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(1.2)INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 57-62页

作者： MA JIPU(Department of Mathematics,nanjing university,nanjing 210093,china) Department of Mathematics Nanjing University Nanjing 210093 China

Let E and F be Banach spaces and f non-linear C1 map from E into F. The main result isTheorem 2.2, in which a connection between local conjugacy problem of f at x0E and a localfine property of f'(x) at x0(see the Definition 1.1 in this paper) are obtained. This theoremincludes as special cases the two known theorems: the finite rank theorem and Berger's Theoremfor non-linear Fredholm operators. Moreover, the thcorem gives rise the further results for somenon-linear semi-Fredholm maps and for all non-linear semi-Wedholm maps when E and F areHilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but alsoreally generalizes them.

关键词： Nonlinear semi-Fredholm maps Conjugacy problem Banach space

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 Department of Mathematics Nanjing University 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.

Study on the thermal stability and electrical properties of the high-k dielectrics (ZrO_2) _x(SiO_2)_(1-x)

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Science china(Technological Sciences) 2009年第8期52卷 2222-2226页

作者： Lü ShiCheng1,2, YIN Jiang1,2, XIA YiDong2,3, GAO LiGang2,3 & LIU ZhiGuo2,3 1 Department of Physics, nanjing university, nanjing 210093, china 2 National Laboratory of Solid Sate Microstructures, nanjing university, nanjing 210093, china 3 Department of Materials Science and Engineering, nanjing university, nanjing 210093, china Department of Physics Nanjing University Nanjing China National Laboratory of Solid Sate Microstructures Nanjing University Nanjing China Department of Materials Science and Engineering Nanjing University Nanjing China

(ZrO2)x(SiO2)1-x (Zr-Si-O) films with different compositions were deposited on p-Si(100) substrates by using pulsed laser deposition technique. X-ray photoelectron spectra (XPS) showed that these films remained amorphous after annealing at 800℃ with RTA process in N2 for 60 s. The XPS spectra indi- cated that Zr-Si-O films with x=0.5 suffered no obvious phase separation after annealing at 800℃, and no interface layer was formed between Zr-Si-O film and Si substrate. While Zr-Si-O films with x >0.5 suffered phase separation to precipitate ZrO2 after annealing under the same condition, and SiO2 was formed at the interface. To get a good interface between Zr-Si-O films and Si substrate, Zr-Si-O films with bi-layer structure (ZrO2)0.7(SiO2)0.3/(ZrO2)0.5(SiO2)0.5/Si was deposited. The electrical properties showed that the bi-layer Zr-Si-O film is of the lowest equivalent oxide thickness and good interface with Si substrate.

关键词： high-k dielectric film pulsed laser deposition pseudo ternary alloy

EIT waves and coronal magnetic field diagnostics

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Science china(Physics,Mechanics & Astronomy) 2009年第11期52卷 1785-1789页

作者： CHEN PengFei Department of Astronomy, nanjing university, nanjing 210093, china Department of Astronomy Nanjing University Nanjing China

Magnetic field in the solar lower atmosphere can be measured by the use of the Zeeman and Hanle effects. By contrast, the coronal magnetic field well above the solar surface, which directly controls various eruptive phenomena, can not be precisely measured with the traditional techniques. Several attempts are being made to probe the coronal magnetic field, such as force-free extrapolation based on the photospheric magnetograms, gyroresonance radio emissions, and coronal seismology based on MHD waves in the corona. Compared to the waves trapped in the localized coronal loops, EIT waves are the only global-scale wave phenomenon, and thus are the ideal tool for the coronal global seismology. In this paper, we review the observations and modelings of EIT waves, and illustrate how they can be applied to probe the global magnetic field in the corona.

关键词： coronal mass ejections (CMEs) magnetic field diagnostics magnetohydrodynamics (MHD)

Regular n-simplices in R^n with vertices in Z^(n)

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Science china Mathematics 2004年第1期47卷 104-113页

作者： XIA Jianguo & QIN HourongDepartment of Mathematics, nanjing Normal university, nanjing 210097, china (email: jgxia@***) Department of Mathematics, nanjing university, nanjing 210093, china Dept. of Math. Nanjing Normal Univ. Nanjing 210097 China Dept. of Math. Nanjing Univ. Nanjing 210093 China

In this paper the Ⅰ and Ⅱ regular n-simplices are introduced. We prove that the sufficient and necessary conditions for existence of an Ⅰ regular n-simplex in Rn are that if n is even then n = 4m(m + 1), and if n is odd then n = 4m + 1 with that n + 1 can be expressed as a sum of two integral squares or n = 4m - 1, and that the sufficient and necessary condition for existence of a Ⅱ regular n-simplex in Rn is n = 2m2 - 1 or n = 4m(m+1)(m 6 N). The connection between regulars-simplex in Rn and combinational design is given.

关键词： regular n-simplex in Rn, quadratic form.

Measures and dimensions of fractal sets in local fields

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Progress in Natural Science:Materials International 2006年第12期16卷 1260-1268页

作者： QIU Hua** and SU Weiyi(Department of Mathematics, nanjing university, nanjing 210093, china) Department of Mathematics Nanjing University Nanjing 210093 China

The study of fractal analysis over the local fields as underline spaces is very important since it can motivate new approaches and new ideas, and discover new techniques in the study of fractals. To study fractal sets in a local field K, in this paper, we define several kinds of fractal measures and dimensions of subsets in K. Some typical fractal sets in K are constructed. We also give out the Hausdorff dimensions and measures, Box-counting dimensions and Packing dimensions, and stress that there exist differences between fractal analysis on local fields and Euclidean spaces. Consequently, the theoretical foundation of fractal analysis on local fields is established.

关键词： local field p-series field Hausdorff measure and dimension Boxcounting dimension Packing measure and dimension Cantor type set.

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 Department of Finance Business School Nanjing University 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

On critical values concerning the evolution of the long period families

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Chinese Journal of Astronomy and Astrophysics 2009年第4期9卷 494-500页

作者： Xi-Yun Hou1,21 Astronomy Department, nanjing university, nanjing 210093, china 2 Institute of Space Environment and Astronautics, nanjing university, nanjing 210093, china Astronomy Department Nanjing University Nanjing 210093 China Institute of Space Environment and Astronautics Nanjing University Nanjing 210093 China

In a previous paper, we proposed another special critical value concerning the evolution of the long period family around the equilateral equilibrium points, besides the two values given by Henrard. Are there any other special critical values？ After studying the stability curves of the long period family carefully, we gave a negative answer. During the study, we found an interesting family of periodic orbits which we called the homo family. We studied the evolution of this family following the increase of μ. With these findings, we were able to explain the origin of the four branches of periodic families emanating from L4 and the stability results of the equilateral equilibrium points.

关键词： celestial mechanics

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.