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.

A Probe into Economic Regionalization Theory Analysis Framework of Conflicts Between Scale Expansion and Transaction costs

The economic regionalization practice led by China local governments has gradually evolved into chaos. Local governments compete to declare for higher-leveled and large-scaled economic regions to obtain more economic resources and policy support in the way of policy game. The author argues that the regionalization chaos is attributed to the reason that the present theoretical support for economic regionalization overemphasizes the economic growth brought about by the economic regionalization but ignores the effect of transaction cost, which leads to constraint loss on the economic regionalization theory analysis framework. Then, the introduction of economic regionalization analysis framework based on the conflicts between scale expansion and transaction costs would establish equilibrium conditions to set up a moderate scale development for economic regions. The author hopes that the acceptance of this framework into the economic regionalization decision-making system would give guidance for making more appropriate regionalization decisions.

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.

快中子诱发蛇纹石混凝土力学性能退化研究

基于三维细观数值模拟方法,考虑快中子辐照(MeV>1.0)诱发的温度与骨料膨胀联合作用对混凝土力学行为及破坏形态的影响规律,该文提出了可有效预测辐照混凝土残余力学性能的二阶段数值模型计算方法,开展了蛇纹石骨料混凝土力学性能退化研究,并借助物理试验进行了模型验证。此外,基于数值模拟结果,提出了蛇纹石骨料膨胀作用下混凝土力学响应及残余力学性能的理论计算公式。该文提出的三维细观数值模型旨在为评估辐照混凝土力学响应及残余力学性能提供有效工具,为揭示辐照混凝土力学性能退化机理提供分析工具,为进行辐照混凝土基准研究提供理论依据,后期可为核反应堆混凝土防护墙延寿评估提供一定的理论指导。

一种针对SAR图像的舰船目标检测算法

由于环境复杂、舰船目标散焦和尺度的多样性,基于SAR图像的舰船目标检测仍然存在一些问题。提出了一种针对SAR图像的舰船目标检测算法。首先,基于可变形卷积构建舰船目标特征细化模块,提高对大长宽比姿态的舰船目标的特征提取能力;其次,在主干网络末尾引入了舰船空间金字塔聚合结构,增强对舰船目标的全局特征提取能力;最后,设计了尺度扩展特征金字塔网络,增强舰船浅层和深层特征信息的交互,提高对多尺度舰船目标的检测能力。实验结果表明,所提算法在HRSID数据集上的mAP达到了93.72%,F1分数达到了89.70%,优于所有比较算法,具有良好的检测效果。

Model of Polysilicon Electro-thermal Micro Actuator and Research of Micro Scale Effect

A type of crank beam electro-thermal micro actuator was prescribed. Mechanical model of the actuator was established, and the static characteristic was analyzed.Comparing the theoretical analysis with experimental data, it is found that the thermodynamic character of material in micro actuator has a different variable regularity contrasted to that used in macro scale machines. It is the micro scale effect that results in the deviation between the simulating result and experimental results. The thermodynamic expression of polysilicon, which was fitted by means of the experimental data concerned, was used to modify the mechanical model. The modified model, in which the micro scale thermodynamic characteristic was considered, was more reasonable and could make the optimal design and control strategies analyzing the straight-line micro actuator more feasible.

Modifed Multifdelity Surrogate Model Based on Radial Basis Function with Adaptive Scale Factor

Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(MMFS)model based on a radial basis function(RBF)is proposed,in which two fdelities of information can be analyzed by adaptively obtaining the scale factor.In the MMFS,an RBF was employed to establish the low-fdelity model.The correlation matrix of the high-fdelity samples and corresponding low-fdelity responses were integrated into an expansion matrix to determine the scaling function parameters.The shape parameters of the basis function were optimized by minimizing the leave-one-out cross-validation error of the high-fdelity sample points.The performance of the MMFS was compared with those of other MFS models(MFS-RBF and cooperative RBF)and single-fdelity RBF using four benchmark test functions,by which the impacts of diferent high-fdelity sample sizes on the prediction accuracy were also analyzed.The sensitivity of the MMFS model to the randomness of the design of experiments(DoE)was investigated by repeating sampling plans with 20 diferent DoEs.Stress analysis of the steel plate is presented to highlight the prediction ability of the proposed MMFS model.This research proposes a new multifdelity modeling method that can fully use two fdelity sample sets,rapidly calculate model parameters,and exhibit good prediction accuracy and robustness.

LAI scale effect research based on compact airborne spectrographic imager data in the Heihe Oasis

As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.

Gene regulatory networks driven by intrinsic noise with two-time scales： a stochastic averaging approach

This work focuses on gene regulatory networks driven by intrinsic noise with two-time scales. It uses a stochastic averaging approach for these systems to reduce complexity. Comparing with the traditional quasi-steady- state hypothesis （QSSH）, our approach uses stochastic averaging principle to treat the intrinsic noise coming from both the fast-changing variables and the slow-changing variables, which yields a more precise description of the underlying systems. To provide further insight, this paper also investigates a prototypical two-component activator-repressor genetic circuit model as an example. If all the protein productions were linear, these two methods would yield the same reduction result. However, if one of the protein productions is nonlinear, the stochastic averaging principle leads to a different reduction result from that of the traditional QSSH.

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.

广东省高等教育规模扩张进程演进及影响因素研究

高等教育作为人才培养的重要渠道,对区域经济发展具有重要影响。该文构建中国情境下高等教育规模扩张机制的理论研究框架。基于广东省21个地级市的面板数据集,运用空间自相关分析、动态空间计量模型,系统揭示广东省高等教育规模的时间演变进程、空间分异特征及影响因素。

同行技术竞争力影响企业劳动收入份额吗?

科技创新是新质生产力的核心要素,企业技术维度的同行竞争力值得关注。本文基于2007—2021年A股上市公司的研究样本,深入探讨了同行技术竞争力对企业劳动收入份额影响及其作用机制。研究结果表明,同行技术竞争力能够显著提升企业劳动收入份额,且该结论在经过系列稳健性检验和内生性讨论后依然成立。机制检验发现,同行技术竞争力通过优化人力资本结构、扩大企业生产规模和缓解融资约束问题,进而提升企业劳动收入份额。横截面检验发现,同行技术竞争力对企业劳动收入份额的提升作用在人力资源丰富和劳动者议价能力低的情形下更显著。进一步研究发现,相较于高管劳动收入份额,同行技术竞争力主要提升了普通员工的劳动收入份额,同时同行技术竞争力还促进了普通员工的岗位数量和薪资水平。

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。

基于日间日内不确定集的中长期电源扩展规划

电源扩展规划(generation expansion planning,GEP)模型常用于为高比例可再生能源电力系统设计可行的规划方案,而对波动性可再生能源(variable renewable energy,VRE)不确定性的合理表征对规划方案的可行性至关重要。随着风光等可再生能源渗透率的增加,波动性可再生能源表现出了不同时间尺度上的不确定性。提出了一种基于日间和日内可再生能源不确定集的长期GEP模型,从而保障不同时间尺度下的电力电量平衡需求。日间不确定集用来描述长期VRE出力的波动性和间歇性,而日内不确定集用作描述日内的典型和极端出力情形,二者共同描述不同时间尺度下VRE出力的不确定性。使用我国电力系统作为算例,将所提方法与典型日法、典型日聚合法和日间电量平衡法进行仿真对比。基于8760 h全年时序生产模拟的结果表明,所提方法能够显著降低不同风光出力情形下电力系统的失负荷和碳排放,但其他方法均无法满足平衡和清洁需求。