课程文献中心 更多>>

关键词： 不定积分   根式代换   三角代换   欧拉变换  

摘要： 本文考虑一道含无理根式的不定积分,借助线性分式变换、根式变换以及三角变换,给出该题在三类变换下的六种解法.对于有的解法,本文还给出了一般公式,并对文中的解法进行了对比和说明.

关键词： 应用数学   课程思政   导数   定积分  

摘要： 本文以应用数学课程中的两个具体教学任务点为案例,探究如何在应用数学的教学环节恰当融入思政元素,使其达到课程思政润物于无声的目的.旨在通过数学教学改革,推动课程思政显性育人与应用数学隐性育人相结合.

关键词： 模糊算法   园林空间   特征分布   三维图像   微分方程  

摘要： 园林空间特征分布具有不可预测性,空间分布规范性较低,提出基于模糊算法的园林空间特征分布模拟研究。利用三维图像收集园林正常数据和隐藏数据,获取该园林空间分布的特征解析函数,分别从数据标准化处理、构造模糊相似矩阵和计算模糊等价矩阵三个步骤探析模糊算法,获取园林空间特征分布的规则程度。建立线性、直角、等距关系的模糊隶属函数,根据规则程度函数构建微分方程,实现园林空间特征分布模拟。仿真结果证明,通过模糊算法对园林空间特征分布模拟情况与实际吻合程度高,模拟数量误差与空间误差均较小,可以作为改善园林空间分布的有效依据。

关键词： Cooperation   Differential evolution   Covariance matrix adaptation   Niching population size   Learning mechanism   Design of experiment  

摘要： In this paper, a knowledge-based differential covariance matrix adaptation cooperative algorithm (DCMAC) is proposed for continuous problems. On the basis of combining successful history-based adaptive DE variants with linear population size reduction (LSHADE) and covariance matrix adaptation evolutionary strategy (CMA-ES), DCMAC proposes a strategy based on knowledge reward and punishment to achieve the purpose of collaborative optimization. Afterward, an adaptive learning mechanism is introduced to optimize the parameters to balance the exploitation and exploration of DCMAC. This process enables the algorithm to have global search capability. Finally, the niching-based population size reduction mechanism is introduced to improve the local search ability of the DCMAC. A weighted mutation strategy with dynamic greedy p value and covariance matrix adaptation (CMA) sampled based on differential vector are presented. Meanwhile, the knowledge acquired in the previous iteration process is adopted in the algorithm to select a mutation strategy for generating the new candidate solutions in the next iteration. The niching population size reduction mechanism is introduced to maintain the diversity of the population and compared with the other classical population size reduction methods. The optimal combination of parameters in the DCMAC algorithm is testified by the design of the experiment. Furthermore, the DCMAC is testified on the CEC2017 benchmark functions. The effectiveness and efficiency of the DCMAC are demonstrated by the experimental results in solving complex continuous problems.

关键词： Atractylodes macrocephala   Transcriptome sequencing   Reference gene   Rhizome growth   Sesquiterpene biosynthesis  

摘要： The rhizome of Atractylodes macrocephala is a kind of traditional Chinese medicine containing a variety of sesquiterpenoids and has a wide range of bioactivities. Due to the lack of genetic information, the rhizome growth and sesquiterpene biosynthesis in A. macrocephala are basically unknown. In this study, the metabolic analysis and transcriptome sequencing of five different tissues (rhizomes, roots, stems, leaves and buds) of A. macrocephala were performed. Over 97.08 Gb clean data obtained from fifteen sequencing samples were assembled into 144,137 unigenes. Transcription factor (TF) analysis revealed that 14 TFs predominantly expressed in the rhizomes might be involved in the regulation of rhizome growth and sesquiterpene biosynthesis. A total of 73 unigenes and 287 CYP450s were annotated to sesquiterpene biosynthesis, and AmFPPS was verified to catalyze the biosynthesis of sesquiterpene. EF-1 alpha was the best reference gene for tissue expression pattern analysis in A. macrocephala by comparing the expression of reference genes in five tissues. Thus, extensive transcriptome data from this work offered a comprehensive transcriptional expression pattern in different tissues of A. macrocephala, which will provide a more valuable resource for further research on molecular mechanisms of the growth and development of rhizome, and the biosynthesis and regulation sesquiterpenes.

关键词： 微分方程   振动准则   Riccati变换  

摘要： 运用Riccati变换,针对α>β和β≥α两种情况研究了一类二阶半线性微分方程的振动性,得到该方程振动的充分条件。

关键词： 自共轭微分算子   Ulam稳定性   Gronwall-Bellman不等式  

摘要： 文章利用自共轭微分算子研究高阶时滞微分方程的Ulam稳定性.首先给出了方程解的存在唯一性结果,在此基础上利用不等式结果得到了方程的Ulam稳定性.

关键词： ARDS   COVID-19   latent class analysis   phenotyping  

摘要： Rationale: Two distinct subphenotypes have been identified in acute respiratory distress syndrome (ARDS), but the presence of subgroups in ARDS associated with coronavirus disease (COVID-19) is unknown. Objectives: To identify clinically relevant, novel subgroups in COVID-19-related ARDS and compare them with previously described ARDS subphenotypes. Methods: Eligible participants were adults with COVID-19 and ARDS at Columbia University Irving Medical Center. Latent class analysis was used to identify subgroups with baseline clinical, respiratory, and laboratory data serving as partitioning variables. A previously developed machine learning model was used to classify patients as the hypoinflammatory and hyperinflammatory subphenotypes. Baseline characteristics and clinical outcomes were compared between subgroups. Heterogeneity of treatment effect for corticosteroid use in subgroups was tested. Measurements and Main Results: From March 2, 2020, to April 30, 2020, 483 patients with COVID-19-related ARDS met study criteria. A two-class latent class analysis model best fit the population (P = 0.0075). Class 2 (23%) had higher proinflammatory markers, troponin, creatinine, and lactate, lower bicarbonate, and lower blood pressure than class 1 (77%). Ninety-day mortality was higher in class 2 versus class 1 (75% vs. 48%;P < 0.0001). Considerable overlap was observed between these subgroups and ARDS subphenotypes. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RT-PCR cycle threshold was associated with mortality in the hypoinflammatory but not the hyperinflammatory phenotype. Heterogeneity of treatment effect to corticosteroids was observed (P = 0.0295), with improved mortality in the hyperinflammatory phenotype and worse mortality in the hypoinflammatory phenotype, with the caveat that corticosteroid treatment was not randomized. Conclusions: We identified two COVID-19-related ARDS subgroups with differential outcomes, similar to previously described ARDS su

关键词： 曲梁   惯性力矩   剪切变形   振动微分方程   Timoshenko梁  

摘要： 振动微分方程的推导与建立是结构动力分析的关键.依据Timoshenko梁理论,计入惯性力矩与剪切变形的影响,通过联立几何变形协调方程与内力平衡方程,推导建立曲梁面内横向弯曲自由振动微分方程与曲梁面内轴向自由振动微分方程.研究结果为曲梁动力学研究提供一定的理论基础.

关键词： 非线性方程组   单调性   投影方法   收敛率分析  

摘要： 在适当的条件下,本文进一步研究带凸约束的单调非线性方程组的超记忆梯度型方法,并建立了它的次线性收敛率.同时,本文还给出求解带凸约束的单调非线性方程组的无导数投影法的更一般的算法框架,并分析了其收敛性及其收敛率.两个说明性的数值计算实例表明了该算法框架的可行性.