eigenvalue. The existence of nonzero solutionsis also considered. 2000 Mathematics Subject Classification35J65, 58E05. 相似文献
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Approximately Local Derivations 总被引:1,自引:0,他引:1
Certain linear operators from a Banach algebra A into a BanachA-bimodule X, which are called approximately local derivations,are studied. It is shown that when A is a C*-algebra, a Banachalgebra generated by idempotents, a semisimple annihilator Banachalgebra, or the group algebra of a SIN or a totally disconnectedgroup, bounded approximately local derivations from A into Xare derivations. This, in particular, extends a result of B.E. Johnson that local derivations on C*-algebras arederivations and provides an alternative proof of it. 相似文献
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In 1903 Minkowski showed that, given pairwise different unitvectors µ1, ..., µm in Euclidean n-space Rn whichspan Rn, and positive reals µ1, ..., µm such thatmi=1µiµi = 0, there exists a polytope P in Rn, uniqueup to translation, with outer unit facet normals µ1, ...,µm and corresponding facet volumes µ1, ..., µm.This paper deals with the computational complexity of the underlyingreconstruction problem, to determine a presentation of P asthe intersection of its facet halfspaces. After a natural reformulationthat reflects the fact that the binary Turing-machine modelof computation is employed, it is shown that this reconstructionproblem can be solved in polynomial time when the dimensionis fixed but is #P-hard when the dimension is part of the input. The problem of Minkowski reconstruction has variousapplications in image processing, and the underlying data structureis relevant for other algorithmic questions in computationalconvexity. 相似文献
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A complete characterization of the categorical quotients of(P1)n by the diagonal action of SL(2, C) with respect to anypolarization is given by M. Polito, in SL(2, C)-quotientsde (P1)n, C. R. Acad. Sci. Paris Sér. I 321 (1995)15771582. In this paper, these categorical quotientsare obtained by certain linear systems on Pn3, dependingon the given polarization. 2000 Mathematics Subject Classification14L24, 14L30 相似文献
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High-accuracy P-stable Methods for y' = f(t, y) 总被引:1,自引:0,他引:1
We obtain a one-parameter family of sixth-order P-stable methodsfor the numerical integration of periodic or near-periodic differentialequations that are defined by initial-value problems of theform: y" = f(t, y), y(t0)= y0, y'(t0)= y0. Our P-stablemethods are symmetric and involve three function evaluationsper step (periteration, in case f(t, y) is non-linear in y).For non-linear problems, starting values for the solution ofthe implicit equations by modified Newton's method are suggestedand illustrated by an example. 相似文献
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It is shown that both the ham sandwich theoremand Richard Rado's theorem on general measure (see [6]), whichis known to be a measure theoretic equivalent of E. Helly'stheorem on convex sets, belong to the same family of resultsabout geometric, extremal properties of measures which are definedon Borel sets in Rn. 相似文献
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We prove that any (real or complex) analytic horizontally conformalsubmersion from a three-dimensional conformal manifold (M3,cM) to a two-dimensional conformal manifold (N2, cN) can be,locally, extended to a unique harmonic morphismfrom the (eaven)-space (H4, g) of (M3, cN) to (N2, cN). Moreover,any positive harmonic morphism with two-dimensional fibres from(H4, g) is obtained in this way. 相似文献