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Branching structure of uniform recursive trees

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Science China Mathematics 2005年第6期48卷 769-784页

作者： feng Qunqiang SU Chun HU Zhishui Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China

The branching structure of uniform recursive trees is investigated in this *** the method of sums for a sequence of independent random variables, the distribution law of ηn, the number of branches of the uniform recursive tree of size n are given first. It is shown that the strong law of large numbers, the central limit theorem and the law of iterated logarithm for ηn follow easily from this method. Next it is shown that ηn and ξn, the depth of vertex n, have the same distribution, and the distribution law of ζn,m, the number of branches of size m, is also given, whose asymptotic distribution is the Poisson distribution with parameter λ = 1/m. In addition, the joint distribution and the asymptotic joint distribution of the numbers of various branches are given. Finally, it is proved that the size of the biggest branch tends to infinity almost sure as n -→∞.

关键词： uniform recursive tree, branch, depth, distribution law, limit theorem.

Distributed Adaptive Synchronization of Complex Dynamical Network with Unknown Time-varying Weights

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International Journal of Automation and computing 2015年第3期12卷 323-329页

作者： Hui-Na feng Jun-Min Li School of Mathematics and Statistics Xidian University

A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical synchronization and all the closed-loop signals are bounded. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible and asymptotical synchronization can be achieved even when the graph of network is not connected. Finally, a simulation example shows the feasibility and effectiveness of the approach.

关键词： Complex dynamical network synchronization distributed control adaptive scheme unknown time-varying parameters.

Hyponormal Toeplitz Operators on the Polydisk

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Acta Mathematica Sinica,English Series 2012年第2期28卷 333-348页

作者： Yu feng LU Yan Yue SHI School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.

关键词： Hyponormality Toeplitz operator Hankel operator polydisk block matrix representation

Hua's Theorem with s Almost Equal Prime Variables

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Acta Mathematica Sinica,English Series 2009年第7期25卷 1145-1156页

作者： Qing feng SUN Heng Cai TANG Department of Mathematics Shandong University Ji'nan 250100 P. R. China

It is proved unconditionally that every sufficiently large positive integer satisfying some necessary congruence conditions can be represented as the sum of s almost equal k-th powers of prime numbers for 2 ≤ k ≤ 10... 详细信息

关键词： the additive theory of prime numbers short intervals circle method

On-line Preconcentration of Trace Nickel from Electrolytic Manganese Using Minicolumn Packed Activated Carbon for Electrothermal Atomic Absorption Spectrometry

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Journal of Wuhan University of Technology(Materials Science) 2004年第4期19卷 17-20页

作者：姚俊 Jishou University

The online flow injection preconcentration and electrothermal atomic absorption spectrometry method were used for the determination of trace nickel in electrolytic manganese samples by sorption on a conical minicolumn packed with activated carbon at pH 9.0. The nickel was eluted from the minicolumn with 10%(v/v) nitric acid. An enrichment factor of 190-fold for a sample volume of 10mL was obtained. The detection limit (DL) of nickel with the use of the preconcentration method was 13ng·g -1in the original solid sample. The precision for 10 replicate determinations at 150ng·g -1 nickel concentration was 5.2% relative standard deviation (RSD). The calibration graph was linear with a correlation coefficient of r=0.9996 up to concentration of 660ng·g -1 nickel.

关键词： online preconcentration nickel electrothermal atomic absorption spectrometry activated carbon electrolytic manganese

On m-ovoids of finite classical polar spaces with an irreducible transitive automorphism group

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Science China Mathematics 2024年第3期67卷 683-712页

作者： Tao feng Weicong Li Ran Tao School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China Department of Mathematics and National Center for Applied Mathematics Shenzhen Southern University of Science and TechnologyShenzhen 518055China Key Laboratory of Cryptologic Technology and Information Security Ministry of EducationShandong UniversityQingdao 266237China School of Cyber Science and Technology Shandong UniversityQingdao 266237China

In this paper, we classify the m-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite familie... 详细信息

关键词： transitive m-ovoids irreducible action finite classical polar spaces primitive divisor

New Kamenev-type Oscillation Criteria for Half-linear Partial Differential Equations

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 535-548页

作者： Ge-feng YANG Zhi-ting XU Cisco School of Informatics Guangdong University of Foreign StudiesGuangzhou510006China School of Mathematical Sciences South China Normal UniversityGuangzhou510631China

We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div（A（x）｜｜ u｜｜^p-2 u）＋〈b（x）,｜｜ u｜｜^p-2 u〉＋c（x）｜u｜^p-2u=0（E）under quite general conditions. These results are extensions of the recent results developed by Sun [Y.C. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 （2004） 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations.

关键词： oscillation half-linear partial differential equations Kamenev-type Damped equation

Research of the traffic characteristics for the real time online traffic classification

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The Journal of China Universities of Posts and Telecommunications 2011年第3期18卷 92-98页

作者： SUN Mei-feng CHEN Jing-tao College of Information Engineering Yangzhou University Yangzhou 225009 China

Aiming at the hysteretic characteristics of classification problem existed in current intemet traffic identification field, this paper investigates the traffic characteristic suitable for the on-line traffic classification, such as quality of service （QoS）. By the theoretical analysis and the experimental observation, two characteristics （the ACK-Len ab and ACK-Len ha） were obtained. They are the data volume which first be sent by the communication parties continuously. For these two characteristics only depend on data＇s total length of the first few packets on the flow, network traffic can be classified in the early time when the flow arrived. The experiment based on decision tree C4.5 algorithm, with above 97% accuracy. The result indicated that the characteristics proposed can commendably reflect behavior patterns of the network application, although they are simple.

关键词： on-line traffic classification traffic characteristics ACK-Len ab ACK-Len ba

Parts-probability-based vehicle detection

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Science China(Information Sciences) 2014年第11期57卷 110-120页

作者： CHEN Long JIANG ZhiGuo feng Hao Image Processing Center School of Astronautics Beihang University Beijing Key Laboratory of Digital Media

Detecting vehicles is important in aerial surveillance. Traditional methods used classifiers to detect vehicles, but a single classifier was limited to detecting vehicles of only one intensity and orientation. Therefore,the task required the use of multiple classifiers of different intensities and orientations. To solve this problem, we first used a latent Dirichlet allocation(LDA) model that improved the previous approaches to vehicle *** text modeling approaches have been generative. They could be used to build probability models of vehicles in different intensities and from various orientations simultaneously using unlabeled data. Using a probability model, we can detect vehicles in a region with high probability. Next, we used a parts-probability model that improves the LDA model. The model effectively encodes spatial structure among visual words by adding spatial relationships among vehicle parts as priors of words. A parts probability model represents a vehicle hierarchically according to parts appearances and a vehicle’s features within the parts to enforce spatial coherency. Then, we used our model to detect vehicles from a collection of images and demonstrate its performs more effectively.

关键词： LDA vehicle detection parts probability model aerial surveillance spatial structure