Dynamic stability of a class of fractional-order nonlinear systems via fixed point theory

In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in $\left(\frac{1}{2},1\right)$. However, the case of the fractional-order belonging to $(0,\frac{1}{2})$ has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.     

A new idea to construct the fractal interpolation function

The aim of this paper is to present a new idea to construct the nonlinear fractal interpolation function, in which we exploit the Matkowski and the Rakotch fixed point theorems. Our technique is different from the methods presented in the previous literatures.     

小孔流速实验中的排水时间和流量系数的研究

本文以水作为理想流体,考虑到水头损失和孔口缩流效应,对小孔流速实验涉及的容器排水问题进行了系统的理论和实验研究.从理论上推导得出了圆柱形容器排水时间的解析解,分析了排水时间和自由液面速度、流量系数之间的规律,提出了排水时间的等效性.实验上,加工了底部开有不同小孔的大型圆柱形容器,测量了容器排水时间随液面高度的变化关系,借助实验结果计算了流量系数值,验证了容器排水时间的等效性关系,实验结果与理论计算符合较好.     

A Ca2+‐, Mg2+‐, and Zn2+‐Based Dendritic Contractile Nanodevice with Two pH‐Dependent Motional Functions

A contractile dendritic motional device is reported where metal ions with biological importance—Ca²⁺ (the main regulatory and signaling species of the natural muscles), Mg²⁺, and Zn²⁺—initiate two kinds of motional functions. The first motional function is the metal‐ion‐induced contraction of a linear strand into a Z‐shaped dinuclear complex, and the second one is the change of the height of Z‐shaped complexes via transmetalation. By means of the pH‐dependent counterligand tren, the two motional features of the machine can depend on alternate additions of acid and base. An optical response is associated with the conversion of the linear form (which is yellow) into the metalated Z‐shaped one (which is red).     

一类双曲型方程的Hamilton算子半群方法

将一类双曲型方程混合问题转换成一阶抽象Cauchy问题,证明所得Hamilton算子矩阵H在相应空间中生成压缩半群,并借助Fourier变换,采用一致连续半群做逼近的方法,得到H所生成的压缩半群,进而给出了问题的古典解.     

一种新的求解拟单调变分不等式的压缩投影算法

2020年Liu和Yang提出了求解Hilbert空间中拟单调且Lipschitz连续的变分不等式问题的投影算法,简称LYA。本文在欧氏空间中提出了一种新的求解拟单调变分不等式的压缩投影算法,简称NPCA。新算法削弱了LYA中映射的Lipschitz连续性。在映射连续、拟单调且对偶变分不等式解集非空的条件下得到了NPCA所生成点列的聚点是解的结论。当变分不等式的解集还满足一定条件时,得到了NPCA的全局收敛性。数值实验结果表明NPCA所需的迭代步数少于LYA的迭代步数,NPCA在高维拟单调例子中所需的计算机耗时也更少。     

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.     

Creeping flow of viscoplastic materials through a planar expansion followed by a contraction

In this work, the creeping flow of a viscoplastic fluid through a planar channel with an expansion followed by a contraction is analyzed numerically. The solution of the conservation equations of mass and momentum is obtained via the finite volume method. In order to model the non-Newtonian behavior of the fluid, it was used the generalized Newtonian fluid constitutive equation. The viscosity function was the one proposed by Souza Mendes and Dutra [Souza Mendes, P.R., Dutra, E.S.S., 2004. Viscosity function for yield-stress liquids. Appl. Rheol. 14, 296–302]. The yielded and unyielded regions are obtained for several combinations of rheological parameters. The influence of these parameters on pressure drop through the cavity is also obtained and analyzed.     

Variation of fiber orientation in turbulent flow inside a planar contraction with different shapes

In this study, we have investigated the influence of shape of planar contractions on the orientation distribution of stiff fibers suspended in turbulent flow. To do this, we have employed a model for the orientational diffusion coefficient based on the data obtained by high-speed imaging of suspension flow at the centerline of a contraction with flat walls. This orientational diffusion coefficient depends only on the contraction ratio and turbulence intensity. Our measurements show that the turbulence intensity decays exponentially independent of the contraction angle. This implies that the turbulence variation in the contraction is independent of the shape, consistent with the results by the rapid distortion theory and the experimental results of axisymmetric contractions. In order to determine the orientation anisotropy, we have solved a Fokker–Planck type equation governing the orientation distribution of fibers in turbulent flow. Although the turbulence variation and the orientational diffusion are independent of the contraction shape, the results show that the variation of the orientation anisotropy is dependent on shape. This can be explained by the variation of the rotational Péclet number, Pe_r, inside the contractions. This quantity is a measure of the importance of the mean rate of the strain relative to the orientational diffusion. We have shown that when Pe_r < 10 turbulence can significantly influence the evolution of the orientation anisotropy. Since in contractions with identical inlet conditions the streamwise position where Pe_r = 10 depends on the shape, the orientation anisotropy is dependent on the variation of rate of strain in a given contraction. We demonstrate the shape effect by considering contraction with flat walls as well as three contractions with different mean rate of strain variation.