Analysis and design of switched normal systems

In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.     

相对论热力学中玻意耳定律与焦耳定律之间的关系

证明在相对论热力学理论系统中,焦耳定律是玻意耳定律的推论,但玻意耳定律不是焦耳定律的推论.     

About Distances between Points on the Plane

Mathematical Notes -     

Airborne virus transmission via respiratory droplets: Effects of droplet evaporation and sedimentation

Airborne transmission is considered as an important route for the spread of infectious diseases, such as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and is primarily determined by the droplet sedimentation time, that is, the time droplets spend in air before reaching the ground. Evaporation increases the sedimentation time by reducing the droplet mass. In fact, small droplets can, depending on their solute content, almost completely evaporate during their descent to the ground and remain airborne as so-called droplet nuclei for a long time. Considering that viruses possibly remain infectious in aerosols for hours, droplet nuclei formation can substantially increase the infectious viral air load. Accordingly, the physical-chemical factors that control droplet evaporation and sedimentation times and play important roles in determining the infection risk from airborne respiratory droplets are reviewed in this article.     

Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation

With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.     

“水体系中物质转化程度的探究”教学设计与实施

以反应的耦合与浓度商为核心概念,以弱电解质的电离、难溶电解质的配位溶解等为问题情境,引导学生基于反应间相互作用视角认识水体系中的物质转化程度。     

基于化学学科核心素养的初高中衔接教学——初三化学“金属的化学性质”

“金属的化学性质”是初高中化学学习的重要内容,该部分内容涉及到重要的化学观念和化学学科核心素养,如元素观、转化观、微粒观、STS观,以及宏观辨识与微观探析、证据推理与模型认知素养。但是初三学生认知水平受限,在教学中不能深入电子转移的微观角度,不能充分认知模型、应用模型。为弥补这一问题,本研究基于化学学科核心素养,进行“金属的化学性质”的初高中衔接教学研究。     

红外光谱结合判别分析对三七道地性及产地的鉴别研究

利用傅里叶变换红外光谱结合判别分析对三七的道地性及产地进行鉴别研究。测试了11个县13个种植点的136株三七主根样品的红外光谱,利用Omnic8.0软件计算了每个样品红外光谱的二阶导数光谱。分别采用1 800~700cm-1光谱范围的红外光谱数据和二阶导数光谱数据,运用逐步判别分析法建立模型对三七的道地性进行判别研究,二阶导数光谱数据建立的模型对三七道地性的识别效果更好,回判正确率为100%,预测正确率为93.4%。采用交叉验证法检验了模型的稳定性,并对此方法进行了外推性验证。用二阶导数光谱数据结合相同的判别方法对三七的产地进行识别,比较了不同光谱范围和不同训练样本数建立的模型判别效果,每个种植点选择8个样本作为训练样本,采用1 500~1 200cm-1光谱范围的数据建立的模型判别效果较好,回判正确率为99.0%,预测正确率为76.5%。结果表明,红外光谱结合判别分析对三七道地性的识别效果好,有望成为实际中鉴别三七道地性的新方法;对三七产地的识别有一定的效果,可作为三七产地鉴别的一种新思路。     

基于抑制性突触可塑性的反馈神经回路兴奋性与抑制性动态平衡

大脑皮层的兴奋性与抑制性平衡是维持正常脑功能的前提, 而其失衡会诱发癫痫、帕金森、抑郁症等多种神经疾病, 因此兴奋性与抑制性平衡的研究是脑科学领域的核心科学问题. 反馈神经回路是脑皮层网络的典型连接模式, 抑制性突触可塑性在兴奋性与抑制性平衡中扮演关键角色. 本文首先构建具有抑制性突触可塑性的反馈神经回路模型; 然后通过计算模拟研究揭示在抑制性突触可塑性的调控下反馈神经回路的兴奋性与抑制性可取得较高程度的动态平衡, 并且二者的平衡对输入扰动具有较强的鲁棒性; 其次给出了基于抑制性突触可塑性的反馈神经回路兴奋性与抑制性平衡机理的解释; 最后发现反馈回路神经元数目有利于提高兴奋性与抑制性平衡的程度, 这在一定程度上解释了为何神经元之间会存在较多的连接. 本文的研究对于理解脑皮层的兴奋性与抑制性动态平衡机理具有重要的参考价值.     

Interaction Between a Slow Magnetohydrodynamic Shock Wave and a Tangential Discontinuity

The self-similar problem of the oblique interaction between a slow MHD shock wave and a tangential discontinuity is solved within the framework of the ideal magnetohydrodynamic model. The constraints on the initial parameters necessary for the existence of a regular solution are found. Various feasible wave flow patterns are found in the steady-state coordinate system moving with the line of intersection of the discontinuities. As distinct from the problems of interaction between fast shock waves and other discontinuities, when the incident shock wave is slow the state ahead of it cannot be given and must to be determined in the process of solving the problem. As an example, a flow in which the slow shock wave incident on the tangential discontinuity is generated by an ideally conducting wedge located in the flow is considered. The basic features of the developing flows are determined.