有限项Hilbert不等式的一些加强式

通过引入参数λ,利用Cauchy不等式及函数单调性,建立了一个推广的有限项Hilbert不等式。     

Holder不等式再推广的几种形式

本文主要对原Holder不等式进行了进一步的推广,将原Holder不等式由2个实数列推广到m(m=2)个实数列,同时给出推广后的Holder不等式的几种不同形式并对其加以数学证明.     

h-差分意义下Hlder不等式的证明及应用

借助于普通意义下Hlder不等式的证明技巧,本文建立了h-差分意义下Hlder不等式.其次利用所建立Hlder不等式得到h-差分意义下的Cauchy-Schwarz不等式和Minkowski不等式.     

Cauchy不等式及推广的应用

在实数域上对Cauchy不等式进行了推广，并给出了Cauchy不等式及推论的应用.     

量子纠缠态制备、操纵的实验研究

量子纠缠是量子信息学中最重要也是最为奇特的一个课题.在量子信息学中,量子信息的处理离不开量子态及其操纵,而量子纠缠态毫无疑问是各种各样的量子态中最重要的一种. 利用光子纠缠态开展了以下实验研究:(1)利用连续波激光束泵浦非线性晶体的自发参量下转换过程,制备出了双光子偏振纠缠态,具有较高亮度和纠缠度,并具有纠缠度可调谐的特点. 利用这种纠缠源,制备了量子信息学中一种重要的混合态——Werner态,采用的方案使得Werner态中纠缠的成分是可控制的.(2)利用线性光学元件以及路径比特概念的引入,在实验上用单光子实现了Buek-Hillery普适克隆机,实验结果表明,对任意的输入纯态,此克隆机输出的2份拷贝与初始态均达到5/6的保真度,与理论计算一致.(3)在实验上利用自发参量下转换系统制备的双光子偏振最大纠缠态及非最大纠缠态进行了CHSH不等式的检验,验证了对于2比特纠缠纯态,"纠缠"等价于"Bell不等式违背"这一结论.(4)除了局域隐变量理论之外,还有一种主要的隐变量理论——环境无关的隐变量理论(NCHV),关于这种隐变量,类似于Bell不等式,有一个Kochen-Specker理论,其主要内容是证明NCHV和量子力学的矛盾. 完成了一个用单光子实现的检验Kochen-Spcker理论的实验,实验结果证明了NCHV是不存在的.     

Sylrester不等式的多种证明方法

Sylrester不等式是高等数学中非常重要的不等式,本文总结了Sylrester不等式的多种证明方法。     

量子物理的基础及其光学实验

在本文就量子物理的基础及其光学实验展开的研究中,笔者主要论述了双缝干涉、量子并协性以及Bell不等式的光学实验验证,希望这一论述内容能够较好的对量子物理的本质进行展示。     

高频数据下商品期货波动率研究——基于不同已实现测度和改进的厚尾分布

商品期货收益率序列存在明显的厚尾现象,将扰动项设定为厚尾分布的波动率模型要优于普通Gaussian分布以及t分布模型。以7种损失函数作为评价准则,在扰动项分别服从偏t分布以及广义双曲线偏t分布时比较了波动率RV、二次幂变差BV以及medRV3种不同已实现测度下Realized GARCH模型对商品期货的波动性预测能力。最后得到扰动项服从ghst分布的Realized GARCH模型具有更优的预测能力。     

Hlder不等式的新证法

通过 Jensen不等式得到一个具有一定使用价值的不等式及其有关推论 ,利用该不等式及其推论证明了著名的 Holder不等式及其推广 ,证明方法简洁明了 .     

产品熟悉度对激活域大小影响的实证研究

激活域是由消费者在制定购买决策时认真考虑的品牌所构成的集合。分别从主观熟悉度和客观熟悉度两个方面检验了产品熟悉度对激活域大小的影响。与以往的结果不同,发现不同熟悉度水平的组别间在激活域大小上不具有显著差异。利用信息搜索成本对结果进行了解释,探讨了研究的理论与管理意义,并提出了未来的研究展望。     

Improved stability criteria for sampled-data systems using modified free weighting matrix

This paper investigates the stability analysis of sampled-data systems in the looped-functional framework. A modified free-weighting matrix inequality with quadratic-type is proposed to reduce conservatism of the integral term. Based on new looped-functional, improved conditions are derived in terms of linear matrix inequalities (LMIs) by utilizing the proposed integral inequality. Numerical examples show the superiority of the proposed condition through comparisons with the most recent results.     

Generalized filtering of one-sided Lipschitz nonlinear systems under measurement delays

This paper addresses the filtering problem for the one-sided Lipschitz nonlinear systems under measurement delays and disturbances using a generalized observer. A generalized architecture for filtering of the one-sided Lipschitz nonlinear systems with output delays is explored, which exhibits diverging manifolds, namely, the conventional static-gain filter and the dynamical filter, and can be employed to render robust stability of the filtering error dynamics. A matrix inequality based framework is obtained by employing a Lyapunov?Krasovskii (LK) functional, whose derivative is exploited through Jensen's inequality, one-sided Lipschitz condition, quadratic inner-boundedness inequality and range of the measurement delay, resulting into L₂ stability for the filtering error system. Generalized filter design for the Lipschitz nonlinear systems with delayed outputs and specific results for the delay-dependent and delay-rate-independent filtering schemes for the one-sided Lipschitz nonlinear systems are deduced from the proposed approach. Convex optimization techniques are employed to achieve a solution for the nonlinear constraints through linear matrix inequalities by employing cone complementary linearization approach. Illustrative numerical examples to demonstrate the effectiveness of proposed method are provided.     

Observer-based exponential stabilization for time-delay systems via augmented weighted integral inequality

In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.     

Stability analysis of nonlinear Hadamard fractional differential system

The stability of the zero solution of a class of nonlinear Hadamard type fractional differential system is investigated by utilizing a new fractional comparison principle. The novelty of this paper is based on some new fractional differential inequalities along the given nonlinear Hadamard fractional differential system. A comparison principle employing the new fractional differential inequality for scalar Hadamard fractional differential system is presented. Based on the new comparison principle, some sufficient conditions for the (generalized) stability and the (generalized) Mittag-Leffler stability are given.     

A generalized multiple-integral inequality and its application on stability analysis for time-varying delay systems

This paper is concerned with the stability analysis of time-delay systems. Lyapunov–Krasovskii functional method is utilized to obtain stability criteria in the form of linear matrix inequalities. The main purpose is to obtain less conservative stability criteria by reducing the estimation gap of the time derivative of the constructed Lyapunov–Krasovskii functional. First, a generalized multiple-integral inequality is put forward based on Schur complement lemma. Then, some special cases of the proposed generalized multiple-integral inequality are given to estimate single and double integral terms in the derivative of Lyapunov–Krasovskii functional. Furthermore, less conservative stability criteria are derived. Finally, three examples are given to illustrate the improvement of the proposed criteria.     

Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality

This paper deals with the problem of delay-dependent stability analysis for neural networks with time-varying delays. First, by constructing an augmented Lyapunov–Krasovskii functional and utilizing a generalized free-weighting matrix integral inequality, an improved stability criterion for the concerned network is derived in terms of linear matrix inequalities. Second, by considering a marginal augmented vector and modifying a Lyapunov–Krasovsii functional, a further enhanced stability criterion is presented. Third, a less conservative stability condition in which a relaxed inequality related to activation functions is added is introduced. Finally, three numerical examples are included to illustrate the advantage and validity of the proposed criteria.     

经济体制和结构变化:基于中国收入不平等总量的实证分析

本文在考虑经济结构变化的基础上,利用LM(最小拉格朗日乘数)单位根检验方法,对我国1952-2000年间的全国基尼系数、GE、城乡基尼系数和内陆一沿海基尼系数等时间序列的数据生成过程的动态特征进行了研究.本文的研究结果表明,4个时间序列均为服从一个断点或两个断点的趋势平稳过程,结构断点出现的时间与我国经济体制改革的时间相吻合.这说明了以政府为导向的经济体制结构的改革对我国收入平等有长期持续效应.     

Event triggered reliable synchronization of semi-Markovian jumping complex dynamical networks via generalized integral inequalities

This paper focuses on the synchronization problem of semi-Markovian jumping complex dynamical networks with time-varying coupling delays against actuator failures. In an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria. By constructing Lyapunov–Krasovski functional, some delay dependent criteria that assures the synchronization of CDN are derived with the help of the general integral inequalities. It should be noted that the general integral inequality used here is general than that of Jensen inequality, the Wirtinger-based inequality, the Bessel-Legendre inequality, the Wirtinger-based double integral inequality, and the auxiliary function-based integral inequalities. The resulting LMIs can be easily verified with the help of the available softwares. Finally, simulation results are proposed to verify the effectiveness of the general integral inequality and designed control law.     

Robust convergence of Cohen–Grossberg neural networks with mode-dependent time-varying delays and Markovian jump

The robust stochastic convergence in mean square is investigated for a class of uncertain Cohen–Grossberg neural networks with both Markovian jump parameters and mode-dependent time-varying delays. By employing the Lyapunov method and a generalized Halanay-type inequality, a delay-dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a pre-specified convergence rate. After some parameters being fixed in advance, the proposed conditions are all in terms of linear matrix inequalities, which can be solved numerically by employing the LMI toolbox in Matlab. Finally, an illustrated example is given to show the effectiveness and usefulness of the obtained results.     

基于相关性分析的土地违法结构与经济结构变化关系探讨

土地违法结构与经济结构关系的研究是保障土地合法利用和经济健康发展的重要课题。通过运用典型多元相关分析与Pearson相关分析法,对1992年～2004年间的土地违法结构变化与经济结构变化进行相关性分析。研究结果表明,经济结构变化与土地违法结构变化是相关的;第一产业生产总值比重与其他违法用地比重呈负相关;建筑业产值比重与破坏耕地比重呈正相关,与其他违法用地比重呈显著正相关,与未经批准占地呈显著负相关;固定资产投资比重与非法批地比重呈负相关。研究结论揭示了土地违法结构变化与经济结构变化之间的确存在一种必然的相关关系。因此,根据经济结构与土地违法结构变化之间的相关关系,应密切注视经济发展中的土地违法结构变化,并制定长期策略,采取多样化措施,在减少土地违法总量同时,重点监控土地违法类型变化,合理确定一定时期应采取的主导调控措施。