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51.
Jean B. Lasserre 《Proceedings of the American Mathematical Society》1998,126(1):189-194
We consider a linear sytem in a Banach lattice and provide a simple theorem of the alternative (or Farkas lemma) without the usual closure condition.
52.
D. B. McReynolds 《Geometriae Dedicata》2007,129(1):47-55
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat n-manifold M, we show that the set of similarity classes of flat metrics on M which occur as a cusp cross-section of a hyperbolic (n + 1)-orbifold is dense in the space of similarity classes of flat metrics on M. The set used for density is precisely the set of those classes which arise in arithmetic orbifolds.
相似文献
53.
54.
This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized
Kalman–Yakubovich–Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence
of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix
and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence
of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of
the proposed approach.
This work was supported by the National Science Foundation of China under Grants 60404007 and 60334030. 相似文献
55.
A. V. Balakrishnan 《Applied Mathematics and Optimization》1995,31(2):177-187
In this paper we generalize the Kalman-Yakubovic lemma to infinite dimensions—or, more precisely, to semigroups of operators over a Hilbert space. The proof differs substantially from the finite-dimensional version and is based on the Paley-Wiener-Helson-Lowdenslager factorization theorem. 相似文献
56.
Zukang Zheng 《中国科学A辑(英文版)》1997,40(9):932-944
The stability of testing hypotheses is discussed. Differing from the usual tests measured by Neyman-Pearson lemma, the regret
and correction of the tests are considered. After the decision is made based on the observationsX
1,X
2, ⋅⋅⋅,X
n, one more piece of datumX
n+1 is picked and the test is done again in the same way but based onX
1,X
2, ⋅⋅⋅,X
n,X
n+l There are three situations: (i) The previous decision is right but the new decision is wrong; (ii) the previous decision
is wrong but the new decision is right; (iii) both of them are right or both of them are wrong. Of course, it is desired that
the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large
as possible. Since the sample size is sometimes not chosen very precisely after the type I error and the type II error are
determined in practice, it seems more urgent to consider the above problem. Some optimal plans are also given.
Project supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation. 相似文献
57.
Duong Minh Duc Tran Vinh Hung Nguyen Tien Khai 《Proceedings of the American Mathematical Society》2007,135(3):921-927
Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.
58.
Yanguang Li 《Journal of Dynamics and Differential Equations》2003,15(4):699-730
For finite-dimensional maps and periodic systems, Palmer rigorously proved Smale horseshoe theorem using shadowing lemma in 1988 [20]. For infinite-dimensional maps and periodic systems, such a proof was completed by Steinlein and Walther in 1990 [30], and Henry in 1994 [9]. For finite-dimensional autonomous systems, such a proof was accomplished by Palmer in 1996 [17]. For infinite-dimensional autonomous systems, the current article offers such a proof. First we prove an Inclination Lemma to set up a coordinate system around a pseudo-orbit. Then we utilize graph transform and the concept of persistence of invariant manifold, to prove the existence of a shadowing orbit. 相似文献
59.
Weishi Liu 《Journal of Dynamics and Differential Equations》2006,18(3):667-691
In this paper, we consider singularly perturbed systems with multiple sets of turning points. Two types of related results contributing to geometric singular perturbation theory are obtained. The first result establishes a new class of invariant manifolds. The second result consists of several exchange lemmas that characterize the evolution of an invariant manifold passing through the vicinity of the slow manifold.Partially supported by NSF Grants DMS-0071931 and DMS-0406998. 相似文献
60.
In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball B n respectively. 相似文献