First order theory of cyclically ordered groups

By a result known as Rieger's theorem (1956), there is a one-to-one correspondence, assigning to each cyclically ordered group H a pair $(G,z)$ where G is a totally ordered group and z is an element in the center of G, generating a cofinal subgroup $〈z〉$ of G, and such that the cyclically ordered quotient group $G/〈z〉$ is isomorphic to H. We first establish that, in this correspondence, the first-order theory of the cyclically ordered group H is uniquely determined by the first-order theory of the pair $(G,z)$. Then we prove that the class of cyclically orderable groups is an elementary class and give an axiom system for it. Finally we show that, in contrast to the fact that all theories of totally ordered Abelian groups have the same universal part, there are uncountably many universal theories of Abelian cyclically ordered groups.     

A note on exact finite difference schemes for modified Lotka–Volterra differential equations

We construct a class of modified Lotka–Volterra ordinary differential equations (ODE’s) and show that a nonlinear change of the dependent variables transform them into a set of coupled, linear ODE’s. Using the latter equations, we calculate the corresponding exact finite difference schemes using a technique given by Mickens. Next, we show how to reconfigure these relations to obtain the exact finite difference representation of the original modified, nonlinear Lotka–Volterra ODE’s.     

左删失数据下ARMA(p,q)模型的估计

在观测数据左删失情形下由K—M估计方法得到,严平稳遍历序列{Xt}的均值和自协方差函数的估计,从而获得ARMA（p,q）模型的参数估计,且所给估计量是强相合估计．     

Hysteresis operators in phase-field models of Penrose-fife type

Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical theory of hysteresis operators developed in the past fifteen years. Well-posedness and thermodynamic consistency were proved for a phase-field system with hysteresis which is closely related to the model advanced by Caginalp in a series of papers. In this note the more difficult case of a phase-field system of Penrose-Fife type with hysteresis is investigated. Under slightly more restrictive assumptions than in the Caginalp case it is shown that the system is well-posed and thermodynamically consistent.     

高中化学新教材习题与课程标准一致性研究*——以“常见无机物及其应用”内容为例

结合本国国情,对SEC一致性分析模式进行本土化改造,构建基于化学学科能力的一致性分析框架,并从内容主题和认知水平等2个维度分析课程标准与3个版本高中化学新教材习题在“常见无机物及其应用”主题的一致性程度。研究结果显示:3个版本高中化学新教材习题与课程标准在内容主题和认知水平维度上均存在统计学意义上的显著一致性。在一致性研究的基础上,分析不同版本教材习题在内容主题和认知水平上的分布重点,并提出教材习题编写建议和使用策略。     

基于Achieve工具的高中化学教科书习题与课程标准的一致性研究

Achieve一致性分析工具从向心性、挑战性和均衡性3个维度,通过内容向心性、表现向心性、挑战的来源、挑战的层次、平衡和范围6个指标来分析评价与课程标准的一致性。选用Achieve一致性分析工具,对2019年人教版《化学第二册(必修)》第七章“有机化合物”课后习题与课程标准必修课程主题“简单的有机化合物及其应用”的一致性进行分析,得出习题与课程标准在各个不同指标的一致性情况。根据研究结果,对课程标准修订、教科书习题设计优化和化学学习评价提出建议。     

WOD样本下密度函数核估计的强相合性

设（Xn,n≥1）是同分布的WOD随机变量序列,具有共同的密度函数f（x）,利用WUOD序列的指数不等式,在适当条件下获得了WOD样本下密度函数核估计的强相合性．     

某光电装置光轴一致性改进分析

某传感器侧挂结构形式的光电装置光轴一致性指标超差。通过对光电装置的光具座、传感器罩等相关零件的结构进行分析,对光具座、传感器罩的相互配合面和光具座的传感器安装面的平面度进行改进设计,提高精度,并适当增加其壁厚;着重对改进前后的光具座进行了模态分析。通过搭建试验装置对改进后的光电装置进行试验测试,对试验测试数据进行分析。试验结果表明,改进措施对提高光电装置光轴一致性有效。     

随机删失场合基于 Synthetic Data 的回归 函数核估计的强相合性

本文改进了文献[ 1] 中窗宽的条件; 并且讨论了随机删失场合基于 Synthetic Data 的回归函数递推核 估计的强相合性,所得结论均与完全样本情况相对应.     

Polynomial Time Uniform Word Problems

We have two polynomial time results for the uniform word problem for a quasivariety Q: (a) The uniform word problem for Q can be solved in polynomial time iff one can find a certain congruence on finite partial algebras in polynomial time. (b) Let Q* be the relational class determined by Q. If any universal Horn class between the universal closure S(Q*) and the weak embedding closure S?(Q*) of Q* is finitely axiomatizable then the uniform word problem for Q is solvable in polynomial time. This covers Skolem's 1920 solution to the uniform word problem for lattices and Evans' 1953 applications of the weak embeddability property for finite partial V algebras.