光谱特征波长的SPA选取和基于SVM的玉米颗粒霉变程度定性判别

利用波长范围在833～2 500 nm的傅里叶变换近红外光谱(Fourier transform near infrared spectroscopy, FT-NIR)对不同霉变程度的玉米颗粒进行检测区分。首先,为避免光谱数据首尾噪声影响,对比四种常见的预处理方法,最终选择移动平均平滑法对原始光谱数据进行预处理;然后为选出合适的样本集划分方法以提高模型预测性能,对常见的四种方法进行对比,最终利用SPXY(sample set partitioning based on joint x-y distance)法进行样本集划分;进一步为减少数据量,降低维度,使用连续投影算法(successive projections algorithm, SPA)提取出7个特征波长,分别为833,927,1 208,1 337,1 454,1 861和2 280 nm;最后,将七个特征波长数据作为输入,选取径向基函数(radial basis function, RBF)作为支持向量机(support vector machine, SVM)核函数,取参数C=7 760 469,γ=0.017 003建立判别模型。SVM模型对训练集和测试集的预测准确率分别达到97.78%和93.33%。另取不同品种的玉米颗粒,以同样的标准挑选样品组成独立验证集,所建立的判别模型对独立验证集的预测准确率达到91.11%。结果表明基于SPA和SVM能有效地对玉米颗粒霉变程度进行判别,所选取的7个特征波长为实现在线霉变玉米颗粒近红外检测提供了理论依据。     

A study of the spatial and temporal evolution of auto-ignition kernels using time-resolved tomographic OH-LIF

In this paper, the spatial and temporal evolution of auto-ignition kernels from methane jets propagating into a NO_x-vitiated, high-turbulence, hot air co-flow was studied by means of time-resolved tomographic laser-induced fluorescence of OH (Tomo OH-LIF). Measurements were performed using a burst dye laser system at 10 kHz for volumetric laser illumination and a multi-camera arrangement (8-views) for detection of the fluorescence signal. Auto-ignition kernels were detected three-dimensionally and tracked using a robust algorithm based on the intensity gradient of the volumetrically reconstructed signals. The size and location of the detected kernels were evaluated for operating conditions with different Reynolds numbers of the fuel jet. Results showed that auto-ignition randomly occurred with high probability in a well defined fairly axisymmetric radial region with strong fluctuations in the main direction of the flow. The increase of the Reynolds number of the fuel jet resulted in a radial spread of the location of auto-ignition events. The statistical evaluation of the orientation and growth of auto-ignition kernels with respect to the mean flow field showed that the kernels were oriented tangentially to the flow and temporally evolve towards this preferential direction as the ignition events progressed.     

Reproducing Kernel for D2(Ω, ρ) and Metric Induced by Reproducing Kernel

An important property of the reproducing kernel of D2(Ω, ρ) is obtained and the reproducing kernels for D2(Ω, ρ) are calculated when Ω = Bn × Bn and ρ are some special functions. A reproducing kernel is used to construct a semi-positive definite matrix and a distance function defined on Ω×Ω. An inequality is obtained about the distance function and the pseudodistance induced by the matrix.     

Fractional Lévy processes on Gel’fand triple and stochastic integration

In this paper, we investigate the long-range dependence of fractional Lévy processes on Gel’fand triple and construct stochastic integral with respect to fractional Lévy processes for a class of deterministic integrands.      

Boundary Behavior of Harmonic Functions for Truncated Stable Processes

For any α∈(0,2), a truncated symmetric α-stable process in ℝ ^d is a symmetric Lévy process in ℝ ^d with no diffusion part and with a Lévy density given by c|x|^−d−α 1_{|x|<1} for some constant c. In (Kim and Song in Math. Z. 256(1): 139–173, [2007]) we have studied the potential theory of truncated symmetric stable processes. Among other things, we proved that the boundary Harnack principle is valid for the positive harmonic functions of this process in any bounded convex domain and showed that the Martin boundary of any bounded convex domain with respect to this process is the same as the Euclidean boundary. However, for truncated symmetric stable processes, the boundary Harnack principle is not valid in non-convex domains. In this paper, we show that, for a large class of not necessarily convex bounded open sets in ℝ ^d called bounded roughly connected κ-fat open sets (including bounded non-convex κ-fat domains), the Martin boundary with respect to any truncated symmetric stable process is still the same as the Euclidean boundary. We also show that, for truncated symmetric stable processes a relative Fatou type theorem is true in bounded roughly connected κ-fat open sets. The research of P. Kim is supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2007-331-C00037). The research of R. Song is supported in part by a joint US-Croatia grant INT 0302167.     

利用再生核解一类变系数偏微分方程

如何求解偏微分方程,已经成为各个领域内非常重视的课题.在再生核空间中,给出了变系数偏微分方程的级数形式精确解,为了数值计算,给出了一个迭代方法,并证明了迭代方法的收敛性.数值算例表明本文方法是有效的而且具有良好的实用性.     

On Approximation Methods Generated by Bochner-Riesz Kernels

Means and families of operators generated by Bochner-Riesz kernels are studied. Some sharp results on their convergence are achieved. The equivalence of the approximation errors of these methods to smoothness quantities related to the Laplacian is proved.      

A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces

Let p∈(0,1] and s≥[n(1/p−1)], where [n(1/p−1)] denotes the maximal integer no more than n(1/p−1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H ^p (ℝ ⁿ ) to some quasi-Banach space ℬ if and only if T maps all (p,2,s)-atoms into uniformly bounded elements of ℬ.      

Gross Laplacian Acting on Operators

In this paper, we introduce a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian, acting on some analytical operators. For this purpose, we use a characterization theorem between this class of operators and their symbols. Applying the quantum Gross Laplacian to the particular case where the operator is the multiplication one, we establishes a relation between the classical and the quantum Gross Laplacians.