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摘要： 为控制高温油管在进油和喷油过程中油管内压力的动态平衡,保证高温油管工作在正常压力范围,首先针对某一高温油管建立并推导出微分方程得到油管内的燃油压力与密度、供油口供油质量与出油口出油质量关于单向阀开启时长的等式模型,求得保持油管内压力稳定的单向阀开启具体时长。找出进出质量的变化与循环次数及每次循环质量变化的关系,以确定单向阀开启时间。之后应用质量守恒原理,建立凸轮角速度和柱塞上下浮动距离之间的关系模型。运用MATLAB软件求解模型,最终得出使高压油管内的压力尽量稳定在100MPa左右的凸轮角速度值。最终根据气压分流理论,得到高压油泵、2个喷油嘴、减压阀同时做周期时长100ms的稳定循环。解决了在双喷射嘴喷射下保持高压油泵和减压阀高温油管压力的控制方案。

关键词： 学术谱系   微分几何学家   学术传统  

摘要： 微分几何学是中国最早从国外移植的现代数学分支之一，经过数代中国微分几何学家的共同努力，微分几何学在中国取得了一些杰出的成就。前人已对微分几何学在中国进行过研究，但是很少进行学术谱系研究。本文围绕微分几何学在中国的成就，绘制早期中国部分微分几何学家谱系，由此探讨微分几何学的中国学术传统，并试图探索早期中国微分几何学发展规律和人才成长规律，从中获得一些关于建设数学强国的启示。

关键词： Differential privacy   deep learning   stochastic gradient descent  

摘要： Private individual information are increasingly exposed through high-dimensional and high-order data, with the wide deployment of learning techniques. These data are typically expressed in form of tensors, but there is no principled way to guarantee privacy for tensor-valued queries. Conventional differential privacy is typically applied to scalar values without a precise definition on the shape of the queried data. Realizing that the conventional mechanisms do not take the data structural information into account, we propose Tensor Variate Gaussian (TVG), a new (epsilon, delta)-differential privacy mechanism for tensor-valued queries. We further introduce two mechanisms based on TVG with an improved utility by imposing the unimodal differentially-private noise. With the utility space available, the proposed mechanisms can be instantiated with an optimized utility, and the optimization problem has a closed-form solution scalable to large-scale problems. Finally, we experimentally test our mechanisms on a variety of datasets and models, demonstrating that TVG is superior than other state-of-the-art mechanisms on tensor-valued queries.

关键词：     singular perturbation   stochastic differential game   Riccati equation   linear qua-dratic   zero sum   slow-fast   two scale  

摘要： We investigate a class of zero-sum linear-quadratic stochastic differential games on a finite time horizon governed by slow and fast state equations. The slow-fast nature of the problem can be leveraged to reformulate the associated generalized Riccati equation as a deterministic singular perturbation problem. In doing so, we show that as the evolutionary speed of the slow and fast processes diverge, the existence of a solution to the associated generalized Riccati equation is guaranteed by the existence of a solution to a decoupled pair of differential and algebraic Riccati equations with a reduced order of dimensionality. Furthermore, we are able to formulate a pair of asymptotic estimates to the value function of the game problem by constructing an approximate feedback strategy and observing the limiting value function.

摘要： 为深刻践行全国高校思想政治工作会议精神，将思政教育融入到高等数学教学中，成了各高校高等数学课程的主要教学目标。导数的概念重要性体现在它是高等数学的重要概念之一，是一种特殊的极限，是后续课程的基础，是微积分思想的灵魂，对于发展高等数学思维有着重要的意义；并且在物理学、经济学等领域都有重要的应用，是开展科学研究必不可少的工具。基于此，本案例强调通过不断创新，探索出在导数的概念中融入思政教育的教学设计，并在课程实践中践行立德树人的根本理念。

关键词： Electric potential   Biomedical monitoring   Sweat glands   Standards   Real-time systems   Immune system   Protocols   Autocorrelation   differential dermal potential   endosomatic   passive monitoring   real-time   settling time  

摘要： In the present pandemic scenario, it is of great importance to have reliable schemes for monitoring the human condition. The aim of this study is to validate the differential dermal potential in terms of the standard endosomatic electrodermal activity (EDA) and determine its usability in real-time applications. The differential dermal potential signal is passively acquired across the intermediate phalanges of the middle and index fingers of the hand or feet of human subjects. A physiological basis for these signals is proposed at the outset of this study. In this study, the signal is acquired from the left hand and is compared with two corresponding standard endosomatic EDA signals that are acquired simultaneously from the same two fingers. The experimental data is acquired while the subjects undergo a change of posture and then settle into a restful static condition. Thereafter, these signals are analyzed to determine their settling time as well as their autocorrelation, statistical, and spectral characteristics. It is found that the differential dermal potential signal is a stable passive signal with low settling time. It is strongly correlated with the difference of the two underlying standard endosomatic EDA signals, though not identical to it. The information in this signal, as obtained from the various characteristics, are interpretable and reliable. The findings in this study validate that this signal can be effectively used for monitoring the human condition.