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941.
Guozhen Lu 《数学学报(英文版)》2000,16(3):405-444
This paper consists of three main parts. One of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie groups. Despite the extensive research after Jerison's work [3] on Poincaré-type inequalities for Hörmander's vector fields over the years, our results given here even in the nonweighted case appear to be new. Such interpolation inequalities have crucial applications to subelliptic or parabolic PDE's involving vector fields. The main tools to prove such inqualities are approximating the Sobolev functions by polynomials associated with the left invariant vector fields on ?. Some very usefull properties for polynomials associated with the functions are given here and they appear to have independent interests in their own rights. Finding the existence of such polynomials is the second main part of this paper. Main results of these two parts have been announced in the author's paper in Mathematical Research Letters [38].The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on (?,δ) domains. Some results of weighted Sobolev spaces are also given here. We construct a linear extension operator which is bounded on different Sobolev spaces simultaneously. In particular, we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev functions. Theorems are stated and proved for weighted anisotropic Sobolev spaces on stratified groups. 相似文献
942.
带概率判断和模糊区间判断的一种排序算法 总被引:4,自引:0,他引:4
对于 AHP中一类判断为模糊、不确定性问题 ,用随机变量和模糊区间描述其判断 ,采用 0 .1~ 0 .9标度 ,建立模糊互补判断矩阵 ,利用数学变换得到模糊一致性判断矩阵 ,给出排序向量算法及公式 ,便于实际应用 相似文献
943.
944.
David R. Brillinger Haiganoush K. Preisler Alan A. Ager John G. Kie Brent S. Stewart 《Bulletin of the Brazilian Mathematical Society》2002,33(3):385-408
The concern is with the properties of stochastic differential equations (SDEs) describing the motion of particles in 3 dimensional
space, on the sphere or in the plane. There is consideration of the case where the drift function comes from a potential function.
There is study of SDEs whose parameters are periodic in time. These are useful for incorporating circadian rhythm in the behavior.
The cases of a seal in a frozen lake in Alaska, an elephant seal migrating a great distance in the Pacific Ocean and of a
group of "free-ranging" elk in a reserve in Oregon are referred to. For the elk nonparametric estimates of the drift and variance
terms of an SDE model are discussed and evaluated and the fit of the model assessed. One issue is how to include explanatories,
beyond location and time, in the model. A number of questions motivated by the wildlife motion concerning diffusion processes
of the type considered are posed at the end of the paper.
Received: 25 April 2002 相似文献
945.
Serhii Dyshko 《Discrete Mathematics》2018,341(11):2995-3002
For a finite vector space over , there are described all the pairs of multisets and of subspaces in such that for all the equality holds. 相似文献
946.
A.P. Bergamasco P.L. Dattori da Silva R.B. Gonzalez 《Journal of Differential Equations》2018,264(5):3500-3526
Let be a vector field defined on the torus , where , are real-valued functions and belonging to the Gevrey class , , for . We present a complete characterization for the s-global solvability and s-global hypoellipticity of L. Our results are linked to Diophantine properties of the coefficients and, also, connectedness of certain sublevel sets. 相似文献
947.
In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness. 相似文献
948.
定义了n维模糊向量的模糊距离、n维模糊度量空间及其完备性的概念,实现了用R上的模糊数度量模糊向量间距离的目的,不仅使得模糊距离的度量更加合理、更加贴切,也创立一套独立于实数的模糊数学分析理论打下了基础。 相似文献
949.
Massimiliano Mella 《Proceedings of the American Mathematical Society》1998,126(8):2199-2204
Let be an -dimensional variety and an ample vector bundle on of rank . We give a complete classification of pairs , with log terminal and such that is not ample. The results we obtain were conjectured by Fujita, and recently by Zhang.
950.
Let X be a Banach space and (,,µ) be a -finite measure space. We consider a strongly continuous d-dimensional semigroup T={T(u):u=(u1,..., ud, ui >0, 1 i d} of linear contractions on Lp((,,µ); X), with 1 p<. In this paper differentiation theorems are proved for d-dimensional bounded processes in Lp((,,µ); X) which are additive with respect to T. In the theorems below we assume that each T(u) possesses a contraction majorant P(u) defined on Lp((,,µ); R), that is, P(u) is a positive linear contraction on Lp((,,µ); R) such that T(u)f(w) P(u)f(·)() almost everywhere on for all f Lp((,,µ); X). 相似文献