共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we give lower bounds for the Mislin genus of thesymplectic groups Sp(m). This result appears to be the exactanalogue of Zabrodsky's theorem concerning the special unitarygroups SU(n). It is achieved by the determination of the stablegenus of the quasi-projective quaternionic spaces QH(m), followingthe approach of McGibbon. It leads to a symplectic version ofZabrodsky's conjecture, saying that these lower bounds are infact the exact cardinality of the genus sets. The genus of Sp(2)is well known to contain exactly two elements. We show thatthe genus of Sp(3) has exactly 32 elements and see that theconjecture is true in these two cases. Independently, we also show that any homotopy type in the genusof Sp(m) fibers over the sphere S4m1 with fiber in thegenus of Sp(m1), and that any homotopy type in the genusof SU(n) fibers over the sphere S2n1 with fiber in thegenus of SU(n1). Moreover, these fibrations are principalwith respect to some appropriate loop structures on the fibers.These constructions permit us to produce particular spaces realizingthe lower bounds obtained. 2000 Mathematics Subject Classification55P60 (primary), 55P15, 55R35 (secondary) 相似文献
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A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Liénard equation.” AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15. 相似文献
4.
A nondegenerate null-pair of the real projective space
consists of a point and of a hyperplane nonincident to this point. The manifold of all nondegenerate null-pairs
carries a natural Kählerian structure of hyperbolic type and of constant nonzero holomorphic sectional curvature. In particular,
is a symplectic manifold. We prove that
is endowed with the structure of a fiber bundle over the projective space
, whose typical fiber is an affine space. The vector space associated to a fiber of the bundle is naturally isomorphic to the cotangent space to
. We also construct a global section of this bundle; this allows us to construct a diffeomorphism
between the manifold of nondegenerate null-pairs and the cotangent bundle over the projective space. The main statement of the paper asserts that the explicit diffeomorphism
is a symplectomorphism of the natural symplectic structure on
to the canonical symplectic structure on
. 相似文献
5.
N. A. Daurtseva 《Mathematical Notes》2005,78(1-2):59-63
Let (M, g
0) be a smooth closed Riemannian manifold of even dimension 2n admitting an almost complex structure. It is shown that the space
of all almost complex structures on M determining the same orientation as the one determined by a fixed almost complex structure J
0 is a smooth locally trivial fiber bundle over the space
of almost complex structures orthogonal with respect to g
0 and determining the same orientation as J
0.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 66–71.Original Russian Text Copyright © 2005 by N. A. Daurtseva. 相似文献
6.
We analyse some Taylor and Runge—Kutta type methods for computing one-dimensional integral manifolds, i.e. solutions to ODEs and DAEs. The distribution defining the solutions is taken to be defined only on the relevant manifold and hence all the intermediate points occuring in the computations are projected orthogonally to the manifold. We analyse the order of such methods, and somewhat surprisingly there does not appear any new order conditions for the Runge—Kutta methods in our context, at least up to order 4. The analysis shows that some terms appearing in the error expansions can be quite naturally expressed in terms of standard notions of Riemannian geometry. The numerical examples show that the methods work reliably and moreover produce qualitatively correct results for Hamiltonian systems although the methods are not symplectic.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
7.
C. M. Wood 《Geometriae Dedicata》1997,64(3):319-330
The energy of a unit vector field on a Riemannian manifold M is defined to be the energy of the mapping M T
1
M, where the unit tangent bundle T
1
M is equipped with the restriction of the Sasaki metric. The constrained variational problem is studied, where variations are confined to unit vector fields, and the first and second variational formulas are derived. The Hopf vector fields on odd-dimensional spheres are shown to be critical points, which are unstable for M=S
5,S
7,..., and an estimate on the index is obtained. 相似文献
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We prove that a Lagrangian submanifold passes through each point of a symplectic manifold in the direction of arbitrary Lagrangian plane at this point. Generally speaking, such a Lagrangian submanifold is not unique; nevertheless, the set of all such submanifolds in Hermitian extension of a symplectic manifold of dimension greater than 4 for arbitrary initial data contains a totally geodesic submanifold (which we call the s-Lagrangian submanifold) iff this symplectic manifold is a complex space form. We show that each Lagrangian submanifold in a complex space form of holomorphic sectional curvature equal to c is a space of constant curvature c/4. We apply these results to the geometry of principal toroidal bundles. 相似文献
10.
This paper deals with the solvability of boundary value problems for singular integral equations of the form (i)-(ii).By an algebraic method we reduce the problem (i)-(ii) to a system of linear algebraic equations which gives all solutions in a closed form.AMS Subject Classification: 47G05, 45GO5, 45E05 相似文献
11.
The method of Magnus series has recently been analysed by Iserles and Nørsett. It approximates the solution of linear differential equations y = a(t)y in the form y(t) = e
(t)
y
0, solving a nonlinear differential equation for by means of an expansion in iterated integrals of commutators. An appealing feature of the method is that, whenever the exact solution evolves in a Lie group, so does the numerical solution.The subject matter of the present paper is practical implementation of the method of Magnus series. We commence by briefly reviewing the method and highlighting its connection with graph theory. This is followed by the derivation of error estimates, a task greatly assisted by the graph-theoretical connection. These error estimates have been incorporated into a variable-step fourth-order code. The concluding section of the paper is devoted to a number of computer experiments that highlight the promise of the proposed approach even in the absence of a Lie-group structure. 相似文献
12.
Yuexin Yan Yingxin Pan Feifei Lu Zhengxin Zhou 《Journal of Nonlinear Modeling and Analysis》2019,1(2):207-220
In this paper, first of all we give the necessary and sufficient con-
ditions of the center of a class of planar quintic differential systems by using
reflecting function method, and provide a simple proof of this results. Sec-
ondly, We use the reflecting integral to research the equivalence of the Abel
equation and some complicated equations and derive their center conditions
and discuss their integrability. 相似文献
13.
On the Attainable Order of Collocation Methods for Delay Differential Equations with Proportional Delay 总被引:3,自引:0,他引:3
To analyze the attainable order of m-stage implicit (collocation-based) Runge-Kutta methods for the delay differential equation (DDE) y′(t) = by(qt), 0 < q ≤ 1 with y(0) = 1, and the delay Volterra integral equation (DVIE) y(t) = 1 + $\tfrac{b}{q}\int {_0^{qt} }$ y(s) ds with proportional delay qt, 0 < q ≤ 1, our particular interest lies in the approximations (and their orders) at the first mesh point t = h for the collocation solution v(t) of the DDE and the iterated collocation solution u it(t) of the DVIE to the solution y(t). Recently, H. Brunner proposed the following open problem: “For m ≤ 3, do there exist collocation points c i = c i(q), i = 1, 2,..., m in [0,1] such that the rational approximant v(h)is the (m, m)-Padé approximant to y(h)? If these exist, then |v(h) ? y(h)| = O(h 2m+1) but what is the collocation polynomial M m(t; q) = K Π i=1 m (t ? c i) of v(th), t ∈ [0, 1]?” In this paper, we solve this question affirmatively, and give the related results between the collocation solution v(t) of the DDE and the iterated collocation solution u it(t) of the DVIE. We also answer to Brunner's second open question in the case that one collocation point is fixed at the right end point of the interval. 相似文献
14.
Tuomela Jukka; Arponen Teijo; Normi Villesamuli 《IMA Journal of Numerical Analysis》2006,26(4):811-846
** Email: jukka.tuomela{at}joensuu.fi*** Corresponding author. Email: arponen{at}maths.warwick.ac.uk**** Email: villesamuli.normi{at}joensuu.fi We analyse some RungeKutta type methods for computing1D integral manifolds, i.e. solutions to ordin-ary differentialequations and differential-algebraic equations. We show thatwe can compute the solutions which respect all the constraintsof the problem reliably and reasonably quickly. Moreover, weshow that the so-called impasse points are regular points inour approach and hence require no special attention. 相似文献
15.
We construct a multiplicative group structure in the class of integro-differential operators specific for a polydisk which was introduced by I. I. Bavrin. We indicate two applications of these operators to solution of functional equations. 相似文献
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17.
B. G. Pachpatte 《Numerical Functional Analysis & Optimization》2013,34(1-2):197-212
In this paper, we study the existence, uniqueness, and other properties of solutions of a system of Volterra integral equations under a general class of perturbations. The representation formula, a simple and classic application of the Leray–Schauder alternative, and a certain integral inequality with explicit estimate are used to establish the results. 相似文献
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考虑时标上一阶拥有积分边界条件的脉冲动力方程,通过上下解方法结合单调迭代技术得到解存在的充分条件,所得结果包括了周期边值问题、初值问题并且改进和丰富了已有文献的结论,并举例说明其应用. 相似文献