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。     

磨矿动力学研究现状及应用

磨矿动力学是描述被磨物料的磨碎速率与磨矿时间之间关系规律的一种数学模型，对分析物料在磨矿过程中的粒级及能量变化具有重要作用。为充分发挥磨矿动力学在磨矿过程中的作用，论文在分析国内外研究现状的基础上，系统介绍了两种典型的磨矿动力学模型：m阶磨矿动力学模型和磨矿总体平衡动力学模型，分析了模型中各参数的含义；以磨矿总体平衡动力学模型为重点，分析了破碎速率函数和破碎分布函数的求解方式，包括零阶产出率法、奥-勒理论简算法、卡普尔G-H算法以及经验公式法等；从物料性质、磨矿介质及配比、磨矿方式及参数、化学添加剂等几个方面分析了影响磨矿动力学模型的因素；指出了磨矿动力学模型在矿物加工工程领域的应用现状并对其未来的研究方向提出展望。研究表明磨矿动力学在矿物加工领域具有广泛而重要的应用，为进一步改善磨矿工艺提供了理论依据。     

Deterministic and probabilistic ship pitch prediction using a multi-predictor integration model based on hybrid data preprocessing,reinforcement learning and improved QRNN

The deterministic and probabilistic prediction of ship motion is important for safe navigation and stable real-time operational control of ships at sea. However, the volatility and randomness of ship motion, the non-adaptive nature of single predictors and the poor coverage of quantile regression pose serious challenges to uncertainty prediction, making research in this field limited. In this paper, a multi-predictor integration model based on hybrid data preprocessing, reinforcement learning and improved quantile regression neural network (QRNN) is proposed to explore the deterministic and probabilistic prediction of ship pitch motion. To validate the performance of the proposed multi-predictor integrated prediction model, an experimental study is conducted with three sets of actual ship longitudinal motions during sea trials in the South China Sea. The experimental results indicate that the root mean square errors (RMSEs) of the proposed model of deterministic prediction are 0.0254°, 0.0359°, and 0.0188°, respectively. Taking series #2 as an example, the prediction interval coverage probabilities (PICPs) of the proposed model of probability predictions at 90%, 95%, and 99% confidence levels (CLs) are 0.9400, 0.9800, and 1.0000, respectively. This study signifies that the proposed model can provide trusted deterministic predictions and can effectively quantify the uncertainty of ship pitch motion, which has the potential to provide practical support for ship early warning systems.     

Application of artificial neural network method to predict the breakage properties of PGE bearing chromite ore

In the present investigation, systematic grinding experiments were conducted in a laboratory ball mill to determine the breakage properties of low-grade PGE bearing chromite ore. The population balance modeling technique was used to study the breakage parameters such as primary breakage distribution (B_{i, j}) and the specific rates of breakage (S_i). The breakage and selection function values were determined for six feed sizes. The results stated that the breakage follows the first-order grinding kinetics for all the feed sizes. It was observed that the coarser feed sizes exhibit higher selection function values than the finer feed size. Further, an artificial neural network was used to predict breakage characteristics of low-grade PGE bearing chromite ore. The predicted results obtained from the neural network modeling were close to the experimental results with a correlation of determination R² = 0.99 for both product size and selection function.     

Changes in polyphenol fractions and bacterial composition after in vitrofermentation of apple peel polyphenol by gut microbiota

The changes in polyphenol fractions after in vitro fermentation of apple peel polyphenol (APP) by gut microbiota as well as the effects of APP on the growth, pH value, short-chain fatty acids (SCFAs) production and intestinal flora composition of gut microbiota fermentation were firstly explored in this study. The relative abundance of Lactobacillus in the APP group was 49.55% with an increment of 49.40% compared with the blank group, while that of Bifidobacterium was 13.32%. Moreover, the flora produced 37.093 ± 0.478 mM of SCFAs including acetic acid, propionic acid, butyric acid and valeric acid during the process of fermentation, thus reduced the environmental pH value. In addition, polyphenol fractions in APP were altered by gut microbiota fermentation to some extent, for example, glycosides were hydrolysed to aglycones. These findings suggested APP as a potential prebiotic agent to alleviate the disorder of intestinal flora.     

A Fusion Kalman Filter and UFIR Estimator Using the Influence Function Method

In this paper, the Kalman filter (KF) and the unbiased finite impulse response (UFIR) filter are fused in the discrete-time state-space to improve robustness against uncertainties. To avoid the problem where fusion filters may give up some advantages of UFIR filters by fusing based on noise statistics, we attempt to find a way to fuse without using noise statistics. The fusion filtering algorithm is derived using the influence function that provides a quantified measure for disturbances on the resulting filtering outputs and is termed as an influence finite impulse response (IFIR) filter. The main advantage of the proposed method is that the noise statistics of process noise and measurement noise are no longer required in the fusion process, showing that a critical feature of the UFIR filter is inherited. One numerical example and a practice-oriented case are given to illustrate the effectiveness of the proposed method. It is shown that the IFIR filter has adaptive performance and can automatically switch from the Kalman estimate to the UFIR estimates according to operating conditions. Moreover, the proposed method can reduce the effects of optimal horizon length on the UFIR estimate and can give the state estimates of best accuracy among all the compared methods.      

Efficiency evaluation of healthcare services in China based on stochastic multicriteria acceptability analysis and directional distance function

Evaluating the efficiency of healthcare services accurately can help in analyzing the rationality of inputs and outputs in such services. Considering the consistency and equity of assessment criteria, this study conducts the stochastic multicriteria acceptability analysis (SMAA-2) with a directional distance function to evaluate the efficiency of healthcare services in 31 provincial administrative regions of mainland China, as observed in 2018. We use SMAA-DDF to explore all the projection directions to the efficient frontier instead of a certain projection direction. We measure the maximum and average efficiencies for each of the 31 provincial healthcare services. Our empirical findings show that only seven provinces achieve optimal healthcare service efficiency; the eastern area performed the best, followed by the central, western, and northeast areas. Furthermore, the path along the projection directions is provided to help inefficient provinces improve their efficiency and obtain the best possible positions.     

Synthesis and performance evaluation of a new drag reducer based on acrylamide/12-allyloxydodecyl acid sodium

Hydraulic fracturing with slickwater is a field-proven stimulation technology used in tight reservoirs. Because of the high pumping rate associated with slickwater fracturing, drag reduction (DR) is critical in minimizing pressure drop and the success of oilfield operations. In this paper, a new type of drag reducer (SPR) was synthesized with acrylamide and 12-allyloxydodecyl acid sodium, and its drag reduction performance was evaluated. The results showed that the new drag reducer features low molecular weight, fast-dissolving rate and low interfacial tension. The algorithm of estimating the drag reduction rate of non-Newtonian fluid SPR was proposed and validated. Empirical or semianalytical models for estimating the friction ratio (σ) or friction factor (λ or f) were used to simulate the turbulence behavior of the SPR drag reducer under different Reynolds numbers (Re). The modified Virk's correlation could accurately model the turbulent behavior of the SPR drag reducer. A unified calculation formula was established in this study for different pipe diameters.