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| 1 | Research progress of the fractional Fourier transform in signal processing显示文摘The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but es-sentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been com-prehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers. | TAO Ran DENG Bing WANG Yue | 2006 | Science in China(Series F)2006，49，1： | 99 |
| 2 | Picard Values and Normal Families of Meromorphic Functions with Multiple Zeros | Wang Yuefei Fang Mingliang Institute of Mathematics, Academia Sinica, Beijing 100080, China Institute of Mathematics, Academia Sinica, Beijing 100080, China Department of Mathematics, Nanjing Normal University, Nanjing 210097, China | 1998 | Acta Mathematica Sinica,English Series1998，14，1： | 99 |
| 3 | L^p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels | Yong Ding Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China Dashan Fan Department of Mathematics, Anhui University and University of Wisconsin-Milwaukee. MW 53201 USA Yibiao Pan Department of Mathematics, University of Pittsburgh. Pittsburgh. Pennsylvania 15260. USA | 2000 | Acta Mathematica Sinica,English Series2000，16，4： | 88 |
| 4 | Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform显示文摘This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method. | QI Lin1, 2, TAO Ran1, ZHOU Siyong1 & WANG Yue1 1. Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China 2. School of Information Engineering, Zhengzhou University, Zhengzhou 450052, China Correspondence should be addressed to QI Lin (email: qilin@bit.edu.cn) | 2004 | Science in China(Series F)2004，47，2： | 143 |
| 5 | Attribute reduction theory and approach to concept lattice显示文摘The theory of the concept lattice is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. This paper proposes the theory of attribute reduction in the concept lattice, which extends the theory of the concept lattice. In this paper, the judgment theorems of consistent sets are examined, and the discernibility matrix of a formal context is introduced, by which we present an approach to attribute reduction in the concept lattice. The characteristics of three types of attributes are analyzed. | ZHANG Wenxiu WEI Ling QI Jianjun | 2005 | Science in China(Series F)2005，48，6： | 70 |
| 6 | Function S-rough sets and law identification显示文摘By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough sets). S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class (law equivalence class) that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets (function singular rough sets). Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identifica- tion. | SHI KaiQuan YAO BingXue | 2008 | Science in China(Series F)2008，51，5： | 68 |
| 7 | Function S-rough sets and security-authentication of hiding law显示文摘Function S-rough sets are defined by R-function equivalence class, which have dynamic characteristic. Function S-rough sets have dynamic characteristic, law characteristic and law-hiding characteristic. Function S-rough sets can generate f-hiding law and - hiding law. By engrafting, crossing, and penetrating between the information security theory and function S-rough sets, the security hiding and the authentication of f- hiding law and - hiding law are given respectively in this paper. The fusion and share between function S-rough sets and information security theory is a new research direction of the application of information law in information system. | SHI KaiQuan1,2 & ZHAO JianLi3 1 School of Mathematics and Computer Sciences, Longyan University, Longyan 364000, China 2 School of Mathematics and System Sciences, Shandong University, Jinan 250100, China 3 School of Mathematics Science, Liaocheng University, Liaocheng 252059, China | 2008 | Science in China(Series F)2008，51，7： | 69 |
| 8 | Mathematic principles of interrupted-sampling repeater jamming (ISRJ)显示文摘Coherent jamming is one of the important trends in modern radar electronic war- fare. High-speed sampling of wideband radio frequency (RF) signals and high iso- lation of two receive-transmit antennas are key technologies for the realization of coherent jamming. However, these technologies present significant challenges to engineering application. In this paper, a novel repeater jamming based on inter- rupted sampling technique is presented. For a jammer with a receive-transmit time-sharing antenna, a radar signal is sampled with a low rate by the jammer. Then, a train of false targets will be achieved after the jamming signal feed the matched filter of a pulse compression radar. For the case of the linear frequency modulated (LFM) pulse compression radars, mathematic principles of the interrupted-sam- pling repeater jamming is developed, and then the efficiency of the jamming is de- scribed and stated as expressions of key parameters which are also beneficial to the jamming design for other coherent radars. | WANG XueSong LIU JianCheng ZHANG WenMing FU QiXiang LIU Zhong XIE XiaoXia | 2007 | Science in China(Series F)2007，50，1： | 53 |
| 9 | Mobius Isoparametric Hypersurfaces in S^(n+1) with Two Distinct Principal Curvatures | Hai Zhong LI Department of Mathematics, Tsinghua University. Beijing 100084. P. R. China Hui Li LIU Department of Mathematics, Northeastern University. Shenyang 110000. P. R. China Chang Ping WANG Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences. Peking University, Beijing 100871, P. R. China Guo Song ZHAO Department of Mathematics, Sichuan University, Chengdu 610064. P. R. China | 2002 | Acta Mathematica Sinica,English Series2002，18，3： | 53 |
| 10 | On the Extension of Isometries between Unit Spheres of E and C(Ω)显示文摘In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too. | GuangGuiDING | 2003 | Acta Mathematica Sinica,English Series2003，19，4： | 52 |
| 11 | Semi-tensor product of matrices and its application to Morgen's problem显示文摘This paper proposes a new matrix product, namely, semi-tensor product. It is a generalization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional data; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgen's problem for control systems is formulated as a numerically solvable problem. | 程代展 | 2001 | Science in China(Series F)2001，44，3： | 50 |
| 12 | Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation显示文摘This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly,both the geometric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics,respectively. Secondly,it puts forward and discusses the definitions and theories of fractional stationary point,fractional equilibrium coefficient,fractional stable coefficient,and fractional grayscale co-occurrence matrix. At the same time,it particularly discusses fractional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly,it discusses in detail the structures and parameters of n×n any order fractional differential mask on negative x-coordinate,positive x-coordinate,negative y-coordinate,positive y-coordinate,left downward diagonal,left upward diagonal,right downward diagonal,and right upward diagonal,respectively. Furthermore,it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly,based on the above-mentioned discussion,it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images. | PU YiFei WANG WeiXing ZHOU JiLiu WANG YiYang JIA HuaDing | 2008 | Science in China(Series F)2008，51，9： | 50 |
| 13 | Decrease-radix design principle for carrying/borrowing free multi-valued and application in ternary optical computer显示文摘In this paper a new theory referred to as the decrease-radix design (DRD) is pro-posed,which is found in the research of logic units of ternary (tri-valued) optical computer. Based on the theory proposed,the principles and the regulations of the DRD for making operation units of multi-valued operation with carrying/borrowing free are also presented. The research work has come to the following important conclusion: let D be a special state contained in n physical informative states,then one may figure out any multi-valued processors within n(n×n) carrying/borrowing free n-valued units by the composition some of n×n×(n-1) simplest basic operating units according to the regulations of DRD proposed in this paper. The detailed systematic way of our design regulations is highlighted step by step in the paper with an example of design of a tri-valued logic optical operating unit. The real ar-chitecture,the procedure,and the experimental results of our sample in tri-valued logic operating unit are given. Finally,a re-constructible model of ternary logical optical processor is introduced. The theory proposed in the paper has laid down a solid foundation for the design of re-constructible carrying/borrowing free operat-ing units in ternary optical computers and can be widely used as the designing reference in a variety of multi-valued logic operating units. | YAN JunYong JIN Yi ZUO KaiZhong | 2008 | Science in China(Series F)2008，51，10： | 41 |
| 14 | Information granules and entropy theory in information systems显示文摘Information granulation and entropy theory are two main approaches to research uncertainty of an information system,which have been widely applied in many practical issues. In this paper,the characterizations and representations of infor-mation granules under various binary relations are investigated in information systems,an axiom definition of information granulation is presented,and some existing definitions of information granulation become its special forms. Entropy theory in information systems is further developed and the granulation monoton-icity of each of them is proved. Moreover,the complement relationship between information granulation and entropy is established. This investigation unifies the results of measures for uncertainties in complete information systems and incom-plete information systems. | LIANG JiYe & QIAN YuHua Key Laboratory of Computational Intelligence and Chinese Information Processing,Ministry of Education School of Computer & Information Technology,Shanxi University,Taiyuan 030006,China | 2008 | Science in China(Series F)2008，51，10： | 41 |
| 15 | Composition Operators on the Bloch Space of Several Complex Variables | Jihuai Shi Luo Luo Department of Mathematics,University of Science and Technology of China,Heifei 230036,P.R.China Fax:(0551)3631760 | 2000 | Acta Mathematica Sinica,English Series2000，16，1： | 43 |
| 16 | Constructing iterative non-uniform B-spline curve and surface to fit data points显示文摘In this paper, based on the idea of profit and loss modification, we present the iterative non-uniform B-spline curve and surface to settle a key problem in computer aided geometric design and reverse engineering, that is, constructing the curve (surface) fitting (interpolating) a given ordered point set without solving a linear system. We start with a piece of initial non-uniform B-spline curve (surface) which takes the given point set as its control point set. Then by adjusting its control points gradually with iterative formula, we can get a group of non-uniform B-spline curves (surfaces) with gradually higher precision. In this paper, using modern matrix theory, we strictly prove that the limit curve (surface) of the iteration interpolates the given point set. The non-uniform B-spline curves (surfaces) generated with the iteration have many advantages, such as satisfying the NURBS standard, having explicit expression, gaining locality, and convexity preserving, etc. | LINHongwei WANGGuojin DONGChenshi | 2004 | Science in China(Series F)2004，47，3： | 47 |
| 17 | A NEW REGULARITY CLASS FOR THE NAVIER-STOKES EQUATIONS IN IR^n显示文摘ANEWREGULARITYCLASSFORTHENAVIER-STOKESEQUATIONSINIR~n￥H.BEIRaODAVEIGA(DepotmentofMathematics,PisaUniversity,Pisa,Italy)Abstra?.. | H. BEIRaO DA VEIGA (Department of Mathematics, Pisa University, Pisa, Italy) | 1995 | Chinese Annals of Mathematics,Series B1995，16，4： | 38 |
| 18 | THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS显示文摘The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables. | LIU TAISHUN (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China)REN GUANGBIN (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China) | 1998 | Chinese Annals of Mathematics,Series B1998，19，4： | 39 |
| 19 | Ternary optical computer principle显示文摘The fundamental principle and the characteristics of ternary optical computer, using horizontal polarized light, vertical polarized light and no-intensity to express information, are propounded in thispaper. The practicability to make key parts of the ternary optical computer from modern micro or integrated optical devices, opto-electronic and electro-photonic elements is discussed. The principle can be applied in three-state optical fiber communication via horizontal and vertical polarized light. | 金翊 何华灿 吕养天 | 2003 | Science in China(Series F)2003，46，2： | 35 |
| 20 | A software architecture centric engineering approach for Internetware显示文摘As a new software paradigm evolved by the Internet, Internetware brings many challenges for the traditional software development methods and techniques. Though architecture-based component composition (ABC) approach is originated in the traditional software paradigm, it supports the engineering of Internetware effectively due to its philosophy, rationales and mechanisms. ABC has three major contributions to the en- gineering of Internetware in detail. First, the feature oriented domain modeling method can structure the “disordered”“software entities” to “ordered Internetware” bottom-up in the problem space. Second, the architecture centric design and analysis method can support the development of self-adaptive Internetware. Third, the component operating platform is a reflective and self-adaptive middleware that not only provides Internetware with a pow- erful and flexible runtime infrastructure but also enables the self-adaptation of the structure and individual entities of Internetware. | MEI Hong HUANG Gang ZHAO Haiyan JIAO Wenpin | 2006 | Science in China(Series F)2006，49，6： | 37 |
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