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31.
Decay of the energy for the Cauchy problem of the wave equation of variable coeffcients with a dissipation is considered.It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coeffcients.In particular,some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given. 相似文献
32.
This paper considers the existence problem of an elliptic equation.which is equivalent to the prescribing conformal Gaussian curvature problem on R2.An existence result is pried.In particular,K(x)is allowed to be unbounded above. 相似文献
33.
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
34.
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
35.
In this paper, we study the Riemannian length of the primal central path in a convex set computed with respect to the local
metric defined by a self-concordant function. Despite some negative examples, in many important situations, the length of
this path is quite close to the length of a geodesic curve. We show that in the case of a bounded convex set endowed with
a ν-self-concordant barrier, the length of the central path is within a factor O(ν
1/4) of the length of the shortest geodesic curve.
This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian
State, Prime Minister’s Office, Science Policy Programming. 相似文献
36.
Envelopes of splines in the projective plane 总被引:2,自引:0,他引:2
In this paper a family of curvesRiemannian cubicsinthe unit sphere and the real projective plane is investigated.Riemannian cubics naturally arise as solutions to variationalproblems in Riemannian spaces. It is remarkable to find thatan envelope of lines generated by a Riemannian cubic in onespace is (nearly) a Riemannian cubic in another space. 相似文献
37.
This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace–Beltrami
operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian
upper bounds.
相似文献
38.
Andrii Khrabustovskyi Holger Stephan 《Mathematical Methods in the Applied Sciences》2008,31(15):1809-1834
We consider a general linear reaction–diffusion system in three dimensions and time, containing diffusion (local interaction), jumps (nonlocal interaction) and memory effects. We prove a maximum principle and positivity of the solution and investigate its asymptotic behavior. Moreover, we give an explicit expression of the limit of the solution for large times. In order to obtain these results, we use the following method: We construct a Riemannian manifold with complicated microstructure depending on a small parameter. We study the asymptotic behavior of the solution to a simple diffusion equation on this manifold as the small parameter tends to zero. It turns out that the homogenized system coincides with the original reaction–diffusion system. Using this and the facts that the diffusion equation on manifolds satisfies the maximum principle and its solution converges to a easily calculated constant, we can obtain analogous properties for the original system. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
39.
We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity.We also study the convergence of the operators introduced by the Riemannian sums.Our result improves some known ones. 相似文献
40.
We consider a Schrödinger differential expression L=ΔA+q on a complete Riemannian manifold (M,g) with metric g, where ΔA is the magnetic Laplacian on M and q≥0 is a locally square integrable function on M. In the terminology of W.N. Everitt and M. Giertz, the differential expression L is said to be separated in L2(M) if for all u∈L2(M) such that Lu∈L2(M), we have qu∈L2(M). We give sufficient conditions for L to be separated in L2(M). 相似文献