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。     

Rheological and viscoelastic properties of colloidal solutions based on gelatins and chitosan as affected by pH

The objective of this study was to evaluate the influence of pH on rheological and viscoelastic properties of solutions based on blends of type A (GeA) or type B (GeB) gelatin and chitosan (CH). Solutions of GeA, GeB, CH, GeA:CH, and GeB:CH were prepared in several pH (3.5–6.0) and analyzed for determination of zeta-potential. Rheological analyses (stationary and dynamic essays) were carried out with blends allowing to study the effect of pH on shear stress, apparent viscosity, loss (G”) and storage (G’) moduli, and angle phase (Tanδ). Zeta potential of all biopolymers decreased linearly as a function of pH. CH presented higher values, and GeB, the lowest one, being the only having negative values at pH > 5. Overall, the pH influenced the rheological and viscoelastic properties of the colloidal solutions: shear stress and apparent viscosity increased as a function of pH. Other assays were carried out at 3% and 5% strain, for GeA:CH and GeB:CH, respectively. In the sol domain, G’ and G” (1 Hz) increased linearly for GeA:CH. But for GeB:CH, they increased in two linear different regions: one function between pH 3.5 and 5.0 and another one between 5.0 and 6.0, being a more important effect was visible in this last domain probably due to the negative net charge of gelatin, above it pI. An effect in two domains was also visible for Tanδ, explained in the same manner as previously. The GeB:CH blends behaved like diluted solutions, and transition temperatures increased as a function of pH.     

Physical and sensory properties of lemon-flavored acidic beverages formulated with nonfat dry milk during storage

Sensory and physical properties of 2 lemon-flavored beverages with 5% and 7.5% wt/wt nonfat dry milk (NFDM) at pH 2.5 were studied during storage. The 2 beverages had similar volatile compounds, but the 5% NFDM had higher aroma and lemon flavor, with a preferred appearance by consumers due to the lower turbidity and viscosity. After 28 d of storage at 4°C, lemon flavor decreased in the 5% NFDM beverage but was still more intense than the 7.5% one. During 70 d of storage, no microorganisms were detected, and the beverages were more stable when stored at 4°C than at room temperature according to changes of physical properties measured for appearance, turbidity, color, particle size, zeta potential, rheological properties, and transmission electron microscopy morphology. Findings of the present study suggest that NFDM may be used at 5% wt/wt to produce stable acidic dairy beverages with low turbidity when stored at 4°C.     

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.     

Influence of tef flour and its association with other flours on the nutritional,technological, and sensory quality of bakery products

The objective of this study was to investigate chemical, technological, and sensory quality of tef in products made exclusively with tef flour and tef flour associated with other flours. The selection of the studies and the extraction of information were carried out through research in several databases. Tef flour was used in cakes, cookies, breads, cupcakes, muffins, and extruded snacks. Bread was the most evaluated product with tef flour associated with other flours or exclusively. Most of the outcomes were with tef (5–50%) associated with other flours. Increased levels of fibers, minerals, antioxidant capacity, and flavonoids were noted according to the percentage of tef. Technological characteristics demonstrated that these products showed intermediate final quality, due to the characteristics of volume, specific volume, firmness, and luminosity. Regarding sensory quality, studies that used (5–35%) tef flour associated with other flours were well-accepted.     

Designing amorphous formulations of polyphenols with naringin by spray-drying for enhanced solubility and permeability

Naringin (NAR), a major flavanone (FVA) glycoside, is a component of food mainly obtained from grapefruit. We used NAR as a food additive to improve the solubility and permeability of hydrophobic polyphenols used as supplements in the food industry. The spray-dried particles (SDPs) of NAR alone show an amorphous state with a glass transition temperature (T_g) at 93.2 °C. SDPs of hydrophobic polyphenols, such as flavone (FVO), quercetin (QCT), naringenin (NRG), and resveratrol (RVT) were prepared by adding varying amounts of NAR. All SDPs of hydrophobic polyphenols with added NAR were in an amorphous state with a single T_g, but SDPs of hydrophobic polyphenols without added NAR showed diffraction peaks derived from each crystal. The SDPs with NAR could keep an amorphous state after storage at a high humidity condition for one month, except for SDPs of RVT/NAR. SDPs with NAR enhanced the solubility of hydrophobic polyphenols, especially NRG solubility, which was enhanced more than 9 times compared to NRG crystal. The enhanced solubility resulted in the increased membrane permeability of NRG. The antioxidant effect of the hydrophobic NRG was also enhanced by the synergetic effect of NAR. The findings demonstrated that NAR could be used as a food additive to enhance the solubility and membrane permeability of hydrophobic polyphenols.