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On the diophantine equation X^2.(1+a^2.Y^4.=-2.

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science China mathematics 2010年第8期53卷 2143-2158页

作者： YUAN PingZhi 1 & ZHANG ZhongFeng 2.1 school of mathematics,South China Normal{2.,guangzhou 510631,China 2.school of mathematics & Computational science,Sun Yat-Sen{2.,guangzhou 5102.5,China school of mathematics South China Normal University Guangzhou China school of mathematics & Computational{2. Sun Yat-Sen University Guangzhou China

Let a≥1 be an *** this paper,we will prove the equation in the title has at most three positive integer solutions.

关键词： algebraic approximations continued fractions elliptic curves quartic equations

Transport network and flow mechanism of shallow ore-bearing magma in Tongling ore cluster area

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science China Earth sciences 2006年第4期49卷 397-407页

作者： DENG Jun1,2. WANG Qingfei1,2., HUANG Dinghua3 , WAN Li4. YANG Liqiang1,2.& GAO Bangfei1,2.1. State Key Laboratory of Geological Processes and Mineral Resources, China university of Geo{2.s, Beijing 100083, China 2. Key Laboratory of Lithosphere Tectonics and Lithoprobing Technology of Ministry of Education, China university of Geo- {2.s, Beijing 100083, China 3. Faculty of Earth {2.s, China university of Geo{2.s, Wuhan 4.0074. China 4. school of {12. and Information {2., guangzhou university, guangzhou 5104.5, China State Key Laboratory of Geological Processes and Mineral Resources China University of Geosciences Beijing China Key Laboratory of Lithosphere Tectonics and Lithoprobing Technology of Ministry of Education China University of Geosciences Beijing China Faculty of Earth sciences China University of Geosciences Wuhan China school of mathematics and Information{2. Guangzhou University Guangzhou China

Abundant studies revealed that shallow intrusions of the Yanshanian epoch resulted in the mass mineralization of the Tongling region. Various evidences showed there existed a concealed magma chamber at ?10 km depth in the middle part of this region during Yanshanian epoch, from which the ore-forming magma was generated and then transported to the superficial layer. Yet the transport network and flow mechanism of the shallow ore-bearing magma, the key problem associ- ated with ore-forming process, was relatively little focused on. Integrate analysis of structural me- chanics, statistical fractal and geological facts suggested that NE trending high-angle fold-related thrust faults and the tessellated basement ones served as the main pathways for the shallow magma’s transporting, moreover, the saddle void spaces among adjacent strata in the folds upon this fault system provided the place for magma’s emplacement. So the folds in the upper part and faults in the lower part of the upper crust constituted the fluid’s transport and emplacement network. During the deformation of geologic body with multi-layer structure, the layers in the upper part tended to fold when received the jacking stress from the lower part, while the lower one inclined to fault undergoing loads of the upper part. And the producing probability of this structure assemblage was highly in- creased in the condition, such as in the Tongling area, that the mechanic rigidity of the lower layers was stronger than that of the upper ones. For the pre-existence of fluid-conducting network, the top magma with high volatile in the magma chamber transported rapidly to the superficial layer in dyking pattern, located in the void spaces of folds, filled and reconstructed them. The sudden drop of pres- sure caused the fluid unmixing from the magma and mass ore-forming elements concentration. Pulse activity of the dyking may be the principal reason why magmatic bodies in the Tongling area were spatially-temporally con

关键词： Tongling, structural network, magma intrusion, fractal, dyke.

A distribution space for Hilbert transform and its applications

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science China mathematics 2008年第12期51卷 2217-2230页

作者： YANG LiHua school of mathematics and Computing{2., Sun Yat-Sen university, {4. 5102.5, China school of mathematics and Computing{2. Sun Yat-Sen University Guangzhou China

In this paper, a new distribution space is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that is the biggest subspace of on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for L p functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space are given and a class of useful nonlinear phase signals is shown to be in . Finally, the applications of the extended Hilbert transform are discussed.

关键词： Hilbert transform distribution time-frequency analysis 4.A15 4.F12

Construction of Boolean functions with maximum algebraic immunity and count of their annihilators at lowest degree

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science China(Information sciences) 2010年第4期53卷 780-787页

作者： DU YuSong* & PEI DingYi school of mathematics and Information{2.s, guangzhou university, {4. 510006, China school of mathematics and Information{2.s Guangzhou University Guangzhou China

Boolean functions used in stream ciphers against algebraic attacks are required to have a necessary cryptographic property-high algebraic immunity (AI). In this paper, Boolean functions of even variables with the maximum AI are investigated. The number of independent annihilators at the lowest degree of Boolean functions of even variables with the maximum AI is determined. It is shown that when n is even, one can get an (n + 1)-variable Boolean function with the maximum AI from two n-variable Boolean functions with the maximum AI only if the Hamming weights of the two functions satisfy the given conditions. The nonlinearity of the Boolean functions obtained in this way is computed. Similarly, one can get an (n + 2.-variable Boolean function with the maximum AI from four n-variable Boolean functions with the maximum AI. The nonlinearity of a class of Boolean functions with the maximum AI is determined such that their Hamming weights are either the maximum or the minimum.

关键词： Boolean function algebraic attack algebraic immunity annihilator nonlinearity

Secure multi-party computation protocol for sequencing problem

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science China(Information sciences) 2011年第8期54卷 1654-1662页

作者： TANG ChunMing 1,2.SHI GuiHua 1 & YAO ZhengAn 3 1 school of mathematics and Information{2.,guangzhou {4.,guangzhou 510006, China 2.tate Key Laboratory of Information Security, Institute of Software{2.,Chinese Academy of{2.s,Beijing 100080,China 3 school of mathematics and Computational{2.,Sun Yat-Sen {4.,guangzhou 5102.5,China school of mathematics and Information{2. Guangzhou University Guangzhou China State Key Laboratory of Information Security Institute of Software Science Chinese Academy of Sciences Beijing China school of mathematics and Computational{2. Sun Yat-Sen University Guangzhou China

In the field of multi-party computation,an important problem is how to construct an efficient and secure multi-party computation protocol for certain specific *** the present study,we make use of a secret sharing scheme to construct an efficient and secure multi-party computation protocol for sequencing *** protocols are perfectly secure against both a passive adversary that can corrupt at most t (n-1)/2.participants, and an active adversary that can corrupt at most t < n/3 *** simplest sequencing problem is the Millionaires' problem.

关键词： secure multi-party computation sequencing problem secret sharing

Atomic Force Microscopy-based Cell Nanostructure for Ligand-conjugated Quantum Dot Endocytosis

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Acta Biochimica et Biophysica Sinica 2006年第9期38卷 646-652页

作者： Yun-Long PAN~1* Ji-Ye CAI~2.Li QIN~3 Hao WANG~4. 1 The First Affiliated Hospital of Jinan university,{2. 510632.China 2.College of Life {2. and Technology,Jinan university,{2. 510632.China 3 Department of Histology and Embryology,Medical College of Jinan university,{2. 510632.China 4.Information and Optoelectronic {2. and Engineering.South China Normal university,{2. 510631,China The First Affiliated Hospital of Jinan universityguangzhou 510632 China College of Life science and Technology Jinan UniversityGuangzhou 510632 China Department of Histology and Embryology Medical College of Jinan UniversityGuangzhou 510632 China school for Information and Optoelectronic science and Engineering South China Normal UniversityGuangzhou 510631 China

While it has been well demonstrated that quantum dots (QDs) play an important role inbiological labeling both in vitro and in vivo,there is no report describing the cellular nanostructure basis ofreceptor-mediated ***,nanostructure evolution responses to the endocytosis of transferrin(Tf)-conjugated QDs were characterized by atomic force microscopy (AFM).AFM-based nanostructureanalysis demonstrated that the Tf-conjugated QDs were specifically and tightly bound to the cell receptorsand the nanostructure evolution is highly correlated with the cell membrane receptor-mediated ***,confocal microscopic and flow cytometry results have demonstrated the specificity anddynamic property of Tf-QD binding and *** found that the internalization of Tf-QD is linearlyrelated to ***,while the nanoparticles on the cell membrane increased,the endocytosis was stillvery active,suggesting that QD nanoparticles did not interfere sterically with the binding and function ***,ligand-conjugated QDs are potentially useful in biological labeling of cells at a nanometerscale.

关键词： quantum dot endocytosis nanostructure atomic force microscopy

On a problem of Skiba from the Kourovka Notebook

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science China mathematics 2004年第1期47卷 96-103页

作者： WANG Yanming & WEI HuaquanLingnan College and school of mathematics, Zhongshan{2., guangzhou 5102.5, China school of mathematics, Zhongshan{2., guangzhou 5102.5, China Department of mathematics, Guangxi Teacher’s College, Nanning 530001, China Lingnan College and school of mathematics Zhongshan University Guangzhou China school of mathematics Zhongshan University Guangzhou China Department of mathematics Guangxi Teacher’s College Nanning China

In this paper, we give a positive answer to a recent open problem of Skiba in Kourovka Notebook without using the odd order theorem and other deep theorems. Some of the techniques are improved.

关键词： supersolvable group c-supple merited subgroup complemented subgroup generalized fitting subgroup saturated formation

Periodic solutions of a 2.th-order nonlinear difference equation

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science China mathematics 2010年第1期53卷 41-50页

作者： ZHOU Zhan 1, YU JianShe 1 & CHEN YuMing 2. school of mathematics and Information{2., guangzhou university, {4. 510006, China 2.Department of mathematics, Wilfrid Laurier university, Waterloo N2. 3C5, Canada school of mathematics and Information{2. Guangzhou University Guangzhou China Department of mathematics Wilfrid Laurier University Waterloo Canada

In this paper, a 2.nth-order nonlinear difference equation is *** the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic *** obtained complement or ... 详细信息

关键词： periodic solution nonlinear difference equation critical point theory

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2.1. Department of mathematics, Hangzhou Normal university, Hangzhou 310036, China 2. Department of Applied mathematics, school of Mathematical {4.s, South China university of Technology, guangzhou 51064., China) Department of mathematics Hangzhou Normal University Hangzhou 310036 China Department of Applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.