THE GRADIENT ESTIMATE OF SUBELLIPTIC HARMONIC MAPS WITH A POTENTIAL

In this paper,we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations.Under some suitable conditions,we give the gradient estimates of these maps and establish a Liouville type result.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

Torque estimation for robotic joint with harmonic drive transmission based on system dynamic characteristics

In the applications of joint control and robot movement,the joint torque estimation has been treated as an effective technique and widely used.Researches are made to analyze the kinematic and compliance model of the robot joint with harmonic drive to acquire high precision torque output.Through analyzing the structures of the harmonic drive and experiment apparatus,a scheme of the proposed joint torque estimation method based on both the dynamic characteristics and unscented Kalman filter(UKF)is designed and built.Based on research and scheme,torque estimation methods in view of only harmonic drive compliance model and compliance model with the Kalman filter are simulated as guidance and reference to promote the research on the torque estimation technique.Finally,a promoted torque estimation method depending on both harmonic drive compliance model and UKF is designed,and simulation results compared with the measurements of a commercial torque sensor,have verified the effectiveness of the proposed method.

A Method for Assessing Customer Harmonic Emission Level Based on the Iterative Algorithm for Least Square Estimation

With the power system harmonic pollution problems becoming more and more serious, how to distinguish the harmonic responsibility accurately and solve the grid harmonics simply and effectively has become the main development direction in harmonic control subjects. This paper, based on linear regression analysis of basic equation and improvement equation, deduced the least squares estimation (LSE) iterative algorithm and obtained the real-time estimates of regression coefficients, and then calculated the level of the harmonic impedance and emission estimates in real time. This paper used power system simulation software Matlab/Simulink as analysis tool and analyzed the user side of the harmonic amplitude and phase fluctuations PCC (point of common coupling) at the harmonic emission level, thus the research has a certain theoretical significance. The development of this algorithm combined with the instrument can be used in practical engineering.

Research on Methods of Parameter Estimation in Combining Forecasting Based on Harmonic Mean

Two kinds of parameter estimation methods (I) and (II) of combining forecasting based on harmontic mean are proposed and compared through a lot of simulation forecasting examples. A very helpful conclusion is obtained, which can lay solid foundations for correct application of the above methods.

An Approach to Harmonic State Estimation of Power System

This paper presents the harmonic state estimation (HSE) based on the Total Least Squares (TLS) through comprehensively considering the harmonic network parameter error and measurement system error. The proposed approach is tested on the IEEE 14–bus harmonic testing system. The satisfied results are obtained.

ON THE UNIVALENCE OF CERTAIN POLYHARMONIC MAPPINGS WITH BOUNDED LENGTH DISTORTIONS

The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappings with bounded length distortions.Then,using these results,we establish five Landau-type theorems for subclasses of polyharmonic mappings F and L(F),where F has bounded length distortion and L is a differential operator.

Partial sums of generalized harmonic starlike univalent functions generated by a (p,q)−Ruscheweyh-type harmonic differential operator

Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruscheweyh-type harmonic differential operator in D.We first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned class.Using this coefficient condition,we then examine ratios of partial sums of f in H.In all cases the results are sharp.In addition,the results so obtained generalize the related works of some authors,and many other new results are obtained.

GRADIENT ESTIMATES FOR POSITIVE SMOOTH f-HARMONIC FUNCTIONS

For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau （i.e., when ： is constant）.

Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite （p.c.f.） self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.

Schauder estimates for parabolic equation of bi-harmonic type

Global Schauder estimates for the initial-value parabolic problem of the hi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order case, first a formal expression of solutions by the Fourier transform is obtained, and then the regularity, uniqueness and existence of solutions using the potential theory and approximation argument are got. out approach is simple and straightforward.

Online LS-SVM for function estimation and classification

An online algorithm for training LS-SVM (Least Square Support VectorMachines) was proposed for the application of function estimation and classification. Online LS-SVMmeans that LS-SVM can be trained in an incremental way, and can be pruned to get sparseapproximation in a decremental way. When a SV (Support Vector) is added or removed, the onlinealgorithm avoids computing large-scale matrix inverse. Thus the computation cost is reduced. Onlinealgorithm is especially useful to realistic function estimation problem such as systemidentification. The experiments with benchmark function estimation problem and classificationproblem show the validity of this online algorithm.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

Harmonic Retrieval Embedded in Hybrid Colored Noise: a Novel Pisarenko Method Based on Cross high order Cumulant

Spectral estimation method is an effective method in the case of parameter estimation of sinusoid signal in noises.It always applies cross spectral estimation theory and high order self spectral estimation methods up to now.Yule Walker equation based on cross fourth order cumulant is developed and Pisarenko method is provided in this paper.Simulation results show that the method is effective to retrieve sinusoid signal frequencies from hybrid colored noises and has good performance.

NEW EFFICIENT ORDER-RECURSIVE LEAST-SQUARES ALGORITHMS

Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.

The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets

In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite （p.c.f.） self-similar sets.

Novel channel estimation model for OFDM in time-varying channel

A new channel estimation method for orthogonal frequency division multiplexing （OFDM） system with large subcarriers and serious intercarrier interference （ICI） is proposed. The channel frequency-domain （ CFD ） matrix of each delay path is factorized to the product of a diagonal delay matrix and a circular ICI matrix in this model. To reduce the coefficient number, the circular ICI ma- trix is squeezed by using Hamming-window as the reshaping pulse in the transmitter. Meanwhile, the elements of the diagonal delay matrix are approximated with a discrete prolate spheroidal basis ex- pansion model （DPS-BEM）. A least-square （LS） estimator is used to estimate the reduced channel coefficients. The proposed method is theoretically derived and simulated. The simulation results in- dicate that the model has good performance and is appropriate for various channel environments. The method also has low complexity and good spectral efficiency.

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR A CLASS OF STOKES EQUATION

A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.

Estimation of a Linear Model in Terms of Intra-Class Correlations of the Residual Error and the Regressors

Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.

Cross-spectral root-min-norm algorithm for harmonics analysis in electric power system

To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root-min-norm algorithm was described,but it is susceptive to noises with unstable performance in different SNRs.So the modified root-min-norm algorithm based on cross-spectral estimation was proposed,utilizing cross-correlation matrix and independence of different Gaussian noise series.Lots of simulation experiments were carried out to test performance of the algorithm in different conditions,and its statistical characteristics was presented.Simulation results show that the modified algorithm can efficiently suppress influence of the noises,and has high frequency resolution,high precision and high stability,and it is much superior to the classic DFT method.