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81.
袁文俊 《数学物理学报(A辑)》2003,23(2):224-230
该文考虑具有控制系数 A\-0 和系数仅有有限个极点的高阶线性齐次微分方程(1.1)。得到了一个复振荡结果,该结果是J. K. Langley[11]等作者在整系数下相应结果的推广。 相似文献
82.
We prove tightness of (r,p)-Sobolev capacities on configuration spaces equipped with Poisson measure. By using this result we construct surface measures on configuration spaces in the spirit of the Malliavin calculus. A related Gauss-Ostrogradskii formula is obtained. 相似文献
83.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
84.
Enrico Leuzinger 《Proceedings of the American Mathematical Society》2004,132(3):919-927
Let be a noncompact semisimple Lie group and an arbitrary discrete, torsion-free subgroup of . Let be the bottom of the spectrum of the Laplace-Beltrami operator on the locally symmetric space , and let be the exponent of growth of . If has rank , then these quantities are related by a well-known formula due to Elstrodt, Patterson, Sullivan and Corlette. In this note we generalize that relation to the higher rank case by estimating from above and below by quadratic polynomials in . As an application we prove a rigiditiy property of lattices.
85.
Understanding of the basic nature of arc root fluctuation is still one of the unsolved problems in thermal arc plasma physics.
It has direct impact on myriads of thermal plasma applications being implemented at present. Recently, chaotic nature of arc
root behavior has been reported through the analysis of voltages, acoustic and optical signals which are generated from a
hollow copper electrode arc plasma torch. In this paper we present details of computations involved in the estimation process
of various dynamic properties and show how they reflect chaotic behavior of arc root in the system. 相似文献
86.
We study solutions of the Cauchy problem for a supercritical semilinear parabolic equation which converge to a singular steady state from below as t→∞. We show that the grow-up rate of such solutions depends on the spatial decay rate of initial data. 相似文献
87.
The bifurcation threshold value of the chaos detection system for a weak signal* 总被引:6,自引:0,他引:6 下载免费PDF全文
Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem. 相似文献
88.
89.
A.?ElmahiEmail author D.?MeskineEmail author 《Annali di Matematica Pura ed Applicata》2005,184(2):161-184
An existence result for a strongly non-linear elliptic equation with natural growth condition on the non-linearity and L1-data is proved. Mathematics Subject Classification (2000) 35J25, 35J60 相似文献
90.
Burgers’ equation is solved numerically with Sobolev gradient methods. A comparison is shown with other numerical schemes presented in this journal, such as modified Adomian method (MAM) [1] and by a variational method (VM) which is based on the method of discretization in time [2]. It is shown that the Sobolev gradient methods are highly efficient while at the same time retaining the simplicity of steepest descent algorithms. 相似文献