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关键词： Soil structure interactions  

摘要： The role of spatially variable soil stiffness and strength on structural performance has been increasingly recognized with the rapid development of geotechnical reliability-based design tools. Performance criteria linked to the angular distortion between foundations and the probability of exceeding certain limit states as a function of linear-elastic soil property autocorrelation have shed light on the link between foundation soils and potential structural damage. However, the role of soil-structure interaction (SSI), especially considering nonlinearity in soil and structural elements, to redistribute shear and flexure within structures that result from differential foundation movements, has been largely neglected. This study presents a critical examination of the effect of nonlinear SSI to redistribute flexural demands within a steel structure founded in soils exhibiting spatial variability and the corresponding differential settlements through a comparison of uncoupled and coupled Monte Carlo simulations (MCS). This study shows that the differential settlement, Delta s, computed using coupled (i.e., SSI) analyses are significantly smaller than those derived from the uncoupled analyses for the random field models (RFMs) used to simulate soil spatial variability. The effect of SSI is to substantially reduce the probability of exceeding selected limit state criteria due to differential movements that vary in magnitude with the level of stringency of the limit state criteria;the most significant reduction corresponds to the structural ultimate limit state (ULS). Furthermore, the effect of SSI on structural performance and the critical scale of fluctuation, S alt , becomes more apparent and beneficial as the severity of differential movement increases. Smaller and/or "allowable" angular distortions are governed by the local footing-to-footing distance, whereas the probability of exceeding the ULS (i.e., yielding of beams) is controlled by the entire structure working t

关键词： 分数阶微分方程   双参数   奇摄动  

摘要： 讨论了一类奇摄动分数阶微分方程边值问题。在适当假设条件下,先求出该问题的外部解,再运用双参数展开理论构造出边界层矫正项,得到解的形式渐近展开式,最后运用极值原理进行余项估计。

关键词： 一致分数阶微分方程   两点边值问题   Leray-Schauder非线性择抉理论   Leray-Schauder度理论  

摘要： 本文运用Leray-Schauder非线性择抉理论和Leray-Schauder度理论得到了一致分数阶微分方程两点边值问题{D^(b)(D^(a)+λ)u(t)=f(t,u(t)),0

关键词： correlated differential privacy   multiparty data release   machine learning  

摘要： Differential privacy(DP)is widely employed for the private data release in the single-party *** utility could be degraded with noise generated by ubiquitous data correlation,and it is often addressed by sensitivity reduction with correlation ***,increasing multiparty data release applications present new challenges for existing *** this paper,we propose a novel correlated differential privacy of the multiparty data release(MP-CRDP).It effectively reduces the merged dataset's dimensionality and correlated sensitivity in two steps to optimize the *** also propose a multiparty correlation analysis *** on the prior knowledge of multiparty data,a more reasonable and rigorous standard is designed to measure the correlated degree,reducing correlated sensitivity,and thus improve the data ***,by adding noise to the weights of machine learning algorithms and query noise to the release data,MP-CRDP provides the release technology for both low-noise private data and private machine learning *** experiments demonstrate the effectiveness and practicability of the proposed method on the utilized Adult and Breast Cancer datasets.

关键词： 金课   常微分方程   线上线下混合式   翻转课堂  

摘要： 针对“常微分方程”课程存在的问题,文章以线上线下混合式“金课”建设为目标,考虑线上资源的构建和线下教学模式的改进以及如何将线上线下模式进行融合,给出调整课程建设方案、丰富教学手段、改良评价考核方式的改革措施。通过多年的实践与建设,“常微分方程”混合式“金课”在课程体系重构、学生实践与创新能力培养等方面取得了一定的成效。

关键词： 二阶微分方程   极值映射   不动点   对称函数   反对称函数  

摘要： 运用具有控制过程的二阶微分方程系统求解极值映射的不动点问题。运用对称函数和反对称函数的偏导数性质以及投影算子性质,证明了具有控制过程的二阶微分方程系统轨迹的聚点是极值映射不动点问题的解。最后给出两个算例说明二阶微分方程系统求解极值映射不动点问题的有效性。

关键词： 平均曲率   算子   不动点指数   径向正解  

摘要： 基于锥上不动点指数理论,讨论含平均曲率算子的拟线性微分系统Dirichlet问题{M(u)+f_(1)(v)=0,x∈B,M(v)+f_(2)(u)=0,x∈B,u|∂B=v|∂B=0径向正解的唯一性,其中M(w)∶=div(■w/√1-|■w|^(2)),f_(i)∈C([0,∞),[0,∞)),i=1,2,B为ℝ^(N)(N≥2)空间中的单位球.

关键词： 导数法   三角函数   高中数学  

摘要： 三角函数是高中数学中常见考点,在解答过程中具有较强的技巧性.本文利用导数法解答三角函数中有关不等式、周期、奇偶性以及三角函数值域等相关问题.

关键词： 实际应用问题   决策方案   命题背景   导数法   数学角度   数学知识   合理构建   数学模型  

摘要： 导数在实际生活中的应用问题一直是高考的热点之一.此类问题通常以实际生活应用为命题背景,进而结合数学知识合理构建相应的数学模型,借助题目条件适当选定相应的变量,寻找各变量之间的关系,并构建对应的数学关系,特别是相应的函数关系,结合函数的求导,利用导数法来转化与解决对应的实际应用问题时,要从数学角度给出合理的、最佳的决策方案.

关键词： 核心素养   数学运算   转化与化归   最值问题   数形结合   数学抽象   不等式恒成立   填空题  

摘要： 利用导数研究函数的性质和解决函数问题是高考考查的重点,核心是研究函数的单调性,涉及极值、最值、零点、不等式恒成立、位置关系等问题。而利用导数研究函数的极值、最值问题是最为常见的类型,考查时选择题、填空题、解答题都会出现,分值在20分左右。解答时,常常需要对问题进行转化,需要学生明确研究对象,构建新的函数,再用导数解决问题。题目中常常含有参数,需要分类讨论,考查学生逻辑是否清晰,推理是否严谨有序,表达是否简洁准确。重点考查数学抽象、数学运算、逻辑推理等核心素养,以及数形结合和转化与化归的思想方法等。