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.     

局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

基于Caputo导数的分数阶非线性振动系统响应计算

研究了含分数阶Caputo导数的非线性振动系统响应的数值计算方法。首先，由Caputo分数阶导数算子的叠加关系，得到含分数阶导数项非线性振动系统状态方程的标准形式。其次，基于Caputo导数与Riemann-Liouville导数和Grunwald-Letnikov导数间的关系，推导计算了Caputo导数的一般数值迭代格式。本文方法不要求状态方程中各分数阶导数阶数相等，弱化了已有算法中对分数阶导数阶数的限制，并可推广到多自由度的情形。随后，选择若干有解析解的算例验证了本文方法的正确性。最后，以多吸引子共存的分数阶Duffing振子系统为例，比较Caputo和GL两种算法所得结果，说明了用GL算法求解存在的问题。     

Electrochemical Characteristics of a Triphenylamine Derivative by Microelectrode Voltammetry

With the objective of understanding the kinetic redox properties of triphenylamine derivatives in association with chemical reactions, for their future application in functional organic semiconductor devices, the electrochemical characteristics of 4‐(2,2‐diphenylethenyl)‐N,N‐bis(4‐methylphenyl)‐benzenamine (TPA) were evaluated. Based on cyclic voltammograms of TPA on Pt disk electrodes with diameters of 300 μm and 10 μm at slow and fast scan rates in an acetonitrile solution, the TPA^.+ is stable, while the TPA²⁺ is unstable. Importantly, the unstable TPA²⁺ appears to break down by a subsequent chemical reaction. A Cottrell plot analysis from chronoamperometry of a solution containing TPA reveals that both the first and second oxidations are one‐electron reactions. Concerning the stabilization mechanism of the first oxidation state of TPA, the results of molecular orbital calculations indicate that the electrons of the HOMO level are distributed in the triphenylamine group, which induces a resonance‐stabilized TPA^.+. Based on these results, TPA/TPA^.+ is suggested to have a sufficient stability for further application in organic semiconductor devices.     

浊度干扰下硝酸盐浓度紫外导数光谱检测方法研究

硝酸盐是水中“三氮”（硝酸盐氮、氨氮、总氮）之一，是反映水体受污染程度的一项重要指标。传统 “现场采样-离线分析” 的硝酸盐化学检测方法操作繁琐、耗时长，难以满足现代水环境实时在线检测需求。由于硝酸根在紫外区具有很强的紫外吸收特性，并且紫外吸收光谱法具有简便快速、可实现实时在线监测等特点，近年来被广泛用于硝酸盐浓度的测量。但使用紫外吸收光谱法检测水体硝酸盐含量时，容易受到水体浊度影响，造成谱线非线性抬升，导致测量误差。目前对浊度补偿算法的研究大都用于水中COD含量的检测，对硝酸盐检测中浊度干扰去除研究较少。为此提出一种基于一阶导数紫外吸收光谱的硝酸盐浓度测量方法，该方法可以减小浊度干扰，从而提高紫外光谱快速检测硝酸盐含量的准确度。通过测量福尔马肼与硝酸钠标准溶液和它们混合溶液在190~300 nm波段的紫外吸收光谱并做一阶导数光谱处理，处理后的光谱采用Savitzky-Golay滤波进行去噪平滑处理，比较浊度与硝酸盐紫外吸收一阶导数光谱特征，分波段研究浊度对硝酸盐紫外一阶导数光谱影响，结果表明硝酸盐导数光谱在220~230 nm波段受浊度影响小；选取220~230 nm波段作为光谱分析区间，以30种不同浓度混合的福尔马肼与硝酸钠溶液作为训练样本，利用偏最小二乘算法建立硝酸盐定量分析模型，使用该建模模型预测剩下的6种不同浓度福尔马肼与硝酸钠混合溶液中硝酸盐的浓度，结果表明福尔马肼干扰下硝酸盐测量结果的预测决定系数（correlation coefficient，R2）为0.994 3，预测均方根误差（root mean square error of prediction，RMSEP）为0.346 9 mg·L-1。为进一步验证该方法的准确性与稳定性，使用该建模模型预测高岭土与硝酸钾配制的混合水样中硝酸盐的浓度，结果表明该方法对高岭土干扰下硝酸盐测量结果的预测决定系数r2为0.991 5，预测均方根误差RMSEP为0.362 8 mg·L-1。综上所述，提出的硝酸盐浓度紫外导数光谱检测方法，采用220~230 nm波段的紫外导数光谱数据，结合PLS建模，可以快速准确测量在浊度干扰下水体硝酸盐的浓度，为发展实际水体硝酸盐在线监测技术与设备提供方法基础。     

一致分数阶非线性微分方程的精确解

同时考虑了Kudryashov方法和Khalil一致分数阶变换,构造了求解一致分数阶非线性微分方程精确解的新方法,并将其用于求解时间-空间一致分数阶Whitham-Boroer-Kaup方程,得到了Whitham-Boroer-Kaup方程新的精确解,验证了该方法的有效性和可行性.     

Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation

This paper proposes a fractional-order simplest chaotic system using a bi-stable locally-active memristor. The characteristics of the memristor and transient transition behaviors of the proposed system are analyzed, and this circuit is implemented digitally using ARM-based MCU. Firstly, the mathematical model of the memristor is designed, which is nonvolatile, locally-active and bi-stable. Secondly, the asymptotical stability of the fractional-order memristive chaotic system is investigated and some sufficient conditions of the stability are obtained. Thirdly, complex dynamics of the novel system are analyzed using phase diagram, Lyapunov exponential spectrum, bifurcation diagram, basin of attractor, and coexisting bifurcation, coexisting attractors are observed. All of these results indicate that this simple system contains the abundant dynamic characteristics. Moreover, transient transition behaviors of the system are analyzed, and it is found that the behaviors of transient chaotic and transient period transition alternately occur. Finally, the hardware implementation of the fractional-order bi-stable locally-active memristive chaotic system using ARM-based STM32F750 is carried out to verify the numerical simulation results.     

Highly sensitive perylene tetra-(alkoxycarbonyl) based colorimetric and ratiometric probes for fluorine detection

Fluoride anion (F^?) affects environmental, biological, and chemical processes significantly. Therefore, its detection has received increasing attention, and sensitive, effective, and convenient probes for F^? detection need to be developed urgently. In this work, two perylene tetra-(alkoxycarbonyl) (PTAC) based colorimetric and ratiometric probes, P1 and P2, were developed for the detection of F^?. The interactions between F^? and these two probes were investigated by absorption, electrochemistry, ¹H NMR, and density functional methods. Both the two probes were complexed with F^? with a ratio of 1:1. The detection limits of P1 and P2 were 0.22 μM and 0.87 μM, respectively. It was worth noting that the absorption peak of P1 showed a 190 nm red shift when sensing F^?, and P1 is the largest red shift value reported in F^? probes based on PTAC derivatives. This phenomenon was resulted from the unique configuration and deprotonation of P1 that can promote the intramolecular charge transfer (ICT). This strategy provides an example for the development of other ion probes based on D-A type ICT mechanism.