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971.
We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity. 相似文献
972.
Shutao Zhang & Yazhou Han 《分析论及其应用》2022,38(2):178-203
For conformal Hardy-Littlewood-Sobolev(HLS) inequalities [22] and reversed conformal HLS inequalities [8] on $\mathbb{S}^n,$ a new proof is given for the attainability
of their sharp constants. Classical methods used in [22] and [8] depends on rearrangement inequalities. Here, we use the subcritical approach to construct the extremal
sequence and circumvent the blow-up phenomenon by renormalization method. The
merit of the method is that it does not rely on rearrangement inequalities. 相似文献
973.
This paper investigates input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems with hybrid delayed impulses. Based on Lyapunov method, some sufficient conditions ensuring ISS and iISS of impulsive systems are obtained, where the time derivative of Lyapunov function is indefinite, and the hybrid effects of delayed impulses are also fully considered. It is shown that the impulsive system is ISS provided that the combined action of time delay existing in impulses, continuous dynamic, and the cumulative strength of hybrid impulses satisfies some conditions, even if the hybrid delayed impulses play a destabilizing effect on ISS. Examples and their simulations are presented to illustrate the applicability of the proposed results. 相似文献
974.
Linear systems whose associated block Jacobi iteration matrixB is weakly cyclic generated by the cyclic permutation = (1,2,...,
p
) in the spirit of Li and Varga are considered. Regions of convergence for the corresponding blockp-cyclic SOR method are derived and the exact convergence domains for real spectra, (B
p
), of the same sign are obtained. Moreover, analytical expressions for two special cases forp = 5 are given and numerical results are presented confirming the theory developed. The tools used for this work are mainly from complex analysis and extensive use of (asteroidal) hypocycloids in the complex plane is made to produce our results.This work was supported in part by AFOSR grant F49620-92-J-0069 and NSF grant 9202536-CCR. 相似文献
975.
N. D. Botkin 《Applied Mathematics and Optimization》1995,32(2):195-210
A randomized algorithm for finding a hyperplane separating two finite point sets in the Euclidean space d and a randomized algorithm for solving linearly constrained general convex quadratic problems are proposed. The expected running time of the separating algorithm isO(dd! (m + n)), wherem andn are cardinalities of sets to be separated. The expected running time of the algorithm for solving quadratic problems isO(dd! s) wheres is the number of inequality constraints. These algorithms are based on the ideas of Seidel's linear programming algorithm [6]. They are closely related to algorithms of [8], [2], and [9] and belong to an abstract class of algorithms investigated in [1]. The algorithm for solving quadratic problems has some features of the one proposed in [7].This research was done when the author was supported by the Alexander von Humboldt Foundation, Germany.On leave from the Institute of Mathematics and Mechanics, Ural Department of the Russian Academy of Sciences, 620219 Ekaterinburg, S. Kovalevskaya str. 16, Russia. 相似文献
976.
It is shown how to represent algebraically all functions that have a zero sum on all -dimensional subspaces ofPG(n,q) or ofAG(n,q). In this way one can calculate the dimensions of related codes, or one can represent interesting sets of points by functions. 相似文献
977.
Jean-Claude Yakoubsohn 《Numerical Algorithms》1995,9(2):223-244
We give a new theorem concerning the convergence of Newton's method to compute an approximate zero of a system of equations. In this result, the constanth
0=0.162434... appears, which plays a fundamental role in the localization of good initial points for the Newton iteration. We apply it to the determination of an appropriate discretization of the time interval in the classical homotopy method. 相似文献
978.
Xiaopu Yan 《Numerical Algorithms》1995,10(2):245-260
Multistep methods for the differential/algebraic equations (DAEs) in the form of
相似文献
979.
已证明小儿厌食症除与缺乏微量元素锌关系密切外,还与其他多种微量元素和宏量元素的缺乏或低下也有关。本院以自行研制的中药强壮灵冲剂治疗小儿厌食症疗效显著。其于浸膏粉经20余种微量元素测定表明含有锌、铁、钴、铜、镍、锰、铬、锗、锶、铝、钡、硒、硅、钛等多种人体必需且品种齐全,含量适度的微量元素。上述元素又恰是患儿体内所缺乏和低下的品种,无疑对患儿全面适度的补充大有裨益.中药强壮灵与西药硫酸锌临床对比研究表明,无论比发锌回升数值以及从厌食等全面疗效统计,中药组均明显优于西药组,并且发现疗效与药物的补锌量不成正相关。说明中药的调理脾胃功能及综合整体治疗作用是其突出优点,值得推广. 相似文献
980.
Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution
belongs to the range of the operator (T
*
T)
v
, o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India. 相似文献
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