On the analysis of vibration equation involving a fractional derivative with Mittag-Leffler law

The present article deals with a fractional extension of the vibration equation for very large membranes with distinct special cases. The fractional derivative is considered in Atangana-Baleanu sense. A numerical algorithm based on homotopic technique is employed to examine the fractional vibration equation. The stability analysis is conducted for the suggested scheme. The maple software package is utilized for numerical simulation. In order to illustrate the effects of space, time, and order of Atangana-Baleanu derivative on the displacement, the outcomes of this study are demonstrated graphically. The results revel that the Atangana-Baleanu fractional derivative is very efficient in describing vibrations in large membranes.     

田字形地震超材料甚低频宽带隙机理

在地球中传播的地震波主要有体波和表面波,而表面波中Rayleigh波对建筑物造成的破坏最为强烈。针对Rayleigh波的振动控制,提出一种田字形超材料结构。相比于传统的地震超材料,这种超材料屏障是由外部口字形框体内部嵌套十字形柱体组成,形成4个可填充区域,其外部框体采用部分埋入的方式,具有高强度、强稳定性、填充方式灵活的特点。应用有限元法计算了田字形超材料的能带结构和传输特性,并通过分析带隙边界处模态振型可知,带隙的打开是由于柱体的局域共振。结合带隙机理可知,柱体结构中土壤填充量不同可改变柱体的质量,形成不同的谐振频率,产生甚低频带隙。为进一步拓宽带隙,设计研究了正、负梯度的质量填充方式,均可得到3.3~13.1 Hz甚低频宽带隙,在谐振频率范围内两者的隔震方式分别为Rayleigh波彩虹捕获和Rayleigh波到体波的转化。最后,采用EI-Centro地震波对填充屏障进行了时程验证,加速度最大幅值衰减超过80%,为地震超材料在减震隔震方面应用提供了新的设计思路和方法。     

Dynamic Modeling of the Feed Drive System of a CNC Metal Cutting Machine

Studying the vibrational behavior of feed drive systems is important for enhancing the structural performance of computer numerical control (CNC) machines. The preload on the screw and nut position have a great influence on the vibration characteristics of the feed drive as two very important operational conditions. Rotational acceleration of the screw also affects the performance of the CNC feed drive when machining small parts. This paper investigates the influence of preload and nut position on the vibration characteristics of the feed drive system of a CNC metal cutting machine in order to be able to eliminate an observed resonance occurred at high rotational speeds of the screw, corresponding to high feed rates. Additionally, rational structural parameters of the feed drive system are selected in order to increase the rotational acceleration for improving the performance of the CNC machine. Experiments and analyses showed that by selecting specific parameters of feed drive system and simultaneously applying a certain value of preload, a 97% increase in rotational acceleration and 30% time reduction considering the vibration resistance at high rotational speeds can be achieved.     

石英晶体板非线性高频振动的拓展伽辽金法分析

针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。     

Tutorial review on validation of liquid chromatography–mass spectrometry methods: Part II

This is the part II of a tutorial review intending to give an overview of the state of the art of method validation in liquid chromatography mass spectrometry (LC–MS) and discuss specific issues that arise with MS (and MS–MS) detection in LC (as opposed to the “conventional” detectors). The Part II starts with briefly introducing the main quantitation methods and then addresses the performance related to quantification: linearity of signal, sensitivity, precision, trueness, accuracy, stability and measurement uncertainty. The last section is devoted to practical considerations in validation. With every performance characteristic its essence and terminology are addressed, the current status of treating it is reviewed and recommendations are given, how to handle it, specifically in the case of LC–MS methods.     

Molecular signal suppression by in situ microextraction in nuclear magnetic resonance spectroscopy

The detailed characterization of complex mixtures by NMR is often hampered by the presence of signals from uninformative compounds, the resonances of which overlap with those of the molecules of interest. We provide here a proof of principle for an approach to NMR signal suppression in complex samples using Molecularly Imprinted Polymers (MIPS). Addition of a few milligrams of polymer to a solution traps the target molecule in typical micromolar to millimolar concentration, thus achieving in situ signal suppression, without altering any other spectral features. This method minimized any manipulation or perturbation of the spectrum and was applied to a complex mixture of known compounds and to a plant extract, in both cases spiked with a compound (bisphenol A), which was subsequently removed by selective binding to a complementary MIP. What is described in this report is comparable with microextraction and may in due course be applied to a large number of analytical challenges. Copyright © 2014 John Wiley & Sons, Ltd.     

不同抗凝比例对凝血四项检测结果的影响

目的观察并分析凝血四项检测结果与不同比例下的全血与抗凝剂之间的关系。方法研究对象取2015年6月来湖北省宜昌市第二人民医院参加体检的110例健康人员,抽取全血血液样本后按照不同比例与抗凝剂混匀,常规分离血浆并测定受试者凝血酶时间(TT)、凝血酶原时间(PT)、激活部分促凝血酶原激酶时间(APTT)以及纤维蛋白原(FIB),并对研究结果相关数据作统计学处理。结果当血液量与抗凝剂比例为1∶5时,标本TT、PT、APTT以及FIB各项指标较1∶9时差异显著而具有统计学意义(P0.05);抗凝比例1∶7的情况下,TT指标差异与1∶9抗凝比例标本相比差异具有统计学意义(P0.05),而PT、FIB以及APTT三项指标差异并无统计学意义(P0.05);抗凝比例为1∶11与1∶13的情况下,TT指标与1∶9抗凝比例标本相比差异具有统计学意义(P0.05),而PT、FIB以及APTT三项指标差异并无统计学意义(P0.05)。结论凝血四项检测工作中,标本质量检测控制最关键的环节在于准确采集血液量,倘若采集血量过多或过少,导致与抗凝剂比例失调往往会影响测定结果准确性,检验科工作人员应予以重视。     

Error Estimates for Semi-Discrete and Fully Discrete Galerkin Finite Element Approximations of the General Linear Second-Order Hyperbolic Equation

In this article, we derive error estimates for the semi-discrete and fully discrete Galerkin approximations of a general linear second-order hyperbolic partial differential equation with general damping (which includes boundary damping). The results can be applied to a variety of cases (e.g. vibrating systems of linked elastic bodies). The results generalize pioneering work of Dupont and complement a recent article by Basson and Van Rensburg.     

Optimal portfolio execution under time-varying liquidity constraints

In this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity.     

Built-in piezoelectric field improved photocatalytic performance of nanoflower-like Bi2WO6 using low-power white LEDs

Photocatalysis technology has been proved to be a potential strategy for removal of organic dyes, however high-power light sources are generally necessary to initiate photocatalytic reaction. In this work, we employed an excellent photocatalyst of Bi₂WO₆ with visible light harvest and meanwhile an intrinsic ferroelectricity, which realized the efficient degradation of organic dye via the synergetic photopiezocatalysis. Through coupling the illumination by a low-power (9 W) LED and the ultrasonic vibration (120 W) by an ultrasonic cleaner, the nanoflower-like Bi₂WO₆ composed of ultrathin nanosheets showed a much more enhanced photopiezocatalysis performance for purification of organic dye than the individual photocatalysis and piezocatalysis. Furthermore, the high mineralization efficiency and the good durability of the Bi₂WO₆ catalyst were demonstrated. The possible mechanism of photopiezocatalysis was finally proposed, where the ultrasound-induced piezoelectric field in Bi₂WO₆ drove photo-generated electrons and holes to diffuse along opposite directions, consequently promoting the separation efficiency of charge carriers. This work indicates that the synergetic photopiezocatalysis by coupling irradiation and ultrasonic vibration is a promising strategy to purify organic pollutants in wastewater.