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101.
We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As a consequence, we calculate the density of states function of the Bochner-Laplacian and establish a symplectic version of the convergence of the induced Fubini-Study metric. We also discuss generalizations of the asymptotic expansion for non-compact or singular manifolds as well as their applications. Our approach is inspired by the analytic localization techniques of Bismut and Lebeau. 相似文献
102.
Gongming WEI 《数学年刊B辑(英文版)》2008,29(3)
A 2-coupled nonlinear Schr(o)dinger equations with bounded varying potentials and strongly attractive interactions is considered.When the attractive interaction is strong enough,the existence of a ground state for sufficiently small Planck constant is proved.As the Planck constant approaches zero,it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4. 相似文献
103.
The classical Three Gap Theorem asserts that for a natural number n and a real number p, there are at most three distinct distances between consecutive elements in the subset of [0,1) consisting of the reductions
modulo 1 of the first n multiples of p. Regarding it as a statement about rotations of the circle, we find results in a similar spirit pertaining to isometries
of compact Riemannian manifolds and the distribution of points along their geodesics.
相似文献
104.
Akhil Ranjan 《Proceedings Mathematical Sciences》2000,110(1):27-34
In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the
sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof.
As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial. 相似文献
105.
The study of the analytic structure of nonlinear ordinary and partial differential equations is shown to provide a unified
approach to determining their properties and finding their solutions.
A course of lectures delivered at the School on Chaos and Nonlinear Dynamics held at the Indian Institute of Science, Bangalore,
India (June 24th–July 18th 1987) 相似文献
106.
107.
This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained. 相似文献
108.
The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obtained as two parameters vary. Some weak resonant and non-resonant double Hopf bifurcation phenomena are observed due to the vanishing of the real parts of two pairs of characteristic roots on the margins of the “death island” regions simultaneously. By applying the center manifold theory, the normal forms near the double Hopf bifurcation points, as well as classifications of local dynamics are analyzed. Furthermore, some quasi-periodic and chaotic motions are verified in both theoretical and numerical ways. 相似文献
109.
Let X,Y be Banach spaces and M a linear manifold in X×Y={{x,y}∣x∈X,y∈Y}. The central problem which motivates many of the concepts and results of this paper is the problem of characterization and construction of all extremal solutions of a linear inclusion y∈M(x). First of all, concept of metric operator parts and metric generalized inverses for linear manifolds are introduced and investigated, and then, characterizations of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds are given by the methods of geometry of Banach spaces. The principal tool in this paper is the generalized orthogonal decomposition theorem in Banach spaces. 相似文献
110.
关于宇宙常数问题是个至今没有解决的问题, 它的来源至今还没有一个共识. 从额外维的流形出发, 给出了宇宙常数的,bulk,流形起源的理论, 得到了不同情况下宇宙常数的取值和宇宙常数随时间演化的函数, 并且得到了可拟合现代天文观测的宇宙常数. 相似文献