数学分层作业研究综述

分层作业的研究有助于发挥数学作业的潜在功能,提升数学作业的质量.基于16篇国内分层作业的文献,采用文献分析法对其进行梳理、剖析.研究发现:一是作业分层对学生的发展具有一定积极作用;二是以学生分层为基础的作业分层设计需对学生进行综合性的考量;三是作业分层的标准较多,目前没有相对统一的标准.本文依据现有的分层作业相关文献,试图就分层作业的功能、实施和发展方向等提供启示.     

二重递归函数及其分层

本文讨论R.Péter[3]所提出的二重递归函数的性质,给出了二重递归函数的另一种等价刻画,即证明了二重速归函数类就是文[6]中所讨论的Z—分层函数类Z=(?).结合文[6]的结论我们便得到了关于二重递归函数类的一种Grzegorezyk型分层和一种更简单的二重递归模式.     

模糊聚类分析在图象分层中的应用

图象数据分层(Image Data Hierarchy)处理技术在图象数据压缩编码、边缘检测、特征提取以及模式识别中有着广泛的应用.本文将模糊聚类方法引入图象分层中,根据图象的特点,将2×2象素块划分为包含均匀和轮廓部分的七种类型,建立了表征图象特征的相似度矩阵,修正了普通的动态聚类法,提出了λ值的自适应控制方案.最后,给出了对一幅标准“USC Girl”数字图象处理的实例以验证本方案的可行性.     

分层教学的Bayes分析

对学校分层教学进行了初步探索 ,提出了分层分班的 Bayes决策 ,介绍了分层分班方法 ,获得了一些结论 ,并完成了对这些结论的证明 ,从理论上论述了分层教学是实施“因材施教”教育原则和素质教育的有效途径 ,给出了应用实例 .     

普通高校公共数学课程分类分层模式优化研究

公共数学课程对实现高校的人才培养目标起着十分重要的作用.本文遵循因材施教的原则,科学设计了公共数学课程体系,采用一种新的教学模式———分类分层教学.提出了分层教学方法、教学内容、考核模式、分层教学管理的改革实施方案,使基础课程更加具有针对性.     

正态分布与分层教学

利用概率论和不等式技巧完善了分层教学数字特征的一般证明,建立了教学效率的数学模型用应用实例,证明了分层教学法的优越性.     

分层教学在初中数学课堂中的运用

分层教学法是新课程改革所提倡的教学方式,从分层教学的概念、应用价值入手,分析分层教学的优势和劣势,合理运用分层教学的优势,并改善其劣势,结合初中数学课堂的特点探究有效分层教学的要点.     

基于聚类分析的中学数学分层教学应用研究

面对班级学生数学能力差异较大的现状，如何“因材施教”是当前所要解决的最大问题.分层教学无疑是大多数教师采用的一种解决措施，但如何科学合理地分层从而更好地挖掘学生的学科素养差异呢?本文中采用人工智能数据分析方法中的K-means聚类分析对中学生数学学科能力进行分层.该方法打破原有分层方法的局限性，从数据中挖掘隐含信息，弥补了教师传统地利用主观判断进行分层的不足，给出定量化分层参考，为进一步提升教学质量奠定基础.     

初中数学分层作业的设计研究

一、"数学分层作业设计"研究的意义"数学分层作业设计"是指教师在设计、布置作业时,根据不同层次学生的各种情况,如课堂表现、掌握程度、已有水平等,设计出不同的、适合各类学生的作业,从而帮助、促使不同层次的学生都能有效地完成作业,通过不同层次的练习达到良好的学习效果.二、"数学分层作业设计"的必要性初中数学作业普遍存在诸多问题:作业机械重复性较多,忽视学生间差距和潜能,形成"一刀切"的局面等.学     

基于分层序列的移动电子商务推荐系统策略研究

移动互联网环境下,移动电子商务快速发展,移动推荐系统成为解决移动信息过载的主要技术和手段.移动电子商务推荐系统中用户策略选择是一个典型的多目标决策问题,目标之间也存在一定的矛盾.基于移动推荐系统的这种特征,借助分层序列法算法的思想,通过元数据的标准化处理,结合移动电子商务中的位置上下文信息获取推荐数据,得到满足用户多目标需求的推荐结果.方法的提出为移动电子商务推荐系统的研究提出了一种新的推荐策略.     

层次P-集合的属性规律发现

P-集合是把动态特性引入到有限普通集合X内,改进有限普通集合X得到的.层次P-集合是对普通P-集合的扩展,具有层次结构和链式结构.利用层次P-集合的性质,研究层次P-集合属性元素与规律,给出层次结构间属性元素的关系及度量,给出链式结构中属性元素的关系及度量,给出属性规律.     

Hierarchical modeling of piezoelectric plates

We use variational techniques to derive a class of two-dimensional models for three-dimensional linearly elastic piezoelectric plates. The models result from a mixed formulation for the original problem within spaces of functions with polynomial dependence in the transverse direction. We show that the resulting system of equations is well-posed, and then discuss the asymptotic consistency of the simplest of such models.     

Hierarchical entropy analysis for biological signals

We develop a hierarchical entropy (HE) method to quantify the complexity of a time series based on hierarchical decomposition and entropy analysis. The proposed method is applied to the Gaussian white noise and the 1/f noise. We prove that the difference frequency components of the Gaussian white noise with the same scale factor have the same value of entropies, and the values decline as the scale factor increases. We also apply the HE method to the 1/f noise, and prove mathematically that a lower frequency component of a 1/f noise is also a 1/f noise and verify numerically that a higher frequency component of a 1/f random vector is approximately equal to a Gaussian random vector. The theoretical results are confirmed by numerical results. Moreover, we show that the HE method is an efficient method to analyze heartbeat signals by applying it to the cardiac interbeat interval time series of healthy young and elderly subjects, congestive heart failure (CHF) subjects and atrial fibrillation (AF) subjects.     

Hierarchical erasure correction of linear codes

Linear codes over finite extension fields have widespread applications in theory and practice. In some scenarios, the decoder has a sequential access to the codeword symbols, giving rise to a hierarchical erasure structure. In this paper we develop a mathematical framework for hierarchical erasures over extension fields, provide several bounds and constructions, and discuss potential applications in distributed storage and flash memories. Our results show intimate connection to Universally Decodable Matrices, as well as to Reed-Solomon and Gabidulin codes.     

Hierarchical management scheme by local fields

In the present paper we propose a new hierarchical management scheme within suitable extensions of 2-adic numbers, in which the subfields are treated as classes, and the communications are realized by computation on elliptic curves. The security of our system is much stronger than that of the traditional public key cryptographic systems.     

The Hierarchical compromise programming

This paper presents a multicriteria decision making method, the Hierarchical Compromise Programming (HCP), which combines a hierarchical structure for the modelization of a problem with the minimization of the distance to an ideal point as a resolution procedure. The proposed method allows the application of a model based on the minimization of a distance function, with tangible and intangible aspects. This research has been partially supported by the project SISDEMA: UN SISTEMA DECISIONAL AMBIENTAL (ref.: PMA-2196 CONSID-DGA)     

系统聚类分析中应注意的两类问题

给出了选用九种相似性度量，用最短距离法聚类，结果互不相同的一个有趣的例子。对该例，用欧氏距离求出距离矩阵后，除用最短距离法聚类结果唯一外，用最长距离法、重心法、类平均法、离差平方和法聚类，结果均不唯一。     

Hierarchical multilabel classification based on path evaluation

Multi-label classification assigns more than one label for each instance; when the labels are ordered in a predefined structure, the task is called Hierarchical Multi-label Classification (HMC). In HMC there are global and local approaches. Global approaches treat the problem as a whole but tend to explode with large datasets. Local approaches divide the problem into local subproblems, but usually do not exploit the information of the hierarchy. This paper addresses the problem of HMC for both tree and Direct Acyclic Graph (DAG) structures whose labels do not necessarily reach a leaf node. A local classifier per parent node is trained incorporating the prediction of the parent(s) node(s) as an additional attribute to include the relations between classes. In the classification phase, the branches with low probability to occur are pruned, performing non-mandatory leaf node prediction. Our method evaluates each possible path from the root of the hierarchy, taking into account the prediction value and the level of the nodes; selecting the path (or paths in the case of DAGs) with the highest score. We tested our method with 20 datasets with tree and DAG structured hierarchies against a number of state-of-the-art methods. Our method proved to obtain superior results when dealing with deep and populated hierarchies.     

A Quasilinear Hierarchical Size-Structured Model: Well-Posedness and Approximation

A finite difference approximation to a hierarchical size-structured model with nonlinear growth, mortality and reproduction rates is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite-difference approximation is proved. Simulations indicate that the monotonicity assumption on the growth rate is crucial for the global existence of weak solutions. Numerical results testing the efficiency of this method in approximating the long-time behavior of the model are presented.     

Hierarchical production planning and scheduling with random demand and production failure

A multiple-objective hierarchical production planning and scheduling model is developed that integrates aggregate type decisions, family disaggregate decisions, lotsizing and scheduling of the jobs. It is assumed that demand and production failure are subject to uncertainties. Stochastic programming with recourse using a constraint sample approximation method is used to incorporate random demand and production failure into the model. The model evaluates final production plans, updates the demand forecasts and proceeds on a rolling horizon manner. Experimental results show that it is sufficient to generate and incorporate into the aggregate type model a small sample of the stochastic constraints from an infinite set of scenarios. A heuristic scheduling algorithm provides detailed information regarding the progress of jobs through work centers. This information is extremely useful in resolving infeasibilities during the production process. Other features of the model are also reported.