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THE STABILITY OF LINEAR MULTISTEP METHODS FOR LINEAR SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2001年第2期19卷 125-130页

作者： Hong-jiong tian Jiao-xun Kuang Lin Qiu Department of Mathematics the University of Manchester Oxford RoadManchester M13 9PLUK Department of Mathematics Shanghai Normal UniversityShanghai 200234China Graduate School of Human Informaticss Nagoya 464-8601Japan

Presents information on a study which focused on the numerical solution of initial value problems for systems of neutral differential equations. Adaptations of linear multistep methods; Linear stability of linear mult... 详细信息

关键词： numerical stability linear multistep method delay differential equations

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基于局部信息熵的智能电网数据离群点识别

电子设计工程 2024年第5期32卷 118-121,126页

作者：田炯秦发宪朱涛国网宁夏电力有限公司中卫供电公司宁夏中卫755000

识别智能电网数据离群点能够准确地确定智能电网数据对象,但是目前提出的识别方法识别精准度较差,识别效率较低。为此,基于局部信息熵研究了一种新的智能电网数据离群点识别方法,通过方差定义选取优选空间,确定优选空间集阈值进行数据... 详细信息

识别智能电网数据离群点能够准确地确定智能电网数据对象,但是目前提出的识别方法识别精准度较差,识别效率较低。为此,基于局部信息熵研究了一种新的智能电网数据离群点识别方法,通过方差定义选取优选空间,确定优选空间集阈值进行数据加权处理,计算优选空间信息熵;通过无量化处理判断临界点数值,得到子空间最优范围。检索与分析离群状态变化情况,计算离群因子,根据概率值增强算法对冗余数据的甄别能力,删除离群点冗余数据,将平均值计入值域,实现智能电网数据离群点识别。实验结果表明,所研究方法精准度最终能够达到95%,识别效率在90%以上。

关键词：局部信息熵智能电网数据离群点离群点识别

Particle Residence Time in Column Flotation Based on Cyclonic Separation

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Journal of China University of Mining and Technology 2007年第3期17卷 349-353页

作者： ZHOU Xiao-hua LIU jiong-tian Department of Mining Engineering University of Kentucky Lexington KY40506 USA School of Chemical Engineering and Technology China University of Mining ＆ Technology Xuzhou Jiangsu 221008 China

The cyclonic static micro-bubble column flotation (FCSMC) is an effective separation device for fine particle treatment. The high mineralization rate and short flotation time of this equipment can be attributed to its unique cyclonic force field. It also has been observed that the presence of a cyclonic force field leads to a lower bottom separation size limit and a reduction of unselective entrainment. The collection zone of the column is considered to consist of two parts,a column separation zone and a cyclonic zone. Total recovery of the collection zone was developed. For our study,we analyzed the particle movement in the cyclonic zone. Particle residence time equations for the cyclonic zone were de-rived by force analysis. Results obtained in this study provide a theoretical foundation for the design and scale-up of the FCSMC.

关键词： column flotation cyclonic separation residence time

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational Mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong tian (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China) department of Mathematics Shanghai Normal University 上海 200234

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

Delay-dependent Stability Analysis of Multistep Methods for Delay Differential Equations

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Acta Mathematicae Applicatae Sinica 2009年第4期25卷 607-616页

作者： Cheng-ming Huang Yang-zi Hu Hong-jiong tian School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Department of Mathematics Shanghai Normal University Division of Computational Science E-Institute of Shanghai Universities Scientific Computing Key Laboratory of Shanghai Universities Shanghai 200234 China

This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of r（0）-stable methods are found. Later, some examples of r（0）-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results.

关键词： Delay differential equations delay-dependent stability asymptotic stability ^-(O)-stability linearmultistep methods general linear methods

Mineralogical characterization and comprehensive utilization of micro-fine tantalum–niobium ores from Songzi

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Rare Metals 2015年第4期34卷 282-290页

作者： Zhi-Tao Yuan Ji-Wei Lu Hui-Fang Wu jiong-tian Liu School of Resources & Civil Engineering Northeastern University Department of Design Northeastern University Engineering and Research Institute Co. Ltd.

The mineralogical characteristics of tantalumniobium ores from Songzi were investigated using mineral liberation analyzer （MLA） and chemical analysis. In particular, the chemical composition, phase composition, particle size, and dissemination characteristics of the ores were studied in detail. Results show that Ta2O5 and Nb2O5 have grades of 0.013 % and 0.011%, respectively. The main valuable minerals in the ores are tantalite, col- umbite, tantalum-niobite, and microlite, and the gangue minerals associated with tantalum-niobium minerals mainly include quartz, kaolinite, illite, feldspar, and mica among others. The minerals are embedded in a complex manner. Tantalum-niobium minerals with most particle sizes of -0.040 mm are disseminated in minerals, such as mica, illite, quartz, and partially intergrown with topaz and zircon, where they could not be easily liberated. Thus, the ores are classified as low-grade, micro-fine, and refractory tantalum-niobium ores. Based on this consideration, the process of classification-gravity concentration-magnetic separation-middlings regrinding and gravity concentration are finally determined and satisfactory indices are obtained. Two rough concentrates are produced： Concentrate I has Ta2O5 and Nb2O5 grades of 7.0292 % and 3.546 %, respectively, as well as recovery of 49.42 % and 35.46 %. By comparison, Concentrate Ⅱ has Ta2O5 and Nb2O5 grades of 7.0292 % and 3.546 %, respectively, as well as recovery of 49.42 % and 35.46 %.

关键词： Mineralogy Tantalum-niobite Comprehensive utilization Micro-fine particles

Directed graph-based distribution network reconfiguration for operation mode adjustment and service restoration considering distributed generation

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Journal of Modern Power Systems and Clean Energy 2017年第1期5卷 142-149页

作者： Haifeng HONG Zhesheng HU Ruipeng GUO Jun MA jiong tian College of Electrical Engineering Zhejiang UniversityHangzhou 310027China Ningxia Electric Power Company State Grid Corporation of ChinaYinchuan 750001China

We present a directed graph-based method for distribution network reconfiguration considering distributed generation. Two reconfiguration situations are considered: operation mode adjustment with the objective of minimizing active power loss(situation Ⅰ) and service restoration with the objective of maximizing loads restored(situation Ⅱ). These two situations are modeled as a mixed integer quadratic programming problem and a mixed integer linear programming problem, respectively. The properties of the distribution network with distributed generation considered are reflected as the structure model and the constraints described by directed graph. More specifically, the concepts of "in-degree" and "out-degree"are presented to ensure the radial structure of the distribution network, and the concepts of "virtual node" and"virtual demand" are developed to ensure the connectivity of charged nodes in every independent power supply *** validity and effectiveness of the proposed method are verified by test results of an IEEE 33-bus system and a 5-feeder system.

关键词： Distribution network Distributed generation Network reconfiguration Directed graph Operation mode adjustment Service restoration

SPURIOUS NUMERICAL SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2006年第2期24卷 181-192页

作者： Hong-jiong tian Li-qiang Fan Yuan-ying Zhang Jia-xiang Xiang Department of Mathematics Shanghai Normal University Division of Computational Science E-Institute of Shanghai Universities Shanghai 200234 China Department of Mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.

关键词： Spurious solution Asymptotic behavior Delay differential equation.

Velocity distribution of the flow field in the cyclonic zone of cyclone-static micro-bubble flotation column

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International Journal of Mining Science and Technology 2013年第1期23卷 89-94页

作者： Deng Xiao-wei Liu jiong-tian Wang Yong-tian Cao Yi-jun School of Chemical Engineering and Technology China University of Mining & Technology

Laboratory experiments have been conducted to study the flow field in a cyclone static micro-bubble flotation column. The method of Particle Image Velocimetry (PIV) was used. The flow field velocity distribution in both cross section and longitudinal section within cyclonic zone was studied for different circulating volumes. The cross sectional vortex was also analyzed. The results show that in cross section as the circulating volume increases from 0.187 to 0.350 m 3 /h, the flow velocity ranges from 0 to 0.68 m/s. The flow field is mainly a non-vortex potential flow that forms a free vortex without outside energy input. In the cyclonic region the vortex deviates from the center of the flotation column because a single tangential opening introduces circulating fluid into the column. The tangential component of the velocity plays a defining role in the cross section. In the longitudinal section the velocity ranges from 0 to 0.08 m/s. The flow velocity increases as does the circulating volume. Advantageous mineral separation conditions arise from the combined effects of cyclonic flow in cross and longitudinal section.

关键词： Cyclone-static micro-bubble flotation column PIV Cyclonic flow field Velocity distribution