Middle-school students’ concept images of geometric translations

This study explored sixth grade students’ concept images of geometric translations and the possible sources of their conceptions in a non-technological environment. The data were gathered through a written instrument, student and teacher interviews and document analyses. Analyses of student responses revealed two major concept images of geometric translations: (a) translation as translational motion, and (b) translation as both translational and rotational motion. Students who held these conceptions showed various levels of understanding, such as conceiving translations as undefined motion, partially-defined motion, and defined-motion of a single geometric figure on the plane. The findings of the study suggested, in general, consistencies between students’ concept images and their concept definitions. However, most of the students’ concept definitions were inconsistent with the formal concept definition of geometric translations.Data analyses also revealed five interpretations of a translation vector: (a) vector as a reference line, (b) vector as a symmetry line, (c) vector as a direction indicator, (d) vector as a parameter, and (e) vector as an abstract tool. Furthermore, classroom instruction, mathematics and science textbooks, real-life examples and everyday language were the major sources of students’ concept images of geometric translations.     

A novel cognitive system model and approach to transformation of information granules

In this paper, a novel cognitive system model is established based on formal concept analysis to exactly describe human cognitive processes. Two new operators, extent–intent and intent–extent, are introduced between an object and its attributes. By analyzing the necessity and sufficient relations between the object and some of its attributes, the information granule concept is investigated in human cognitive processes. Furthermore, theories of transforming arbitrary information granule into necessary, sufficient, sufficient and necessary information granules are addressed carefully. Algorithm of the transformation is constructed, by which we can provide an efficient approach to the conversion among information granules. To interpret and help understand the theories and algorithm, an experimental computing program is designed and two cases is employed as case study. Results of the small scale case are calculated by the method presented in this paper. The large-scale case is calculated by the experimental computing program and validated by the proposed algorithm. The considered framework can provide a novel convenient tool for artificial intelligence researches.     

STUDENT TEACHERS’ UNDERSTANDING OF RATIONAL NUMBER: PART-WHOLE AND NUMERICAL CONSTRUCTS

Previous research has shown that secondary school students’ understanding of fractions is dominated by the part-whole concept to the possible detriment of their understanding of a fraction as a number in its own right. The present paper reports on an investigation into the understanding of intending primary teachers in this area. Four representatives of a cohort of sixty students on a PGCE course specialising in the lower primary age range were asked detailed questions probing their knowledge of fractions. The conclusion was that the part-whole concept dominates. All of the students were familiar with the numerical concept from their work on the PGCE course, but they reverted to the more familiar part-whole ideas in attempting to solve problems.     

A general approach to fuzzy concepts

The paper proposes a flexible way to build concepts within fuzzy logic and set theory. The framework is general enough to capture some important particular cases, with their own independent interpretations, like “antitone” or “isotone” concepts constructed from fuzzy binary relations, but also to allow the two universes (of objects and attributes) to be equipped each with its own truth structure. Perhaps the most important feature of our approach is that we do not commit ourselves to any kind of logical connector, covering thus the case of a possibly non‐commutative conjunction too. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一种新的概念格增量维护算法

形式概念分析在数据分析以及机器学习领域得到了广泛的应用,作为核心数据结构的概念格的构造算法一直是形式概念分析领域的研究热点.根据概念外延的补集性质,给出并证明了概念的生成定理和超概念的生成定理,并以此为基础提出了一种新的概念格的增量维护算法,包括概念的生成和序关系建立算法,并给出了一个应用示例.     

On computable formal concepts in computable formal contexts

We introduce and study the notions of computable formal context and computable formal concept. We give some examples of computable formal contexts in which the computable formal concepts fail to form a lattice and study the complexity aspects of formal concepts in computable contexts. In particular, we give some sufficient conditions under which the computability or noncomputability of a formal concept could be recognized from its lattice-theoretic properties. We prove the density theorem showing that in a Cantor-like topology every formal concept can be approximated by computable ones. We also show that not all formal concepts have lattice-theoretic approximations as suprema or infima of families of computable formal concepts.     

国际市场营销管理与决策信息系统(IMMADIS)原型研究

分析归纳了国际市场营销管理与信息的特征，把系统目标分解为三级，依此提出的国际市场营销管理与决策信息系统结构模式，充分考虑了计算机在企业管理中应用的优势与特点，同时又考虑到国情，便于企业开发实施。     

Reactor design and energy concepts for a plasma process of acetylene black production

Acetylene black can be produced from methane decomposition in a plasma reactor. Different types of plasma reactor are designed for this purpose and a parametric analysis of the system is made. Carbon yield in the reactor seems to be dependent on methane flow rate and plasma power. The results obtained from various types of material analysis of the product obtained show that in some conditions carbon produced under plasma has qualities similar to acetylene black obtained by classical processes.     

Macroscopic and Micromechanical Approaches to the Modelling of the Osmotic Swelling in Clays

The osmotic swelling in clays has been extensively studied at the physico-chemical scale. The present paper addresses the question of the modelling of this phenomenon from the mechanical point of view. First, the classical macroscopic thermodynamic framework for saturated porous continua is extended in order to take into account the solid-salt interaction through the concept of macroscopic activity coefficient of the salt. The micromechanical approach then incorporates this interaction through the concept of swelling pressure which is used for describing the internal forces in the fluid phase at the microscopic scale. The results of a physico-chemical theory for the solid-salt interaction, such as the e.d.l. theory, can be introduced in both approaches. Each of them leads to the identification of a deviation, of chemical origin, to Terzaghi's effective stress principle. Besides, the micromechanical approach allows us to clearly differentiate the mechanical and the chemical parts of clay materials elasticity.