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Preemptive Semi-online Algorithms for Parallel Machine Scheduling with Known Total Size

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Acta Mathematica Sinica,English Series 2006年第2期22卷 587-594页

作者： Yong HE Hao ZHOU Yi Wei JIANG State Key lab of CAD & CG Zhejiang University Department of mathematics Zhejiang University

This paper investigates preemptive semi-online scheduling problems on m identical parallel machines, where the total size of all jobs is known in advance. The goal is to minimize the maximum machine completion time or maximize the minimum machine completion time. For the first objective, we present an optimal semi-online algorithm with competitive ratio 1. For the second objective, we show that the competitive ratio of any semi-online algorithm is at least （2m-3）/（m-1） for any m〉2 and present optimal semi-online algorithms for m = 2, 3.

关键词： Semi-online Preemptive scheduling Competitive analysis

Stability of Julia sets for a quadratic random dynamical system

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Science China mathematics 2002年第11期45卷 1381-1389页

作者：龚志民邱维元王键 lab of mathematics for Nonlinear Science Fudan University Shanghai China Department of mathematics Xiangtan University Xiangtan China Business School Xiangtan University Xiangtan China

For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + Cn and the sequence (Fn) of iterates Fn: = fcn ο ? ο fc1 are considered. The Fatou set F(Cn) is defined as the set of all $z \in \hat {\mathbb{C}}: = {\mathbb{C}} \cup \left\{ \infty \right\}$ such that (Fn) is normal in some neighbourhood of z, while the complement J(Cn) of F(cn) (in $\hat {\mathbb{C}}$ ) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(Cn) in the case where (cn) is bounded. A problem put forward by Brück is solved.

关键词： Fatou set, Julia set, random iterates, stability.

Pores-Preserving Face Cleaning Based on Improved Empirical Mode Decomposition

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Journal of Computer Science & Technology 2009年第3期24卷 557-567页

作者：刘艳丽徐晓刚郭延文王进段鑫陈曦彭群生 State Key lab of CAD & CG Zhejiang University Department of mathematics Zhejiang University State Key lab of Novel Software Technology Nanjing University

In this paper, we propose a novel method of cleaning up facial imperfections such as bumps and blemishes that may detract from a pleasing digital portrait. Contrasting with traditional methods which tend to blur facial details, our method fully retains fine scale skin textures （pores etc.） of the subject. Our key idea is to find a quantity, namely normalized local energy, to capture different characteristics of fine scale details and distractions, based on empirical mode decomposition, and then build a quantitative measurement of facial skin appearance which characterizes both imperfections and facial details in a unified framework. Finally, we use the quantitative measurement as a guide to enhance facial skin. We also introduce a few high-level, intuitive parameters for controlling the amount of enhancement. In addition, an adaptive local mean and neighborhood limited empirical mode decomposition algorithm is also developed to improve in two respects the performance of empirical mode decomposition. It can effectively avoid the gray spots effect commonly associated with traditional empirical mode decomposition when dealing with high-nonstationary images.

关键词： image enhancement empirical mode decomposition normalized local energy

Some Notes on Generalized Cyclotomic Sequences of Length pq

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Journal of Computer Science & Technology 2008年第5期23卷 843-850页

作者：陈智雄李胜强 Key lab of Applied mathematics Putian University Key lab of Network Security and Cryptology Fujian Normal University National Key lab of Communication University of Electronic Science and Technology of China

We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Ding-Helleseth（DH, for short）-generalized cyclotomic sequences. We present some new pseudo-random properties of DH-generalized cyclotomic sequences using the theory of character sums instead of the theory of cyclotomy, which is a conventional method for investigating generalized cyclotomic sequences.

关键词： stream cipher generalized cyclotomic sequence pseudo-random binary sequence character sum correlation

Simulation of nuclei morphologies for binary alloy

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Science China mathematics 2010年第11期53卷 2927-2936页

作者： LI DaMing1, & ZHANG PingWen2 1Department of mathematics, Shanghai Jiaotong University, Shanghai 200240, China 2Key lab of mathematics and Applied mathematics, Center for Applied Physics and Technology and School of Mathematical Sciences, Peking University, Beijing 100871, China Department of mathematics Shanghai Jiaotong University Shanghai China Key lab of mathematics and Applied mathematics Center for Applied Physics and Technology and School of Mathematical Sciences Peking University Beijing China

We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is su?ciently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered.

关键词： nucleation crystal morphology string method

Symbolic Computation and q-Deformed Function Solutions of （2＋1）-Dimensional Breaking Soliton Equation

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Communications in Theoretical Physics 2007年第2期47卷 270-274页

作者： CAO Li-Na WANG Deng-Shan CHEN Lan-Xin School of mathematics and Computer Science Central University for Nationalities Beijing 100081 China mathematics Mechanization Key lab Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of mathematics Shijiazhuang University Shijiazhuang 050035 China

In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the （2＋1）-dimensional Breaking soliton equation are derived by using the extended multiple Riccatl equations expansion method.

关键词： q-deformed hyperbolic functions symbolic computation Riccati equation soliton-like solution

Twice Q-polynomial distance-regular graphs of diameter 4

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Science China mathematics 2015年第12期58卷 2683-2690页

作者： MA JianMin KOOLEN Jack H. College of mathematics & Information Science and Hebei Key lab of Computational mathematics & Applications Hebei Normal University School of Mathematical Sciences University of Science and Technology of China

It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.

关键词： distance-regular graph P-or Q-polynomial structure tight

Performance analysis of switched linear systems under arbitrary switching via generalized coordinate transformations

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Science China(Information Sciences) 2019年第1期62卷 108-118页

作者： Meili LIN Zhendong SUN mathematics and Physics Institute Fujian University of Technology Key lab of Systems & Control Academy of Mathematics & Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

For a continuous-time switched linear system, the spectral abscissa is defined as the worst-case divergence rate under arbitrary switching, which is critical for characterizing the asymptotic performance of the switched system. In this study, based on the generalized coordinate transformations approach, we develop a computational scheme that iteratively produces sequences of minimums of matrix set μ1measures,where the limits of the sequences are upper bound estimates of the spectral abscissa. A simulation example is presented to illustrate the effectiveness of the proposed scheme.

关键词： generalized coordinate transformation matrix set measure spectral abscissa switched linear system

The Controllability, Observability, and Stability Analysis of a Class of Composite Systems with Fractional Degree Generalized Frequency Variables

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IEEE/CAA Journal of Automatica Sinica 2019年第3期6卷 859-864页

作者： Cuihong Wang Yafei Zhao YangQuan Chen IEEE the Department of mathematics and Computer Science Shanxi Normal University the Mechatronics Embedded Systems and Automation(MESA) Lab

This paper is concerned with fundamental properties of a class of composite systems with fractional degree generalized frequency variables, including controllability, observability and stability. Firstly, some necessary and sufficient conditions are given to guarantee controllability and observability of such composite systems. Then we prove that the stability problem of such composite systems can be reduced to judging whether a fractional degree polynomial is stable. Finally, the stability analysis result is applied in the supervisory control of fractional-order multi-agent systems, and an example is provided to illustrate the effectiveness of the proposed methods.

关键词： Composite system controllability fractionalorder system observability stability