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151.
A nonlinear inequality and application to global asymptotic stability of perturbed systems
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The goal of this work is to present a new nonlinear inequality which is used in a study of the Lyapunov uniform stability and uniform asymptotic stability of solutions to time‐varying perturbed differential equations. New sufficient conditions for global uniform asymptotic stability and/or practical stability in terms of Lyapunov‐like functions for nonlinear time‐varying systems is obtained. Our conditions are expressed as relation between the Lyapunov function and the existence of specific function which appear in our analysis through the solution of a scalar differential equation. Moreover, an example in dimensional two is given to illustrate the applicability of the main result. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
152.
Juan Enrique Martínez-Legaz 《Optimization》2015,64(1):87-96
This article surveys the main contributions of K.-H. Elster to the theory of generalized conjugate functions and its applications to duality in nonconvex optimization. 相似文献
153.
154.
Ramn Carrazana-Escalona Miguel Enrique Snchez-Hechavarría Ariel vila 《Entropy (Basel, Switzerland)》2022,24(3)
Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously to Theil entropy analysis. The behavior of Theil entropy and its decomposable property was investigated using exponents in the range of [−1, 2], on the spectrum of synthetic and physiological signals. Our results suggest that the best spectral decomposition method to analyze the spectral inequality of physiological oscillations is the Lomb–Scargle method, followed by Theil entropy analysis. Moreover, our results showed that the exponents that provide more information to describe the spectral inequality in the tested signals were zero, one, and two. It was also observed that the intra-band component is the one that contributes the most to total inequality for the studied oscillations. More in detail, we found that in the state of mental stress, the inequality determined by the Theil entropy analysis of heart rate increases with respect to the resting state. Likewise, the same analytical approach shows that cellular calcium oscillations present on developing interneurons display greater inequality distribution when inhibition of a neurotransmitter system is in place. In conclusion, we propose that Theil entropy is useful for analyzing spectral inequality and to explore its origin in physiological signals. 相似文献
155.
Xu Bing Cai Guanghui 《高校应用数学学报(英文版)》2007,22(3):316-324
A maximal inequality for the partial sum of NA sequence is constructed.By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discussed.The results obtained extend the results of Liang(1999, 2000). 相似文献
156.
给出了函数f(x)和g(x)单调性的证明.据此,得到了著名的Minc H和Sathre L不等式最好的界. 相似文献
157.
通过构造随机变量的方法,并结合凸函数的性质,证明了数学分析中的一些著名不等式,证明方法简明、独特. 相似文献
158.
本文在Sobolev-Lorentz空间W2L2,q(R4)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp Moser-Trudinger and Adams ... 相似文献
159.
NA序列部分和的矩完全收敛性 总被引:4,自引:0,他引:4
讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果. 相似文献
160.