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CONDITIONS FOR OPTIMAL SOLUTIONS OF UNBALANCED PROCRUSTES PROBLEM ON STIEFEL MANIFOLD

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Journal of Computational Mathematics 2007年第6期25卷 661-671页

作者： zhenyue zhang Yuyang Qiu keqin du Department of Mathematics Zhejiang University Hangzhou 310027 China

We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions： given matrices A ∈ R^n×n and B ∈ R^n×k, n 〉 k, minimize the residual ‖AQ- B‖F over the Stiefel manifold of orthonormal matrices. Theoretical analysis on necessary conditions and sufficient conditions for optimal solutions of the unbalanced Procrustes problem is given.

关键词： Procrustes problem Stiefel manifold Necessary condition Sufficient condition.

FAST PARALLELIZABLE METHODS FOR COMPUTING INVARIANT SUBSPACES OF HERMITIAN MATRICES

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Journal of Computational Mathematics 2007年第5期25卷 583-594页

作者： zhenyue zhang Hongyuan Zha Wenlong Ying Department of Mathematics Zhejiang University Hangzhou 310027 China College of Computing Georgia Institute of Technology Atlanta GA 30332 USA

We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We present an accurate convergence analysis of the algorithm without using the big O notation. We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates. Several numerical examples are given which compare some aspects of the existing algorithms and the new algorithms.

关键词： Eigenvalue Invariant subspace Hermitian matrix QR method Parallelizable method.

A New Criterion on k-Normal Elements over Finite Fields

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Chinese Annals of Mathematics,Series B 2020年第5期41卷 665-678页

作者： Aixian zhang keqin FENG Department of Mathematical Sciences Xi’an University of TechnologyXi’an 710054China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al.(2013).Several methods to construct k-normal elements were presented by Alizadah et al.(2016)and Huczynska et al.(2013),and the criteria on k-normal elements were given by Alizadah et al.(2016)and Antonio et al.(2018).In the paper by Huczynska,S.,Mullen,G.,Panario,*** Thomson,D.(2013),the number of k-normal elements for a fixed finite field extension was calculated and *** this paper the authors present a new criterion on k-normal elements by using idempotents and show some *** criterion was given for usual normal elements before by zhang et al.(2015).

关键词： Normal basis Finite field Idempotent Linearized polynomial Gauss

Effect of particle gradation on pore structure and seepage law of solution in weathered crust elution-deposited rare earth ores

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International Journal of Mining Science and Technology 2023年第10期33卷 1261-1272页

作者： Defeng Liu Wenxin Yan zhenyue zhang Ruan Chi School of Resource and Safety Engineering Wuhan Institute of TechnologyWuhan 430073China Key Laboratory for Green Chemical Process of Ministry of Education Wuhan Institute of TechnologyWuhan 430073China

Both CT and Avizo software were used to explore the effect of particle gradation on the evolution characteristics of pore structure and seepage paths in weathered crust elution-deposited rare earth ores during *** results showed that the pore areas in four kinds of ore samples before leaching were mainly concentrated in 10^(4)–10^(7)μm^(2),whose pore quantities accounted for 96.89%,94.94%,90.48%,and 89.45%,respectively,while the corresponding pore volume only accounted for 30.74%,14.55%,7.58%,and 2.84%of the total pore *** the decrease of fractal dimension,the average pore throat length increased,but pore throat quantities,the average pore throat radius and coordination number *** with that before leaching,the change degree of pore structure during leaching increased with the fractal dimension *** example,the reduction rate of the average coordination number of ore samples was 14.36%,21.30%,28.00%,and 32.90%,*** simulation results indicated that seepage paths were uniformly distributed before leaching while the streamline density and seepage velocity increased with the fractal dimension ***,the phenomenon of the streamline interruption gradually reduced during leaching while preferential seepage got more obvious with the decrease of the fractal dimension.

关键词： Weathered crust elution-deposited rare earth ores Particle gradation Pore structure Seepage law Fractal dimension

Local concentration of middle and heavy rare earth elements in the col on the weathered crust elution-deposited rare earth ores

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Journal of Rare Earths 2018年第5期36卷 552-558页

作者： zhenyue zhang Ningjie Sun Zhengyan He Ru'an Chi School of Minerals Processing and Bioengineering Central South University Changsha 410083 China Key Laboratory for Green Chemical Process of Ministry of Education Wuhan Institute of Technology Wuhan 430073 China

This present study focused on investigating the content and relative enrichment multiple of rare earth elements（REEs） in different terrain of weathered ore body, and the value of light rare earth elements/middle and heavy rare earth elements（LREEs/HREEs）, in order to understand the mobilization and redistribution of HREEs, Furthermore, the abrasion pH was investigated as well, The results show that the average contents of HREEs in the knap, ridge and col are 37.26, 61.71, and 271.3 μg/g, respectively. The value of LREEs/HREEs is decreased from 16.78 to 7.914 between knap and col and the relative enrichment multiple of HREEs is as follows： CCol-HREEs 〉 CRidge-HREEs 〉 0. It is indicated the HREEs is concentrated in the col and the enrichment degree of HREEs is stronger than the ridge and the knap. Rare earth elements fractionation is exhibited in the different terrain of weathered ore body. Based on this study, the finding that HREEs concentrate in the lower terrain of weathered crust elution-deposited rare earth ores, such as in the col, would become a marker or indicator to search for middle and heavy rare earth enriched zone.

关键词： Weathered crust elution-deposited rareearth ores Topography conditions Middle and heavy rare earth elements Local concentration

Trajectory optimization of multiple quad-rotor UAVs in collaborative assembling task

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Chinese Journal of Aeronautics 2016年第1期29卷 184-201页

作者： Chen Yongbo Yu Jianqiao Mei Yuesong zhang Siyu Ai Xiaolin Jia zhenyue School of Aerospace Engineering Beijing Institute of Technology

A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial vehicles in the collaborative assembling task. Firstly, the path planning process is solved by a novel parallel intelligent optimization algorithm, the central force optimization-genetic algorithm （CFO-GA）, which combines the central force optimization （CFO） algorithm with the genetic algorithm （GA）. Because of the immaturity of the CFO, the convergence analysis of the CFO is completed by the stability theory of the linear time-variant discrete-time sys- tems. The results show that the parallel CFO-GA algorithm converges faster than the parallel CFO and the central force optimization-sequential quadratic programming （CFO-SQP） algorithm. Then, the trajectory planning problem is established based on the path planning results. In order to limit the range of the attitude angle and guarantee the fight stability, the optimized object is changed from the ordinary six-degree-of-freedom rigid-body dynamic model to the dynamic model with an inner-loop attitude controller. The results show that the trajectory planning process can be solved by the mature SQP algorithm easily. Finally, the discussion and analysis of the real-time per- formance of the hierarchic optimization strategy are presented around the group number of the wav^oints and the eoual interval time.

关键词： Hierarchic optimizationstrategy Parallel CFO-GA algorithm Path planning Six,degree-of-freedom rigid-body dynamic model Trajectory optimization Trajectory planning

Enhancing mineral liberation of a Canadian rare earth are with microwave pretreatment

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Journal of Rare Earths 2018年第2期36卷 215-224页

作者： Chengbin Zhong Caili Xu Renliang Lyu zhenyue zhang Xiaoyan Wu Ru'an Chi Key Laboratory for Green Chemical Process of Ministry of Education School of Chemical Engineering & PharmacyWuhan Institute of Technology School of Minerals Processing and Bioengineering Central South University

Liberation. as an attribute of mineralogy characteristic. whose impacts on finely disseminated Canadian rare earth ore was studied with microwave pretreatment. Samples of a light rare earth ore along with mostly ankerite and biotite as dominant gangue minerals as well as bastnaesite, strontianite and goethite as dominated minerals were exposed to further comminution by ball mill and microwave pretreatment fragmentation. Mineralogical characteristics were analyzed by using a mineral liberation analyzer（MLA）.The results indicated that tight association mutually penetrates among dominated minerals in the range size of -300 ＋ 212 μm and 212 ＋ 150 μm and gangue minerals in the form of adjacent type. fine vein type. shell type and packing type. Temperature in the ore samples pre-treated by microwave can rapidly rise to 250 ℃ with microwave power of 0-1.5 kW and microwave time of 0-2 min. Applying the microwave pretreatment merely reduces the hardness of the ore causing the fracture of rare earth ore, but this does not transform or change the original mineralogy characteristics of the ore samples. On the basis of above study. the liberation value of bastnaesite, strontianite and goethite with microwave pretreatment is greater than with conventional comminution when the liberation class is above 75%. The distribution of particle size of rare earth ore samples is better with microwave pretreatment than with conventional comminution for particle size of 7.4 × 10^（-5） m. With microwave pretreatment, the theoretical grade-recovery of bastnaesite. strontianite and goethite in the rare earth ore attains better results than with conventional comminution at a given grade.

关键词： MLA Bastnaesite Strontianite Goethite Mineralogy Rare earths

Enhancing the powering ability of triboelectric nanogenerator through output signal’s management strategies

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Nano Research 2023年第9期16卷 11783-11800页

作者： Changxin Qi zhenyue Yang Jinyan Zhi Ruichao zhang Juan Wen Yong Qin Institute of Nanoscience and Nanotechnology School of Materials and EnergyLanzhou UniversityLanzhou 730000China

As a new branch of efficient and low-cost mechanical energy conversion technology,triboelectric nanogenerator(TENG)is a potential solution to provide a long-term power supply for the Internet of Things(IoT)sensors and portable electronic ***,due to inherent working properties of TENG itself such as extremely high internal impedance,pulse,and alternating current(AC)output,TENG can not directly supply power to loads such as batteries *** on these,we describe TENG’s performance from a new perspective of powering *** consists of two aspects:the ability to transport charge effectively and the ability to output high power quality current *** order to push forward the developments and applications of TENG,it is necessary to improve its power supply capacity from different ***,in recent years,a variety of output signal’s management strategies aiming at effectively managing the generated electricity and significantly improving powering ability of TENG have obtained significantly ***,this paper discusses the working mechanisms and different load characteristics of TENG at first to clarify the electric performance of ***,on basis of theoretical analysis,the output signal’s management strategies are elaborated from four aspects:improving the cycle output electricity of TENG,increasing the surface charge density of TENG,improving the power quality of TENG-based energy harvesting system,promoting the application of TENG through integrated circuit(IC)technology and TENG network,and the relevant principles and applications are discussed ***,the advantages and disadvantages of the above output signal’s management strategies are summarized and discussed,and the future development of the output signal’s management strategies for TENG is prospected.

关键词： triboelectric nanogenerator(TENG) inherent working properties TENG-based energy harvesting system powering ability output signal’s management strategies.

Toward Energy-Efficiency Optimization of Pktgen-DPDK for Green Network Testbeds

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China Communications 2018年第11期15卷 199-207页

作者： Guo Li Dafang zhang Yanbiao Li keqin Li College of Computer Science and Electronic Engineering Hunan University Department of Computer Science State University of New York

The packet generator （pktgen） is a fundamental module of the majority of soft- ware testers used to benchmark network pro- tocols and functions. The high performance of the pktgen is an important feature of Future Internet Testbeds, and DPDK is a network packet accelerated platform, so we can use DPDK to improve performance. Meanwhile, green computing is advocated for in the fu- ture of the internet. Most existing efforts have contributed to improving either performance or accuracy. We, however, shifted the focus to energy-efficiency. We find that high per- formance comes at the cost of high energy consumption. Therefore, we started from a widely used high performance schema, deeply studying the multi-core platform, especially in terms of parallelism, core allocation, and fre- quency controlling. On this basis, we proposed an AFfinity-oriented Fine-grained CONtrolling （AFFCON） mechanism in order to improve energy efficiency with desirable performance. As clearly demonstrated through a series of evaluative experiments, our proposal can reduce CPU power consumption by up to 11% while maintaining throughput at the line rate.

关键词： CPU affinity DPDK energy-effi-cient NUMA packet generator