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A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

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Acta Mathematica Scientia 2006年第2期26卷 193-201页

作者：刘秀贵 school of Mathematical Sciences and LMPC nankai university Tianjin 300071China

In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres ;π-6S which is represented by hngoγ^-3 ∈ Ext^6tA（Zp, Zp） in the Adams spectral sequence, where t = 2p^n（p- 1）＋ 6（p^2 ＋p ＋ 1）（p- 1） and p ≥ 7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s ＋ 6 in the stable homotopy groups of spheres πt1-8-6S which is represented by bygoγ^s＋3 ∈ Ext^s＋6＋t1Atl （Zp, Zp） in the Adams spectral sequence, where n≥ 4, 0 ≤ s 〈 p - 4, t1 = 2p^n（p- 1）＋ 2（p- 1）（（s ＋ 3）p^2 ＋（s ＋ 3）p ＋（s ＋ 3））＋ s.

关键词： Stable homotopy groups of spheres Adams spectral sequence Toda-Smith spectrum May spectral sequence

Twisted Product and Cohomology

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Acta Mathematica Sinica,English Series 1997年第1期13卷 76-80页

作者： Zheng Qibing (Department of Mathematics,nankai university,tianjin 300071,china) Department of Mathematics Nankai University Tianjin China

Let H be a Hopf algebra,H1 be a sub-Hopf algebra of H,H2 be the quotient Hopt algebra of H modular H1.This paper gives a simplified complex by defining a new base for the cobar complex and proves that the cobar comple... 详细信息

关键词： DGA Twisted product Hopf algebra The cohomology algebra of a coalgebra

Recent studies on chemistry of novel μ-CO-containing butterfly Fe/E (E=S,Se,Te) cluster salts

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Science china Chemistry 2009年第1期52卷 1-14页

作者： SONG LiCheng Department of Chemistry, State Key Laboratory of Elemento-Organic Chemistry, nankai university, tianjin 300071, china Department of Chemistry State Key Laboratory of Elemento-Organic Chemistry Nankai University Tianjin China

This article describes recent developments in chemical study on a series of butterfly-shaped μ-CO-containing Fe/E (E = S, Se, Te) cluster salts. These salts include eleven novel cluster anions, which are the single butterfly one μ-CO-containing [(μ-RE)(μ-CO)Fe2(CO)6]- (A), the double butterfly two μ-CO-containing {[(μ-CO)Fe2(CO)6]2(μ-EZE-μ)}2- (B, E = S; C, E = Se), the triple butterfly three μ-CO- containing {[(μ-CO)Fe2(CO)6]3[(μ-SCH2CH2)3N]}3- (D), {[(μ-CO)Fe2(CO)6]3[1,3,5-(μ-SCH2)3C6H3]}3- (E), {[(μ- CO)Fe2(CO)6]3[(μ-SCH2)3CMe]}3- (F), the double butterfly one μ-CO-containing {[(μ-CO)Fe2(CO)6] [Fe2(CO)6][(μ-SCH2)3CMe]} - (G) derived in situ from F, the quadruple butterfly four μ-CO-containing {[(μ- CO)Fe2(CO)6]4[1,2,4,5-(μ-SCH2)4C6H2]}4- (H), the triple butterfly two μ-CO-containing {[(μ-CO)Fe2(CO)6]2 [Fe2(CO)6][1,2,4,5-(μ-SCH2)4C6H2]}2- (I) derived in situ from H, the quadruple butterfly four μ-CO-con- taining {[(μ-CO)Fe2(CO)6]4[(μ-SCH2)4C]}4- (J), and the triple butterfly two μ-CO-containing {[(μ-CO)Fe2 (CO)6]2[Fe2(CO)6][(μ-SCH2)4C]}2- (K) derived in situ from J. This article describes not only the synthetic methods for formation of such anionic cluster (A-K) salts, but also their novel reactions leading to various new types of butterfly Fe/E cluster complexes. All these findings described in this article are important both theoretically and practically.

关键词： butterfly cluster synthesis structure reaction mechanism

SOME NEW FAMILIES OF FILTRATION FOUR IN THE STABLE HOMOTOPY OF SPHERES

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 93-102页

作者： LIN JINKUN(Department of Mathematics,nankai university,tianjin 300071,china E-mail:jklin@***) Department of Mathematics Nankai University Tianjin 300071 China

This paper proves the existence of 4 families of nontrivial homotopy elements in the stablehomotopy of spheres which are represented by in the ternis of the Adams spectral sequence respectively, where and are thekno... 详细信息

关键词： Stable homotopy of spheres Adams spectral sequence Derivations ofmaps M-module spectra

CRITERION FOR SL(2,Z)-MATRIX TO BE CONJUGATE TO ITS INVERSE

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 455-460页

作者： LONG YIMINGnankai Institute of Mathematics, nankai university, tianjin 300071, china. E-mail: longym@***. nankai Institute of Mathematics Nankai University Tianjin 300071 China

This paper gives a necessary and sufficient condition for a matrix in SL(2, Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of second degree. It yields an algorithm to determine this conjugation in finite steps based on the elementary number theory.

关键词： SL(2 Z) matrix Inverse Mixed stability

A Fibration of Categories over H_B

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Acta Mathematica Sinica,English Series 1997年第4期13卷 553-562页

作者： Chen Jixiang Department of Mathematics. nankai university, tianjin 300071, china Department of Mathematics Nankai University Tianjin China

K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split... 详细信息

关键词： Fibration of categories Track homotopy Adjoint functor

Lipschitz functions on Banach spaces which are actually on Asplund spaces

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Chinese Science Bulletin 1997年第24期42卷 2051-2054页

作者： CHENG Lixin Shi Shuzhongnankai Institute of Mathematics, nankai university, tianjin 300071, china nankai Institute of Mathematics Nankai University Tianjin China

SINCE Namioka and Phelps, starting with Asplund’s pioneering work, introduced the no-tion of Asplund spaces (those are Banach spaces on which every continuous convex function isFrechet differentiable on a dense G_δ subset) and proved that the dual of an Asplund space hasthe Radon-Nikodym property (RNP), the study of differentiability properties of functions oninfinite dimensional spaces has continued widely and deeply (see, for instance, Phelps andGiles). The research attained a great achievment after Stegall’s theorem: If the dualspace E~* has the RNP, then E is an Asplund space. Because of the N-Ph-S theorem, we

关键词： mathematics Lipschitz function Radon-Nikodym property subdifferential Banach space.

Photocatalytic decolourization of reactive dyes

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Journal of Environmental Sciences 1992年第1期4卷 97-105页

作者： You Daoxin, Xie Huasheng Dai ShuguiDepartment of Environmental Science, nankai university, tianjin 300071, china

The photocatalytic degradation of reactive dyes with solar-irradiated TiO2 was investigated in these experiments which showed that: (1)the decolourization efficiency are determined by pH value, catalyst amount and light intensity; (2) the reactive dyes decolourized rapidly (cleavageld be biologically degradated more easily, the toxicity decreased considerably after *** results demonstrated that the photocatalytic process would become an efficient and safe method for colour wastewater treatment and would be very useful for explaining the reaction mechanism and decolourising structure-reactivity relationship. of the azo linkage), but the intermediates needed more time to transform to further degradation products, and finally to produce CO2; (3) the main products were identified to be alkanes and alkyl amines which cou

关键词： reactive dyes photocatalytic degradation wastewater treatment.

On　the　H_∞　Control　for　Linear　Time-Delay　Systems

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Journal of Systems Engineering and Electronics 1998年第3期9卷 23-28页

作者： Chen Wanyi (College of Mathematics, nankai university, tianjin 300071, P. R. china ) College of Marhematics Nankai University Tianjin 300071 P. R. China

In this paper, we study the H∞ control of time-delay linear systems either with some　norm-bounded uncertainties or not with (for systems not in the scope of the nominal systems of the former ones). As linear time-delay systems are infinite dimensional in natural, some new sufficient conditions in Riccati equation form are offered, which extends current related results. We also point out a mistake appeared in a recently published paper.

关键词： Time-delay Uncertainty Stabilization Riccati equation