Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.     

非对称信息条件下供应链管理质量控制策略

研究非对称信息条件下供应链管理的质量控制问题·建立了供应链合作关系中的购买商和供应商的质量成本模型,其中包括供应商的生产理性约束条件·分析了非对称信息条件下购买商与供应商质量成本的委托代理关系,质量水平的不可观测性则表现为供应商的信息隐匿·实质上,这是一个委托代理中的逆向选择问题·购买商的质量成本是目标函数,供应商质量成本的一阶条件转化为状态空间方程,运用极大值原理求解该问题的最优质量控制·并进行了非对称信息条件下供应链的质量控制仿真实验·     

大螺旋藻氨基酸成分的研究

通过对大螺旋藻的游离氨基酸和全氨基酸的组成成分分析表明大螺旋藻有较高的氨基酸营养，全氨基酸成分与极大螺旋藻及钝顶螺旋藻的成分很相似．因此大螺旋藻与极大螺旋藻、钝顶螺旋藻同样，可被开发利用．     

带有极大值项的二阶中立型差分方程的振动性

考虑带有极大值项的二阶中立型差分方程Δ2(xn pnxn-k) qnmaxs∈[n-l,n]rsxs=0,n∈N的振动性,获得了所有解振动的充分条件。     

带有极大值项的中立型差分方程的振动性与非振动性

研究带有极大值项的一阶中立型差分方程Δ(xn+pnxn-k)+qnmaxs∈[n-l,n]rsfs(xs)=0,获得了所有解振动的充分条件,同时也研究了非振动解的渐近性质.     

Lagrange乘数法的部分应用

Lagrange乘数法主要用于求函数在满足约束条件下的极值问题,但联立方程求驻点及确定条件极值是较困难的事。文章将其应用于条件最值的求解、不等式的证明及隐函数极值的求解,提出在实际解题过程中的技巧,以展现Lagrange乘数法独特而简捷的效果。     

Determination of different arsenic species in food‐grade spirulina powder by ion chromatography combined with inductively coupled plasma mass spectrometry

A “two‐step” pressurized microwave‐assisted extraction method coupled with ion chromatography with inductively coupled plasma mass spectrometry for the determination of different arsenic species in spirulina samples was developed. The extraction method used H₂O₂/H₂O (1:5, v/v) as solvent to extract all arsenic species except arsenite, which was extracted by using water as solvent. The extraction method had a satisfactory recovery (>96%) and took a short time (20.0 min). With our method, all arsenic species in spirulina samples were completely separated and determined with recoveries of 84–105% and relative standard deviations of 2–4%. Food‐grade spirulina powder samples from seven provinces (Inner Mongolia, Zhejiang, Fujian, Hainan, Yunnan, Jiangsu, and Guangxi) in China were analyzed using the optimized protocol. Arsenate was detected at the concentration range of 170–394 ng/g in all the spirulina samples. Dimethylarsinic acid was detected at the concentration range of 32–839 ng/g in spirulina from above‐six provinces except Guangxi. Monomethylarsonic acid (67 ± 3 ng/g) was detected only in spirulina from Yunnan province. Arsenite was detected at the concentration range of 28–147 ng/g in spirulina from above five provinces except Hainan and Guangxi. Five unknown organic arsenic species were found in spirulina from above six provinces except Guangxi.     

对单变量三次函数求极值的一种简便方法

本文给出单变量三次函数是否存在极值的一种简便判别法，由稳定点个数来判别单变量三次函数是否存在极值，并求其极大（小）值。     

Asymptotic Expansions for the Distribution of the Maximum of Gaussian Random Fields

Some asymptotic results are proved for the distribution of the maximum of a centered Gaussian random field with unit variance on a compact subset S of ^N . They are obtained by a Rice method and the evaluation of some moments of the number of local maxima of the Gaussian field above an high level inside S and on the border S. Depending on the geometry of the border we give up to N+1 terms of the expansion sometimes with exponentially small remainder. Application to waves maximum is shown.     

螺旋藻对铁的富集作用研究

研究螺旋藻的富铁规律和如何提高螺旋藻有机铁比率及含量，从而为更好地利用开发螺旋藻这一宝贵的生物资源提供依据。研究结果表明，螺旋藻对铁离子具有较强烈的吸附和密集作用，藻体中有机铁含量较高，最低可达284ppm，最高可达349ppm；螺旋藻培养过程中应适当给予添加剂以增加培养基中的铁离子浓度，如0．01—0．03gm/L，可望有效增加螺旋藻中有机铁含量。