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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,{2., nanjing 2.0093, 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.

Lipschitz classes on local fields

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Science China mathematics 2007年第7期50卷 1005-1014页

作者： Wei-yi SU~(1+) Guo-xiang CHEN~2.1 department of mathematics,{2. university,{2. 2.0093,China 2.department of mathematics,{2. Audit university,{2. 2.1815,China 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Nanjing Audit University Nanjing 211815 China

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is ***,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and ***,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2.ln 3).

关键词： local field Holder type space Lipschitz class Cantor type fractal function 11F85 46F05 43A2. 2.A80 2.A78

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2. WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics,{2., nanjing 2.0093, China 2. department of mathematics, Henan university, Kaifeng 475001, China 3. department of Applied mathematics, Southeast university, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

Y_CΩ_(2.)are easy terms

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Chinese Science Bulletin 1998年第20期43卷 1707-1709页

作者： ZHAO Xishun 1 and WANG Ju 2.1. department of mathematics,{2., nanjing 2.0093, China 2. Institute of Software, Chinese Academy of Sciences, Beijing 100080, China department of mathematics Nanjing University Nanjing China Institute of Software Chinese Academy of Sciences Beijing China

For any natural number n≥1, Y CΩ 2. is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2. =M is consistent, where Y C is Curry fixed point combinator, Ω 2. ≡ω 2. ω 2. and ω 2. ≡λ***...x (there are 2. occurrences of x after λx ). This result is a partial solution to Jacopini’s conjecture: Y CΩ n is an easy term for any natural number n≥2.

关键词： λβ-calculus Kuper’s theorem easy term.

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 2.0093, China 2.{2. of Earth Sciences, nanjing university, nanjing 2.0093, China 3. Modern Analysis Center, nanjing university, nanjing 2.0093, 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.-3.2.%. 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-0.70-0.2., 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.

L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of mathematics,{2. Agricultural university,{2. 2.0095, China department of mathematics, nanjing university,{2. 2.0008, China) [a] department of mathematics Nanjing Agricultural University Nanjing China [b] department of mathematics Nanjing University Nanjing China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

A new sequential learning algorithm for RBF neural networks

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Science China(Technological Sciences) 2004年第4期47卷 447-460页

作者： YANG Ge1, LV Jianhong1 & LIU Zhiyuan2.1. department of Power Engineering, Southeast university,{2. 2.0096, China 2. department of Power Engineering,{2. Institute of Technology,{2. 2.0013, China 1. department of Power Engineering Southeast University 210096 Nanjing China 2. department of Power Engineering Nanjing Institute of Technology 210013 Nanjing China

Due to their inherent imperfections, it is hard to use the static neural networks for nonlinear time-varying process modeling and prediction, and the minimal resource allocation network (MRAN) is difficult to be realized for its too many regulation parameters. A new sequential learning algorithm for radial basis function (RBF) neural networks based on local projection named Local Projection Network (LPN) is proposed in this paper. The results of validation for several benchmark problems with the new algorithm show that the presented LPN not only has the same level as M-RAN in network size and precision of the outputs, but also has fewer regulation parameters and is more predictable.

关键词： radial basis functions, local projection network, minimal resource allocation network, learning algorithm.

Reducing component estimation for varying coefficient models with longitudinal data

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Science China mathematics 2008年第2期51卷 250-272页

作者： TANG QingGuo~(1,2.) WANG JinDe~2.1 Institute of Sciences,People’s Liberation Army university of Science and Technology,nanjing 2.0007,China 2.2. of mathematics,nanjing university,nanjing 2.0093,China 1. Institute of Sciences People’s Liberation Army University of Science and Technology Nanjing 210007 China 2. department of mathematics Nanjing University Nanjing 210093 China

Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical *** this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- *** asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are *** asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of *** sample properties of our procedures are studied through Monte Carlo simulations.

关键词： varying coefficient model longitudinal data nonparametric estimation reducing component estimators asymptotic normality 62.07

On the variational principle for the topological pressure for certain non-compact sets

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Science China mathematics 2010年第4期53卷 1117-1128页

作者： PEI Yu 1 & CHEN ErCai 1,2.1 department of mathematics,{2. Normal university,{2. 2.0097,China 2.Center for Nonlinear Science,{2. university,{2. 2.0093,China 1. department of mathematics Nanjing Normal University Nanjing 210097 China2. Center for Nonlinear Science Nanjing University Nanjing 210093 China

Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous *** assume that the dynamical system satisfies g-almost product property and the uniform separation *** compute the topological pressure of saturated sets under these two *** the uniform separation property does not hold,we compute the topological pressure of the set of generic *** give an application of these results to multifractal analysis and finally get a conditional variational principle.

关键词： uniform separation property g-almost product property topological pressure of non-compact sets variational principle BS-dinmension