Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-A: The Factorizational Theory for Chebyshev Asymptotic Scales

This paper, divided into three parts (Part II-A, Part II-B and Part II-C), contains the detailed factorizational theory of asymptotic expansions of type (?)?, , , where the asymptotic scale?, , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of . It follows two pre-viously published papers: the first, labelled as Part I, contains the complete (elementary but non-trivial) theory for;the second is a survey highlighting only the main results without proofs. All the material appearing in §2 of the survey is here reproduced in an expanded form, as it contains all the preliminary formulas necessary to understand and prove the results. The remaining part of the survey—especially the heuristical considerations and consequent conjectures in §3—may serve as a good introduction to the complete theory.

Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-C: Constructive Algorithms for Canonical Factorizations and a Special Class of Asymptotic Scales

This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymptotic scale at an endpoint. These algorithms arise quite naturally in our asymptotic context and prove very simple in special cases and/or for scales with a small numbers of terms. All the results in the three Parts of this work are well illustrated by a class of asymptotic scales featuring interesting properties. Examples and counterexamples complete the exposition.

DEFECT AND IMPROVEMENT OF TWO-TIME EXPANSION METHOD IN NONLINEAR OSCILLATIONS

In this paper, the defect of the Two-Time Expansion method is indicated and an improvement of this method is suggested. Certain examples.in which the present method is used, are given. Moreover, the paper shows the equivalence of the improved Two-Time Expansion Method and the method of KBM(Kryloy-Bogoliuboy-Mitropolski).

The Factorizational Theory of Finite Asymptotic Expansions in the Real Domain: A Survey of the Main Results

After studying finite asymptotic expansions in real powers, we have developed a general theory for expansions of type (*) ,x → x0 where the ordered n-tuple forms an asymptotic scale at x0 , i.e. as x → x0, 1 ≤ i ≤ n – 1, and is practically assumed to be an extended complete Chebyshev system on a one-sided neighborhood of x o. As in previous papers by the author concerning polynomial, real-power and two-term theory, the locution “factorizational theory” refers to the special approach based on various types of factorizations of a differential operator associated to . Moreover, the guiding thread of our theory is the property of formal differentiation and we aim at characterizing some n-tuples of asymptotic expansions formed by (*) and n -1 expansions obtained by formal applications of suitable linear differential operators of orders 1,2,…,n-1. Some considerations lead to restrict the attention to two sets of operators naturally associated to “canonical factorizations”. This gives rise to conjectures whose proofs build an analytic theory of finite asymptotic expansions in the real domain which, though not elementary, parallels the familiar results about Taylor’s formula. One of the results states that to each scale of the type under consideration it remains associated an important class of functions (namely that of generalized convex functions) enjoying the property that the expansion(*), if valid, is automatically formally differentiable n-1 times in two special senses.

Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-B: Solutions of Differential Inequalities and Asymptotic Admissibility of Standard Derivatives

Part II-B of our work continues the factorizational theory of asymptotic expansions of type (*) , , where the asymptotic scale , , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of x0. The main result states that to each scale of this type it remains as-sociated an important class of functions (namely that of generalized convex functions) enjoying the property that the expansion (*), if valid, is automatically formally differentiable n ? 1 times in the two special senses characterized in Part II-A. A second result shows that formal applications of ordinary derivatives to an asymptotic expansion are rarely admissible and that they may also yield skew results even for scales of powers.

Risk Management Strategy for Agricultural Operation Subjects in Simple Scale Expansion Mode

Agricultural operation subject is a main body of the market economy. At present,the simple scale expansion mode is a major mode of agricultural operation in China. According to some hypothesis,scale expansion will inevitably bring high income,but such hypothesis has serious defects. The operation mechanism of the simple scale expansion mode includes farmer operation mechanism,professional farmer operation mechanism,and " company + farmers" operation mechanism. In the production and operation,they will be faced with different natural risks,technical risks,market risks and policy risks. Besides,their risk control ability is also varied. Therefore,it is required to take different agricultural risk management strategies. The " company + farmers" production and operation subjects have the highest ability of risk management. Other subjects should learn their experience.

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.

Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time

This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Maxkov chains often have large state spaces, which make the computa- tional tasks ihfeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε〉 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Maxkov chains including also tran- sient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions axe constructed. Then error bounds are obtained.

基于深度学习的光纤麦克风频带扩展

光纤麦克风具有体积小、精度高、抗干扰能力强等优点,能在复杂环境下拾取目标语音.然而,在采集语音过程中,光纤麦克风受响应带宽限制,出现了高频成分缺失情况,进而降低语音短时客观可懂度(short-time objective intelligibility,简称STOI)和信噪比(signal-to-noise ratio,简称SNR).将时间卷积模块(temporal convolutional module,简称TCM)引入Wave-U-Net,提出TCM_Wave-U-Net.在此基础上,提出频域卷积递归神经网络(convolutional recurrent neural networks,简称CRN)与时域TCM_Wave-U-Net协同的网络(简称协同网络).实验结果表明:协同网络具有较强的泛化性和鲁棒性.该文研究结果为光纤麦克风的语音保真拾取奠定了基础.

基于改进YOLOX算法的光学卫星影像车辆目标检测

为了改善光学卫星影像中车辆目标检测准确率低、速度慢的问题,提出一种基于改进YOLOX算法的卫星影像车辆目标检测方法。首先,以轻量化模型YOLOX的S版本为基线,采用CSPDarknet—53替换原主干特征提取网络,引入基于卷积块的注意力模块(CBAM)提高特征提取时对车辆目标的关注度。其次,扩充主干特征提取网络输出尺度,并在特征强化提取部分设计了一个双向特征金字塔网络(BFP-net),采用亚像素卷积上采样、横向的跳跃连接和纵向的跨尺度连接实现对不同层级、尺度特征的复用,使得最后输出特征层充分融合了分类和定位信息。实验结果表明:本文算法对large-vehicle和small-vehicle两类车辆的检测准确率分别为88.98%和86.58%,相较于原算法,平均检测准确率提高了5.36%,检测速度达到了58.37fps,具有更好的检测效果。

大型7085铝合金筒形件淬火残余应力及其消减工艺研究

以大型7085铝合金筒形件为研究对象,研究了在最大程度保证铝合金大锻件性能的同时尽可能减小其淬火残余应力的方法。基于Abaqus平台,分别建立了大型筒形件淬火有限元模型和淬火后冷胀形有限元模型,考虑了淬火工艺和冷胀形工艺间的数据继承关系,分析了工艺参数对锻件性能及残余应力的影响规律。针对大型7085铝合金筒形件的淬火过程,将7085铝合金的等温转变曲线和时间-温度-性能曲线写入Abaqus用户子程序USDFLD中,计算了大型筒形件在不同淬火工艺条件下的析出相含量和分布、对应的硬度变化以及残余应力分布,获得了35℃的淬火水温是最优的选择。在消减淬火残余应力的冷胀形工艺中,基于不同的淬火水温条件开展了胀形量、胀形道次和每道次之间环转动角度的正交模拟实验,结果显示胀形量对残余应力消减的影响最显著,胀形量为4.5%时大型7085铝合金筒形件的应变均匀性最好且残余应力消减最充分。将仿真获得的优化淬火工艺和胀形方案应用于生产试制,所获得的大型筒形件各项力学性能达到设计要求,其残余应力实测结果与仿真结果对比具有较好的一致性。

在优秀与平等之间:高等教育规模扩张进程中精英教育的发展

精英高等教育阶段,追求优秀、培养精英是大学的基本理念。20世纪中叶以来,高等教育的发展理念以平等主义逐渐取代精英主义,而随着以平等为目的的高等教育规模不断扩张,大学精英教育的特质也被高等职业教育和尖端科学研究的普适性所取代。但精英教育逐渐被大众教育取代,也使曾经以精英主义为理念的大学越发难以培养出英才。当今我国已经迈入普及高等教育阶段,规模扩张的进程还在继续,在此背景下,只有从平等主义理论和精英主义理论角度来审视优秀与平等之间的矛盾,才能在规模扩张进程中把握大众教育与精英教育的合理尺度,从而实现高等教育的高质量发展。

基于密集多尺度特征的遥感影像水体提取

针对传统遥感影像水体提取方法和基于深度学习的经典目标提取模型的提取结果存在丢失边缘细节信息和准确率低的问题,提出了基于深层特征编码-水体识别解码的多尺度特征密集连接网络结构。首先利用深层特征编码结构中的普通卷积提取影像中水体的特征信息,然后利用密集多尺度特征模块提取水体的多尺度特征和保留全局信息,最后利用水体识别解码结构对图像中的水体进行预测。实验结果表明:本文方法的提取结果精度优于经典全卷积神经网络模型,在测试集上的像元精度达到98.56%,交并比达到78.91%,有效保留了水体的完整性和细节边缘信息,实现了水体的精细化提取。

高等教育的多中心布局能提高城市创新水平吗

创新驱动发展战略的深入实施有赖于高等教育,但高校作为资源依赖型组织,往往受制于政府目标和市场力量,这种独立性的相对欠缺所带来的高等教育规模扩张,直接推动了高等教育在省域空间的多中心布局,这是否有碍于高等教育对经济社会良序发展的促进作用?以2004—2019年23个省份231个城市作为研究样本,采用固定效应模型和工具变量法进行实证研究,结果表明:第一,高校自主性欠缺所带来的省域高等教育布局多中心化趋势,会对省域内城市的创新水平带来负向影响。第二,基础设施建设的挤出效应是城市创新关键机制。与地方政府博弈互为表里的省域多中心化进程,将通过基础设施建设,放大地方高校规模扩张所具有的投资拉动属性,并最终挤出城市创新;省域层面知识溢出所带来的网络外部性和城市层面的集聚外部性虽然有利于城市创新,但难以克服多中心布局所带来的负面效应。第三,异质性研究发现,多中心布局只是促进了形式公平,但实际上经济发展水平更差、行政级别更低城市的创新水平受到更为明显的负向影响,中心城市对邻近区域创新水平的溢出效应也间接被削弱。因此,加快转变地方政府的经济增长逻辑和尊重高校主体性地位,避免盲目扩张,是优化省域高等教育布局、提高城市创新水平、助推城市经济高质量发展的有效路径。

银行竞争如何影响企业进口——来自中国工业企业的经验证据

中国政府将扩大进口规模、优化进口结构、提高进口质量作为经济“新常态”下的发展战略。本文利用2000—2013年中国制造业微观企业数据和银行分支机构数据,深入分析了银行竞争对企业进口的影响效应及其作用机制。结果表明,银行竞争显著促进了企业进口规模扩大,传导渠道为融资约束缓解和生产规模扩张。异质性分析表明,银行竞争对非国有企业、中小规模企业、一般贸易企业、信息不透明企业及消费品进口的促进作用更大。进一步研究发现,股份制和城市商业银行竞争在更大程度上促进了企业(尤其是中小企业)进口。此外,银行竞争还显著促进了进口高质量发展,包括促进了进口多样化和提高了进口质量,以及延长了进口持续期。本研究不但从新的角度诠释了中国进口快速发展的动因,而且对下一步银行业的深化改革具有重要的政策启示。

多尺度残差群网络的图像去雨算法

雨天作为一种常见的天气条件会对计算机视觉造成一定影响,图像中会出现雨纹与细节模糊,从而需要一种高效的单幅图像去雨算法来改善图像质量。现有图像去雨算法大多只关注于去除雨纹,而忽略了恢复去雨后图像的细节信息。针对此,为了更好地检测雨纹提出了浅层特征提取模块和深层特征提取模块,其中,浅层特征提取模块选取残差密集块,深层特征提取模块选取两个双注意力模块和两个卷积层作为残差块构成的残差群。为了恢复图像细节信息,提出了一种包含全局分支和局部分支的多尺度细节恢复模块。在合成数据集和真实数据集上的大量实验表明,所提算法的PSNR和SSIM分别达到了40.41 dB和0.989,同时保留了图像细节信息。

改进小波变换下的永磁同步电机机械故障识别

针对永磁同步电机部件参数具有延续性关联性特征,机械故障特征难以提取,导致识别精准度较低的问题,研究改进小波变换下的永磁同步电机机械故障识别技术。建立永磁同步电机内定子、转子的同步状态参数数学模型,通过三相方程按照正弦分布变化规律,得到在电机正常同步状态下各项参数的周期性数据,以该值作故障状态特征提取的初始参照。以永磁同步电机内高、低频作为特征提取尺度,基于改进小波包变换完成电机机械故障特征信号重构提取;基于Kalman滤波残差估计算法计算重构信号的故障残差值,与初始状态对比,完成故障识别。经过实验证明,所提方法识别精准度高,可以识别出短路故障下的三相定子电流和电机输出转矩,具有一定的实用价值。

基于行车噪声的伸缩缝损伤识别缩比试验

伸缩缝出现损伤后行车产生的噪声会发生改变,为得到损伤伸缩缝行车噪声特征,本研究搭建了含无损和损伤类型为路面破损导致伸缩缝钢筋外露的GQF-C型伸缩缝的缩比路面装置,利用声音采集系统采集小车通过伸缩缝产生的噪声,分别在时域和频域中对采集噪声进行分析。研究结果表明,损伤伸缩缝噪声信号的频率成分主要集中在0~2000 Hz,伸缩缝出现损伤之后,时域波形、频率成分、能量和无量纲指标等均会发生明显的变化,因此跳车噪声可以用于伸缩缝的健康状态评估。

高寒河流健康评价研究

科学评价河流健康状况可以有效推进中小河流系统治理,加强河流管理保护。选取5个准则层、15个指标,采用标度扩展法与改进熵权法计算各指标的主客观权重,构建模糊评价模型,评价高寒河流降曲河的健康状况。结果表明,降曲河整体Ⅰ级隶属度为0.811,现状为非常健康状态。其中下游L6和L8河段社会服务功能准则层的健康等级为Ⅱ级,存在防洪未达标等问题。其他河段的综合评价级别均为Ⅰ级,但也反映出岸坡稳定性差、鱼类资源量减少的问题。构建的模型客观反映了降曲河的河流健康状况,为降曲河治理提供科学支撑;评价标准和体系可为同类型河流健康评价提供参考。