Variation of student numerical and figural reasoning approaches by pattern generalization type,strategy use and grade level

This paper explored variation of student numerical and figural reasoning approaches across different pattern generalization types and across grade level. An instrument was designed for this purpose. The instrument was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. Analysis of data showed that the numerical reasoning approach seems to be more dominant than the figural reasoning approach for the near and far pattern generalization types but not for the immediate generalization type. The findings showed that for the recursive strategy, the numerical reasoning approach seems to be more dominant than the figural reasoning approach for each of the three pattern generalization types. However, the figural reasoning approach seems to be more dominant than the numerical reasoning approach for the functional strategy, for each generalization type. The findings also showed that the numerical reasoning was more dominant than the figural reasoning in lower grade levels (grades 4 and 5) for each generalization type. In contrast, the figural reasoning became more dominant than the numerical reasoning in the upper grade levels (grades 10 and 11).     

运用综合手段研究铅锌硫化物精矿的氧化和鉴定其产物

南京关口每年从国外进口铅、锌精矿达几百万吨,随着我国国民经济的发展,作为重要有色金属来源的该矿种的进口量仍将逐年增加。硫化物精矿在运输和储存过程中都有可能发生氧化,由此导致金属品位的波动是常见现象,然而此前在这方面的报导甚少。为此,作者以铅锌硫化物精矿为例对其进行了模拟状态下的氧化实验并采用能谱、光学显微镜、化学物相分析、X射线衍射分析、扫描电镜等手段对氧化前及氧化后的样品进行了鉴定。结果表明,在模拟精矿储运条件下两种精矿的氧化皆甚为明显,铅精矿为1.5%,而锌精矿达到了14.5%,由此引起的品位变化是不可忽视的。鉴于有色金属硫化物精矿在储运过程中呈现了它们的易氧化性并对品位产生影响,所以有关这类矿产品的商贸过程中涉及取样、样品加工和保管、公证等问题,均应在科学实验基础上规范化。     

耕地模糊综合定级体系初探

本文探讨了耕地模糊综合定级法的基本原理、特点和数学模型以及技术路线 ,并运用此法对耕地进行模拟定级 ,最后就此法的实际应用进行客观评价 .     

Stationary problem of third-grade fluids in two and three dimensions: existence and uniqueness

This paper is devoted to the stationary problem of third-grade fluids in two and three dimensions. In two dimensions, we show existence of solutions and uniqueness, for a boundary of class C^2,1 and small data, by generalizing the method used by J.M. Bernard for the stationary problem of second-grade fluids (we deal with a polynomial of four degrees instead of two degrees). Contrary to the case of two dimensions, the resolution of the problem of third-grade fluids in three dimensions requires the physical condition |α₁+α₂|<(24νβ)^1/2. From this condition, we derive two “pseudo ellipticities” for the operator ν|A(u)|²+(α₁+α₂)tr(A(u)³)+β|A(u)|⁴, where A(u) is a 3-order symmetric matrix such that tr(A(u))=0. Thus, with, in addition, a sharp estimate of the scalar product (|A(u)|²A(u)-|A(v)|²A(v),A(u)-A(v)), we are able to prove existence of solutions and uniqueness, for a boundary of class C^2,1 and small data, in three dimensions.

Résumé

Cet article est consacré au problème stationnaire des fluides de grade trois en dimension deux et trois. En dimension deux, nous montrons l’existence de solutions et l’unicité, pour une frontière de classe C^2,1 et une donnée petite, en généralisant la méthode utilisée par J.M. Bernard pour le problème stationnaire des fluides de grade deux (nous avons affaire à un polynôme de degré quatre au lieu de deux). Contrairement au cas de la dimension deux, la résolution du problème des fluides de grade trois en dimension trois requière la condition physique |α₁+α₂|<(24νβ)^1/2. De cette condition, nous déduisons deux “pseudo matrice” pour l’opérateur ν|A(u)|²+(α₁+α₂)tr(A(u)³)+β|A(u)|⁴, où A(u) est une matice symétrique d’ordre 3 à trace nulle. De là, avec, en plus, une fine estimation du produit scalaire (|A(u)|²A(u)-|A(v)|²A(v),A(u)-A(v)), nous sommes capables de prouver l’existence de solutions et l’unicité, pour une frontière de classe C^2,1 et une donnée petite, en dimension trois.     

A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation and work due to deformation are considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case).     

基于灰色关联的虚拟企业伙伴选择

虚拟企业组建时,面对网络上众多且又处于分散无序状态的潜在合作资源,往往难以找到合适的合作伙伴.研究了虚拟企业选择伙伴的指标体系,应用层次分析法计算出各指标的权重,并借鉴灰色关联度理论较好地解决虚拟企业网络化资源伙伴的选择问题.     

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.     

Nonsingular systems of generalized Sylvester equations: An algorithmic approach

We consider the uniqueness of solution (i.e., nonsingularity) of systems of r generalized Sylvester and ?‐Sylvester equations with n×n coefficients. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ?‐Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition and leads to a backward stable O(n³r) algorithm for computing the (unique) solution.