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991.
Christian Pötzsche 《Applicable analysis》2013,92(6):687-722
This work on implicit nonautonomous difference equations (iterations) is devoted to an abstract technical result on the existence of attractive invariant manifolds. We investigate their existence, smoothness and their asymptotic phase property using invariant foliations. Such results lay the basic foundation of further investigations on discretization methods of evolutionary differential equations. 相似文献
992.
Zhong-yuan LIU 《应用数学学报(英文版)》2013,29(2):415-424
Let BR be the ball centered at the origin with radius R in RN ( N ≥2). In this paper we study the existence of solution for the following elliptic systemu -△u+λu=p/(p + q)κ(| x |)) u(p-1)vq1,x ∈BR1,-△u+λu=p/(p + q)κ(| x |)) upv(q-1)1,x ∈BR1,u > 01,v > 01,x ∈ BR1,(u)/(v)=01,(v)/(v)=01,x ∈BRwhereλ > 0 , μ > 0 p ≥ 2, q ≥ 2,ν is the unit outward normal at the boundary BR . Under certainassumptions on κ ( | x | ), using variational methods, we prove the existence of a positive and radially increasing solution for this problem without growth conditions on the nonlinearity. 相似文献
993.
The authors prove the Schwarz lemma from a compact complex Finsler manifold to another complex Finsler manifold and any complete complex Finsler manifold with a non-positive holomorphic curvature obeying the Hartogs phenomenon. 相似文献
994.
We introduce stable estimation procedures for several aspects of a sufficient dimension-reduction matrix. We first propose a stable method for estimating structural dimension, which only selects the correct directions in the central subspace with no false positive selection. We then provide a Grassmann manifold sparse estimate for the central subspace. By using subsampling, we develop an ensemble method to obtain a stable nonsparse estimate for the central subspace. This ensemble idea is also used to stabilize the choice of the number of slices in sliced inverse methods. Theoretical results are established, and the efficacy of the proposed stable methods is demonstrated by simulation studies and the analysis of Hitters’ salary data. Supplementary materials for this article are available online. 相似文献
995.
996.
Alfonso Ruiz-Herrera 《Journal of Difference Equations and Applications》2013,19(1):96-113
This paper is devoted to show that Hirsch's results on the existence of a carrying simplex are a powerful tool to understand the dynamics of Kolmogorov models. For two and three species, we prove that there is exclusion for our models if and only if there are no coexistence states. The proof of this result is based on a result in planar topology due to Campos, Ortega and Tineo. For an arbitrary number of species, we will obtain dominance criteria following the notions of Franke and Yakubu. In this scenario, the crucial fact will be that the carrying simplex is an unordered manifold. Applications in concrete models are given. 相似文献
997.
Guy Jumarie 《数学学报(英文版)》2012,28(9):1741-1768
In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one (Jumarie) has proposed recently an alternative referred to as (local) modified Riemann-Liouville definition, which directly, provides a Taylor’s series of fractional order for non differentiable functions. We examine here in which way this calculus can be used as a framework for a differential geometry of fractional order. One will examine successively implicit function, manifold, length of curves, radius of curvature, Christoffel coefficients, velocity, acceleration. One outlines the application of this framework to Lagrange optimization in mechanics, and one concludes with some considerations on a possible fractional extension of the pseudo-geodesic of thespecial relativity and of the Lorentz transformation. 相似文献
998.
999.
流形学习是一种新的非线性维数约简方法,近年来正引起可视化等领域研究者的高度重视.为加深对流形学习的理解,介绍了流形学习的基本原理,总结了其研究进展和分类方法,最后阐述了几种常用的流形学习方法的基本思想、算法步骤和各自的优缺点.通过在人工数据集Swiss-Roll上进行实验,将各类方法在近邻值选取和噪声影响等方面进行了对比分析,结果表明:与传统的线性维数约简方法相比,流形学习方法能够有效地发现观测样本的低维结构.最后对流形学习未来的研究方向作出展望,以期在这一领域取得更大进展. 相似文献
1000.
G.R. AnsarifarH.A. Talebi H. Davilu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(1):414-425
This paper presents a new algorithm for designing dynamic sliding-mode controllers. The proposed controller is based on dynamic sliding manifolds to circumvent the difficulties associated with the conventional sliding mode controllers in the face of non-minimum phase systems. Unlike previous works, a proper and easy to implement algorithm is presented for designing the dynamic sliding manifold which facilitates the design of the controller. The output tracking problem in nonlinear non-minimum phase systems with matched and unmatched disturbances and matched nonlinearities is addressed. Then, the performance of the dynamic sliding mode controller is significantly improved by combining the given dynamic sliding manifold with online parameter adaptation. Simulations results are presented to demonstrate the effectiveness of the proposed sliding mode controller in terms of performance, robustness and stability. 相似文献