To avoid the poles and unreachable points, the barycentric rational Hermite interpolation (BRHI) can select the interpolation weights to acquire appropriate BRI functions. When approaching the interpolated function with horizontal asymptotes, the rational Hermite interpolation function is unable to keep the original horizontal asymptotes. In this paper, a barycentric rational Hermite interpolation method with horizontal asymptotes is proposed. Firstly, the condition of level preserving asymptotes is studied for BRHI. Secondly, an optimal weights optimization model is constructed by using the minimum Lebesgue constant as the objective function. The constraint conditions of optimization model of the BRHI include no pole, no inaccessible point, the interpolation function level preserving asymptotes, and the normalization of barycentric weights. Finally, the barycentric rational Hermite interpolation with horizontal-preserving asymptotes is obtained. The effectiveness of the algorithm is proved by numerical examples.
The impact of air pollutants on the human respiratory system has received more and more attention. However, due to the differences in human characteristics and the strength of protective measures, different people have different symptoms in air pollution and viral infection environments. In this paper, an SI1I2P dynamic model of respiratory diseases infected by virus under air pollution is established by introducing air pollutant concentration compartment. Qualitative research shows that there are seven equilibria in the system, the daily average emission and clearance rate of pollutants are the key parameters affecting the existence and stability of equilibria. In this paper, by using Sotomayor’s theorem and center manifold theory, it is proved that the system undergoes saddle–node bifurcation or Bogdanov–Takens bifurcation of co-dimension 3 at the boundary equilibrium, and exhibits saddle–node bifurcation at the endemic equilibrium. Numerical simulation results show that wearing masks in haze weather can not only reduce the number of allergic patients, but also reduce the number of viral patients. In addition, reducing the daily average emission of air pollution and increasing its clearance rate can also reduce the number of allergic patients. It is worth mentioning that this measure is more effective in controlling viral respiratory diseases.
为研究天长市全民健身中心体育场金属屋面的抗风揭性能,针对该项目金属屋面的结构类型,进行了足尺实验研究.通过沙袋堆载法模拟风荷载,先对实验构件施加正向风荷载,再施加负向风荷载的方式,来检验金属屋面的抗风揭性能,同时检验其极限承载能力,利用有限元软件进行模拟分析,和实测结果进行对比.
基于合肥市蜀山区某蓄水池基坑工程,根据实际工程资料,结合现场地质勘测并通过MIDAS/GTS NX有限元分析软件对其进行数值模拟.分析基坑开挖时出现的基坑围护结构位移、基坑底部隆起以及基坑外侧表面土体沉降的变形机制及影响因素,研究结果表明:该基坑开挖工程的各项围护结构位移均在预警值以下,基坑外侧表面土体沉降均在预警值以下,围护结构水平位移随着地连墙厚度增大而减小,但水平位移减小到一定程度趋于稳定,在地连墙厚度为1200mm时效果最佳.支护结构中锚杆的水平向夹角并非越大越好,在25°时效果最佳,此时支护结构变形有所减小.
新工科背景注重培养学生的创新能力和问题解决能力,而课程思政旨在通过教育引导学生树立正确的世界观、人生观和价值观,提高学生的思想道德素质和社会责任感.离散数学作为一门基础课程,在计算机科学、逻辑推理、密码学和安全性、决策分析和优化等领域具有重要意义.针对当前离散数学课程教学中存在的主要问题,结合实际教育工作,将"新工科"与"课程思政"理念融入教学体系中,并从教材内容、授课方法、思政案例以及评估方式等方面探索具体改革策略.着眼于培养创新能力、问题解决能力以及社会责任感,进而培养出富有创造力与实践能力的优秀工程技术人才.
