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1.
《Indagationes Mathematicae》2021,32(1):55-85
We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows. 相似文献
2.
Ieva
Dauickait Amos S. Lawless Jennifer A. Scott Peter Jan van Leeuwen 《Numerical Linear Algebra with Applications》2020,27(5)
We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds. 相似文献
3.
4.
本文是文[1-7]的继续,研究变权综合问题,从确定变权的经验公式入手引出了变权原理,给出了变权的公理化定义,讨论了与之有关的均衡函数及其梯度向量。 相似文献
5.
本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果 相似文献
6.
Xuguang Lu 《Journal of statistical physics》2006,124(2-4):517-547
The paper considers macroscopic behavior of a Fermi–Dirac particle system. We prove the L
1-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi–Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ
*|γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫0
π
b(cos θ)sin 3θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff–Young inequality, the L
∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy. 相似文献
7.
We present a new approach to study the convergence of Newton's method in Banach spaces, which relax the conditions appearing in the usual studies. The approach is based on the bound required for the second derivative of the operator involved. An application to a nonlinear integral equation is presented. 相似文献
8.
9.
Agnieszka Kaamajska 《Mathematical Methods in the Applied Sciences》2006,29(11):1307-1325
The weak limits of sequences {f(uν)}ν∈? where uν's are vector‐valued µ‐measurable functions defined on a compact set Ω and f is (possibly) discontinuous are investigated. As shown by the author (J. Conv. Anal. (to appear)), they are described in terms of integral formulae involving parametrized measures independent of f, similarly as in the classical theorem by Young and its generalization due to DiPerna and Majda. In the present paper we describe the supports of the involved parametrized measures. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
10.