n-X余挠模与咒．妊余挠维数

在余挠模的基础上引入了n-X余挠模的定义,对n—X-余挠模作了等价刻画．并且引入了模与环上的n-X余挠维数,讨论了n-X余挠维数与其它同调维数之间的关系,推广了一些已有的结论．     

最小二乘法求作拟合直线

静态测试中,检测系统可以在一定的区间内用一个线性函数表达测试数据的变化规律,确定此线性函数即拟合直线的方法常采用最小二乘法.机械工程中,通过对应变测试可以分析与研究零件或结构的受力状况以及工作状态.根据实验输入输出测试数据,用最小二乘法求解拟合直线方程,以此计算的测量误差,均未超出测试数据的极限偏差.     

基于学生的理解水平制定课程目标——以“小数乘法运算”为例

课程目标的制定要基于学生的理解水平.学生对小数乘法运算的理解是有限的、有层次的.由低到高,理解的3个水平为:程序理解、直观理解,抽象理解、形式理解.学生学习了分数乘法运算后对小数乘法运算的理解水平显著提高.导致学生理解水平较低的主要原因是欠缺分数知识、不理解分数乘法的意义.因而,要按照学生的理解水平,制定适切的课程目标,不可过高地强调对小数乘法运算的理解;要加强分数意义教学.     

Critical couplings in topological-insulator waveguide-resonator systems observed in elastic waves

Waveguides and resonators are core components in the large-scale integration of electronics, photonics and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e. no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting and intense wave–matter interactions, using phonons, photons or even electrons. The present work further enhances confidence in using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.     

关于亚直不可约环上的导子

讨论了亚直不可约环上的导子。首先证明了一些简单的引理,接着讨论了导子作用在亚直不可约环上的问题,并给出了亚直不可约环的中心元与交换性的若干条件。最后,就一对导子在亚直不可约环上的共同作用进行了探讨。     

国际碳中和战略行动与科技布局分析及对我国的启示建议

实现碳达峰、碳中和是以习近平同志为核心的党中央做出的重大战略决策，将带来经济社会广泛而深刻的系统性变革。科技是支撑碳中和目标的核心驱动力。文章在梳理碳中和相关概念基础上，分析了发达国家/地区和国际组织碳中和的战略行动和科技布局特点，发现：各主要国家通过立法监管、能源战略、技术路线图、碳市场等政策行动全面推动碳中和目标；在科技方面，重点布局可再生能源、氢能、储能、先进核能、碳捕集利用与封存（CCUS）等变革性绿色低碳技术，抢占未来绿色工业革命科技制高点。文章针对实现碳中和的“减排”和“增汇”两条根本路径，围绕“构建零碳能源体系”“再造低碳产业流程”“生态固碳增汇/负排放”三大方向提出了需要重点布局的14个重要科技问题研究，以引导超过70项关键技术突破。在分析碳中和国际行动和关键科技问题基础上，围绕加强碳达峰、碳中和行动顶层设计，强化面向碳中和的科技研发体系，建立零碳能源体系和新型电力系统，构建低碳产业体系，前瞻部署生态固碳等负排放技术，以及加强系统性解决方案在碳中和行动中的应用6个方面，提出了加强我国碳中和战略科技布局的建议。     

Lessons from the famous 17th-century paradox of the Chevalier de Méré

We take advantage of a combinatorial misconception and the famous paradox of the Chevalier de Méré to present the multiplication rule for independent events; the principle of inclusion and exclusion in the presence of disjoint events; the median of a discrete-type random variable, and a confidence interval for a large sample. Moreover, we pay tribute to our original bibliographic sources by providing two computational tools to facilitate the students' insights on these topics.