共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove the exponential decay of the derivative of the gluing maps with respect to the gluing parameter. 相似文献
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We generalize the well-known Baker's superstability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary commutative complex semisimple Banach algebra. It was shown by Ger that the superstability phenomenon disappears if we formulate the stability question for exponential complex-valued functions in a more natural way. We improve his result by showing that the maximal possible distance of an -approximately exponential function to the set of all exponential functions tends to zero as tends to zero. In order to get this result we have to prove a stability theorem for real-valued functions additive modulo the set of all integers .
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In this paper, we consider a class of nonlinear impulsive delay differential equations. By establishing an exponential estimate for delay differential inequality with impulsive initial condition and employing Banach fixed point theorem, we obtain several sufficient conditions ensuring the existence, uniqueness and global exponential stability of a periodic solution for nonlinear impulsive delay differential equations. Furthermore, the criteria are applied to analyze dynamical behavior of impulsive delay Hopfield neural networks and the results show different behavior of impulsive system originating from one continuous system. 相似文献
5.
We prove that the admissibility of any pair of vector-valued Schäffer function spaces (satisfying a very general technical condition) implies the existence of a “no past” exponential dichotomy for an exponentially bounded, strongly continuous cocycle (over a semiflow). Roughly speaking the class of Schäffer function spaces consists in all function spaces which are invariant under the right-shift and therefore our approach addresses most of the possible pairs of admissible spaces. Complete characterizations for the exponential dichotomy of cocycles are also obtained. Moreover, we involve a concept of a “no past” exponential dichotomy for cocycles weaker than the classical concept defined by Sacker and Sell (1994) in [23]. Our definition of exponential dichotomy follows partially the definition given by Chow and Leiva (1996) in [4] in the sense that we allow the unstable subspace to have infinite dimension. The main difference is that we do not assume a priori that the cocycle is invertible on the unstable space (actually we do not even assume that the unstable space is invariant under the cocycle). Thus we generalize some known results due to O. Perron (1930) [14], J. Daleckij and M. Krein (1974) [7], J.L. Massera and J.J. Schäffer (1966) [11], N. van Minh, F. Räbiger and R. Schnaubelt (1998) [26]. 相似文献
6.
Robust exponential stability and stabilizability of linear parameter dependent systems with delays 总被引:1,自引:0,他引:1
T. Botmart 《Applied mathematics and computation》2010,217(6):2551-2566
The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results. 相似文献
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Jae Gug Bae 《Journal of Mathematical Analysis and Applications》2009,353(1):1-7
With the introduction of a new parameter n, Kim recently generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. In this paper, we answer some of Kim's conjectures about the inequalities between Kim's generalized upper bound and the original one. We also see the validity of Kim's generalization for some further negative values of x for the case in which the n is rational with both numerator and denominator odd. The range of its validity for negative x is investigated through the study of the zero distribution of a certain family of quadrinomials. 相似文献
9.
Jin-Xing Cai 《Mathematische Zeitschrift》2002,240(3):511-519
Received: 15 October 1999; in final form: 13 June 2000 / Published online: 29 April 2002 相似文献
10.
William Arveson 《Journal of Functional Analysis》2007,248(1):202-224
Starting with a unit-preserving normal completely positive map acting on a von Neumann algebra—or more generally a dual operator system—we show that there is a unique reversible system (i.e., a complete order automorphism α of a dual operator system N) that captures all of the asymptotic behavior of L, called the asymptotic lift of L. This provides a noncommutative generalization of the Frobenius theorems that describe the asymptotic behavior of the sequence of powers of a stochastic n×n matrix. In cases where M is a von Neumann algebra, the asymptotic lift is shown to be a W∗-dynamical system (N,Z), and we identify (N,Z) as the tail flow of the minimal dilation of L. We are also able to identify the Poisson boundary of L as the fixed algebra Nα. In general, we show the action of the asymptotic lift is trivial iff L is slowly oscillating in the sense that
11.
Truong Xuan Duc Ha 《Journal of Mathematical Analysis and Applications》2006,316(1):346-356
In this paper we present two set-valued variants of the Ekeland variational principle involving the Clarke normal cone and establish sufficient conditions for a set-valued map to have a weak minimizer or a properly positive minimizer when it satisfies Palais-Smale type conditions. 相似文献
12.
This paper presents a discrete and distributed time-delays dependent simultaneous approach to deterministic and uncertain stochastic high-order neural networks. New results are proposed in terms of linear matrix inequality (LMI) by exploiting a novel Lyapunov–Krasovskii functional and by making use of novel techniques for time-delay systems. Some constraints of systems are removed, and new results cover some recently published works. Two numerical examples are given to show the usefulness of presented approach. 相似文献
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Yun Chen Anke Xue Renquan Lu Shaosheng Zhou 《Nonlinear Analysis: Theory, Methods & Applications》2008
The issue of robustly exponential stability for uncertain neutral-type systems is considered in this paper. The uncertainties are nonlinear and the delays are time-varying. In terms of a linear matrix inequality (LMI), the new sufficient stability condition with delay dependence is presented. The model transformation and bounding techniques for cross terms are avoided based on an integral inequality. Two illustrative examples are proposed to show the effectiveness of our method. 相似文献
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This paper concerns the study of Lipschitzian stability of fully parameterized generalized equations in which both single-valued and set-valued functions depend on parameters. Various relationships between the Lipschitz-like and metric regularity properties of the solution mapping, the base mapping, or field mapping in the fully perturbed generalized equations are established by using the Dontchev–Hager Fixed Point Theorem. The implicit mapping theorem for metric regularity is also extended to fully parameterized generalized equations. 相似文献
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In the article, we derive an explicit formula for the double exponential map on spaces of constant curvature. In addition, we consider some applications of the resulting formula to computing the principal symbol of the product of two pseudodifferential operators on a manifold with connection. 相似文献
17.
Let F={P(m,F); mMF} be a multidimensional steep natural exponential family parameterized by its domain of the means MF and let VF(m) be its variance function. This paper studies the boundary behaviour of VF. Necessary and sufficient conditions on a point
of ∂MF are given so that VF admits a continuous extension
to the point
. It is also shown that the existence of
implies the existence of a limit distribution
concentrated on an exposed face of
containing
. The relation between
and
is established and some illustrating examples are given. 相似文献
18.
In this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity. The conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated. Namely, the smallness of the kernels is replaced by the smallness of the set where the kernel is flat. This work extends previous works and improves in particular a recent result by Pata [16]. This is established by introducing two lemmas, an idea due to Pata and using the energy method. 相似文献
19.
Miomir S. Stankovi?Sladjana D. Marinkovi? Predrag M. Rajkovi? 《Applied mathematics and computation》2011,218(6):2439-2448
In the recent development in various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In last two decades, the Tsallis and Kaniadakis versions have found a lot of applications. In this paper, we consider the deformations which have two purposes. First, we introduce them like beginning of a more general mathematical approach where the Tsallis and Kaniadakis exponential functions are the special cases. Then, we wish to pay attention to the mathematical community that they have a lot of interesting properties from mathematical point of view and possibilities in applications. Really, we will show the differential and difference properties of our deformations which are important for the formation and explanation of continuous and discrete models of numerous phenomena. 相似文献
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It is known that if a projective variety X in P
N
is reflexive with respect to the projective dual, then the Gauss map of X defined by embedded tangent spaces is separable, and moreover that the converse is not true in general. We prove that the
converse holds under the assumption that X is of dimension two. Explaining the subtleness of the problem, we present an example of smooth projective surfaces in arbitrary
positive characteristic, which gives a negative answer to a question raised by S. Kleiman and R. Piene on the inseparability
of the Gauss map.
相似文献