Strong asymptotics in Lagrange interpolation with equidistant nodes

In this paper we prove three conjectures of Revers on Lagrange interpolation for f_λ(t)=|t|^λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants L_N( f_λ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max_|t|1| |t|^λ−L_N( f_λ,t)|. The proofs are based on strong asymptotics for |t|^λ−L_N( f_λ,t), 0|t|<1.     

Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

本征导电聚合物的智能性

在化学掺杂或电化学掺杂过程中，性质发生可逆性变化的本征导电聚合物是一种潜在的智能材料，可望实现或部分实现传感、处理和执竽功能，适于制成电机执行器、智能窗、化学分离与释放体系、传感器和非线性光学器件等。     

Synthesis and degradation of intelligent hydrogels containing polyacetal segments

Intelligent hydrogels were first obtained by copolymerization of telechelic poly(1,3-dioxolane) (pDXL) with acrylic acid, acrylamide, N-isopropylacrylamide respectively. The synthesis and characterization of the networks were discussed. The swelling behavior of the hydrogel was dependent on the solubility parameter of the solvents and hydrogels. The networks containing polyacetal segments (pDXL) can degrade by acid in different solvents. DXL and few other cycle molecules measured by GC-MS analysis were formed after degradation. According to the degradation products, the polymerization mechanism can be testified.     

智能性水凝胶

“智能”材料具有传感、处理和执行功能，水凝胶作为智能材料其应用前景良好。本文综述了智能水凝胶的近期研究发展，以Ｆｌｏｒｙ的溶胀理论着重探讨了刺激响应性，并介绍了化学机械现象及凝胶相转变。     

Evolutionary variational inequalities with a volterra term

The mathematical model of the injection molding process is characterized by evolutionary inequalities with an elliptic principal part and a Volterra term. Existence and uniqueness of the solution of these problems are derived by means of an argument based on the Banach fixed point theorem. Regularity results are obtained by using the penalty and Rothe method. The results can be considered as a starting point for the numerical treatment and for the application to injection molding.     

基于荧光光谱技术的菜籽油氧化状态智能评价

菜籽油在加工及贮藏过程中，易受氧气、温度、光照等因素的影响，产生氧化酸败现象。为准确判断油脂氧化程度，实现不同氧化模式下菜籽油品质的快速判别，采用三维同步荧光光谱技术结合平行因子分析法及BP神经网络法建立菜籽油氧化状态的智能评价模型。以冷榨菜籽油为原料，将样品分别置于常温、Schaal烘箱、高温模式中氧化处理，期间采集菜籽油的三维同步荧光光谱数据及理化指标，当理化指标超出国标限定范围时，停止采集数据。结果表明，菜籽油中荧光物质在不同氧化模式中的演变规律呈显著差异，氧化温度对菜籽油荧光光谱有明显影响。常温氧化350 d与第1 d相比，菜籽油的特征荧光峰位置无变化，仅在激发波长Ex为620和660 nm附近荧光峰强度发生微弱变化；Schaal烘箱氧化26 d后，在激发波长Ex为620和660 nm附近荧光峰强度显著减弱，且在激发波长Ex为350～450 nm之间有新的荧光峰生成；高温氧化48 h后，Ex为620和660 nm处荧光峰消失，在Ex为400～550 nm处产生显著荧光峰，相对Schaal烘箱氧化，荧光波长发生一定程度红移，这是由于高温氧化过程中油脂氧化生成的物质稳定性较差引起的。利用平行因子分析法对三维同步荧光光谱数据进行分解获取有效的二维荧光光谱数据，当组分数为6，Δλ=60 nm时激发波长的载荷值最大，不同样品间差异最显著。选定Δλ=60 nm波段的二维荧光光谱数据用于智能评价，作为BP神经网络模型的输入值，以极性组分作为模型输出值，分别对菜籽油三种氧化模式数据建模训练。实验结果表明，三种氧化模式对应的训练集、验证集、测试集模型相关系数r均能达到0.9以上，其中常温氧化模式中验证集及测试集模型的相关系数r为1，输出值与目标值较接近，模型的预测效果较好；综合三种氧化模式数据建模，对应训练集、验证集、测试集模型的相关系数分别为0.999，0.913和0.988，均方误差均较小，说明该模型能准确判断菜籽油的不同氧化状态。因此，三维同步荧光光谱技术结合平行因子分析法、BP神经网络法建立快速检测模型能实现菜籽油不同氧化状态的判别，为菜籽油的氧化程度的评价提供新方法，同时为其他食用油的品质评价提供参考。     

基于RFID的智能跟踪机器人的设计

针对国内各种智能机器人的智能跟踪难这一现状,设计出一种基于RFID技术的智能跟踪的机器人,能实现对携有特定电子标签的目标进行实时跟踪。该机器人以STC89C51单片机为核心,采用有源RFID读写器(HR6020C)和电子标签(WS-HT06)构建定位系统,采用单片机控制L298来驱动机器人的两个后轮,整个系统通过单片机进行整合、计算、处理数据,并发出指令,控制机器人对目标进行跟踪,进而达到机器人的智能跟踪的目的。实验结果表明,该机器人达到了智能跟踪的要求。     

基于MXenes的功能纤维的制备及其在智能可穿戴领域的应用

在电子信息和物联网技术的推动下,人类对可穿戴电子器件和智能织物的需求愈发突出,功能纤维作为智能可穿戴设备的重要载体,近年来获得快速发展。功能纤维的性能很大程度上取决于纤维的基础构筑单元。过渡金属碳/氮化物(MXenes)作为一种新兴的二维材料,凭借其高电导率、优异的可加工性能、可调节的表面特性以及出色的机械强度等优点,受到了极大的关注,也逐渐成为构筑功能纤维的重要单元。本文将主要综述MXenes的湿化学、熔融盐、无氟试剂刻蚀等方法和力学、电学、光学和化学稳定性等性能,阐述基于该材料制备的功能纤维在传感、储能以及其他智能领域的应用,最后讨论了基于MXenes材料的功能纤维的未来应用前景和技术挑战。