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Fast algorithms for singular value decomposition and the inverse of nearly low-rank matrices

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National Science Review 2023年第6期10卷 24-27页

作者： Chen Xu Weiwei Xu Kaili Jing Department of Mathematics and statistics University of Ottawa School of Mathematics and statistics Xi'an Jiao Tong University School of Mathematics and statistics Nanjing University of Information Science and Technology

PROBLEM Matrix computation is a fundamental task in science and engineering;it is recognized as one of the seven computational’giants’of massive data analysis [1],analogous to the seven’dwarfs’in highperformance *** recent years,as the scale of datasets rapidly grows,analysts and engineers frequently need to deal with big matrices with a nearly lowrank *** big size of a matrix brings great numerical hurdles to matrix *** this work,we focus on two typical tasks in matrix computation:singular value decomposition (SVD) and matrix inverse on nearly low-rank matrices that are potentially of big sizes.

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Existence of Periodic Solutions for Neutral Functional Differential Equations with Nonlinear Difference Operator

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Acta Mathematica Sinica,English Series 2016年第12期32卷 1541-1556页

作者： Shi Ping LU College of Mathematics & statistics Nanjing University of Information Science & Technology

In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.

关键词： Neutral functional differential equation condensing operator topological degree periodic solution

Synchronization of impulsively coupled complex networks

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Chinese Physics B 2012年第5期21卷 126-132页

作者：孙文陈忠陈士华 School of information and Mathematics Yangtze University School of Mathematics and statistics Wuhan University

We investigate the synchronization of complex networks,which are impulsively coupled only at discrete *** on the comparison theory of impulsive differential systems,a distributed impulsive control scheme is proposed for complex dynamical networks to achieve *** proposed scheme not only takes into account the influence of all nodes to network synchronization,which depends on the weight of each node in the network,but also provides us with a flexible method to select the synchronized state of the *** addition,it is unnecessary for the impulsive coupling matrix to be ***,the proposed control scheme is applied to a chaotic Lorenz network and Chua＇s circuit *** simulations are used to illustrate the validity of this control scheme.

关键词： complex network impulsive control scheme synchronization

Optimal operating policy for a controllable queueing model with a fuzzy environment

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第2期10卷 311-318页

作者： Chuen-horng LIN Jau-chuan KE Department of information Management Department of Applied statistics National Taichung Institute of Technology

We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle,a set of parametric nonlinear programs is developed to find the upper and lower bounds of the minimal average total cost per unit time at the possibility level. The membership functions of the minimal average total cost are further constructed using different values of the possibility level. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the object value is expressed and governed by the membership functions,the optimization problem in a fuzzy environment for the controllable queueing models is represented more accurately and analytical results are more useful for system designers and practitioners.

关键词： Controllable queue Fuzzy sets Membership function Nonlinear programming

Adaptive quantile regression with precise risk bounds

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Science China Mathematics 2017年第5期60卷 875-896页

作者： TIAN MaoZai CHAN Ngai Hang School of statistics Lanzhou University of Finance and Economics School of statistics and information Xinjiang University of Finance and Economics Center for Applied statistics School of StatisticsRenmin University of China Department of statistics The Chinese University of Hong Kong

An adaptive local smoothing method for nonpaxametric conditional quantile regression models is considered in this paper. Theoretical properties of the procedure are examined. The proposed method is fully adaptive in the sense that no prior information about the structure of the model is assumed. The fully adaptive feature not only allows varying bandwidths to accommodate jumps or instantaneous slope changes, but also al- lows the algorithm to be spatially adaptive. Under general conditions, precise risk bounds for homogeneous and heterogeneous cases of the underlying conditional quantile curves are established. An automatic selection algo- rithm for locally adaptive bandwidths is also given, which is applicable to higher dimensional cases. Simulation studies and data analysis confirm that the proposed methodology works well.

关键词： adaptive smoothing automatic bandwidths conditional quantile risk bounds robustness

Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic

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Chinese Journal of Electronics 2014年第4期23卷 767-772页

作者： ZHENG Dabin YU Long HU Lei Faculty of Mathematics and statistics Hubei University School of Mathematics and statistics Central China Normal University State Key Laboratory of information Security Institute of Information Engineering CAS

Let n=me and p be an odd prime. Let Fp be a finite field and Fpn be its n th field extension. By some polynomial GCD computations, this paper characterize the bentness and semi-bentness of two classes of p-ary quadratic functions from Fpn to Fp with coefficients in Fpe. Moreover, the enumeration formulas of constructed bent functions are obtained for some special cases of m. The results generalize some previous related work.

关键词： Quadratic bent function Quadratic semibent function Greatest common divisor Block cyclic matrix

Covariate-adaptive designs with missing covariates in clinical trials

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Science China Mathematics 2015年第6期58卷 1191-1202页

作者： LIU ZhongQiang YIN JianXin HU FeiFang Center for Applied statistics and School of statistics Renmin University of China School of Mathematics and information Science Henan Polytechnic University

Many covariate-adaptive randomization procedures have been proposed and implemented to balance important covariates in clinical trials. These methods are usually based on fully observed covariates. In practice,the covariates of a patient are often partially missing. We propose a novel covariate-adaptive design to deal with missing covariates and study its properties. For the proposed design, we show that as the number of patients increases, the overall imbalance, observed margin imbalance and fully observed stratum imbalance are bounded in probability. Under certain covariate-dependent missing mechanism, the proposed design can balance missing covariates as if the covariates are observed. Finally, we explore our methods and theoretical findings through simulations.

关键词： missing stratum imbalance restored strata absolute partially minimization margin exclusive

Equicontinuity of Maps on a Dendrite with Finite Branch Points

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Acta Mathematica Sinica,English Series 2017年第8期33卷 1125-1130页

作者： Tai Xiang SUN Guang Wang SU Hong Jian XI Xin KONG College of information and statistics Guangxi University of Finance and Economics College of Mathematics and information Science Guangxi University

Let （T, d） be a dendrite with finite branch points and f be a continuous map from T to T. Denote by w（x, f） and P（f） the w-limit set of x under f and the set of periodic points of f, respectively. Write Ω（x, f） = {yl there exist a sequence of points xk ∈ T and a sequence of positive integers n1 〈 n2 〈 … such that lim k→∞ Xk = X and lim k→∞ f nk （xk） = y}. In this paper, we show that the following statements are equivalent：（1） f is equicontinuous. （2） w（x, f） = Ω（x, f） for any x ∈ T. （3） ∩ ∞ n=1 f n（T） = P（f）, and w（x, f） is a periodic orbit for every x ∈ T and map h： x → w（x, f）（x ∈ T） is continuous. （4） Ω（x, f） is a periodic orbit for any x ∈ T.

关键词： Dendrite map equicontinuity periodic point ε-limit set

FAMILIES OF p-ARY SEQUENCES WITH LOW CORRELATION AND LARGE LINEAR COMPLEXITY

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Journal of Systems Science & Complexity 2014年第6期27卷 1305-1319页

作者： CAI Han ZENG Xiangyong HU Lei Faculty of Mathematics and statistics Hubei University State Key Laboratory of information Security Institute of Information EngineeringChinese Academy of Sciences

This paper generalizes a method of generating shift sequences in the interleaved construction proposed by *** the new shift sequences,some new families of p-ary sequences with desired properties can be obtained.A lowe... 详细信息

关键词： Auto-correlation cross-correlation linear complexity low correlation p-ary sequence.