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关于稳定性的几个基本定理 总被引:13,自引:0,他引:13
本文给出了非自治常微分方程稳定性,一致稳定性,渐近稳定性与一致渐近稳定性的几个定理。这些定理允许Lyapunov函数的导数为变号函数,放宽了Marachkov定理对系统状态变量变化率有界的要求,推广了文[4-7]的相应结果。 相似文献
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Qing MENG 《数学年刊B辑(英文版)》2019,40(3):429-438
In this paper, the author first introduces the concept of
generalized algebraic cone metric spaces and some elementary results
concerning generalized algebraic cone metric spaces. Next, by using
these results, some new fixed point theorems on generalized
(complete) algebraic cone metric spaces are proved and an example is
given. As a consequence, the main results generalize the
corresponding results in complete algebraic cone metric spaces and
generalized complete metric spaces. 相似文献
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王松敏 《数学物理学报(A辑)》2014,34(5)
通常所说的代数体函数都是由不可约方程确定出来的.最近,孙与高~([1-2])研究代数体函数的四则运算时把这一要求去掉了.该文对可约方程确定出来的代数体函数进行了研究,探讨了其单值解析分支及分支点,论证了代数体函数的第一、二基本定理及对数导数引理对于可约代数体函数同样成立. 相似文献
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The tree metric theorem provides a combinatorial four-point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A related weaker four point condition characterizes dissimilarity maps derived from circular split systems known as Kalmanson metrics. The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics, and Robinsonian matrices, and the theorems that relate them. As with tree metrics and ultrametrics, the link between PC-trees and PQ-trees is established via the Gromov product. 相似文献
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首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的Landsberg空间为Berwald空间,这些条件可以是具有闭的Cartan型形式,S曲率为零或平均Berwald曲率为零. 相似文献
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Wen-Ling Huang 《Geometriae Dedicata》1999,78(3):315-325
In the present paper the relation between the fundamental theorem of Sn(F) and the fundamental theorem ofP Sn(F)is studied geometrically. 相似文献
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Christian Ketterer 《Journal of Geometric Analysis》2017,27(3):1951-1994
Motivated by a classical comparison result of J. C. F. Sturm, we introduce a curvature-dimension condition CD(k, N) for general metric measure spaces, variable lower curvature bound \(k\) and upper dimension bound \(N\ge 1\). In the case of non-zero constant lower curvature, our approach coincides with the celebrated condition that was proposed by Sturm (Acta Math 196(1):133–177, 2006). We prove several geometric properties as sharp Bishop–Gromov volume growth comparison or a sharp generalized Bonnet–Myers theorem (Schneider’s Theorem). In addition, the curvature-dimension condition is stable with respect to measured Gromov–Hausdorff convergence, and it is stable with respect to tensorization of finitely many metric measure spaces provided a non-branching condition is assumed. We also briefly describe possible extensions for variable dimension bounds. 相似文献
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Nguyen Xuan Tan 《Mathematische Nachrichten》1986,129(1):205-218
Several results concerning generalized probabilistic spaces, fixed points of mappings on topological spaces are obtained and applied to yield some new theorems on fixed points for mappings on generalized probabilistic metric spaces. 相似文献
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Variational Principles, Minimization Theorems, and Fixed-Point Theorems on Generalized Metric Spaces
J.S. Ume 《Journal of Optimization Theory and Applications》2003,118(3):619-633
In this paper, we prove a new minimization theorem by using the generalized Ekeland variational principle. We apply our minimization theorem to obtain some fixed-point theorems. Our results extend, improve, and unify many known results due to Kui, Ekeland, Takahashi, Caristi, iri, and others. 相似文献
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Kazuyuki Hasegawa 《Monatshefte für Mathematik》2000,131(1):37-48
We prove the fundamental theorems for affine immersions into hyperquadrics (including affine spaces) with arbitrary codimension,
which are generalizations of those for isometric immersions into space forms. As applications, the fundamental theorems for
equiaffine immersions into hyperquadrics with arbitrary codimension are obtained.
(Received 10 February 2000) 相似文献
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We improve a recent result of Mauduit and Sárk?zy (2000) on the well-distribution measure of pseudorandom sequences and complement
another of their results on the correlation measure.
Received 12 September 2000; in revised form 1 March 2001 相似文献
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We improve a recent result of Mauduit and Sárk?zy (2000) on the well-distribution measure of pseudorandom sequences and complement
another of their results on the correlation measure. 相似文献