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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 ( 8015 )   PDF (195KB) ( 2446 )   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. References | Related Articles | Metrics

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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 ( 1802 )   PDF (294KB) ( 1676 )   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 concluded. References | Related Articles | Metrics

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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 ( 2052 )   PDF (283KB) ( 1950 )   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 $K_{n-2,n}$ contains exactly $\frac{(n-2)(n-3)}{2}$ many 4-cycles. References | Related Articles | Metrics

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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 ( 1899 )   PDF (257KB) ( 1751 )   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. References | Related Articles | Metrics

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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 ( 2259 )   PDF (343KB) ( 2010 )   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 optimality. References | Related Articles | Metrics

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Regression credibility model with correlation risk under balanced loss function HUANG Wei-zhong 2013, 2013 (1):  30-40.  Abstract ( 2229 )   PDF (334KB) ( 2009 )   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. References | Related Articles | Metrics

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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 ( 1995 )   PDF (328KB) ( 1857 )   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. References | Related Articles | Metrics

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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 ( 1709 )   PDF (198KB) ( 1895 )   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. References | Related Articles | Metrics

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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 ( 1823 )   PDF (363KB) ( 1812 )   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 $D$. References | Related Articles | Metrics

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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 ( 2434 )   PDF (1368KB) ( 2065 )   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\,$(\widetilde{C}_4,\,L)$. References | Related Articles | Metrics

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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 ( 1828 )   PDF (265KB) ( 1796 )   Save We showed that all the left cells in the Weyl group $E_{6}$ were left-connected, verifying a conjecture of Lusztig in our case. References | Related Articles | Metrics

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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 ( 2340 )   PDF (558KB) ( 1902 )   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 $(2n-1,2)$. References | Related Articles | Metrics

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Properties of strongly infinite ${\bm{C^{\ast}}}$-algebras LIANG Yue-liang 2013, 2013 (1):  104-114.  Abstract ( 1738 )   PDF (211KB) ( 1985 )   Save null References | Related Articles | Metrics

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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 ( 2092 )   PDF (1871KB) ( 2005 )   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. References | Related Articles | Metrics

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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 ( 1972 )   PDF (2347KB) ( 1916 )   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. References | Related Articles | Metrics

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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 ( 2399 )   PDF (896KB) ( 2032 )   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. References | Related Articles | Metrics

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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 ( 2392 )   PDF (1053KB) ( 2149 )   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. References | Related Articles | Metrics