5连通图中的可去边

An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G- e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e （x）. The existence of removable edges of k-connected graphs and some properties of 3-connected and 4-connected graphs have been investigated [1, 11, 14, 15]. In the present paper, we investigate some properties of 5-connected graphs and study the distribution of removable edges on a cycle and a spanning tree in a 5- connected graph. Based on the properties, we proved that for a 5-connected graph G of order at least 10, if the edge-vertex-atom of G contains at least three vertices, then G has at least （3│G│ ＋ 2）/2 removable edges.     

Design procedure for photonic crystal fibers with ultra-flattened chromatic dispersion

A simple design procedure is used to generate photonic crystal fibers (PCFs) with ultra-flattened chromatic dispersion. Only four parameters are required, which not only considerably saves the computing time, but also distinctly reduces the air-hole quantity. The influence of the air-hole diameters of each ring of hexagonal PCFs (H-PCF, including 1-hole-missing and 7-hole-missing H-PCFs), circular PCFs (C-PCF), square PCFs (S-PCF), and octagonal PCFs (O-PCF) is investigated through simulations. Results show that regardless of the cross section structures of the PCFs, the 1st ring air-hole diameter has the greatest influence on the dispersion curve followed by that of the 2nd ring. The 3rd ring diameter only affects the dispersion curve within longer wavelengths, whereas the 4th and 5th rings have almost no influence on the dispersion curve. The hole-to-hole pitch between rings changes the dispersion curve as a whole. Based on the simulation results, a procedure is proposed to design PCFs with ultra-flattened dispersion. Through the adjustment of air-hole diameters of the inner three rings and hole-to-hole pitch, a flattened dispersion of 0±0.5 ps/(nm·km) within a wavelength range of 1.239 – 2.083 μm for 5-ring 1-hole-missing H-PCF, 1.248 – 1.992 μm for 5-ring C-PCF, 1.237 – 2.21 μm for 5-ring S-PCF, 1.149 – 1.926 μm for 5-ring O-PCF, and 1.294 – 1.663 μm for 7-hole-missing H-PCF is achieved.     

Dimension Results for Space-anisotropic Gaussian Random Fields

Let X = {X(t) ∈ R~d, t ∈ R~N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R~d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.     

利用AAO模板制备SERS基底检测SudanⅠ

通过模板法制备大面积、可控的、可重复的、热点集中的金纳米结构阵列,并在纳米结构阵列上通过化学修饰分子,吸附更多苏丹红Ⅰ分子至金纳米的SERS增强区域,实现其高灵敏的表面增强拉曼分析检测。以多孔阳极氧化铝为模板,通过真空蒸镀金,约200 nm厚度,复制氧化铝的孔洞结构,用碱液将氧化铝模板腐蚀去除,可得到氧化铝模板的互补结构,即大面积的、均匀的金半球纳米结构阵列。在金纳米结构阵列上修饰十二硫醇,硫醇巯基端与纳米金相结合,碳链端自组装形成非极性的疏水环境,疏水环境可以捕获苏丹红Ⅰ分子,使其吸附至纳米金结构表面的SERS增强区域,实现苏丹红Ⅰ的SERS检测。由于SERS基底表面的金半球纳米结构均匀、规整,在激光光斑的区域内,苏丹红Ⅰ的SERS信号均匀、稳定,可以对苏丹红Ⅰ进行定量分析。苏丹红Ⅰ的拉曼峰强度对数与浓度对数之间呈线性关系,线性相关系数达0.99,线性范围为5×10-4～10-7mol·L-1,回收率范围77%～117%。此方法的检测限可达到4×10-8mol·L-1,与国标的高效液相色谱的检测限相当。     

钒取代型多金属氧酸盐对酪氨酸酶的抑制作用

测定了自制的α-1,2,3-K6H[SiW9V3O40]、α-1,2-K6[SiW10V2O40]和α-K5[SiW11VO40](以下分别简写为α-SiW9V3、α-SiW10V2和α-SiW11V)钒取代多金属氧酸盐对蘑菇酪氨酸酶活性的抑制作用。 结果表明,在pH=6.8的NaH2PO4-Na2HPO4缓冲溶液中,α-SiW9V3对酪氨酸酶有较强的抑制作用,表现为对酶稳态活力的抑制作用和对迟滞时间的延长作用,在DMSO溶液中,其IC50为0.6841 mmol/L,0.7 mmol/L α-SiW9V3可使单酚酶的迟滞时间由235 s延长至650 s,增加了2.77倍。 α-SiW9V3对酪氨酸酶单酚酶的抑制为可逆作用过程,抑制类型为混合型,其抑制常数KI、KIS分别为4.22和2.39 mmol/L。 α-SiW10V2不溶于DMSO,故未研究其对酶的抑制作用,α-SiW11V对酪氨酸酶抑制作用很弱。     

Approximation of level continuous fuzzy-valued functions by multilayer regular fuzzy neural networks

This paper proves the capability of approximation by four-layer regular fuzzy neural networks on the set of all level continuous fuzzy-valued functions according to level convergence. A numerical example is given to illustrate the results.     

Exponential periodic attractor of impulsive BAM networks with finite distributed delays

In this paper, we investigate a class of impulsive bidirectional associative memory (BAM) networks with both periodic coefficients and finite distributed delays. New criteria are established for the existence of an exponential periodic attractor, which generalize and improve the previously known results. Our criteria are less restrictive and can be applied to impulsive or non-impulsive BAM networks with a broad range of activation functions without differentiability and strict monotonicity. Moreover, our results are given in terms of system parameters and finite delay kernels of impulsive BAM networks by employing inequality technique, M-matrix and spectral theory. Finally, an example is given to show the feasibility and effectiveness of our results.     

一致光滑的等价条件

给出了一个新的关于赋范空间的光滑模,从而得到了一个一致光滑空间的等价刻画。