一类分数阶微积分的中值定理及应用

Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形，以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础，我们得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理，并给出其在计算方面的一些应用。     

Study of planar structure applying reciprocity technique combined with MGEC and analysis of discontinuity

The 3D structure electromagnetic computation presents several difficulties related to the volume mesh. In fact, the entire volume space must be taken into account even the smallest details. In this article, we propose a formulation based on the reciprocity theorem combined with the generalized equivalent circuit method to model a planar 3D structure with both coaxial and planar excitation. The major advantage of this formulation is the fact to reduce the computational volume into 2D ones in the discontinuity plane. In addition, we focused on the calculation of the discontinuity between the excitation source and the planar structure to determine the exact behavior of the electric coaxial excitation model. The obtained current density, electric field distributions, and the input impedance are presented and discussed in the following sections. An approximately good agreement of input impedance with those obtained by the simulator and measurement is shown.     

Weighted preliminary-summation-based principal component analysis for non-Gaussian processes

For industrial chemical process, preliminary-summation-based principal component analysis (PS-PCA), an amended PCA method was recently provided for coping with both Gaussian and non-Gaussian characteristics. By summing the training and monitoring data respectively, PS-PCA is capable of resolving the issue of non-Gaussian processes and achieves higher fault detection rate than the traditional PCA. However, in the PS-PCA summation operation, all data samples are regarded as the same weight, which results in the fault information of newly-samples may be diluted, leading to significant detection delays. To address this challenge, in this paper, we propose a novel weighted PS-PCA (WPS-PCA) method that employs an exponential weighting scheme to put more emphasis on recent information. Subsequently, a mathematical argument demonstrates that when the number of variables is enough plentiful, the obtained summation combined with the generalized central limit theorem conforms to approximately a Gaussian distribution. The kurtosis relationships indicate this conversion will bring out well-pleasing feasibility for conventional PCA. Ultimately, the proposed technique verifies detection performance using the Tennessee Eastman process, which is compared with the existing PCA and PS-PCA schemes, in terms of the fault detection time and fault detection rate. The simulation studies reveal that the proposed method is efficient and superior.     

一类Hilfer型分数阶微分方程解的存在和唯一性

用Banach不动点定理和上下解方法研究了α(1<α <2)阶数和β(0≤β ≤1)类型Hilfer分数阶微分方程的解,给出了方程解的存在和唯一性,并通过例证验证了本文所得结果的有效性.     

Robust Linear Interpolation and Extrapolation of Stationary Time Series in Lp

To deal with uncertainty of the spectral distribution, we consider minimax interpolation and extrapolation problems in L^p for stationary processes. The interpolation and extrapolation problems can be regarded as a linear approximation problem on the unit disk in the complex plane. Although the robust one-step-ahead predictor and interpolator has already been considered separately in the previous literature, we give two conditions for the uncertainty class to find the minimax interpolator and extrapolator in the general framework from both the point of view of the observation set and the point of view of evaluation on the interpolation and extrapolation error under the L^p-norm. We show that there exists a minimax interpolator and extrapolator for the class of spectral densities ε-contaminated by unknown spectral densities under our conditions. When the uncertainty class contains spectral distribution functions which are not absolutely continuous to the Lebesgue measure, we show that there exists an approximate interpolator and extrapolator in L^p such that its maximal interpolation and extrapolation error is arbitrarily close to the minimax error when the spectral distributions have densities. Our results are applicable to the stationary harmonizable stable processes.     

On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model

We derive the limit theory of the Gaussian stable quasi maximum likelihood estimator for the stationary EGARCH(1,1) model when the squared innovation process has marginals with regularly varying tails. We derive regularly varying rates and limiting stable distributions. We perform Monte Carlo experiments to assess the extent of the parameter space corresponding to the invertibility condition, and the quality of the asymptotic approximation.     

Levelized cost of energy definition – An economic paradox

Using mean value theorem for integrals we show that the well-known LCOE definition is incorrect.