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。     

Breeding schemes with optimum-contribution selection or truncation selection for beef cattle destined for use on dairy females

We tested the hypothesis that the size of a beef cattle population destined for use on dairy females is smaller under optimum-contribution selection (OCS) than under truncation selection (TRS) at the same genetic gain (ΔG) and the same rate of inbreeding (ΔF). We used stochastic simulation to estimate true ΔG realized at a 0.005 ΔF in breeding schemes with OCS or TRS. The schemes for the beef cattle population also differed in the number of purebred offspring per dam and the total number of purebred offspring per generation. Dams of the next generation were exclusively selected among the one-year-old heifers. All dams were donors for embryo transfer and produced a maximum of 5 or 10 offspring. The total number of purebred offspring per generation was: 400, 800, 1,600 or 4,000 calves, and it was used as a measure of population size. Rate of inbreeding was predicted and controlled using pedigree relationships. Each OCS (TRS) scheme was simulated for 10 discrete generations and replicated 100 (200) times. The OCS scheme and the TRS scheme with a maximum of 10 offspring per dam required approximately 783 and 1,257 purebred offspring per generation to realize a true ΔG of €14 and a ΔF of 0.005 per generation. Schemes with a maximum of 5 offspring per dam required more purebred offspring per generation to realize a similar true ΔG and a similar ΔF. Our results show that OCS and multiple ovulation and embryo transfer act on selection intensity through different mechanisms to achieve fewer selection candidates and fewer selected sires and dams than under TRS at the same ΔG and a fixed ΔF. Therefore, we advocate the use of a breeding scheme with OCS and multiple ovulation and embryo transfer for beef cattle destined for use on dairy females because it is favorable both from an economic perspective and a carbon footprint perspective.     

A charge sharing–based switching scheme for SAR ADCs

This paper presents an energy-efficient switching scheme for successive approximation register (SAR) analogue-to-digital converter (ADC). The proposed scheme employs charge recycling method to keep the capacitor arrays free of transitional energy between bit generations except reset phase. In comparison with the conventional switching scheme, the proposed one achieves 100% transitional energy saving without considering reset phase. In addition, configuration of a 10-bit SAR ADC shows that the proposed switching scheme reduces the capacitor area by 25% compared with the conventional switching scheme.     

A Reliable Stochastic Numerical Analysis for Typhoid Fever Incorporating With Protection Against Infection

In this paper, a reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection has been considered. We have compared the solutions of stochastic and deterministic typhoid fever model. It has been shown that the stochastic typhoid fever model is more realistic as compared to the deterministic typhoid fever model. The effect of threshold number T* hold in stochastic typhoid fever model. The proposed framework of the stochastic non-standard finite difference scheme (SNSFD) preserves all dynamical properties like positivity, bounded-ness and dynamical consistency defined by Mickens, R. E. The stochastic numerical simulation of the model showed that increase in protection leads to low disease prevalence in a population.     

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.     

A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients

In this paper, a combined compact finite difference method (CCD) together with alternating direction implicit (ADI) scheme is developed for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. The proposed CCD-ADI method is second-order accurate in time variable and sixth-order accurate in space variable. For the linear hyperbolic equation, the CCD-ADI method is shown to be unconditionally stable by using the Von Neumann stability analysis. Numerical results for both linear and nonlinear hyperbolic equations are presented to illustrate the high accuracy of the proposed method.     

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.