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关键词： 广义常微分方程   测度泛函微分方程   Lyapunov泛函   稳定   渐进稳定   指数稳定  

摘要： 利用广义常微分方程与测度泛函微分方程的等价关系,定义了测度泛函微分方程的稳定,渐进稳定及指数稳定的概念,并借助此概念及Lyapunov泛函证明了测度泛函微分方程稳定性的相关定理。

关键词： 高等数学   混合式教学   教学改革   定积分的概念  

摘要： 高等数学作为大学生必修的一门重要的基础理论课,对培养学生的抽象思维能力、自主学习能力和促进专业发展有着重要的作用,因此提高高等数学的教学质量就显得至关重要。而线上线下混合式教学是基于信息化技术课堂的模式,弥补了传统教学的不足。为了实现良好的教学效果,文章主要以高等数学中“定积分的概念”为例,从线上、线下、线上三个阶段探索线上线下混合式教学模式在高等数学教学中的应用。

关键词： 微分方程数值解法   超短激光   脉冲光   传输特性   有效拉比频率  

摘要： 针对已有方法进行超短激光脉冲光传输特性计算时,在输入光中心波长为800 nm~920 nm的范围内存在波形畸变捕捉率较低的问题,因此,将微分方程数值解法应用于超短激光脉冲光传输特性计算中。在对吸收进行忽略的情况下,根据脉冲光斑的实际传播情况对超短激光脉冲光传输进行模拟。通过麦克斯韦方程组获取在无自由电荷、非导电、非磁的介质内对光电场特性进行描述的方程,基于微分方程数值解法构建超短激光脉冲光传输方程。根据构建的超短激光脉冲光传输方程,在介质系统模型中对超短激光脉冲光传输特性进行计算。为证明基于微分方程数值解法的超短激光脉冲光传输特性计算方法实现了性能提升,将该方法与已有方法进行三次对比实验,实验结果证明该方法的波形畸变捕捉率高于实验中的已有方法,对于超短激光脉冲光技术的发展有很大意义。

关键词： 函数   极限存在   连续   可导   可微  

摘要： 函数极限的存在性、连续、可导与可微四者之间的关系是微分学的重要内容,特别是多元函数的四者之间的关系是难点内容,搞清楚它们之间的关系,对学生学好微分学非常重要.基于作者在教学过程中的一些思考和总结,本文给出一元函数和多元函数(以二元函数为例)的极限存在、连续、可导与可微的关系图,对于有推出或者等价关系的给予证明,没有推出关系的举出反例.

关键词： Electrooptical modulators   Imaging techniques   Nonlinear microscopy   Raman scattering   Raman spectroscopy   Stimulated scattering  

摘要： Percutaneous endoscopic lumbar discectomy (PELD) is the major effective treatment for lumbar disc herniation, and rapid histological identification of dissected tissue is critical to guide the discectomy. In this work, we revealed the histological features of different types of peridural tissues of the lumbar spine by label-free multi-modal nonlinear optical microscopy. Stimulated Raman scattering (SRS) was used to extract lipid and protein distributions, while second harmonic generation (SHG) and two-photon excited fluorescence (TPEF) signals were applied to image the collagen and elastin fibers at the same time. Our results demonstrated that the nonlinear optical features of the dura and adjacent soft tissues were significantly different, showing the potentials of our method for intraoperative differentiation of these critical tissues and improving the surgical outcome of PELD.

关键词： diagnosis   metastasis   ACCP  

摘要： A global trend towards greater health awareness with a resulting reduction in smoking has contributed to the improved control and early detection of lung cancer.[1]Furthermore,developments in diagnostic technologies have enhanced the detection of multifocal lung cancer,characterized by multiple cancerous *** lung cancer can be divided into multiple primary lung cancer(MPLC)and pulmonary metastasis-associated lung cancer intrapulmonary metastases(IM)according to the types of *** differential diagnosis of MPLC and IM is clinically important because of the direct impacts on tumor-node-metastasis staging and the implications for the treatment of lung *** diagnostic criteria for MPLC were first proposed by Martini and Melamed in 1975[2]and were subsequently revised and supplemented by the American College of Chest Physicians(ACCP)in 2003.[3]These ACCP standards currently provide the main diagnostic criteria for the clinical differential diagnosis of MPLC and *** and IM differ in terms of their clonal origins,which could provide a useful basis for multi-gene detection to assist the diagnosis of multifocal lung cancer.

关键词： Differential operator   Universality   Hypercyclicity   Universal Taylor series   Multiple universality   Disjoint universality  

摘要： For a simply connected domain G, we study the problem of disjoint universality for the sequences of operators T-alpha,T-n : H(G) -> H(G), defined by T-alpha,T-n(f)(z) = Sigma(n)(j=0) f((j))(z)/j(!) (alpha z)(j), where alpha is an element of C -{0}. Note that T-alpha,T-n(f)(z) is the nth partial sum j=0 of the Taylor expansion of f around z on (alpha + 1)z. The motivation to study such sequences comes from universal Taylor series, by changing the role of the center of expansion. (c) 2021 Elsevier Inc. All rights reserved.

关键词： 高职数学   不定积分第一类换元法   教法  

摘要： 本文结合高职数学的教学实际，对“不定积分第一类换元法”的教学方法进行了分析、探讨，总结出适应高职学生数学基础的教学方法。对于有效地化解教学难点，提高高职数学教学效果有一定的探索意义。

关键词： Long-term price guidance   Stochastic differential method   Flexible energy   Power market  

摘要： With the increasing generation of renewable energy in power markets, the mismatch between power production and power demand in the power market is becoming more serious. Power prices in the short term guided the balance of load and demand. Although short-term power price guidance can provide certain benefits, short-term power price guidance disrupts the potential long-term market balance and provides sustainable development challenges. This paper adopts a stochastic differential method to guide flexible energy service providers for long-term price guidance with addressing the challenges of long-term market imbalances. After knowing power production, the stochastic differentiation method guides load power demand to follow changes in power production by a reasonable power price. The stochastic differential method utilizes energy flexibility for long-term price guidance with cost mini-mization in a long-term market environment. The power demand results of Zhaoqing considering the water tower model show that the long-term price guidance mechanism based on the stochastic differ-ential method saves 12.39% of the operating cost with RMB 782.6987 million each year. The long-term price guidance based on the stochastic differential method mobilizes the energy flexibility by indi-rectly control the demand of flexible energy systems through reasonable price signals. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： 基本不等式   导数   权方和不等式   轮换式  

摘要： 双变量或多元变量的代数式最值(或取值范围等)问题,是历年高考考查的热点,掌握基本的解题思路与方法,合理变形,创新思维,触类旁通,变式拓展,有利于学生深入理解此类问题。