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    25 January 2013, Volume 2013 Issue 1 Previous Issue    Next Issue
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    Sufficient and necessary condition for the chromatic equivalence of a class of graphs
    MA Hai-cheng, LI Sheng-gang
    2013, 2013 (1):  1-6. 
    Abstract ( 7969 )   PDF (195KB) ( 2429 )   Save
    A necessary and sufficient condition for the adjoint equivalence of two graphs with the adjoint minimum real root at least $-$4 was given. Based on this result, a necessary and sufficient condition of the chromatic equivalence for the complement graphs of these graphs can be naturally obtained.
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    Linear arboricity of an embedded graph on a surface of large genus
    LV Chang-qing, FANG Yong-lei
    2013, 2013 (1):  7-10, 23. 
    Abstract ( 1760 )   PDF (294KB) ( 1661 )   Save
    The linear arboricity of a graph $G$ is the minimum number
    of linear forests which partition the edges of $G$. This paper
    proved that if $G$ can be embedded on a surface of large genus
    without 4-cycle and $\Delta(G)\geq (\sqrt{45-45\varepsilon}+10)$,
    then its linear arboricity is $\lceil \frac{\Delta}{2}\rceil$, where
    $\varepsilon=2-2h$ if the orientable surface with genus
    \,$h(h>1)$\,or $\varepsilon=2-k$ if the nonorientable surface with
    genus \,$k(k>2)$. It improves the bound obtained by J. L. Wu. As an
    application, the linear arboricity of a graph with fewer edges were
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    Estimating the number of short cycles in simple planar graphs
    TANG Bao-xiang, SHI Li-hua, REN Han
    2013, 2013 (1):  11-16. 
    Abstract ( 2006 )   PDF (283KB) ( 1931 )   Save
    This paper showed that the number of the shortest cycles
    in a planar graph of order $n$ is at most $O(n^{2})$ and the bound
    is the best possible (subject to the power of $n$) since $K_{n-2,n}$
    exactly $\frac{(n-2)(n-3)}{2}$ many 4-cycles.
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    Determination of a convex body by the volume of its polar bodies
    WU Li-rong
    2013, 2013 (1):  17-23. 
    Abstract ( 1839 )   PDF (257KB) ( 1718 )   Save
    Using tools of spherical harmonics and Hamburger's moment,
    we proved that an origin-symmetric convex body containing a sphere
    of radius $\delta$ in its interior is determined in
    ${\mathbb{R}}^{n}$ by the volume of its polar bodies with respect to
    all the points near the sphere.
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    Bayesian linear unbiased estimator and its robustness under the matrix loss function
    QIU Hong-bing, LUO Ji
    2013, 2013 (1):  24-29, 53. 
    Abstract ( 2218 )   PDF (343KB) ( 1990 )   Save
    It was proved that the Bayesian linear unbiased estimator
    of the unknown parameters in a general linear model under the
    quadratic loss function is also the Bayesian linear unbiased
    estimator under the matrix loss function. The robustness of the
    Bayesian linear unbiased estimator of the unknown parameter in terms
    of error distributions was also discussed; moreover, the necessary
    and sufficient conditions are obtained, under which the Bayesian
    linear unbiased estimator of the unknown parameters hold its
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    Regression credibility model with correlation risk under balanced loss function
    HUANG Wei-zhong
    2013, 2013 (1):  30-40. 
    Abstract ( 2185 )   PDF (334KB) ( 1973 )   Save
    Firstly the relation between the credibility premium under
    balanced loss function and  quadratic loss function was given. Then
    the linear regression credibility premium with correlation risk
    under balanced loss function was derived. At last the credibility
    premium was expressed in balanced loss function when the target
    estimator was specialized, meanwhile the regression credibility
    model with equal correlation  and common effect risk under balanced
    loss function was discussed.
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    Convergence theorems for the fixed points of two finite families of set-valued asymptotically nonexpansive mappings
    SONG Chuan-jing, WU Jian-rong
    2013, 2013 (1):  41-46, 75. 
    Abstract ( 1949 )   PDF (328KB) ( 1847 )   Save
    The common fixed points of two finite families of
    set-valued asymptotically nonexpansive mappings were studied in real
    uniformly convex Banach spaces. A finite-step iteration process for
    these two families was introduced, and some strong convergence
    theorems for this scheme were proved. The results improve and extend
    some recent relative results.
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    Small-amplitude limit cycles of some non-smooth Li\'{e}nard systems
    LIU Xia, LIU Yan-wei
    2013, 2013 (1):  47-53. 
    Abstract ( 1676 )   PDF (198KB) ( 1861 )   Save
    Based on the results by HAN Mao-an, et al. for computing
    some focus values of non-smooth Li\'{e}nard systems, the number of
    limit cycles bifurcated from the origin of some more general
    non-smooth Li\'{e}nard systems were given by using maple process.
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    Normal families related to shared values
    LI San-hua, LIU Zhong-dong, WU Gao-xiang
    2013, 2013 (1):  54-60, 75. 
    Abstract ( 1788 )   PDF (363KB) ( 1795 )   Save
    Let $\F$ be a family of meromorphic functions on a domain
    $D$, $a$ and $b$ be two nonzero finite complex numbers($\frac{a}{b}$
    not positive integer). If for every $f \in \F$, $f(z) = a
    \Rightarrow f^{(k)}(z) = a$, and the zeros multiplicity of $f - a$
    is at least $k$, and $|f(z) - a| \geq \varepsilon$ ($\varepsilon >
    0)$ whenever $f^{(k)}(z) = b$, then $\F$ is normal on $D$.
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    Cells of the affine Weyl group $\widetilde{\bm C}_{\bm 4}$ in quasi-split case
    YUE Ming-shi
    2013, 2013 (1):  61-75. 
    Abstract ( 2382 )   PDF (1368KB) ( 2036 )   Save
    The affine Weyl group $(\widetilde{C}_4,\,S)$ can be
    considered as the fixed point set of the affine Weyl group
    $(\widetilde{A}_7,\,\widetilde{S})$ under a certain group
    automorphism $\alpha$. Let
    $\widetilde{l}:\widetilde{A}_7\longrightarrow \mathbf{\mathbf{N}}$
    be the length function of\,$\widetilde{A}_7$. The restriction of
    $\widetilde{l}$ on $\widetilde{C}_4$, denoted by $L$, is a weighted
    function on $\widetilde{C}_4$. This paper classified the cells in
    weighted Coxteger group\,$(\widetilde{C}_4,\,L)$.
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    Left-connectedness of left cells in the Weyl Group of type E6
    MI Qian-qian, SHI Jian-yi
    2013, 2013 (1):  76-90. 
    Abstract ( 1793 )   PDF (265KB) ( 1775 )   Save
    We showed that all the left cells in the Weyl group $E_{6}$
    were left-connected, verifying a conjecture of Lusztig in our
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    Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$
    HUANG Qian
    2013, 2013 (1):  91-103, 114. 
    Abstract ( 2294 )   PDF (558KB) ( 1884 )   Save
    The fixed point set of the affine Weyl group
    ($\widetilde{A}_{2n},\widetilde{S}$) under a certain group
    automorphism $\alpha$ with $\alpha\,(\widetilde{S}) = \widetilde{S}$
    can be considered as the affine Weyl group ($\widetilde{C}_n,S$).
    Then the left and two-sided cells of the weighted Coxeter group
    ($\widetilde{C}_n,\widetilde{\ell}$), where $\widetilde{\ell}$ is
    the length function of $\widetilde{A}_{2n}$, can be given an
    explicit description  by studying the fixed point set of the affine
    Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under $\alpha$. We
    describe the cells of ($\widetilde{C}_n,\widetilde{\ell}$)
    corresponding to the partitions
    $\textbf{k}\textbf{1}^{\textbf{2n+1-k}}$ with $1\leqslant k
    \leqslant 2n+1$ and $(2n-1,2)$.
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    Properties of strongly infinite ${\bm{C^{\ast}}}$-algebras
    LIANG Yue-liang
    2013, 2013 (1):  104-114. 
    Abstract ( 1698 )   PDF (211KB) ( 1935 )   Save
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    Giant magneto-impedance on glass-coated microwires with copper layer
    WANG Rui-li, RUAN Jian-zhong, KONG Xiang-hong, YANG Wei, WANG Jiang-tao, ZHAO Zhen-jie
    2013, 2013 (1):  115-120. 
    Abstract ( 2057 )   PDF (1871KB) ( 1993 )   Save
    The amorphous wires of nominal compositions Fe73.0Cu1.0Nb2.0Si13.5B9.0 were prepared by glass-coating melt-spinning method. Then, the wires were annealed at 480~650 ℃ for 30 min in nitrogen atmosphere. The composite wires with copper layer using electroless deposition were produced, a thin layer of copper deposited onto the microwires annealed at 570 ℃. The morphology of composite microwires was observed using SEM. The giant magnetoimpedance effect on the samples was investigated. The results show that soft magnetic properties of the specimen can improve its MI ratio. The electromagnetic interactions between the ferromagnetic core and the copper layer can also affect MI ratio.
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    Study on the conductivity of P(MMA-St)/MWNTs composites after temperature modification
    ZHI Hui, XU Xue-cheng
    2013, 2013 (1):  121-127, 138. 
    Abstract ( 1933 )   PDF (2347KB) ( 1907 )   Save
    Methyl methacrylate-styrene copolymer/multiwalled carbon nanotubes (P(MMA-St)/MWNTs) composites were prepared via situ emulsion polymerization and the influence of temperature modification on the conductivity of the composites was studied. The results indicated that the conductivity of the composite in the threshold value was increased by 2 orders of magnitude after temperature modification at 200 ℃ for 1 h. The relationship between the structure, interaction and properties of the composites were initiated by FTIR, XPS and XRD. After temperature modification some ester and acid in the PMMA change into anhydride. The change can prolong the effective conjugation and enhance the interaction between copolymers and MWNTs that the conductivity of composites improved.
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    Simultaneous determination of phenolic pollutants in wastewater using CE-AD
    LI Zi-cheng, TANG Wan-rong, ZHU Jin-kun, WANG Qing-jiang, HE Pin-gang, FANG Yu-zhi
    2013, 2013 (1):  128-138. 
    Abstract ( 2367 )   PDF (896KB) ( 2003 )   Save
    A method based on capillary electrophoresis coupled with amperometric detection (CE-AD) was developed for the simultaneous determination of phenols: 2,4-dichlorophenol, p-nitrophenol, o-cresol, m-cresol and p-cresol. The effects of working electrode potential, pH and concentration of running buffer, separation voltage and injection time on CE-AD were investigated. Under the optimum conditions, the aim analytes could be separated in buffer solution of Na2HPO4-NaOH at pH 11.38 within 25 min. A 300 μm diameter carbon disk electrode generated good current responses at +0.78 V ( vs SCE) for all analytes. The current responses were linear with concentrations over three orders of magnitude with detection limits at 10-7mol/L (S/N=3) and the recoveries were in the range of 94.0%~107.0%. This method could be successfully applied to the analysis of actual sample from coking plants with satisfactory results.
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    Newly recorded plants in Shanghai (VI)
    LI Hong-qing, XIONG Shen-zhan, CHEN Ji-yun, GUI Ping, HU Chao
    2013, 2013 (1):  139-144. 
    Abstract ( 2359 )   PDF (1053KB) ( 2124 )   Save
    A newly exotic genus Kickxia Dumort.(Scrophulariaceae) is recorded in Shanghai and China. And 11 newly recorded species are found in Shanghai, namely, Kickxia elatine (L.) Dumort., Amaranthus polygonoides L., Ampelopsis japonica (Thunb.) Makino, Asarum forbesii Maxim., Ammannia multiflora Roxb., Elymus shandongensis B. Salomon, Rorippa dubia (Pers.) H. Hara, Cardamine scutata Thunb., Corydalis sheareri S. Moore, Basella alba L. and Melochia corchorifolia L. respectively.
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