数学公式的教学法浅析

公式教学是数学教学内容的一项重要内容 ,在实际教学中 ,应重视对公式的结构分析 ,注意公式的范围和变形 ,揭示公式间的联系 ,促进知识的内化 ,这样有助于学生理解和掌握运用公式。     

简单快速判断手性碳原子R/S构型

一种用右手螺旋法来判断手性碳原子R／S构型的方法，在掌握这种方法以后，可逆用这种方法来写出已知命名的含手性碳原子的化合物的立体化学式或Fischer投影式.     

Seismic response analysis of damper-connected adjacent structures with stochastic parameters

Dynamic response analysis of damper connected adjacent multi-story structures with uncertain parameters is carried out. A formula of the multi degree of freedom （MDOF） for the structure-damper system with stochastic parameters is derived. The uncertainties of mass and stiffness are taken into consideration firstly. The ground acceleration is represented by Kanai-Tajimi filtered non-stationary process. The mean square random responses of structural displacement and story drift are chosen as the optimization objective. The variations of mean square responses of top floor displacements and bottom story drifts in neighboring structures with the damper stiffness and damping coefficient are analyzed in detail. Through the parametric study, the acquiring optimum parameters of damper are regarded as numerical results. Then, a reducing order model of the MDOF system for adjacent structures with mean parameters is presented. The explicit expressions for determining optimal parameters of Kelvin model-defined damper which is used to connect adjacent single degree of freedom （SDOF） structures subjected to a white-noise excitation are employed to achieve the appropriate damper parameters, which are called theory results. Through a comparative study, it can be found that the theory values of damper parameters are consistent with the results based on extensive parametric studies. The analytical results can be obtained by using the first natural frequencies and the total mass of the adjacent deterministic structures with mean parameters. The analytical formulas can be used to find appropriate parameters of damper between adjacent structures for engineering applications. The performance of damper is investigated on the basis of mitigations of mean square random responses of inter-story drifts, displacements and accelerations in adjacent structures. The numerical results demonstrate the robustness of coupled building control strategies.     

图的拓扑指标Z_2(G)

分子图的拓扑指标Z2(G)是反映分子性能的一个重要指标,在文[3]中,我们给出了任一自然数是否可作为某分子图的拓扑指标Z2(G)的一个结论,本文在此基础上讨论了拓扑指标Z2(G)界定的一个递归关系;同时给出了它的一个下界.     

劲性钢筋轻骨料混凝土梁斜截面承载力的计算

用极限状态法的计算理论并结合充满型钢试验中得出的试验参数，在考虑轻骨料砼与颈性钢筋的共同工作性能前提下，利用叠加法，建立了劲性钢筋轻骨料砼梁斜截面承载力的近似计算表达式。由于该近似计算表达式靠近现行的钢筋混凝土结构设计规范，易于被工程界所接受。该公式概念清晰，计算简便、适合手算，适用性较强。     

PRACTICAL ANALYSIS OF ORTHOTROPIC PLATES SUPPORTED IN ONE DIRECTION

A practical method for computing the one-way rectangular orthotropicplate(isotropic plate as a special case)is suggested in this paper.The supported condi-tions in two opposite edges may be simply supported,continuous or supportednonsymmetrically and the other two opposite edges are slide-supported or free.A series ofsimplified formulas are given for calculating the bending moments along the cross section(loaded section),in which the acting point of the concentrated load or the center of a rec-tangular uniform load is located.The valid range and accuracy of these formulas were stud-ied and the approximate results were examined and compared extensively with those by thetriangular series solution or finite element method.     

美国大学生资助需求公式及对中国的启示

美国大学生资助需求公式是上世纪中期发展起来的,用于判断一个大学生是否需要资助,需要资助的金额是多少。其理论基础是高等教育成本需要家庭和社会共同分担,维护高等教育公平。其基本结构是学生入学成本减去家庭预期贡献。公式的核心内容是计算大学生家庭可以用于高等教育的资金。美国大学生资助需求公式可以为建立中国大学生资助需求公式提供借鉴。     

大一无机化学教学中引入化学热力学的一点浅见

ΔG变化值反映体系变化自发趋向的可能性、程度;当体系处于平衡时,应用化学等温式就可求算平衡常数K。将这一思路应用于溶液中的化学平衡,能很简结地得出与实验相当吻合的数据。为拓宽热力学在无机化学教学中的产用,必须在教学中增加ΔG°变化在溶液平衡中的产用,而这增加不作精密处理,采取直接引入的方法。     

CAN READABILITY FORMULAS BE USED TO SUCCESSFULLY GAUGE DIFFICULTY OF READING MATERIALS?

A grade level of reading material is commonly estimated using one or more readability formulas, which purport to measure text difficulty based on specified text characteristics. However, there is limited direction for teachers and publishers regarding which readability formulas (if any) are appropriate indicators of actual text difficulty. Because oral reading fluency (ORF) is considered one primary indicator of an elementary aged student's overall reading ability, the purpose of this study was to assess the link between leveled reading passages and students’ actual ORF rates. ORF rates of 360 elementary‐aged students were used to determine whether reading passages at varying grade levels are, as would be predicted by readability levels, more or less difficult for students to read. Results showed that a small number of readability formulas were fairly good indicators of text, but this was only true at particular grade levels. Additionally, most of the readability formulas were more accurate for higher ability readers. One implication of the findings suggests that teachers should be cautious when making instructional decisions based on purported “grade‐leveled” text, and educational researchers and practitioners should strive to assess difficulty of text materials beyond simply using a readability formula.     

由系统物理性质确定化学反应的动力学常数——微分法

根据系统物理性质与物质浓度之间的关系式，推导出用微分法确定化学反应动力学常数的一般公式，并举例介绍了公式的使用方法．     

辅助变元之于命题与量化布尔公式的作用

使用辅助变元来引入定义,在知识表达中是一个流行和有力的技巧,能够得到更短、更自然的编码而无需冗长的重复.这篇论文中,我们形式地定义了辅助变元的概念,检验了其表达力并讨论了有趣的相关应用.我们把以下两者联系起来:一是,反复使用中间结果而不通过定义重复;二是,布尔函数其他表达中的相似概念.特别的,我们表明带定义的命题逻辑与具有任意输出端的布尔线路以及约束变元满足Horn性质的存在量化布尔公式(记作(E)HORNb)具有相同的表达力.本文还考虑了定义结构的限制,以及命题定义的扩充.特别的,我们检验了正命题定义与带存在量化的正定义之间的关系(或等价地,检验了(E)HORNb公式和约束变元未被Horn限定的存在量化的CNF公式(记作(E)CNF*)之间的关系).对命题定义的进一步扩充,是允许在定义中使用任意的量词,或等价地,允许布尔公式的嵌入.我们还证明了,量化CNF公式中的约束变元的表达力,是由子句中被约束部分的极小不可满足子公式或极小假子公式的结构所决定的.     

Developing an approach for teaching and learning about Lewis structures

ABSTRACT

This study explores first-year university students’ reasoning as they learn to draw Lewis structures. We also present a theoretical account of the formal procedure commonly taught for drawing these structures. Students’ discussions during problem-solving activities were video recorded and detailed analyses of the discussions were made through the use of practical epistemology analysis (PEA). Our results show that the formal procedure was central for drawing Lewis structures, but its use varied depending on situational aspects. Commonly, the use of individual steps of the formal procedure was contingent on experiences of chemical structures, and other information such as the characteristics of the problem given. The analysis revealed a number of patterns in how students constructed, checked and modified the structure in relation to the formal procedure and the situational aspects. We suggest that explicitly teaching the formal procedure as a process of constructing, checking and modifying might be helpful for students learning to draw Lewis structures. By doing so, the students may learn to check the accuracy of the generated structure not only in relation to the octet rule and formal charge, but also to other experiences that are not explicitly included in the formal procedure.     

Unique-MU(2)和SYM-MU(2)的结构和复杂度

SAT问题(可满足性问题)是计算机科学的核心问题,研究问题的方法很多,利用极小不可满足公式的性质来研究SAT问题是近几年兴起的一个热点研究方向. 文章主要利用,(1,*)-消解和分裂方法研究了差为2的唯一极小不可满足公式集(Unique-MU(2))和差为2的对称极小不可满足公式集(SYM-MU(2))的结构和复杂度.     

Use of salivary cortisol measurements in young infants: a note of caution

In order to investigate possible contamination of saliva samples with formula or breast milk obtained from young infants for cortisol assays, we measured cortisol concentrations in 3 common infant milk formulas and in breast milk before and after defatting and extraction using a commercial radioimmunoassay kit. Cortisol concentrations obtained prior to defatting and extraction were equal to or higher than (1.64-82.80 micrograms/dL) levels reported for salivary cortisol levels reported in newborn infants (0.09-2.08 micrograms/dL). Cortisol concentrations obtained after the defatting and extraction were lower (0.02-0.15 micrograms/dL), indicating that values obtained prior to defatting and extraction were due to cross-reacting substances as well as cortisol. As saliva samples are not routinely defatted or extracted prior to being assayed, high cortisol levels and interfering substances in formula and breast milk could contaminate salivary cortisol measurements in young infants. The present study suggests that appropriate controls should be taken when making salivary cortisol measurements in young infants to help ensure accurate results.     

Lucene相似度计算方法研究和改进

Lucene中的相似度计算可以让用户得到与查询词相似程度最高的文本,以及文本与查询词的相似程度,因此是Lucene搜索引擎的一个很重要的部分。最后的得分通过评分公式来实现,它的性能直接影响了评分结果,因此针对评分公式算法加以改进,改进后的Lucene相似度计算评分公式更准确地为用户提供所需要的信息。     

Statistical Power for School-Based RCTs With Binary Outcomes

Abstract

This article develops a new approach for calculating appropriate sample sizes for school-based randomized control trials (RCTs) with binary outcomes using logit models with and without baseline covariates. The theoretical analysis develops sample size formulas for clustered designs where random assignment is at the school or teacher level using generalized estimating equation methods. The article focuses on the impact parameter pertaining to rates and proportions rather than to the log odds of response, which has been the focus of the previous literature. The article also compiles intraclass correlations (ICCs) for the clustered design for a range of binary outcomes using data from seven education RCTs. These ICCs and the power formulas are then used to conduct a power analysis using a provided SAS macro; the key finding is that sample sizes of 40 to 60 schools that are typically included in clustered RCTs for student test score or behavioral scale outcomes will often be insufficient for binary outcomes. A key reason is that the potential for precision gains from regression adjustment is likely to be smaller for binary outcomes.     

Differential instructional productivity indices

Teaching load formulas to provide for differential program productivity ratios are in wide use. However, the various sets of differential weights on student credit hours (SCH) in use tend to be the result of historical accident, negotiation, or limited cost studies. To bring a unity into these formulas, a new statistical methodology applied to three years of teaching load data from 21 major public universities has yielded an objective, broadly applicable set of SCH weight factors. Those weights give promise of providing comparison of instructional productivity via unobtrusive measures. A table of optimum weighting factors for upper division and graduate SCH (relative to lower division) is presented by NCES Code discipline division. The weights derived from analysis are then compared with those developed by more traditional means.     

MAX—MU（2）的结构和复杂度

SAT问题(可满足性问题)是理论计算机科学的核心问题,研究SAT问题的方法很多,利用极小不可满足公式的性质来研究SAT问题是近几年的一个热点研究方向.文章主要利用(1,*)-消解和分裂方法研究了差为2的极大极小不可满足公式集(MAX-MU(2))的结构和复杂度.     

Experimental and numerical investigation of buckling in rectangular steel plates with groove-shaped cutouts

Steel plates are widely used in various structures, such as the deck and bodies of ships and bridges, and in the aerospace industry. In many instances, these plates are subjected to axial compression loads that predispose the sheets to instability and buckling. In this study, we investigate the buckling and post-buckling behaviors of steel plates having groove-shaped cutouts of various dimensions and angles using finite element method (FEM) (by ABAQUS software) and experimental tests (by an Instron servohydraulic machine). Boundary conditions were clamped by supports at upper and lower ends and free supports at the other edges. The results of both numerical and experimental analyses are compared, which show a very good agreement between them. Finally, based on the experimental findings, formulas are presented for the determination of the buckling load of such plates.     

Educational Transfer as Transformation: A Case Study about the Emergence and Implementation of Dual Apprenticeship Structures in a German Automotive Transplant in the United States

The apprenticeship system in Germany is carried out both by companies and vocational schools (the Dual System). The question of whether the German Dual System is transferable is currently being asked in vocational education and training research. The analysis of current transfer discourses alludes to a research desideratum: the actual approaches consider either the input or the output of an educational transfer, but the transfer process in relation to its input and output has not been investigated to date. We focus on this desideratum. In the present case study, the processes emergence and implementation of dual apprenticeship structures is analysed in relation to its input and output in a German automotive transplant in the United States. Transplant organisations provide an ideal case to explore the transfer phenomenon because they have been transferred from a familiar context to a foreign context. The research questions are: firstly, why and how did the need emerge to implement dual apprenticeship structures in the German transplant in the United States (input); secondly, how and in which way have these structures been implemented (process); and thirdly, how can the implemented structures be characterised: as an imitation, adaptation or transformation of the original model (output)? The central findings of the case study are: firstly, that growing contradictions in the production system triggered the implementation process; secondly, that the original Dual System was transformed within the implementation process; and thirdly, that this transformation led to innovative solutions. These findings may not be valid for every transfer at any time, but they reflect that educational transfer of dual apprenticeship structures can be more than just a more or less successful imitation or adaptation.