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961.
962.
A simple characterization of weighted Sobolev spaces with bounded multiplication operator 总被引:1,自引:0,他引:1
In this paper we give a simple characterization of weighted Sobolev spaces (with piecewise monotone weights) such that the multiplication operator is bounded: it is bounded if and only if the support of μ0 is large enough. We also prove some basic properties of the appropriate weighted Sobolev spaces. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials. 相似文献
963.
The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under
certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that
under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge
to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence
problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson
(JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established
in the paper. All the results are verified and analyzed by numerical experiments.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471074, 10771116) and the Doctoral
Program of the Ministry of Education of China (Grant No. 20060003003) 相似文献
964.
V. N. Margaryan H. G. Ghazaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(3):157-178
A two-dimensional linear differential operator P(D) = P(D 1, D 2) is called almost hypoelliptic if all derivatives D α P of the characteristic polynomial P(ζ) = P(ζ 1, ζ 2) are estimated by P(ζ). Assuming that {Ω κ = (x 1, x 2) ∈ E 2 : |x 1| < κ, x 2 ∈ R 1}, the paper proves that if the width κ of the strip Ω κ exceeds some C = C(P) > 0, then all solutions {u} of the almost hypoelliptic equation P(D)u = 0 in a Sobolev space are infinitely smooth functions with respect to x 1. 相似文献
965.
Some new results on the rigidity of automorphism groups and the regularity of(?)-Neumann operator in group actions are presented. 相似文献
966.
Tong Xiaojiao Zhou Shuzi Dept. of Appl.Math. Hunan Univ. Changsha . Dept.of Math. Changsha Univ.of Electric Power Changsha 《高校应用数学学报(英文版)》2000,(2)
§ 1 IntroductionIn this paper we study the following nonlinear equality constrained optimization prob-lem:minimize f(x) ,subjectto h(x) =0 ,(P)where h(x) =(h1 (x) ,h2 (x) ,...,hm(x) ) T,f and hi(i=1 ,2 ,...,m) are Rn→R twice conti-nously differentiable(m≤n) .Many authors have studied the problem(P) with trustregion method(see,references[1~ 3 ] ) .These methods have the same property:to enforce strict monotonicity for meritfunction at every iteration.Paper[4 ] shows thatstrictmonotonic … 相似文献
967.
George A. Anastassiou 《Semigroup Forum》2009,78(1):54-67
Here we present Poincaré type general L
p
inequalities regarding semigroups, cosine and sine operator functions. 相似文献
968.
In this paper we obtain a necessary and sufficient condition for Toeplitz operators with generalized circulant symbols to be hyponormal. 相似文献
969.
We develop a finite-difference scheme for approximation of a system of nonlinear PDEs describing the Q-switching process.
We construct it by using staggered grids. The transport equations are approximated along characteristics, and quadratic nonlinear
functions are linearized using a special selection of staggered grids. The stability analysis proves that a connection between
time and space steps arises only due to approximation requirements in order to follow exactly the directions of characteristics.
The convergence analysis of this scheme is done in two steps. First, some estimates of the uniform boundedness of the discrete
solution are proved. This part of the analysis is done locally, in some neighborhood of the exact solution. Second, on the
basis of the obtained estimates, the main stability inequality is proved. The second-order convergence rate with respect to
the space and time coordinates follows from this stability estimate. Using the obtained convergence result, we prove that
the local stability analysis in the selected neighborhood of the exact solution is sufficient. 相似文献
970.
Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72], the resulting composed map has a periodic orbit which is stable. 相似文献