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    25 May 2012, Volume 2012 Issue 3 Previous Issue    Next Issue
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    Least Q-eigenvalue of a graph
    HE Chang-xiang, ZHOU Min
    2012, 2012 (3):  1-5. 
    Abstract ( 2183 )   PDF (250KB) ( 2472 )   Save
    We showed that: If $G$ is a non-bipartite connected graph, then $q(G)\geqslant \frac{1}{n(D+1)}$, where $g(G)$ is the least $Q$-eigenvalue of $G$, and $D$ is the diameter of $G$. Some relations between the least $Q$-eigenvalue of $G$ and that of its subgraph were given.
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    Toroidal embeddings of K7
    ZHAO Wen-zhou, SHI Li-hua, WU Hao, REN Han
    2012, 2012 (3):  6-12,40. 
    Abstract ( 2181 )   PDF (2280KB) ( 2557 )   Save
    In this paper, we showed that there are exactly $2\times5!$ embeddings of $K_7$ in the torus. All of such embeddings are triangular permitting $Gr\ddot{u}nbaum$ coloring.
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    Star edge coloring of $d$-dimensional grids
    DENG Kai, LIU Xin-sheng, TIAN Shuang-liang
    2012, 2012 (3):  13-16. 
    Abstract ( 2371 )   PDF (243KB) ( 2618 )   Save
    The star chromatic index of graph $G$ is denoted by $\chi_{s}^{\prime}(G)$. In this paper, we studied the relationship between  $\chi_{s}^{\prime}(G)$, $|V(G)|=\nu$, and $|E(G)|=\varepsilon$, and proved that $\lceil\frac{8\varepsilon}{3\nu}\rceil\leqslant\chi_{s}^{\prime}(G)$ for $\Delta(G)\geqslant2$. The star chromatic index of 2-dimensional grid was obtained. We also got the attainable bounds for the star chromatic index of hypercubes and $d$-dimensional grids.
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    Oscillation criteria of a class of second-order dynamic equations on time scales
    YANG Jia-shan
    2012, 2012 (3):  17-23. 
    Abstract ( 2701 )   PDF (267KB) ( 2246 )   Save
    The oscillation for a class of second-order nonlinear variable delay dynamic equations on time scales with nonlinear neutral term was discussed. Using the time scales theory and some necessary analytic techniques, and by introducing parameter function and the generalized Riccati transformation, some sufficient
    conditions for the oscillation of the equations were obtained. Some existing results in the literature are improved and extended.
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    Right-passage probabilities of $\emph{\textbf{SLE}}_{\bm {\kappa}}$ and critical percolation
    2012, 2012 (3):  24-29. 
    Abstract ( 2847 )   PDF (544KB) ( 2516 )   Save
    This paper derived the probability formula for a chordal $SLE_{\kappa}$ trace across a given point in upper half plane $\mathbb{H}$. And on the basis of the left-passage probability, established the probability formula for a critical percolation in a closed unit circle without a given point. Finally, according to the relationship of exploration process and $SLE_{6}$, got that with the same starting and ending point, the trace of $SLE_{6}$ has the same distribution of self-avoiding walk.
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    Pricing extendible option under jump-fraction process
    PENG Bin, PENG Fei
    2012, 2012 (3):  30-40. 
    Abstract ( 2329 )   PDF (238KB) ( 2745 )   Save
    A valuation framework for extendible options is constructed when the underlying asset obeys a fractional process with jump. Under the risk neutral environment, an analytic formula for the call option with one extendible maturity is derived by solving the expected present value of cashflow and conditioning jumps for the underlying asset. Moreover, some special cases of the formula are discussed. These results are generalized to the option with$ M $extendible maturity. Its value will converge in the limit to the value of perpetual extendible option as the number of extendible maturity increases to infinite. Extrapolated technique with two
    points is presented to yield a simple and efficient computation procedure to calculate the limit. Numerical results are provided to illustrate provided that our pricing expressions are easy to implement.
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    Weighted finite difference methods for two-sided space-time fractional diffusion equations
    MA Wei-yuan, LIU Hua
    2012, 2012 (3):  41-48,70. 
    Abstract ( 3504 )   PDF (315KB) ( 3327 )   Save
    A weighted finite difference scheme was proposed in order to solve initial-boundary value problems of space-time fractional diffusion equations. Their stability was analyzed by means of discrete energy method. Using mathematical induction, we proved that the scheme was convergent under the same condition. Illustrative
    example was included to demonstrate the validity and applicability of the scheme.
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    Two formulations and solutions of the inverse problems for Lie symmetries in dynamics of a Birkhoffian system
    LONG Zi-xuan, ZHANG Yi
    2012, 2012 (3):  49-55. 
    Abstract ( 2181 )   PDF (251KB) ( 2605 )   Save
    First, the determining equations, the structure equations and the conserved quantities of Lie symmetries for a Birkhoffian system were given; then two formulations and solutions of the inverse problems of Lie symmetries for the system were presented. The results show that the same Birkhoffian(Birkhoff's functions) and
    first integral can correspond to different Birkhoff's functions(Birkhoffian) and different Lie symmetries, and can also correspond to the same Lie symmetry and different Birkhoff's functions(Birkhoffian).
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    Limit theorems in infinitesimal non-commutative probability spaces
    CUI Han-zhe, XUE Yi-feng
    2012, 2012 (3):  56-60,96. 
    Abstract ( 2732 )   PDF (322KB) ( 2405 )   Save
    This paper proved the central limit theorems in infinitesimal non-commutative probability spaces using $R$ transform under both one-dimension and multi-dimension cases. Also Poisson limit theorem was proved using the moments-cumulants formula. Lastly, the relation between the standard semicircular elements and free poisson elements was figured out by combinatorial analysis.
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    Normal criterion concerning differential polynomials and omitted functions
    WANG Xue, LIU Xiao-jun, CHEN Qiao-yu
    2012, 2012 (3):  61-70. 
    Abstract ( 1983 )   PDF (282KB) ( 2274 )   Save
    In this paper, we proved: Let $k\geqslant 2$ be a positive integer, $\mathcal{F}$ be a family of holomorphic functions, all of whose zeros have multiplicities at least $k$, and let $h(z)$, $a_1(z)$, $a_2(z)$, $\cdots$, $a_k(z)$ are all nonequivalent to $0$ on $D$. If for any  $f\in\mathcal{F}$, the following two conditions are satisfied: (a)~$f(z)=0\Rightarrow |f^{(k)}(z)+a_1(z)f^{(k-1)}(z)+\cdots+a_k(z)f(z)|<|h(z)|$; (b)~$f^{(k)}(z)+a_1(z)f^{(k-1)}(z)+\cdots+a_k(z)f(z)\neq h(z),$~ where ~$a_1(z), a_2(z),\cdots ,a_k(z)$ and $f$ have no common zeros, then $\mathcal{F}$ is normal on $D$.
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    Direct sum decomposition of $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm s}{\bm l}_{\bf 2}\textbf{)}$ about principal indecomposable modules
    TONG Zhao-jia, HU Nai-hong
    2012, 2012 (3):  71-84,96. 
    Abstract ( 4333 )   PDF (444KB) ( 2352 )   Save
    This paper described a class of irreducible modules of the restricted two-parameter quantum group $\overline{U}_{r,s}(sl_2)$, and constructed all its principal indecomposable modules.  Finally, the minimal polynomial of the action of the Casimir element on $\overline{U}_{r,s}(sl_2)$ and all the conjugate classes of the
    primitive idempotents of $\overline{U}_{r,s}(sl_2)$ were obtained.
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    Realization of ${\bm B}_{\bm 2}$ type finite W-algebras
    ZENG Yang, SHU Bin
    2012, 2012 (3):  85-96. 
    Abstract ( 3156 )   PDF (357KB) ( 2456 )   Save
    In this paper we constructed an explicit set of generators for the finite W-algebras associated to all nilpotent orbits of $B_{2}$ type Lie algebras. We also computed the relations for these generators. The results give realization of $B_{2}$ type finite W-algebras.
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    Research of codec and geometric correction method for true 3D volumetric display images
    TIAN Feng, CAI Wen, ZHAO Fan, CHEN Ming, ZHANG Wen-jun
    2012, 2012 (3):  97-102. 
    Abstract ( 2451 )   PDF (1076KB) ( 2345 )   Save
    By introducing a true 3D display model, volumetric display technique based on visual voxel was explained. To solve the low-resolution problem of true 3D LED displayer, multi-machine synchronization projection method was proposed. With serial section images of true 3D display, the codec algorithm for true 3D display was studied and geometric correction model based on ray tracing method was built. The experiment proves that this method can build a practical and high-resolution true 3D displayer and can display the object exactly.
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    Accurate eye location in near-infrared images based on ellipse fitting
    JIN Jun-cai, TONG Wei-qing, LIANG Xiao-ni, CHEN Qiang, MEI Yue-ping, LIU Dan
    2012, 2012 (3):  103-110. 
    Abstract ( 2830 )   PDF (3011KB) ( 4184 )   Save
    This paper presents a novel approach to precisely locate eye position in near-infrared facial images. In this approach, we first determine the face region and initial eye position using face detection classifier based on Haar features and AdaBoost algorithm. Then we detect the eye edge in the eye region using Sobel operator, fit it into an elliptical contour. Finally, the center point of eye is located by the center of the fitted ellipse. With 120×120 normalized face images, the experiments show that the proposed approach is accurate. The average error is less than 1.5 pixels and the processing time is about 7 ms.
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    Analysis of tidal characteristics of the tide gauges in the Changjiang Estuary
    YANG Zheng-dong, ZHU Jian-rong, WANG Biao, LIN Tang-yu
    2012, 2012 (3):  111-119. 
    Abstract ( 6955 )   PDF (1190KB) ( 5216 )   Save
    Based on the measured water levels at Hengsha, Majiagang, Baozhen and Yonglongsha tide gauges in 2009, the tidal temporal and spatial variations, tidal constituents, tidal form and distortion at these gauges in the Changjiang Estuary were analyzed. There exist tidal daily inequalities that mainly occur during high tide levels, and are more significant during neap tides than spring tides in March and September while are more significant during spring tides than neap tides in June and December. The monthly maximum and minimum tidal ranges in each month at the tide gauges were given out statistically. The tidal range in the estuary varies monthly with two peaks: the maximum tidal range reaches the maximum values in March and September, and reaches the minimum values in June and December. The minimum tidal range reaches the maximum values in June and December, and reaches the minimum values in March and September. The tidal range in the South Branch reduced toward upstream due to the river discharge and friction. The tidal range at Yonglongsha tidal gauge is the largest among the 4 tidal gauges because the North Branch has small river discharge division ratio and funnel shape bathymetry. The tide is mainly composed by the 4 semi-diurnal tidal constituent (M 2S 2N 2K 2), 4 diurnal tidal constituent (K 1O 1P 1Q 1) and 3 shallow water tidal constituent (M 4MS 4M 6). The semi-diurnal tidal constituents M 2 and S 2 are the predominant ones, and the shallow water tidal constituents M 4 and MS 4 are apparent due to the shallow water in the estuary. The tidal form number in the South Branch is larger than 0.25, indicating where the tide is an irregular semi-diurnal tide type there, and is smaller than 0.25 in the North Branch, indicating where the tide is a regular semi-diurnal tide type. The tidal distortion coefficients in the 4 tidal gauges are all larger than 0.1, indicating that the tide at the tide gauges has significant distortion in the Changjiang Estuary, especially at Yonglongsha in the North Branch with tidal distortion coefficient 0.173.
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    Magnetic properties of the core CX21 off the Yangtze Estuary and its influencing factors
    MA Hong-lei, ZHANG Wei-guo, HU Zhong-xing, JIA Tie-fei, DONG Chen-yin, LIU Ying
    2012, 2012 (3):  120-129,153. 
    Abstract ( 2462 )   PDF (2400KB) ( 2206 )   Save
    Core CX21(122°30′ E,30°00′ N) is 340 cm in length, obtained off the Yangtze Estuary, China. In this study, magnetic, geochemical and particle size analyses were conducted on sediments from the core CX21 to determine the major factors (including early diagenesis, particle size and sediment provenance) that control the down-core variations of magnetic properties. Results indicate that there are strong positive relationships between χARM, χARM/SIRM and χARM/χ and the fractions finer than 16 μm. χ, SIRM, χfd and χfd% display relatively weak, but positive correlations with the finer fractions (2—4 μm and 4—8 μm). This suggests that particle size plays an important role in the variation of magnetic properties. Iron species analysis using the BCR method indicates that sediments below 170 cm experienced more reducing environment than that above, which is consistent with the phenomena of stronger reductive diagenesis of magnetic minerals. Ti, an element insensitive to redox conditions, reveals sediment provenance changes in the core CX21. The increase of Ti toward the surface is accompanied by an increase of concentration related magnetic parameters (χ and SIRM), suggesting that sediment source is also a main factor influencing magnetic properties. In spite of the difference in sedimentation rate and particle size composition, CX21 and the previously studied core Y7 show similar down core variations of magnetic properties, implying that magnetic properties can be used as a tool for core correlation in area off the Yangtze Estuary.
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    Application of RBPs for the habitat assessment of Suzhou Creek
    CAO Min, WU E-nuo, CHE Yue, CHEN Ting
    2012, 2012 (3):  130-137. 
    Abstract ( 4744 )   PDF (1371KB) ( 2799 )   Save
    As an important part of river health evaluations, habitat assessment has received more and more attention. Practice progresses of foreign river habitat assessment are reviewed and the basic thinking with working procedure of habitat assessment in American Rapid Bioassessment Protocols (RBPs) is introduced in this paper. Then, an empirical study has been carried out on Suzhou Creek in Shanghai. The result indicates that: Suzhou Creek has been strongly affected by human activity, and its habitat quality varies mostly between better to bad levels. Scores of the habitat quality of main streams are close to that of branches, while habitat quality of upstream areas is better than that of lower-middle reaches areas, and rural areas is better than urban areas. Result shows that Rapid Bioassessment Protocols (RBPs) has important referential value to the river habitat assessment in China.
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    Discharge pattern of rural domestic sewage and the efficiency of soil infiltration in Shanghai
    REN Xiang-yu, SHANG Zhao-yi, CHE Yue, YANG Kai, ZHONG Chun-jie
    2012, 2012 (3):  138-144. 
    Abstract ( 2657 )   PDF (1722KB) ( 2580 )   Save
    A field investigation was made in respect of the volume and quality of domestic sewage in 3 villages in Baoshan District of Shanghai, where pilot experiments of domestic sewage treating system had been performed. Meanwhile, a study on the water usage and discharge pattern in rural areas and an assessment of efficiency of soil infiltration system were made by continuous monitoring data. And an evaluation of the contribution by septic tank and treating system was also made. Finally, suggestions on the promotion and management of domestic sewage treating system in Shanghai was provided.
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    Screening the ecological toxicity of sediments in black-odors rivers using  Xenopus tropicalis embryos
    YANG Bo, ZHU Pan, YUAN Jing, LIU Zhen, HUANG Min-sheng, SHI hua-hong
    2012, 2012 (3):  145-153. 
    Abstract ( 2428 )   PDF (1237KB) ( 2380 )   Save
    To assess the pollution and management effects of the black-odors rivers from Wenzhou, we screened the toxocity of aqueous sediment extracts and interstitial water of rivers using Xenopus tropicalis  embryos. The surface sediment samples were collected for 5 times from September to December in 2010. The embryos were exposed to the extracting solution of the sediments (1∶4) for the first to the fourth tests and in the interstitial water for the fifth test for 48 h. Our results showed that all the embryos treated with samples from S1 died after 48 h of exposure during the 5 tests. This suggested that the sediments in S1 showed very high toxicity. Compared with the control, the body length of embryos treated with aqueous sediments extracts from Shanxia River was significantly decreased, but the body length of embryos treated with those from Jiushan River was decreased only in the third test. The percent of malformations were higher in Shanxia River than that in Jiushan River. Especially, the percent of malforation was up to 100% in S2-S4, but the highest of percent of malformations was only 70% (J2) and 40 (J1) in Jiushan River. The interstitial water of sediments in Shanxia River led to the death of all embryos. These results suggested that the toxicity of sediments in Shanxia River was generally higher than that in Jiushan River, and that the interstitial water was more toxic than aqueous sediments extracts. Our study indicates that the sediments of the black-odors rivers have adverse effects on the development of X. tropicalis embryos and show significant ecological toxicity. In addition, X. tropicalis embryos can be used for screening the hazards of sediments effectively.
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    Computational and experimental identification of novel microRNAs in rats
    WANG Lin, ZHANG Shuang, DONG Su-zhen
    2012, 2012 (3):  154-160,170. 
    Abstract ( 2096 )   PDF (893KB) ( 2799 )   Save
    The number of miRNAs in rat genome in miRBase is much less than that of mouse and human. One effective method to identify new miRNAs is to utilize the homolog- based bioinformatrical method. In this report, this method was applied to predict new miRNAs of rats. The known miRNAs sequences were downloaded from miRBase, and used as query sequences to search the rat genome at UCSC Genome Bioinformatics by BLAT analysis. New miRNAs were selected based on commonly- used miRNA standards. As a result, 45 new miRNAs were obtained. Nine of them were chosen to be validated by RT- PCR, and most of them were found expressed in brain, heart, lung, kidney, muscle, spleen, testis and liver. Based on the results, miRNA cluster analysis and miRNA gene family analysis were performed in rat genome.
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    Antiproliferative and apoptotic activities of novel curcumin analogs in human liver cancer cell lines
    LI Yu-bo, WEN Ying, MA Ming-liang, WU Liang-chun, WEN Ke, ZHAO Zheng
    2012, 2012 (3):  161-170. 
    Abstract ( 2781 )   PDF (2235KB) ( 4206 )   Save
    Antiproliverative and apoptotic activities of the novel curcumin analogs (CCM series) against human liver carcinoma Bal-7402 and SMMC-7721 cells were investigated by MTT assay. The cell cycle distribution and apoptosis of SMMC-7721 cells induced by CCM-5 and CCM-14 were analyzed using flow cytometry. The expressions of caspase-3 and its activated form p17 in SMMC-7721 cells were further determined by western blot. CCM-5 and CCM-14 exhibited, in a concentration-dependent manner, the stronger antiproliferative role than those of curcumin and the other CCM compounds. Their apoptotic effects on the SMMC-7721 cells were also found to be significantly elevated as compared with the control group (P<0.01). Cell cycle distribution appeared that, as the concentrations of the compounds increased in SMMC-7721 cells, the G0/G1 phase cells decreased while the S phase and the G2/M phase cells, and the SubG1 peak increased. Furthermore, both CCM-5 and CCM-14 could activate caspase-3 expression in the SMMC-7721 cells. Collectively, our data suggest that CCM-5 and CCM-14 can restrain proliferation and promote apoptosis in SMMC-7721 cell, and the molecular mechanism underlying these actions against the cancer cells of the compounds may involve in the activation of caspase-3.
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