Some inequalities for the generalized linear distortion function

In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.

A New Definition for Generalized First Derivative of Nonsmooth Functions

In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

Empirical Likelihood Inference for Generalized Partially Linear Models with Longitudinal Data

In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.

On Generalized High Order Derivatives of Nonsmooth Functions

In this paper, we proposed a Extension Definition to derive, simultaneously, the first, second and high order generalized derivatives for non-smooth functions, in which the involved functions are Riemann integrable but not necessarily locally Lipschitz or continuous. Indeed, we define a functional optimization problem corresponding to smooth functions where its optimal solutions are the first and second derivatives of these functions in a domain. Then by applying these functional optimization problems for non-smooth functions and using this method we obtain generalized first derivative (GFD) and generalized second derivative (GSD). Here, the optimization problem is approximated with a linear programming problem that by solving of which, we can obtain these derivatives, as simple as possible. We extend this approach for obtaining generalized high order derivatives (GHODs) of non-smooth functions, simultaneously. Finally, for efficiency of our approach some numerical examples have been presented.

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.

A New General Linear Convolution Model for fMRI Data Process

General linear model (GLM) is the most popular method for functional magnetic resource imaging (fMRI) data analysis . However, its theory is imperfect. The key of this model is how to constitute the design-matrix to model the interesting effects better and separate noises better. For the purpose of detecting brain function activation , according to the principle of GLM,a new convolution model is presented by a new dynamic function convolving with design-matrix,which combining with t-test can be used to detect brain active signal. The fMRI imaging result of visual stimulus experiment indicates that brain activities mainly concentrate among v1and v2 areas of visual cortex, and also verified the validity of this technique.

A New Vector-Valued Padé-Type Approximation in the Inner Space

A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas are presented. The expressions of this Pad′e-type ap- proximants are provided with the generating function form and the determinant form.

Safety Performance Functions for Traffic Signals:Phasing and Geometry

A significant proportion of urban crashes,especially serious and fatal crashes,occur at traffic signals.Many of the black-spots in both Australia and New Zealand cities occur at high volume and/or high-speed traffic signals.Given this,crash reduction studies often focus on the major signalised intersections.However,there is limited information that links the phasing configuration,degree of saturation and overall cycle time to crashes.While a number of analysis tools are available for assessing the efficiency of intersections,there are very few tools that can assist engineers in assessing the safety effects of intersection upgrades and new intersections.Safety performance functions have been developed to help quantify the safety impact of various traffic signal phasing configurations and level of intersection congestion at low and high-speed traffic signals in New Zealand and Australia.Data from 238 signalised intersection sites in Auckland,Wellington,Christchurch,Hamilton,Dunedin and Melbourne was used to develop crash prediction models for key crash-causing movements at traffic signals.Different variables(road features)effect each crash type.The models indicate that the safety of intersections can be improved by longer cycle times and longer lost inter-green times,especially all-red time,using fully protected right turns and by extending the length of right turn bays.The exception is at intersections with lots of pedestrians where shorter cycle times are preferred as pedestrian crashes increase with longer wait times.A number of factors have a negative impact on safety including,free left turns,more approach lanes,intersection arms operating near or over capacity in peak periods and higher speed limits.

一类非线性系统的广义伴随线性方程分析研究

非线性输出频率响应函数是线性系统理论中频率响应函数在非线性系统中的一种推广,越来越多的学者已将其应用在结构损伤检测及故障诊断中.基于Volterra级数理论与由非线性微分方程描述的单输入单输出非线性系统的广义频率响应函数递归计算公式,利用多重积分性质和多维傅里叶变换,将广义频率响应函数映射到了一维频域中,推导出了一类非线性系统的广义伴随线性方程计算公式.研究表明,这类系统的第n阶非线性输出响应是以系统输入激励和前n-1阶非线性输出响应的组合函数作为广义激励作用到系统各阶广义伴随线性方程中的输出响应,最后通过求解一系列线性微分方程可得到这类非线性系统的任意阶非线性输出响应,其结果弥补了伴随线性方程无法求解这类非线性系统的不足.同时,针对广义伴随线性方程的数值计算问题,论文提出了一种耦合计算法,提高了计算非线性输出响应的精度,为非线性输出频率响应函数的计算提供了一种新思路.最后利用广义伴随线性方程与线性算子理论研究了两种典型非线性系统中非线性现象产生的原因,研究结果为非线性系统的分析与设计提供了一种有效途径.

一种提高整体拟合程度的对数分布广义翁氏模型新解法

广义翁氏模型已有解法在进行参数优选线性拟合时普遍存在生产初期拟合点离散偏差性较强的问题,这些偏差点与整体拟合趋势线的偏离程度较大,且偏差点的位置相对较为集中,加大了偏差点对整体拟合程度的影响,进一步影响了模型参数的优选准确性。针对模型已有解法存在的问题,本文从模型拟合点的分布形式研究出发,提出了一种对数分布广义翁氏模型新解法,区别于已有解法以时间t作为线性拟合函数自变量,新解法以时间对数ln(t)作为线性函数的自变量,拟合点的分布形态也从均匀分布转变为对数分布。实际应用表明,新解法使生产初期参数拟合点分布相对更加分散,分布趋势也更贴近整体拟合点的趋势,参数拟合初期拟合点偏离误差平均值减少了2.1%,参数拟合曲线整体偏离误差平均值减少了1.7%,模型新解法对应的产量偏离误差较模型已有解法平均值减少2.87%,表明模型新解法相对模型已有解法更能够提高产量的整体拟合程度。

基于平滑GMS模型和改进扩张状态观测器的复合摩擦补偿

摩擦力是影响直线伺服系统低速运行与点对点定位精度的主要非线性扰动。广义麦克斯韦(generalized Maxwellslip,GMS)摩擦模型虽然可以准确描述摩擦特性用于前馈补偿,但其存在切换点过渡时振荡的问题,同时易受测量噪声和摩擦参数变化等影响。为此,该文提出基于平滑GMS模型和改进扩张状态观测器(extended state observer,ESO)的复合摩擦补偿策略。首先,引入过渡用双曲正切函数以解决GMS模型中在切换点的反复穿越问题,并给出该模型的离线辨识方法。其次,设计基于模型信息的四阶ESO补偿剩余摩擦力与未知扰动,并引入切比雪夫滤波器整定观测器增益,以降低扰动观测与噪声敏感之间的冲突。为验证所提摩擦补偿策略的有效性,在小型高精度永磁同步直线电机定位平台上进行定位实验。实验结果验证了所提摩擦补偿策略的可行性和有效性。

基于RBF-LADRC的虚拟同步发电机控制策略

随着大规模分布式发电技术的出现,为支持微电网的稳定运行,提出虚拟同步发电机(VSG)技术。由于VSG常用的电压电流双闭环控制存在动态响应时间久、抗扰动能力弱的缺点,考虑LADRC对扰动具有更优异的动态响应速度,该文提出一种用于VSG电压外环控制的线性自抗扰控制方案,并采用RBF对LADRC中的关键参数进行在线整定,以实现控制器的实时优化。在Matlab/Simulink平台下搭建仿真模型,并对所提出的改进策略与传统控制策略进行仿真对照,结果显示该策略可有效提高并网环境下虚拟同步发电机功率和频率稳定性。

线弹性迭代的等肢角钢输电塔极限承载力研究

为了规避现有的构件截面广义屈服函数表达形式繁琐的缺点,同时弥补函数不等比例加载的不足,以逐步回归分析为基础,建立了等肢角钢简化的齐次广义屈服函数,提出了一种高效线弹性迭代方法,用以分析输电塔在构件强度方面的极限承载力。首先,利用最小二乘法建立等肢角钢齐次广义屈服函数;然后通过逐步回归分析,逐个剔除函数中影响不显著的各项,简化上述齐次广义屈服函数,同时保证其较高的拟合精度;最后,基于弹性模量调整策略,提出了一种高效线弹性迭代方法,用以等肢角钢输电塔的极限承载力分析。结果表明:所建立的简化形式的齐次广义屈服函数,不仅精度高,而且项数少,克服了现有传统的广义屈服函数表达形式繁琐、不等比例加载,以及由此带来的计算结果不稳定等问题。通过对比传统方法,验证了所述方法在分析输电塔构件强度方面的极限承载力具有高精度和高计算效率的特点。

基于积分滑模观测器的直线振荡电机谐振频率跟踪控制

现有直线振荡电机(LOM)无位置传感器谐振频率跟踪控制方法存在行程观测精度低、抗干扰能力差等问题,容易导致谐振频率跟踪精度低、频率振荡严重。为提高谐振频率跟踪控制性能,该文研究了一种基于积分滑模观测器(ISMO)的新型谐振频率跟踪控制方法。首先,基于LOM工作在系统谐振频率点时行程-电流相位差为90°的特点,提出一种双互相关函数比值方法,消除了行程变化对谐振频率跟踪控制的影响。其次,采用积分滑模面及新型趋近律设计ISMO,并利用二阶广义积分器获取行程估算信号,大大提高了行程估算精度。最后,对比实验结果表明,所提方法能够有效提高谐振频率跟踪精度、稳定时间及抗干扰能力。

超高压容器开孔处裂纹最深点处应力强度因子的计算方法

由于超高压容器开孔处的应力梯度变化很大,通常由最小二乘法拟合的三次多项式往往与实际的应力分布之间存在较大偏差。针对这一问题,提出了一种分段插值求解的计算方法。首先,基于应力强度因子及通用权函数的理论,推导出了常数插值、线性插值、二次插值求解的计算公式;其次,结合工程实例,基于无裂纹体的弹性应力分析,对比分析了常规最小二乘法与常数插值、线性插值、二次插值的应力分布表征精度及应力强度因子计算结果,确定了线性插值和二次插值方法的可靠性;然后,分析了数据采集量对线性插值和二次插值计算结果的影响,确定了线性插值方法的实用性;最后,对线性插值与有限元分析的计算结果进行了分析验证。研究结果表明:应力分布表征精度为“最小二乘法<常数插值<线性插值<二次插值”,计算结果相对误差约为15%;随着采集数据量的增加,采用线性插值方法的计算结果能较快收敛,更适合于工程计算;线性插值与有限元法的计算结果高度一致,证明了线性插值计算的可靠性。

CONNECTION BETWEEN THE ORDER OF FRACTIONAL CALCULUS AND FRACTIONAL DIMENSIONS OF A TYPE OF FRACTAL FUNCTIONS

The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.

ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

ESTIMATION METHOD FOR SOLUTIONS TO GENERAL LINEAR SYSTEM OF VOLTERRA INTEGRAL INEQUALITIES INVOLVING ITERATED INTEGRAL FUNCTIONALS

An estimation method for solutions to the general linear system of Volterra- type integral inequalities containing several iterated integral functionals is obtained. This method is based on a result proved by the present second author in Journ. Math. Anal. Appl.(1984). A certain two-dimensional system of nonlinear ordinary differential equations is also discussed to demonstrate the usefulness of our method.

THE REALIZATION OF LINEAR SHIFT-VARIANT FILTERS THROUGH STATE FEEDBACK

In this paper a new method to realize rational generalized transfer functions of linearshift-variant digital filters through state feedback is presented In some practical applications therequired characteristics of the filter change slowly.Under these circumstances,the proposedmethod is very effective and the resulting filter structure is simple.A numerical example isprovided to show the performance of the method.