粘合运算对图的控制参数的影响

简单图G的粘合运算G_(uv)指的是重合G的两个顶点{u,v}并且去掉重边和环所得到简单图的运算．本文考虑了粘合运算对图的4个控制参数γ(G),Γ(G),β(G),i(G)的影响．刻画了图G_(uv)与图G的控制参数γ(G),Γ(G),γ(G),i(G)之间的关系．及给出γ(G_(uv))=γ(G)-1和β(G_(uv)=β(G)-1的充要条件．     

Efficient hedging with coherent risk measure

The idea of efficient hedging has been introduced by Föllmer and Leukert. They defined the shortfall risk as the expectation of the shortfall weighted by a loss function, and looked for strategies that minimize the shortfall risk under a capital constraint. In this paper, to measure the shortfall risk, we use the coherent risk measures introduced by Artzner, Delbaen, Eber and Heath. We show that, for a given contingent claim H, the optimal strategy consists in hedging a modified claim ?H for some randomized test ?. This is an analogue of the results by Föllmer and Leukert.     

Semidefinite programming in combinatorial optimization

We discuss the use of semidefinite programming for combinatorial optimization problems. The main topics covered include (i) the Lovász theta function and its applications to stable sets, perfect graphs, and coding theory, (ii) the automatic generation of strong valid inequalities, (iii) the maximum cut problem and related problems, and (iv) the embedding of finite metric spaces and its relationship to the sparsest cut problem. Part of this work is supported by NSF contract 9623859-CCR, a Sloan Foundation Fellowship, and ARPA Contract N00014-95-1-1246.     

基于快速轮廓转动力矩特征的激光主动成像目标识别

针对激光主动成像的图像特性,提出一种基于快速轮廓转动力矩的目标识别方法。将转动力矩的概念引入目标识别中,提出的快速轮廓转动力矩特征(FCTF)不仅包含了轮廓的尺寸、位置、规则度以及目标的亮暗等信息,同时对于旋转、尺度缩放等变换具有不变性。采用转动力矩的快速计算方法,提高了识别算法的计算效率。识别算法首先使用最大稳定极值区域(MSER)算法检测出目标特征区域,并将其变换为圆形区域,然后结合快速转动力矩特征算法提取出目标区域的局部不变特征,最后输入训练好的支持向量机分类器进行识别。实验结果表明相比于已有的激光主动成像目标识别方法,所提算法对于旋转、仿射变换均具有更高的识别率,同时单帧平均运算时间为9.68 ms,满足激光主动成像目标识别系统实时性的要求。     

稳定同位素稀释-气相色谱质谱联用法测定水产品中甲基汞和乙基汞

建立了测定水产品中甲基汞和乙基汞的气相色谱质谱联用分析方法。采用6.0 mol/L HCl超声辅助提取,在NaCl存在下,提取液中甲基汞和乙基汞可被甲苯萃取,再用半胱氨酸反萃取,加入CuSO4释放出的甲基汞和乙基汞与四苯硼钠反应,生成甲基苯基汞和乙基苯基汞,经DB-5MS毛细柱分离,选择离子监测方式(SIM)质谱检测,以d3-甲基汞作为内标的稳定同位素稀释法定量。甲基汞和乙基汞标准曲线的线性范围均为1~500μg/L,国家标准参考物质(GBW 10029)6次测定的甲基汞(以汞计)平均值为0.828 mg/kg,相对标准偏差为3.2%,与证书参考值(0.84±0.03)mg/kg(以汞计)一致。鱼、虾和贝类等不同种类水产品中甲基汞和乙基汞的平均加标回收率分别为94%~101%和81%~104%,相对标准偏差在1.9%~4.7%和3.1%~8.2%范围内(n=6),样品的检出限为0.1~0.3μg/kg(S/N=3)。方法灵敏,准确,可用于水产品中甲基汞和乙基汞的测定。     

稳定同位素稀释气相色谱-质谱联用测定化妆品中5种磷酸三酯类化合物

根据不同化妆品的基质特性探讨优化不同的提取净化方法,建立了稳定同位素稀释气相色谱-质谱联用测定化妆品中5种磷酸三酯类化合物(OPEs)的方法。膏霜乳液类和蜡基类化妆品经溶剂提取后,采用ENVI-Carb固相萃取柱净化;粉剂类和水剂类化妆品经溶剂提取、浓缩后直接检测。样液经DB-5MS(30 m×0.25 mm×0.25μm)色谱柱分离,GC-MS的选择离子监测(SIM)模式检测,以保留时间和特征离子丰度比定性,稳定同位素稀释内标法定量。在优化的实验条件下,5种磷酸三酯类化合物在各自的线性范围内相关系数大于0.9995,方法检出限为1.0~30μg/kg,平均回收率为89.5%~105%,相对标准偏差(n=6)为2.9%~9.1%。本方法净化效果好,可有效消除基质效应,且有较好的回收率,可用于不同类型的化妆品基质中磷酸三酯类化合物的测定。     

Stochastic classical solutions for space–time fractional evolution equations on a bounded domain

Space–time fractional evolution equations are a powerful tool to model diffusion displaying space–time heterogeneity. We prove existence, uniqueness and stochastic representation of classical solutions for an extension of Caputo evolution equations featuring time-nonlocal initial conditions. We discuss the interpretation of the new stochastic representation. As part of the proof a new result about inhomogeneous Caputo evolution equations is proven.     

Computing reconstructions from nonuniform Fourier samples: Universality of stability barriers and stable sampling rates

We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this kind arise in various imaging applications, where Fourier samples are taken along radial lines or spirals for example.Specifically, we consider finite-dimensional reconstructions, where a limited number of samples is available, and investigate the rate of convergence of such approximate solutions and their numerical stability. We show that the proportion of Fourier samples that allow for stable approximations of a given numerical accuracy is independent of the specific sampling geometry and is therefore universal for different sampling scenarios. This allows us to relate both sufficient and necessary conditions for different sampling setups and to exploit several results that were previously available only for very specific sampling geometries.The results are obtained by developing: (i) a transference argument for different measures of the concentration of the Fourier transform and Fourier samples; (ii) frame bounds valid up to the critical sampling density, which depend explicitly on the sampling set and the spectrum.As an application, we identify sufficient and necessary conditions for stable and accurate reconstruction of algebraic polynomials or wavelet coefficients from nonuniform Fourier data.     

Gromov–Hausdorff stability of linkage-based hierarchical clustering methods

A hierarchical clustering method is stable if small perturbations on the data set produce small perturbations in the result. These perturbations are measured using the Gromov–Hausdorff metric. We study the problem of stability on linkage-based hierarchical clustering methods. We obtain that, under some basic conditions, standard linkage-based methods are semi-stable. We also prove that, avoiding exotic examples, introducing any unchaining condition in the algorithm always produces unstable methods.     

The play operator,the truncated variation and the generalisation of the Jordan decomposition

The play operator minimalizes the total variation on intervals, [0,T],T > 0, of functions approximating uniformly given regulated function with given accuracy and starting from a given point. In this article, we link the play operator with the so‐called truncated variation functionals, introduced recently by the second‐named author, and provide a semi‐explicit expression for the play operator in terms of these functionals. Generalisation for time‐dependent boundaries is also considered. This gives the best possible lower bounds for the total variation of the outputs of the play operator and its Jordan‐like decomposition. Copyright © 2014 John Wiley & Sons, Ltd.