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• Author or Editor: Ji Gao
Clear All Modify Search  # Normal structure and Pythagorean approach in Banach spaces

Author: Ji Gao

## Summary

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $X$ \end{document} be a real Banach space and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S(X) = \{x \in X: \|x\| = 1\}$ \end{document} be the unit sphere of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $X$ \end{document}. The parameters \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $E_{\epsilon}(X)=\sup\{\alpha_{\epsilon}(x): x \in S(X)\}$ \end{document}, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $e_{\epsilon}(X)=\inf\{\alpha_{\epsilon}(x): x \in S(X)\}$ \end{document}, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $F_{\epsilon}(X)=\sup\{\beta_{\epsilon}(x): x \in S(X)\}$ \end{document}, and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $f_{\epsilon}(X)=\inf\{\beta_{\epsilon}(x): x \in S(X)\}$ \end{document}, where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\alpha_{\epsilon}(x) = \sup\{\| x + \epsilon y \|^{2}+ \| x - \epsilon y \|^{2}: y \in S(X)\}$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\beta_{\epsilon}(x) = \inf\{\| x + \epsilon y \|^{2}+ \| x - \epsilon y \|^{2}: y \in S(X)\}$ \end{document}, are defined and studied. The main result is that a Banach space \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $X$ \end{document} with \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $E_{\epsilon}(X) < 2 + 2\epsilon +\frac{1}{2}\epsilon^{2}$ \end{document} for some \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $0\leq \epsilon \leq 1$ \end{document} has uniform normal structure.

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# The permutation of integers with small least common multiple of two subsequent terms

Authors: Yong-Gao Chen and Cheng-Shuang Ji

## Abstract

Erdős, Freud and Hegyvári  constructed a permutation a 1,a 2,… of positive integers with for an absolute constant c>0 and all i≧3. In this note, we construct a permutation of all positive integers such that for any >0 there exists an i 0 with for all ii 0.

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# The Enthalpy of Solution in Water of Complexes of Zinc with Methionine

Authors: M. Ji, Sh. Gao and Q. Shi

## Abstract

The enthalpies of solution in water of L- -methionine and its zinc complexes Zn(Met)Cl2, Zn(Met)2Cl2·2H2O, Zn(Met)(NO3)2·1/2H2O, Zn(Met)3(NO3)2·H2O and Zn(Met)SO4·H2O have been measured at 298.15 K. The standard enthalpy of formation of met(aq) has been calculated. The experimental results have been discussed.

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# Thermal Behaviour of RE(His)(NO3)3⋅H2O

Authors: M. Ji, J. Liu, S. Gao, R. Hu and Q. Shi

## Abstract

The thermal decomposition behaviour of the complexes of rare earth metals with histidine: RE(His)(NO3)3 H2O (RE=La—Nd, Sm—Lu and Y; His=histidine) was investigated by means of TG-DTG techniques. The results indicated that the thermal decomposition processes of the complexes can be divided into three steps. The first step is the loss of crystal water molecules or part of the histidine molecules from the complexes. The second step is the formation of alkaline salts or mixtures of nitrates with alkaline salts after the histidine has been completely lost from the complexes. The third step is the formation of oxides or mixtures of oxides with alkaline salts. The results relating to the three steps indicate that the stabilities of the complexes increase from La to Lu.

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# Hybrid documents co-citation analysis: making sense of the interaction between science and technology in technology diffusion

Authors: Ji-ping Gao, Kun Ding, Li Teng and Jie Pang

## Abstract

The paper presents a methodology called hybrid documents co-citation analysis, for studying the interaction between science and technology in technology diffusion. Our approach rests mostly on patent citation, cluster analysis and network analysis. More specifically, with the patents citing Smalley RE in Derwent innovations index as the data sets, the paper implemented hybrid documents co-citation network through two procedures. Then spectrum cluster algorithm was used to reveal the knowledge structure in technology diffusion. After that, with the concordance between network properties and technology diffusion mechanisms, three indicators containing degree, betweenness and citation half-life, were calculated to discuss the basic documents in the pivotal position during the technology diffusion. At last, the paper summarized the hybrid documents co-citation analysis in practise, thus concluded that science and technology undertook different functions and acted dominatingly in the different period of technology diffusion, though they were co-activity all the time.

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# A co-word analysis of digital library field in China

Authors: Gao-Yong Liu, Ji-Ming Hu and Hui-Ling Wang

## Abstract

The aim of this study is to map the intellectual structure of digital library (DL) field in China during the period of 2002–2011. Co-word analysis was employed to reveal the patterns of DL field in China through measuring the association strength of keywords in relevant journals. Data was collected from Chinese Journal Full-Text Database during the period of 2002–2011. And then, the co-occurrence matrix of keywords was analyzed by the methods of multivariate statistical analysis and social network analysis. The results mainly include five parts: seven clusters of keywords, a two-dimensional map, the density and centrality of clusters, a strategic diagram, and a relation network. The results show that there are some hot research topics and marginal topics in DL field in China, but the research topics are relatively decentralized compared with the international studies.

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# Thermal Behaviour of the Complexes of Zinc Amino Acids

Authors: J. Liu, Y. Hou, S. Gao, M. Ji, R. Hu and Q. Shi

## Abstract

The eight solid complexes of zinc with L- -methionine or L- -histidine were prepared. The thermal decomposition processes of these complexes were determined by means of TG-DTG. The results show that their decomposition processes can be divided into three steps except for the complex Zn(Met)2 the decomposition of which is completed in one step. All the final products are ZnO.

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# The Enthalpy of Solution in Water of Histidine Complexes of Re Nitrates

Authors: M. Ji, J. Liu, S. Gao, B. Kang, R. Hu and Q. Shi

## Abstract

The enthalpies of solution in water of RE(His)(NO3)3 H2O (RE=La—Nd, Sm—Lu, Y) were measured calorimetrically at 298.15 K, and the standard enthalpies of formation of RE(His)aq 3+ (RE=La—Nd, Sm—Lu, Y) were calculated. The plot of the enthalpies of solution vs. the atomic numbers of the elements in the lanthanide series exhibits the tetrad effect .

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# A journal co-citation analysis of library and information science in China

Authors: Chang-Ping Hu, Ji-Ming Hu, Yan Gao and Yao-Kun Zhang

## Abstract

This paper aims to reveal the relationship and structure of library and information science (LIS) journals in China. 24 core LIS journals in China are selected and the relevant data of journal co-citation are retrieved from Chinese Journal Full-Text Database constructed by China National Knowledge Infrastructure during the period of 1999–2009. By calculating mean co-citation frequencies and correlation coefficients, we find that there is a strong relationship among LIS journals in China. Utilizing the methods of cluster analysis, multidimensional scaling analysis and factor analysis, we analyze the data of journal co-citation. LIS journals in China are divided into four clusters. The relatedness among journals is shown manifestly through their locations in the two-dimensional map. A three-factor solution is obtained with the factor loading of each journal. Finally, we interpret and discuss the results to get some conclusions and also expect to describe the network characters of journal co-citation in future research.

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# Exploring antibiotic resistant mechanism by microcalorimetry

## Determination of thermokinetic parameters of metallo-β-lactamase L1 catalyzing penicillin G hydrolysis

Authors: Hui-Zhou Gao, Qi Yang, Xiao-Yan Yan, Zhu-Jun Wang, Ji-Li Feng, Xia Yang, Sheng-Li Gao, Lei Feng, Xu Cheng, Chao Jia and Ke-Wu Yang

## Abstract

In an effort to probe the reaction of antibiotic hydrolysis catalyzed by B3 metallo-β-lactamase (MβL), the thermodynamic parameters of penicillin G hydrolysis catalyzed by MβL L1 from Stenotrophomonas maltophilia were determined by microcalorimetric method. The values of activation free energy ΔG θ are 88.26, 89.44, 90.49, and 91.57 kJ mol−1 at 293.15, 298.15, 303.15, and 308.15 K, respectively, activation enthalpy ΔH θ is 24.02 kJ mol−1, activation entropy ΔS θ is −219.2511 J mol−1 K−1, apparent activation energy E is 26.5183 kJ mol−1, and the reaction order is 1.0. The thermodynamic parameters reveal that the penicillin G hydrolysis catalyzed by MβL L1 is an exothermic and spontaneous reaction.

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