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971.
For a fundamental group of a compact orientable manifold, a condition is specified that is sufficient to guarantee the presence
of a “virtual” epimorphism onto a free non-Abelian group. A consequence is deriving a strong Tits alternative. An arbitrary
noncompact finitely generated discrete subgroup in PO(3, 1) either is large or is virtually Abelian. An application is provided
to the problem of uniform exponential growth for lattices in a 3-dimensional hyperbolic space and of growth of Betti numbers
for lattices in a hyperbolic n-dimensional space, where n is an odd number.
Supported by RFBR (project No. 08-01-00067), by DFG grant Gr 627-11, and by Forschergruppe “Spektrale Analysis, asymptotical
Verteilungen und stochastische Dynamiken,” Billfold University. (G. A. Noskov)
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 174–189, March–April, 2009. 相似文献
972.
The initial boundary value problem for linear elastodynamic system for viscoporous materials is considered. Exponential decay of solutions via the linear boundary feedback is established. Existence of solutions is obtained through the method of c0‐semigroups. Exponential stabilization is derived via a proper collection of ideas of observability inequality, energy identity and c0‐semigroup of contractions. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
973.
Salim A. Messaoudi Michael Pokojovy Belkacem Said‐Houari 《Mathematical Methods in the Applied Sciences》2009,32(5):505-534
In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one‐dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle—a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
974.
G. Harman 《Acta Mathematica Hungarica》2009,124(3):289-298
We continue the study of sums of the form
begun by Indlekofer and Kátai. Here |Y
n
|,|X
p
| ≦ 1 and α is irrational. We prove one conjecture of Kátai, disprove another by both authors, and give what may be a close to best possible
result valid for all irrational α.
相似文献
975.
Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations 总被引:1,自引:0,他引:1
This paper investigates the dynamics of a class of recurrent neural networks where the neural activations are modeled by discontinuous functions. Without presuming the boundedness of activation functions, the sufficient conditions to ensure the existence, uniqueness, global exponential stability and global convergence of state equilibrium point and output equilibrium point are derived, respectively. Furthermore, under certain conditions we prove that the system is convergent globally in finite time. The analysis in the paper is based on the properties of M-matrix, Lyapunov-like approach, and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend previous works on global stability of recurrent neural networks with not only Lipschitz continuous but also discontinuous neural activation functions. 相似文献
976.
In the present paper we obtain a sufficient condition for the exponential dichotomy of a strongly continuous, one-parameter
semigroup , in terms of the admissibility of the pair . It is already known the equivalence between the -admissibility condition and and the hyperbolicity of a C
0-semigroup , when we assume a priori that the kernel of the dichotomic projector (denoted here by X
2) is T(t)-invariant and is an invertible operator. We succeed to prove in this paper that the admissibility of the pair still implies the existence of an exponential dichotomy for a C
0-semigroup even in the general case where the kernel of the dichotomic projector, X
2, is not assumed to be T(t)-invariant.
相似文献
977.
Jun Cheng Jie Cang Shi-Jun Liao 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):450-478
A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated
by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies exponentially with
the magnitude of the stream function, while remaining constant on a particular streamline. The so-called Dubreil–Jacotin transformation
is used to transfer the original exponentially nonlinear boundary-value problem in an unknown domain into an algebraically
nonlinear boundary-value problem in a known domain. Convergent series solutions are obtained not only for small amplitude
water waves on a weak current but also for large amplitude waves on a strong current. The nonlinear wave-current interaction
is studied in detail. It is found that an aiding shear current tends to enlarge the wave phase speed, sharpen the wave crest,
but shorten the maximum wave height, while an opposing shear current has the opposite effect. Besides, the amplitude of waves
and fluid velocity decay over the depth more quickly on an aiding shear current but more slowly on an opposing shear current
than that of waves on still water. Furthermore, it is found that Stokes criteria of wave breaking is still valid for waves
on a shear current: a train of propagating waves on a shear current breaks as the fiuid velocity at crest equals the wave
phase speed. Especially, it is found that the highest waves on an opposing shear current are even higher and steeper than
that of waves on still water. Mathematically, this analytic method is rather general in principle and can be employed to solve
many types of nonlinear partial differential equations with variable coefficients in science, finance and engineering. 相似文献
978.
Svetlana Jankovi? 《Journal of Mathematical Analysis and Applications》2009,355(2):811-6134
The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on paper [X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (2) (1997) 389-401], referring to mean square and almost sure exponential stability. 相似文献
979.
Akira Saito 《Discrete Mathematics》2009,309(16):5000-1723
We consider 2-factors with a bounded number of components in the n-times iterated line graph Ln(G). We first give a characterization of graph G such that Ln(G) has a 2-factor containing at most k components, based on the existence of a certain type of subgraph in G. This generalizes the main result of [L. Xiong, Z. Liu, Hamiltonian iterated line graphs, Discrete Math. 256 (2002) 407-422]. We use this result to show that the minimum number of components of 2-factors in the iterated line graphs Ln(G) is stable under the closure operation on a claw-free graph G. This extends results in [Z. Ryjá?ek, On a closure concept in claw-free graphs, J. Combin. Theory Ser. B 70 (1997) 217-224; Z. Ryjá?ek, A. Saito, R.H. Schelp, Closure, 2-factors and cycle coverings in claw-free graphs, J. Graph Theory 32 (1999) 109-117; L. Xiong, Z. Ryjá?ek, H.J. Broersma, On stability of the hamiltonian index under contractions and closures, J. Graph Theory 49 (2005) 104-115]. 相似文献
980.
基于输出反馈的一类大型互联非线性系统的鲁棒全局指数稳定 总被引:4,自引:1,他引:3
研究基于输出反馈的一类新的大型互联非线性不确定系统的鲁棒全局指数稳定问题,通过构造每个子系统收敛的状态观测器,并对观测器的状态作线性变换,得到鲁棒分散输出反馈控制器.当该反馈控制律作用于该系统时,闭环系统是全局指数稳定的. 相似文献