Heisenberg群上次椭圆 p-Laplace方程的增长性估计

首先利用Heisenberg群上的Hardy型不等式,通过基本的微积分运算建立了若干不等式,然后建立了次椭圆p-Laplace方程的解在原点附近的增长性估计.最后给出了具有广义有限能量的函数的Lp-估计.     

关于digamma函数的一个不等式

建立了关于digamma函数的一个新不等式.     

关于积分型Hilbert定理的一个改进

通过建立一个权函数的不等式,改进了Hilbert定理,作为应用,建立了一个Hilbert类积分不等式及其加强式。     

关于多个函数的Hardy-Hilbert不等式的推广

引入参数A,B,A,建立了涉及多个函数的Hardy-Hilbert积分不等式,并考虑了它的等价形式及相应的级数不等式,并证明了当λ=1时,其常数因子是最佳的.     

关于一个加强的Hardy-Littlewood-Polya不等式

应用改进的Euler-Maclaurin求和公式,得到权系数不等式,从而建立了一个加强的Hardy-Littlewood-Polya不等式.     

关于Chebyshev函数的加权Landau''''s型不等式

本文在L~2上建立了关于Chebyshev多项式T_n(x)的Landau's型不等式。利用T_n(x)的正交性,建立了代数多项式p_n(x)的加权Landau's型不等式,并指出其不等式的系数在某种意义上是最好可能的。     

积分中值定理的应用以及加强

本文以实例的形式,列举了积分中值定理在求极限、判定某些性质点、估计积分值等方面的应用.并探讨了积分中值定理的加强,即"ξ"的范围由闭区间缩小到开区间.通过比较加强的积分中值定理和原积分中值定理在不等式证明方面应用的差别,表明了积分中值定理在加强后,更具有应用性.     

和极大似然估计不等式约束平差模型建立

由于测绘工具的飞速发展,测量工作变得也越来越简单,精度也越来越高。但数据处理在测绘工作中仍旧占据重要的位置。其中尤其是不等式约束平差是现代数据处理的趋势。以往的研究中大多以最小二乘模型为研究平台。最小二乘虽然是测绘科学中最为经典的数学模型,然而不难发现最小二乘不具有抗差性能。和极大似然估计则不同,它能抗拒粗差。但是在不等式约束中的应用以往还没这方面的研究。本文通过将和极大似然估计模型引入不等式约束平差问题,并建立相应平差模型。     

不等式的缩放是高等数学的灵魂

通过具体例子说明不等式的放大与缩小在极限计算、泰勒公式应用、级数敛散的判定中的重要作用;阐明了高等数学与初等数学的本质区别;涵盖了高等数学学习方法的重要内容.对系统把握高数的抽象性与极强的逻辑性认识有一定帮助;特别是给出了在闲区间上具有单项二阶导数的函数平均值的限的估计新结论.     

关于三角形内切圆半径的两个不等式的探讨

在教学和科研中,尹华焱、杨学枝等一批教学工作者提出了大批三角形有关的不等式,本文解决了有关三角形内切圆半径及角平分的一个不等式,并在此基础上建立了一个有关内切圆半径和外接圆半径的新不等式。     

Fault diagnosis for a kind of nonlinear systems by using model-based contribution analysis

For the purpose of fault detection and isolation (FDI), reconstruction-based contribution (RBC) analysis is carried out in a model-based way. A bank of adaptive observers are designed for a set of potential faults. From these observers, fault estimates and fault signatures are directly available, thus contribution functions are conveniently constructed to accomplish the FDI work. This integrated design of contribution analysis and adaptive observer takes advantages of both data-driven and model-based approaches, and the diagnosis performance is improved. Furthermore, quantitative isolability analysis is also studied by similarity measurement of the obtained fault signatures. Simulation study with a nonlinear unmanned aerial vehicle (UAV) model shows the effectiveness of the proposed method.     

Robust distributed tracking control for linear multi-agent systems based on distributed intermediate estimator

This paper considers the distributed tracking control problem for linear multi-agent systems with disturbances and a leader whose control input is nonzero and not available to any follower. Based on the relative output measurements of neighboring agents, a novel distributed observer-based tracking protocol is proposed, where the distributed intermediate estimators are constructed to estimate the leader’s unknown control input and the states of the tracking error system simultaneously, then a distributed tracking protocol is designed based on the derived estimates. It is proved that the states of the tracking error system are uniformly ultimately bounded and an explicit tracking error bound is obtained. A simulation example of aircrafts verifies the effectiveness of the proposed method.     

Adaptive finite-time consensus of a class of disturbed multi-agent systems

In this paper, the finite-time exponential consensus problem is addressed for a class of multi-agent systems against some disturbed factors, which include system uncertainties, communication perturbations, and actuator faults. All disturbed factors are supposed to be influenced by internal and external effects of systems. The internal effects are described in terms of dependency on the system states, while the external actions are restricted by constant bounds. To obtain the information of the rate of dependency on the states and constant bounds, an adaptive mechanism is designed to estimate the rate and bounds. Based on these estimates, a distributed adaptive sliding mode controller is constructed to eliminate the effects of those disturbed factors. Then exponential consensus of the closed-loop adaptive multi-agent system is achieved within a finite time based on Lyapunov stability theory. The efficiency of the developed adaptive consensus control strategy is verified by a coupled system with four F-18 aircrafts of decoupled longitudinal model.     

R＆D项目中止决策的Fuzzy动态综合评判

企业在研究R＆D项目评价的关键是解决二个问题.一是项目在某时间点上的静态评价;二是项目在时间序列上的动态评价.本文引入Fuzzy理论及时间序列的动态评价方法,建立了R＆D项目中止决策的Fuzzy动态综合评判模型.另外还对时间序列的权重向量做了探讨.根据某企业的R＆D项目的调查,给出了一个案例.     

High-speed train localization algorithm via cooperative multi-classifier network using distributed heterogeneous signals

Long-distance high-speed train localization based on distributed optical fiber sensors (DOFS) has been a challenging issue due to the large-scale heterogeneous sensor nodes. It requires a competent localization algorithm to be capable of strong generalization and quick response. This paper proposes a cooperative multi-classifier network (CMCN) for locating HSTs based on heterogeneous DOFS signals by adaptive modeling of the local characteristics. The proposed CMCN is composed of adaptive feature extraction, lightweight base classifiers and spatial boostrap aggregating (SBA). First, the heterogeneous signals are adaptively transformed to an optimal intrinsic mode function for extracting the statistical features of base classifiers. The base classifiers are constructed based on dynamic soft-margin support vector machine to model local characteristics without computationally burdensome kernel functions by introducing a dynamic penalty factor. The factor is automatically initialized by evaluating the regional consistency before training. Furthermore, the SBA estimates the location of HSTs based on the local states of nodes. It can cooperate with base classifiers for enhanced accuracy by searching for the interval with maximum regional consistency. Finally, a trial is conducted in a high-speed railway in China in long-term running of 92 days. The results prove feasibility and accuracy of the proposed algorithm.     

Resilient strategy design for cyber-physical system under active eavesdropping attack

We consider a remote state estimation process under an active eavesdropper for cyber-physical system. A smart sensor transmits its local state estimates to a remote estimator over an unreliable network, which is eavesdropped by an adversary. The intelligent adversary can work in passive eavesdropping mode and active jamming mode. An active jamming mode enables the adversary to interfere the data transmission from sensor to estimator, and meanwhile improve the data reception of itself. To protect the transmission data from being wiretapped, the sensor with two antennas injects noise to the eavesdropping link with different power levels. Aiming at minimizing the estimation error covariance and power cost of themselves while maximizing the estimation error covariance of their opponents, a two-player nonzero-sum game is constructed for sensor and active eavesdropper. For an open-loop case, the mixed Nash equilibrium is obtained by solving an one-stage nonzero-sum game. For a long term consideration, a Markov stochastic game is introduced and a Nash Q-learning method is given to find the Nash equilibrium strategies for two players. Numerical results are provided to show the effectiveness of our theoretical conclusions.     

HOSPITAL COSTS AND INFORMATION THEORY CASE MIX INDEXES: RESULTS FOR QUEENSLAND

The use of information theory as a basis for the construction of scalar case mix indexes for hospitals is well established but to date no results arising from an application of these indexes to Australian hospitals have been published. This paper provides a simplified explanation of the information theory approach and constructs the indexes for Queensland public hospitals. The usefulness of the indexes is then demonstrated with two applications. First, they are used to explain the variation in average cost per case between the hospitals in the study and are found to account for a small but statistically significant amount of such variation. Second, they are employed to provide estimates of state mean average and marginal costs by case type in Queensland. The resulting estimates are all both positive and plausible, characteristics not commonly found in estimates obtained using other techniques.     

A note on the coherence-based signal-to-noise ratio estimation in systems with periodic inputs

Coherence plays a very important role in linear systems analysis, since, in addition to quantify the similarity between signals, it is related to other quantities of interest, such as the signal-to-noise ratio (SNR). The sampling distribution of coherence estimates between Gaussian signals is well established, and hence, in this particular case, the statistics of SNR can be readily found if it is calculated from coherence estimates. However, in some applications, one of the signals is periodic, leading to a different coherence sampling distribution, which has been recently investigated. This work aims at developing analytical expressions for bias, variance and the probability density function of coherence-based SNR estimates under this particular assumption. Routines for obtaining this latter as well as critical values of the estimates are also provided.     

German employee inventors’ compensation records: A window into the returns to patented inventions

This paper uses a novel data source, namely German employee inventors’ compensation records compiled in compliance with the German Employee Invention Act of 1957 to estimate the returns to patented inventions. In contrast to patent value estimates obtained from surveys and renewals, these records primarily provide a measure of the value of the use of the invention and not the value of patent protection. While indicators of patent value explain much of the variation in these patent value estimates, the values are only weakly correlated with the estimated renewal value of the patents. The distribution of patent value from these records is highly skew, with the vast majority of the returns earned by a select set of high valued patents, consistent with finding for other measures of patent value. The value estimates however are considerably lower than recent survey estimates with most of the patents having little or no realized value, suggesting that the returns appropriated through the use of an invention may represent only a fraction of the value of a patented invention.