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Linear Maps Preserving Projections of Jordan Products on the Space of Self-Adjoint Operators

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Journal of Mathematical Research with Applications 2012年第2期32卷 235-240页

作者： Meifeng WANG,Guoxing JI college of mathematics and information science,Shaanxi normal university,Shaanxi 710062,china college of mathematics and information science Shaanxi Normal University Shaanxi 710062

Let Bs(H) be the real linear space of all self-adjoint operators on a complex Hilbert space H with dim H ≥ *** is proved that a linear surjective map on Bs (H) preserves the nonzero projections of Jordan products of two operators if and only if there is a unitary or an anti-unitary operator U on H such that (X)=λU XU,X∈Bs(H) for some constant λ with λ∈{1,1}.

关键词： self-adjoint operator Jordan product projection linear map.

Development and application of ergodicity model with FRCM and FLAR for hydrological process

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science china(Technological sciences) 2009年第2期52卷 379-386页

作者： WANG HongRui1, FENG QiLei2, LIN Xin3 & ZENG WenYi4 1 college of Water science, Key Laboratory for Water and Sediment sciences of the Ministry of Education, Beijing normal university, Beijing 100875, china 2 School of science, Beijing Institute of Education, Beijing 100011, china 3 School of Mathematical sciences, Beijing normal university, Beijing 100875, china 4 college of information science and Technology, Beijing normal university, Beijing 100875, china 1. college of Water science Key Laboratory for Water and Sediment Sciences of the Ministry of Education Beijing Normal University Beijing 100875 China 2. School of science Beijing Institute of Education Beijing 100011 China 3. School of Mathematical sciences Beijing Normal University Beijing 100875 China 4. college of information science and Technology Beijing Normal University Beijing 100875 China

In this paper, a new ergodic property analysis model of hydrological process is proposed based on fuzzy-rough c-means clustering (FRCM), autocorrelogram, and fuzzy least absolute regression (FLAR). A precipitation time series (1951―2004) from Shanghai Hydrology Station is then analyzed with the model. The results show that the precipitation time series of April, May, June, and September has er-godic property. We conclude that in the long run, the precipitation of April, May, June, and September will not keep decreasing; it will converge to its mean value in some period.

关键词： hydrological process ergodic autocorrelogram fuzzy-rough c-means clustering fuzzy least absolute regression

Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

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science china mathematics 2011年第3期54卷 555-572页

作者： DENG ShengFu1, GUO BoLing2 & WANG TingChun2,3 1Department of mathematics, Zhanjiang normal university, Zhanjiang 524048, china 2Institute of Applied Physics and Computational mathematics, Beijing 100088, china 3 college of Math and Physics, Nanjing university of information science and Technology, Nanjing 210044, china 1. Department of mathematics Zhanjiang Normal University Zhanjiang 524048 China2. Institute of Applied Physics and Computational Mathematics Beijing 100088 China3. College of Math and Physics Nanjing University of Information Science and Technology Nanjing 210044 China

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

关键词： homoclinic orbits heteroclinic orbits peakon wave solutions compacton wave solutions periodic cusp wave solutions

Resolution method for overlapping peaks based on the fractional-order differential

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science china Chemistry 2007年第6期50卷 797-805页

作者： LI YuanLu1, YU ShengLin2 & ZHENG Gang2 1 college of information & Control, Nanjing university of information science & Technology, Nanjing 210044, china 2 college of Automation Engineering, Nanjing university of Aeronautics and Astronautics, Nanjing 210016, china 1. college of information & Control Nanjing University of Information Science & Technology Nanjing 210044 China 2. college of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders. Also, equations between the differential order and the zero-crossing of the fractional-order differential of the specified peak signals are proposed according to the variation of the zero-crossing of the specified peak signals at different orders. Characteristic paramters of the Gaus- sian peak, Lorentzian peak, and Tsallis peak can be estimated using estimator I and estimator II which are obtained by the equations above. As a result, a new method is presented to resolve the overlapped peaks signal. Firstly, a fractional-order differential of the specified peak signals is obtained with the fractional-order differentiation filter. Then, characteristic paramters of the specified peak signals can be extracted using estimator I and estimator II. Finally, the Tsallis peak is used as a model to assign the overlapping peak signals correctly. Experimental results show that the proposed method is efficient and effective for the simulated overlapping peaks and detected overlapping voltammetric peak signals.

关键词： fractional-order differentiation filter, fractional-order differential, overlapping peaks, voltammetric peak

Checking for normality in linear mixed models

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science china mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,ZHU LiXing 2,3 & FANG Yun 4 1 School of Finance and Statistics,East china normal university,Shanghai 200241,china 2 School of Statistics and mathematics,Yunnan university of Finance and Economics,Yunnan 650221,china 3 The Department of mathematics,Hong Kong Baptist university,Hong Kong 999077,china 4 mathematics and science college,Shanghai normal university,Shanghai 200234,china 1. School of Finance and Statistics East China Normal University Shanghai 200241 China2. School of Statistics and Mathematics Yunnan University of Finance and Economics Yunnan 650221 China3. The Department of Mathematics Hong Kong Baptist University Hong Kong 999077 China4. Mathematics and Science College Shanghai Normal University Shanghai 200234 China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

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science china mathematics 2006年第10期49卷 1392-1404页

作者： XU Yichao,CHEN Minru & MA Songya Academy of mathematics and Systems science, Chinese Academy of sciences, Beijing 100080, china college of mathematics and information sciences, Henan university, Kaifeng 475001, china Academy of mathematics Systems science Chinese Academy of Sciences Beijing 100080 China college of mathematics information sciences Henan University Kaifeng 475001 China

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso (D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F).In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN,F)) and Iso (D(VN, F))(0), where G(0) is the unit connected component of the Lie group G.

关键词： holomorphic automorphism group, homogeneous Siegel domain, normal Siegel domain, complex homogeneous bounded domain.

A novel key pre-distribution scheme for wireless distributed sensor networks

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science china(information sciences) 2010年第2期53卷 288-298页

作者： PEI DingYi 1 , DONG JunWu 1 & RONG ChunMing 2 1 college of mathematics and information science, Guangzhou university, Guangzhou 510006, china 2 university of Stavanger, N-4036, Stavanger, Norway 1. college of mathematics and information science Guangzhou University Guangzhou 510006 China2. University of Stavanger N-4036 Stavanger Norway

A novel key pre-distribution scheme for sensor networks is proposed, which enables sensor nodes to communicate securely with each other using cryptographic techniques. The approach uses the rational normal curves in the projective space with the dimension n over the finite field F q . Both secure connectivity and resilience of the resulting sensor networks are analyzed. By choosing the parameters q and n properly, this key pre-distribution scheme has some advantages over the previous known schemes. In addition, if the number of the rational normal curves in the scheme becomes too large for an application, the size may be reduced by choosing a part of the curves randomly. This reduction has, shown by our experiments, only minimal impact on secure connectivity and resilience of the resulting sensor network.

关键词： sensor network key pre-distribution scheme combinatorial design rational normal curve projective space finite field

基于CRI算法的蕴涵算子族L-λ-R_0模糊系统的函数逼近性及概率表示

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四川师范大学学报（自然科学版） 2009年第6期32卷 746-750页

作者：彭家寅内江师范学院四川省高等学校数值仿真重点实验室四川内江641112 内江师范学院数学与信息科学学院四川内江641112

针对蕴涵算子族L-λ-R0,讨论了基于CRI算法的模糊系统的函数逼近的泛性及概率表示.首先证明了蕴涵算子族L-λ-R0模糊系统只具有阶跃输出能力,不具有函数逼近泛性;其次揭示了蕴涵算子族L-λ-R0模糊系统的概率意义,给出了其概率分布.

关键词：模糊系统蕴涵算子族L-λ-R0 CRI算法条件数学期望概率分布

Investigation of 'chazi'(damaged-enamels)on Chenghua doucai Porcelains

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science china(Technological sciences) 2009年第6期52卷 1722-1729页

作者： DU Feng1 & SU BaoRu2 1 Institute of Chemistry & Molecular Engineering,Qingdao university of science & Technology,Qingdao,china 2 college of information science & Technology,Qingdao university of science & Technology,Qingdao,china Institute of Chemistry & Molecular Engineering Qingdao University of Science & Technology Qingdao China college of information science & Technology Qingdao University of Science & Technology Qingdao China

At the end of the 1950s,Sun Yingzhou considered that the 'chazi'(damaged colour)on Chenghua doucai imperial porcelain as a defect was originally produced in firing process during Chenghua period(1465―1487).Researchers in china have accepted his *** any fragment with the 'chazi' has never been found in several tons of Chenghua imperial sherds excavated from Ming imperial kiln site in *** china,few scholars have questioned the formation of 'chazi',and further investigated *** researchers at the Research Laboratory in the British Museum,employing unde-structive EDXRF,have analyzed the chemical composition of the 'chazi'(damaged colour)on a Chen-ghua doucai stem cup in the museum,and they have confirmed that the 'chazi'(damaged colour)was caused by the fire of the Jianfu palace in the Forbidden City in *** on their research,the authors studied the colour chemical principle of the 'chazi's' formation *** to the ceramic technology principle,scientific reasoning for the 'chazi' was carried *** the help of the history of Qing court,the brainteaser of the 'chazi' was totally uncovered,the misunderstanding for the 'chazi' has also been *** research also suggests that employing modern science and technology is a direction to study Chinese ancient ceramic further.

关键词： Chenghua doucai porcelains court eunuchs the set on fire at the Jianfu palace ’chazi’(damaged-enamels) the British Museum colour chemical principle archaeology using science and technology