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An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of mathematics, university of Science and Technology of China, Hefei 230026, China 2. department of mathematics, beijing normal university, beijing 100875, China department of mathematics University of Science and Technology of China Hefei China department of mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of mathematics, Chinese Academy of Sciences, beijing 100080, China 2. department of mathematics, beijing normal university, beijing 100875, China Institute of mathematics Chinese Academy of Sciences Beijing China department of mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.

Direct Electrochemistry of Myoglobin in DDAB-Clay Composite Films

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Chinese Chemical Letters 2000年第1期11卷 79-80页

作者： Nai Fei HU Zhen LI Hong Yan MA (department of Chemistry, beijing normal university, beijing, 100875) department of Chemistry Beijing Normal University Beijing 100875 China

Ordered films were made by casting a mixture of aqueous dispersions of didodecyldimethylammonium bromide (DDAB)-clay composite and myoglobin (Mb) solution on pyrolytic graphite (PG) electrodes. The Mb-DDAB-clay film electrodes showed stable and reversible cyclic voltammetric responses in buffers and can catalyze the reduction of id (TCA).

关键词： myoglobin didodecyldimethylammonium bromide clay composite film electrode electrochemistry electrocatalysis

The information entropy of a static dilaton black hole

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Science China(Physics,Mechanics & Astronomy) 2008年第2期51卷 113-125页

作者： LIU chengZhou Institute of Theoretical Physics, Binzhou university, Binzhou 256600, China department of Physics, beijing {4. university, beijing 100875, China Institute of Theoretical Physics Binzhou University Binzhou China department of Physics Beijing Normal University Beijing China

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

关键词： black hole entropy holographic principle non-commutative quantum field theory event horizon loop quantum gravity

The localization of 1-cohomology of transitive Lie algebroids

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Science China mathematics 2006年第2期49卷 277-288页

作者： chen Zhuo & LIU Zhangju department of mathematics, Capital normal {4., beijing 100037, China School of Mathematical Science, Peking {4., beijing 100871, China department of mathematics Capital Normal University Beijing China School of Mathematical Science Peking University Beijing China

For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases.

关键词： transitive Lie algebroid representation cohomology localization.

The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 663-674页

作者： Yong-ping Liu, Gui-qiao Xudepartment of mathematics, beijing normal {4., beijing 100875, China department of mathematics, Tianjin normal Univesity, Tianjin 300074. China department of mathematics Beijing Normal University Beijing China department of mathematics Tianjin Normal Univesity Tianjin China

The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the correspondi... 详细信息

关键词： Multivariate function classes average width non-linear width

Formation of 3-Arylpyrazolines and 1-Aroylethyl-3-arylpyrazolines via 3-Aroylethylsydnone with HCl in Ethyl Acetate

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Chinese Chemical Letters 1998年第9期9卷 803-804页

作者： Zhan Bin ZHANG cheng Lie YIN Yong Ren WU (department of Chemistry, beijing normal {4., beijing 100875) department of Chemistry Beijing Normal University Beijing 100875 China

Treatment of 3-aroylethylsydnone 1 with HCl leads to 3-arylpyrazoline 2 or 1-aroylethyl-3-arylpyrazoline 3 under different conditions.

关键词： sydnone pyrazoline hydrolysis

Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces

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Acta Mathematica Sinica,English Series 1998年第1期14卷 67-76页

作者： Li Xiaochun Lu Shanzhen department of mathematics, beijing normal {4., beijing 100875, China

Let 01, w2 ∈A1 （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqα,p（w1; w2） to the homogeneous weighted Herz spaces Kqα,p（w1;w2）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqα,p（w1, w2） is also investigated.

关键词： Strongly singular convolution operator Hardy space

The studies on neurogenesis induced by brain injury inadult ring dove

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Cell Research 1998年第2期8卷 151-158页

作者： ZUO MING XUE(Biology department, beijing normal university, beijing100875, China) Biology department Beijing Normal University Beijing China

It was the first time demonstrated by us that the number of newborn neurons was increajsed after making lesion in forebraill of adult ring dove (Streptopelia risoria)by means of autoradiography and *** in the adult avian is restricted to the telencephalon. In doves with bilateral electrolytic lesion of nucleus ectostriatum (E), the mean number of proliferating cells in the lateral ventricular zone (LVZ) and newborn neurons in the forebrain increased by 1.95 times and 2.38times respectively as compared with that in intact doves. The most relllarkable increase of neurogenesis induced by nucleus ectostriatum lesions was found at the anteriorposterior level 3 (L3), where the lesion site was *** results showed that the electrolytic brain lesion altered the distribution pattern of proliferating cells in theLVZ and resulted in increase of the number of newborn neurons in the non-VZ areas of forebrain. The changes in number and distribution pattern of proliferating cells in LVZ and newborn neurons in forebrain may be dependent on site of lesion. Studies on the relationship between proliferating cells in LVZ and newly generated neurons in non-VZ areas may help to understand the mechanism of brain plasticity and development.

关键词： Autoradiography neurogenesis brain lesion ring dove