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Rank theorems of operators between Banach spaces

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Science china Mathematics 2000年第1期43卷 1-5页

作者： MA Jipudepartment of Mathematics, nanjing university, nanjing 210093, china 1. department of Mathematics Nanjing University 210093 Nanjing China

LetE andF be Banach spaces, andB(E,F) all of bounded linear operators onE intoF. LetT 0 ∈B( E,F) with an outer inverseT 0 # ∈B( F,E). Then a characteristic condition ofS=(I + T0 # (T-T0)-1 T0 # with T∈B(E, F) and ∥ T0 # (T - T0 ∥ < 1, being a generalized inverse ofT, is presented, and hence, a rank theorem of operators onE intoF is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.

关键词： rank theorem generalized inverse operator-value map.

Electrochemical Properties of Polypyrrole-Coated Microelectrode Array and the Fabrication of Polypyrrole-Based Microelectronic Devices

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Chemical Research in Chinese Universities 1995年第2期11卷 163-169页

作者： CAI Chen-xin,JU Huang-xian and CHEN Hong-yuan (department of chemistry,nanjing university,nanjing,210093) nanjing UNIV DEPT CHEMNANJING 210093PEOPLES R CHINA

Conducting polymers have been studied extensively. An interesting property of the conducting polymer is that the conductivity of some polymers, such as polypyrrolc, polyaniline, poly(3-methylthiophene) etc. , is affected by the voltage applied to them. For polypyrrole, the oxidized state is an electronic conductor and the reduced state is essentially insulating. Using this property, one can fabricate the polymer-based electronic devices. Experimental results of Pickun

关键词： Microelectrode Microeiectrode array Chemically modified electrode Polymer-based electronic devices Polypyrrole

One-step estimation for varying coefficient models

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Science china Mathematics 2005年第2期48卷 198-213页

作者： TANG Qingguo & WANG Jinde department of Mathematics, nanjing university, nanjing 210093, china Institute of Sciences, PLA university of Science and Technology, nanjing 210007, china 1. department of Mathematics Nanjing University 210093 Nanjing China 2. Institute of Sciences PLA University of Science and Technology 210007 Nanjing China

A one-step method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing two-step estimation method. It is shown that the one-step estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.

关键词： varying coefficient model, one-step estimation, asymptotic distribution, optimal convergence rate.

A New One-Pot Synthesis of Macroheterocycles Using Mannich Reaction

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Chinese Chemical Letters 1997年第10期8卷 845-846页

作者： Min Min YANG Jin Qi ZHANG Zhen SHEN (department of chemistry, nanjing university, nanjing 210093) nanjing UNIV DEPT CHEMNANJING 210093PEOPLES R CHINA

Three N,N-heterylmethyl derivates of diaza-18-crown-6(I) are readily prepared by the reaction of (I) with paraformaldehyde and heterocyclic compounds in dry benzene.

关键词： A New One-Pot Synthesis of Macroheterocycles Using Mannich Reaction

Relationship between bioaccumulation，distribution of MET and lipid content of aquatic organisms

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Journal of Environmental Sciences 1995年第2期7卷 212-217页

作者： Liu Zhengtao Zhou Fengfan Jin Hongjun(department of Environmental Sciences , nanjing university , nanjing 210093 , china) Dept of Envmtl Sciences Nanjing University Nanjing China China

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关键词： MET bioaccumulation distribution acute toxicity : lipid content.

Study on lithogeochemistry of Middle Jurassic basalts from southern china represented by the Fankeng basalts from Yongding of Fujian Province

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Science china Earth Sciences 2006年第10期49卷 1020-1031页

作者： ZHOU Jincheng1,2, JIANG Shaoyong1,2, WANG Xiaolei1,2, YANG Jinghong 1,2 & ZHANG Mengqun 3 1. State Key Laboratory of Mineral Deposit Research, nanjing university, nanjing 210093, china 2. department of Earth Sciences, nanjing university, nanjing 210093, china 3. Modern Analysis Center, nanjing university, nanjing 210093, china 1. State Key Laboratory of Mineral Deposit Research Nanjing University Nanjing 210093 China 2. department of Earth Sciences Nanjing University Nanjing 210093 China 3. Modern Analysis Center Nanjing University Nanjing 210093 China

There exists an E-W trending Middle Jurassic volcanic zone in southern china. The Fankeng basalts in the Yongding basin of Fujian Province are considered to be a typical example. The Fankeng basalts have TiO2 contents in the range of 1.92%-3.21%. They are classified as high-Ti basalts. They also have higher total Fe (averaging FeO* = 11.09%). The Middle Jurassic Fankeng basalts from southwestern Fujian have obvious distinctive lithogeochemical features from early Cre- taceous basalts from southeastern coast of china. They have higher HFSE, such as Th, Nb, Ta, Zr and Ti. Their element ratios related with HFSE, such as Zr/Ba, La/Nb, La/Ta ,Zr/Y, Ti/Y, Ba/Nb, K/Ti and Rb/Zr are similar to those of OIB. The most samples have ε Nd(T) of-0.70-0.24, which are near chondrite. Some samples have higher ε Nd(T) of ***, these basaltic magmas might be derived from depleted asthenospheric mantle. The lithogeochemical characteristics of the Fankeng basalts may be caused by interaction between asthenosphere and lithosphere at the time. The (Early-) Middle Jurassic basalts and gabbros from southeastern Hunan, southern Jiangxi and northern Guangdong provinces show similar geochemical features to those of the Fankeng basalts from the Yongding of Fujian. Occurrence of these OIB-type basalts in the area may be regarded as the petrological mark of upwelling of asthenosphere at the time. Upwelling of asthenosphere has led to tectonic extension and the formation of rifted basin in the area.

关键词： interaction between asthenosphere and lithosphere, lithogeochemistry, basalts, Middle Jurassic, southern china.

A local probability exponential inequality for the large deviation of an empirical process indexed by an unbounded class of functions and its application

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Science china Mathematics 2004年第6期47卷 821-830页

作者： ZHANG Dixindepartment of Finance, Business School, nanjing university, nanjing 210093, china 1. department of Finance Business School Nanjing University 210093 Nanjing China

A local probability exponential inequality for the tail of large deviation of an empirical process over an unbounded class of functions is proposed and studied. A new method of truncating the original probability space and a new symmetrization method are given. Using these methods, the local probability exponential inequalities for the tails of large deviations of empirical processes with non-i.i.d. independent samples over unbounded class of functions are established. Some applications of the inequalities are discussed. As an additional result of this paper, under the conditions of Kolmogorov theorem, the strong convergence results of Kolmogorov on sums of non-i.i.d. independent random variables are extended to the cases of empirical processes indexed by unbounded classes of functions, the local probability exponential inequalities and the laws of the logarithm for the empirical processes are obtained.

关键词： empirical process large deviation unbounded class of functions local probability exponential inequality

Depth zonation of Arenigian acritarchs in South china

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Chinese Science Bulletin 1997年第3期42卷 248-251页

作者： XU Wanhongdepartment of Earth Sciences, nanjing university, nanjing 210093, china department of Earth Sciences Nanjing University Nanjing China

STAPLIN revealed that palaeoenvironment changes seem to control acritarch distribution patterns. However, scientists have been puzzled by the fact that characteristic offshore acritarchs occur with nearshore ones. This note demonstrates depth zonation of Arenigian acritarchs in South china and reveals the variation of water depth in South china during the Arenig Age.

关键词： South china Arenigian acritarch depth zonation.

Galactic kinematics and structure defined by open clusters

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Research in Astronomy and Astrophysics 2009年第12期9卷 1285-1302页

作者： Zi Zhu department of Astronomy Nanjing University Nanjing 210093 China

On the basis of recently published astrophysical parameters of the open clusters, we have selected 301 clusters with measurements of their kinematical parameters to trace the local structure and kinematics of the Galactic disk. The present sample covers a range of over 3.0 kpc from the Sun and gives significant estimates of the disk structure and kinematical parameters of the Galaxy. We derive the disk scale height, vertical displacement of the Sun to the Galactic plane, solar motion with respect to the local standard of rest, circular speed of the Galactic rotation, Galactocentric distance from the Sun, etc. We found that the average scale height of the disk defined by the open clusters is Zh = 58 ± 4pc, with a vertical displacement of the Sun below the Galactic plane of z0 -= - 16±4 pc. Clusters with ages older than 50 Myr are less concentrated in the average plane （Zh=67 ±6pc） than the younger clusters （Zh = 51±5pc）. Using the approximation of axisymmetric circular rotation, we have derived the distance to the Galactic center from the Sun R0 = 8.03 ±0.70 kpc, which is in excellent agreement with the best estimate of the Galactocentric distance. From a kinematical analysis, we found an agedependent rotation of the Galaxy. The older clusters exhibit a lower velocity of vorticity, but have the same shear as the younger clusters. The mean rotation velocity of the Galaxy was obtained as 235 ± 10 km s-1.

关键词： Galaxy: disk -- Galaxy: kinematics and dynamics -- Galaxy: open clustersand associations: general -- Galaxy: structure