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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.

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, Beijing 100871, china) Beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

Study on impurity desorption induced by femtosecond pulse laser based on a stochastic process model

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Science china(Technological Sciences) 2006年第1期49卷 78-88页

作者： CHI Yinsheng1, LIN Xiaohui1, ZHUANG Ping1 & CHEN Yunfei1,2 1. department of Mechanical Engineering, southeast university, nanjing 210096, china 2. Key Laboratory of MEMS of china Educational Ministry, southeast university, nanjing 210096, china department of Mechanical Engineering Southeast University Nanjing 210096 China Key Laboratory of MEMS of china Educational Ministry Southeast University Nanjing 210096 China

With the advantages on non-equilibrium heating and desorption induced by electronic transition, the femtosecond pulse laser introduces a new way for solving the problem of impurity pollution adsorbed on a solid thin film in micro-electro-mechanical systems (MEMS). A model based on stochastic processes was established for stimulated desorption induced by the femtosecond pulse laser to interpret the interaction of the opti-cally excited hot electrons with the adsorbed molecules in a metal substrate. Numerical simulation results reveal a time-dependent desorption probability of adsorbed molecules and indicate that how key parameters of femtosecond pulse laser, such as incident laser energy flux, pulse duration, and wavelength of pulse, have a great effect on the desorption probability.

关键词： desorption, femtosecond pulse laser, stochastic process.

A predict-correct projection method for monotone variant variational inequalities

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Chinese Science Bulletin 1998年第15期43卷 1264-1267页

作者： HAN Qiaoming 1 and HE Bingsheng 2 1. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, china 2. department of mathematics, nanjing university, nanjing 210093, china Institute of Applied mathematics Chinese Academy of Sciences Beijing China department of mathematics Nanjing University Nanjing China

A predict_correct projection method is presented for solving monotone variant variational inequalities, which could exploit the advantages and overcome the difficulties of both explicit and implicit projection methods.

关键词： variant variational inequality explicit projection method implicit projection method predict_correct projection method.

On generalized k-syzygy modules

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Science china mathematics 2007年第5期50卷 675-682页

作者： Chong-hui HUANG & Zhao-yong HUANG department of mathematics, nanjing university, nanjing 210093, china College of mathematics and Physics, Nanhua university, Hengyang 421001, china department of mathematics Nanjing University Nanjing China College of mathematics and Physics Nanhua University Hengyang China

In this paper, we first introduce the notion of generalized k-syzygy modules, and then give an equivalent characterization that the class of generalized k-syzygy modules coincides with that ofω-k-torsionfree modules. We further study the extension closure of the category consisting of generalized k-syzygy modules. Some known results are obtained as corollaries.

关键词： generalized k-syzygy module ω-k-torsionfree module extension closure

Duality theorem for weak L-R smash products

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Applied mathematics(A Journal of Chinese Universities) 2010年第4期25卷 481-488页

作者： ZHOU Xiao-yan LI Qiang ZHANG Liang-yun department of mathematics, nanjing Agricultural university, nanjing 210095, china department of mathematics Nanjing Agricultural University Nanjing China

This paper gives a duality theorem for weak L-R smash products, which extends the duality theorem for weak smash products given by Nikshych.

关键词： Weak Hopf algebras weak L-R smash products duality theorem.

Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1 and DAI Yonglong 2 1. department of mathematics, Shanghai university, Shanghai 201800, china 2. department of mathematics, Zhongshan university, Guangzhou 510275, china department of mathematics Shanghai University Shanghai China department of mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

Existence of Invariant Tori for Certain Weakly Reversible Mappings

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Acta Mathematica Sinica,English Series 2002年第4期18卷 701-718页

作者： Bao She WEI department of mathematics, nanjing university. nanjing 210093. P. R. china department of mathematics Nanjing University Nanjing 210093 P. R. China

In this paper, we consider certain mappings. M, sufficiently close to an integrable one, which is weakly reversible with respect to the mappings G sufficiently close to an involution of type (m.n). where m, n∈Z_+ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for proving the existence of a Cantor family of m-tori invariant under the reversible mappings M and the reversing mapping G.

关键词： Weakly reversible mappings Weakly undegenerate condition Invariant tori

Perturbations of the radical of nest algebras

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Chinese Science Bulletin 1998年第7期43卷 556-560页

作者： LU Fangyan 1 and LU Shijie 2 1. department of mathematics, Suzhou university, Suzhou 215006, china 2. department of mathematics, Zhejiang university, Hangzhou 310027, china department of mathematics Suzhou University Suzhou China department of mathematics Zhejiang University Hangzhou China

Let R N and K-N be the radical ideal and the compact operator ideal of nest algebra T(N) respectively. It is proved thatR-N+K-N=span{T∈T(N)∶TT(N)NCT}=span{T∈T(N): #σ′(ST)≤1, S∈T(N)}.

关键词： nest algebras radical perturbation.