On the Stable Method Computing Values of Unbounded Operators

Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.

Empirical Line Method Using Spectrally Stable Targets to Calibrate IKONOS Imagery

By using speetrally stable targets, the empirical line （EL） method was tested to correct the multispectral IKONOS imagery acquired over Putuo Mountain, Zhejiang, China. A series of calibration targets, which were spectrally stable over time, were selected to establish the linear predicted equation. Subsequently, a series of spectrally stable validation targets were selected to assess the accuracy of the equations. And, validation targets, which were speetrally unstable over time, were used to test the feasibility of using the EL method to calibrate the archival remotely sensed data. Ground reflectance measurements for each target were made using an ASD FieldSpec spectroradiometer. A Trimble GeoXTTM GPS unit with sub-meter accuracy was used to estimate the target position accurately. Linear regression equations for four tKONOS bands were derived. The coefficients of determination for the blue, green, and red bands were all greater than 0.9800 and it was 0.9697 for the near infrared band. It was concluded that reasonable results could be obtained by using speetrally stable targets.

QUAD METHOD FOR IDENTIFYING RELATIVELY STABLE STATIONS

The QUAD(Quasi-Accurate Detection of gross errors) method which is originally developed to detect gross errors in the geodetic data is extended and used to select and identify relatively stable stations. The formulas and algorithm are described in detail. Some problems that should be noticed in the use of this method are discussed. Finally, this method is applied to some data observed in North China as an example.

对称α-stable与高斯的混合噪声中信号检测的几种新方法

文章首先对现有α-stable噪声中信号检测的几种方法进行概述、分析.在将背景噪声拓展为对称α-stable分布噪声和高斯噪声的混合噪声(一种更接近实际工程的噪声模型)时,基于一种可逼近于对称α-stable分布的表达式,提出了几种基于低阶矩理论的信号检测新方法.它们分别是:改进的矩方法、局部次最优新方法.它们有简单的表达式,容易实现.蒙特卡罗仿真试验结果表明,这几种新方法是行之有效的,检测性能优于现有的一些方法.

Alpha-stable分布粗糙土壤表面电磁散射研究

采用空间域合成法生成高度起伏遵守Alpha-stable分布的粗糙土壤表面,运用矩量法研究了锥形入射波入射时粗糙土壤表面的电磁散射特性。数值计算了散射系数随散射角的变化关系,分析了稳定性系数、归一化尺度参数、互相关长度、入射波频率、土壤湿度对散射系数的影响。结果表明,稳定性系数、归一化尺度参数、互相关长度、入射波频率、土壤湿度对散射系数均有较大的影响,遵守不同的规律。

PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

Efficient Elliptic Solver for the Mild Slope Equation Using BI-CGSTAB Method

The elliptic mild slope equation is used to simulate linear wave propagation over variable sea bed topography with mild slopes. The governing equation is discretized by the finite difference method. Based on the BI-CGSTAB technique, an attractive variant bf BI-Conjugate Gradients (BI-CG) method, the obtained linear algebraic system of equations is solved. Numerical experiments show that the BI-CGSTAB method is efficient for solving the elliptic mild slope equation. The results obtained by the BI-CGSTAB-Based method are much the same as those obtained by other authors with different solution methods, but the convergence rate is much faster than that of other methods.

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.

Stable response of low-gravity liquid non-linear sloshing in a circle cylindrical tank

Under pitch excitation, the sloshing of liquid in circular cylindrical tank includes planar motion, rotary motion and rotary motion inside planar motion. The boundaries between stable motion and unstable motion depend on the radius of the tank, the liquid height, the gravitational intension, the surface tensor and the sloshing damping. In this article, the differential equations of nonlinear sloshing are built first. And by variational principle, the Lagrange function of liquid pressure is constructed in volume intergration form. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived. At last, these equations are solved by multiple-scales method. The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail. The result indicates that variation of amplitude frequency response characteristics of the system with Bond, jump, lag and other nonlinear phenomena of liquid sloshing are investigated.

Study of dynamic stable control for a leg-wheeled robot

In order to realize the dynamic stable motion control for a leg-wheeled robot, this paper presents a layered control architecture. It is composed of three levels, i.e. the supervisor level, coordinator level and leg level. The supervisor level is for the task definition and planning, while the coordinator level does the dynamic stable control and the leg level executes the real-time control command. First, we build the efficient Newton-Euler dynamics equations of the robot. Then, the stability control is realized by properly distributing ground reaction forces applied by the legs. We also use Simplex method to optimize the ground reaction force distribution and verify the control method by experimental and numerical results.

A LOWER BOUND OF STABLE STATIONARY TRAJECTORIES

It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.

STABLE AND UNSTABLE STATIONARY TRAJECTORIES

The stability of stationary trajectories of a particular autonomous system is studied.The proof of the result is based upon continuation methods.

Construction of highly-stable graphene hollow nanospheres and their application in supporting Pt as effective catalysts for oxygen reduction reaction

The construction and surface modification of three-dimensional(3D) graphene structures have been recognized as effective ways to prepare high-performance graphene-based composites in energy-related applications. Herein, on the basis of well-defined morphology and efficient electron conduction, the 3D highly-stable graphene hollow nanospheres have been synthesized by using sacrificial template method. The asprepared 3D graphene nanospheres exhibit superior mechanical stability, electrochemical stability, and strong hydrophobicity, which may accelerate the emission of H2O in acidic medium-based ORR. Accordingly, the 3D highly-stable graphene nanospheres are used to confine tiny Pt nanoparticles(3Dr-GO@Pt HNSs) for ORR in acidic medium, exhibiting superior activity with 4-electron-transfered pathway. Meanwhile,dramatically improved durability are achieved in terms of both ORR mass activity and electrochemically surface area compared to those of commercial Pt/C.

Alpha-stable粗糙面与下方目标的复合电磁散射研究

基于Alpha-stable分布在通信、电子、雷达等领域的应用,采用空间域合成法生成高度起伏遵守Alphastable分布的粗糙土壤表面,根据四成分模型模拟粉沙壤土的介电常数,运用矩量法研究了锥形入射波入射下粗糙土壤表面与下方三角形截面柱体的复合电磁散射问题.数值计算了散射系数随散射角的变化关系,分析了稳定性系数、归一化尺度参数、互相关长度、入射波频率、土壤湿度、三角形截面柱边长、目标方位角、三角形截面柱埋藏深度对散射系数的影响.该研究结果在军事、民用、通信、工业等多领域具有一定的理论价值.

Study of plasma-based stable and ultrawideband electromagnetic wave absorption for stealth application

A plasma-based stable,ultra-wideband electromagnetic（EM） wave absorber structure is studied in this paper for stealth applications.The stability is maintained by a multi-layer structure with several plasma layers and dielectric layers distributed alternately.The plasma in each plasma layer is designed to be uniform,whereas it has a discrete nonuniform distribution from the overall view of the structure.The nonuniform distribution of the plasma is the key to obtaining ultra-wideband wave absorption.A discrete Epstein distribution model is put forward to constrain the nonuniform electron density of the plasma layers,by which the wave absorption range is extended to the ultra-wideband.Then,the scattering matrix method（SMM） is employed to analyze the electromagnetic reflection and absorption of the absorber structure.In the simulation,the validation of the proposed structure and model in ultra-wideband EM wave absorption is first illustrated by comparing the nonuniform plasma model with the uniform case.Then,the influence of various parameters on the EM wave reflection of the plasma are simulated and analyzed in detail,verifying the EM wave absorption performance of the absorber.The proposed structure and model are expected to be superior in some realistic applications,such as supersonic aircraft.

Proposal for Generalized Exergy and Entropy Properties Based on Stable Equilibrium of Composite System-Reservoir

The present theoretical study represents a proposal aimed at investigating about the possibility of generalizing the canonical entropy-exergy relationship and the reservoir concept. The method adopted assumes the equality of pressure and chemical potential as necessary conditions of mutual stable equilibrium between a system and a reservoir in addition to the equality of temperature that constitutes the basis for defining entropy as deriving from energy and exergy concepts. An attempt is made to define mechanical and chemical entropy as an additional and additive component of generalized entropy formulated from generalized exergy property. The implications in exergy method and the possible engineering applications of this approach are outlined as future developments among the domains involved.

A Bayesian Approach for Stable Distributions:Some Computational Aspects

In this work, we study some computational aspects for the Bayesian analysis involving stable distributions. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, the use of a latent or auxiliary random variable facilitates to obtain any posterior distribution when being related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to daily price returns of Abbey National shares, considered in [1], and the other is the length distribution analysis of coding and non-coding regions in a Homo sapiens chromosome DNA sequence, considered in [2]. Posterior summaries of interest are obtained using the OpenBUGS software.

Robust Linear Regression Models:Use of a Stable Distribution for the Response Data

In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.

Multi-scale seismic full waveform inversion in the frequency-domain with a multi-grid method

Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.

Numerical simulation of solitary wave propagation based on MPS method

The concept of candidate particle set is introduced in the MPS gridless numerical method to generate neighboring particle set ma- trix, which can reduce the CPU time to 1/11 of that before introduction. The Bi-CGSTAB （bi-conjugate gradient stabilized） algorithm is applied to solving the Poisson pressure equation, by which the solving speed is significantly accelerated. The process of solitary waves propagating over a numerical flume and interacting with a vertical wall is simulated. The simulated results of water surface elevation are in good agreement with the analytical solution as well as the measured data. The predicted maximum values of the run-up of solitary waves with various relative incident wave heights agree well with the measured results.