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。     

Weighted regularized extreme learning machine to model the discharge coefficient of side slots

In the current research, a modern learning machine algorithm named “Weighted Regularized Extreme Learning Machine (WRELM)" is implemented for the first time for the simulation of the coefficient of discharge of side slots. For this purpose, an effective variable on the coefficient of discharge of side slots is firstly introduced, then five distinctive WRELM models are produced by it for the estimation of the coefficient. In the next stage, a database is created for verification of WRELM results. it should be mentioned that 70% of the data are utilized for training the WRELM models, while the rest (i.e. 30%) for testing them. After that, the optimal number of hidden layer neurons as well as the best activation function of the WRELM algorithm are chosen. In addition, the best regularization parameter and also the weight function of the WRELM are achieved. By conducting a sensitivity analysis, the most effective variable for the simulation of the coefficient of discharge along with the WRELM superior model is introduced. The WRELM superior model estimates values of the coefficient of discharge with the maximum exactness and the highest correlation. For instance, the estimations of the correlation coefficient and scatter index for this model are computed to be 0.930 and 0.051, respectively. The sensitivity analysis shows that the ratio of the side slot crest height to its length and the Froude number should be considered as the most important input variables. A comparison between the WRELM with the ELM displays that the former works much better. Furthermore, an uncertainty analysis is executed for both models. Eventually, an equation is suggested for the estimation of the coefficient of discharge and a partial derivative sensitivity analysis is performed on it.     

基于小波变换的分数阶微分算法在肝脏肿瘤CT图像纹理增强中的应用

图像纹理增强过程中容易丢失平滑区域纹理细节，而分数阶微分增强虽然能够非线性保留平滑区域纹理细节，但对频率分辨率敏感。针对这个问题，提出一种基于小波变换的分数阶微分纹理增强算法，应用于平扫计算机断层扫描（CT）图像的肝脏肿瘤区域的纹理增强。首先，通过小波变换将图像感兴趣区分解成多个子带分量；其次，基于分数阶微分定义构造一个带补偿参数的分数阶微分掩膜；最后，使用该掩膜与每个高频子带分量进行卷积并利用小波逆变换重组图像感兴趣区。实验结果表明，该方法在使用较大分数阶次显著增强肿瘤区域的高频轮廓信息的同时，有效地保留了低频平滑的纹理细节：增强后的肝细胞癌区域与原区域相比，信息熵平均增加36.56%，平均梯度平均增加321.56%，平均绝对差值平均为9.287；增强后的肝血管瘤区域与原区域相比，信息熵平均增加48.77%，平均梯度平均增加511.26%，平均绝对差值平均为14.097。     

Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

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.     

Theoretical and experimental studies of a new aniline derivative corrosion inhibitor for mild steel in acid medium

4-Chloro-N-(pyridin-2-ylmethyl)aniline (CPYA) was synthesized by a simple and inexpensive method and tested as a corrosion inhibitor in acid medium for mild steel by using gravimetric studies and electrochemical measurements. An average maximum efficiency of 96.0% was achieved at 4.59 mmol/L. Corrosion kinetic and thermodynamic parameters were also analyzed. Surface analyses (atomic force microscopy and scanning electron microscopy) show that protection is enabled by adsorption on the metal, forming a film. Quantum chemical calculations were performed to access information regarding the molecular structure in the corrosive medium and to support interpretation of the results obtained by experimental methods.     

Assessing smoke toxicity of burning combustibles by four expressions for fractional effective dose

Toxicity of smoke generated in a fire is difficult to measure accurately. That is because gas sensors for measuring rapidly varying concentrations of toxic gases are not yet developed. Simple expressions are searched for quick measurement in assessing smoke toxicity practically. Four equations on calculating fractional effective dose (FED) related to toxic effluents were reported in the literature, each based on different assumptions. FED value was proposed to be calculated based on peak carbon monoxide concentration and peak carbon dioxide concentration, and transient carbon monoxide, carbon dioxide, and oxygen concentrations. The four values were compared in this article using literature data on toxic gases from different materials measured by (i) cone calorimeter; (ii) full-scale burning tests; and (iii) tunnel full-scale tests. Measured carbon monoxide, carbon dioxide, and oxygen concentrations by standard equipment of oxygen consumption calorimeters were used to calculate the four FED values. It is found that the values of FED based on peak carbon monoxide and carbon dioxide concentrations (denoted as FED₂) are similar to the average values of FED calculated from the updated equation in the literature using the oxygen consumption calorimeters. Putting the values of FED₂ in fire safety design guides is then recommended.     

Robust adaptive passivity-based PIλD control

In this article, we develop proportional, fractional-integral, and derivative () controllers for the regulation and tracking problems of nonlinear systems. The analytic results are obtained by extending the passivity-based approach to include fractional operators. Robustness under parametric uncertainty is dealt with by a combination with an adaptive scheme. It is also shown their robustness under additive noise and their robustness under uncertainty in the derivation order. The advantages in the controlled system performance and in the control energy consumption in comparison to classic PI and proportional integral derivative controllers are illustrated for the quadratic boost converter and a benchmark system in the literature.     

Unsteady free convection of second‐grade nanofluid with a new time‐space fractional heat conduction

The Caputo and Caputo–Fabrizio derivative are applied to study a second‐grade nanofluid over a vertical plate. A comparative analysis is presented to study the unsteady free convection of a second‐grade nanofluid with a new time–space fractional heat conduction. The governing equations with mixed time–space fractional derivatives are non‐dimensionalized and solved numerically, and a comparison between the Caputo and the Caputo–Fabrizio models is made. It is found that the temperature is higher for the Caputo–Fabrizio fractional model than the Caputo model, but the higher velocity only exists near the vertical plate for the Caputo–Fabrizio model than the Caputo model. Moreover, the velocity for the Caputo model will exceed the Caputo–Fabrizio model as y evolves.     

氟橡胶的红外光谱研究

采用红外(IR)光谱,包括一维红外光谱、二阶导数红外光谱、四阶导数红外光谱和去卷积红外光谱对氟橡胶(FKM)的分子结构进行了研究。试验发现:氟橡胶的红外吸收模式主要包括CH2不对称伸缩振动模式(νasCH2-FKM)、CH2对称伸缩振动模式(νsCH2-FKM)、CH2弯曲伸缩振动模式(δCH2-FKM)、CF2不对称伸缩振动模式(νasCF2-FKM)、CF2对称伸缩振动模式(νsCF2-FKM)和CFCl伸缩振动模式(νCFCl-FKM)等。研究发现:氟橡胶的去卷积IR光谱的谱图分辨能力要优于相应的一维IR光谱、二阶导数IR光谱和四阶导数IR光谱。此研究拓展了IR光谱在氟橡胶结构及应用研究的范围。