高中物理临界极值问题的处理方法

临界极值问题是高中物理中比较常见的问题,只有掌握临界极值问题的处理方法,才能为高中物理问题的解决提供依据.通过总结物理知识发现,存在临界极值问题的包括静摩擦力临界极值问题、运动学中的追及和相遇类问题、传送带上的临界速度问题等,对于不同物理量的临界和极值问题,需要运用不同的处理方法.本文主要分析高中物理部分临界极值问题的相关处理方法.     

利用导数求解高中物理中的极值问题

“应用数学知识处理物理问题的能力”是高中物理学习中的一项重要内容.高三学生已经学习了导数的概念和简单的求导方法.应用导数求极值问题是十分方便的,下面举例说明导数求解极值问题的方法.     

不等式在极值问题中的应用

极值问题的求解方法甚多,但通常可归结为不等式问题,由不等式的性质及求解方法予以解决.那么,不等式在极值问题中有何应用?本文主要从以下三个方面的极值问题进行探讨:(1)代数函数的极值问题;(2)三角函数的极值问题;(3)几何中的极值问题.通过对这三个方面的探讨,以体现不等式在极值问题求解中的灵活性和重要性.     

巧用数学知识 妙解物理极值问题

极值问题是高中物理中一个常见问题。处理极值问题的方法叫做极值法。高中物理中的极值问题可以分为两类：一类是直接指明变化的某物理量,要求得出最值;另一类是通过求出某量的极值,进而以此为依据解出与之相关的问题。 解答极值问题可以从物理过程的分析着手,也可以从数学方法的角度思考,还可以综合运用物理、数学相关知识和方法分析得出。     

物理中几种常见的极值问题的数学处理方法

物理问题中常会涉及至求极值的问题，要求同学们有较高的数学能力，体现了高考中“应用数学处理物理问题”的能力要求，现就高中物理中常见的几种极值问题的处理方法作一下归纳和总结。     

高中物理临界极值问题的处理方法

临界极值问题在物理学中极为常见,总结中学物理知识,物理临界极值问题主要有静摩擦力的范围引出的临界极值问题,运动学中追及、相遇类极值问题,物体在竖直面内做圆周运动的临界问题,传送带上的临界速度问题,临界出射点问题,某物理量取极值求解临界问题六种,本文重点探究后四种问题的处理办法。     

巧解条件极值问题

对多元条件极值问题中只有一个附加条件的类型进行了探讨,应用拉格朗日乘数法证明出几个函数极值问题。并且给出它们应用的一些例题。不少极值问题经过转化都能直接应用这几个命题而得出结论。这些命题的应用对于解决实际生活中的条件极值问题具有重要意义。     

高中物理中几种求极值的方法

极值问题在解物理习题时经常碰到,若用高等数学中函数求导的方向处理,则较为容易,但对中学生而言却难以掌握,如果我们在解题过程中巧妙地应用数学手段,思路上不局限于只是求解物理问题那么,许多看似抽象的物理问题就能迎刃而解,本文列举了几类求中学物理极值问题的方法,供大家在解题时参考.一、作图法求极值点到直线的所有连线中垂直距离最短,这一几何知识是同学们所熟悉的,我们应用这一知识就可以巧妙地求解力学问题.     

物理中的极值问题

中学物理中的极值问题，除了涉及物理过程的分析，还要应用数学手段进行处理．     

关于平面解析几何中极值问题的求解

介绍了求平面解析几何极值问题的六种方法，同时通过典型 例题，展示了 这些方法在解析几何极值问题中的实际应用。     

Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence

Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the “Groupitizing” ability in 1209 third to eighth graders (mean age at first timepoint = 10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures the ability to use grouping cues to access the exact value of a set. Groupitizing improves each year from late childhood to early adolescence (d = 3.29), is a central predictor of math achievement (beta weight = .30), is linked to conceptual processes in mathematics (minimum d = 0.69), and helps explain the dynamic between the ongoing development of non-symbolic number concepts, systemic educational inequities in school associated with SES, and mathematics achievement (minimum beta weight = .11) in ways that explicit symbolic measures may miss.     

Individual versus collaborative problem solving: divergent outcomes depending on task complexity

Many studies have tested external supports for promoting productive collaboration, but relatively few have examined what features characterize naturally productive collaborative tasks. Two lines of research have come to distinct conclusions on the primary task feature associated with productive collaboration: demonstrability versus complexity. This study examined the problem-solving performance of 110 seventh grade students on a demonstrable mathematical task, including 69 in three traditional math classrooms (for whom the task was complex) and 41 in two accelerated math classrooms (for whom the task was not complex). Students were further assigned to one of four conditions split by two factors: grouping (individual versus dyad) and number of problems (one or two). For the accelerated math classes, individuals performed significantly better than dyads. For the traditional math classes, dyads performed significantly better than individuals and exceeded the truth-wins criterion (a theoretical maximum indicating how individuals would perform if they shared knowledge perfectly). A complex-demonstrable task framework is proposed for characterizing naturally productive collaborative tasks.     

经济理论中最小二乘法线性拟合参数估计的等价性问题

在当今西方经济学至少是所谓的"高级"西方经济理论中,数学已经成为阐述理论内容的基本要素或者说是通用语言.线性回归模型是最常用的经济计量模型,用于研究风险、保险、资产组合等经济问题,也可以用作经济预测.本文研究了线性回归模型中的参数估计问题,运用最小二乘法进行参数估计的数学分析基础.最小二乘法只是使用了函数的稳定点而没有运用数学分析的极值理论里的第一充分条件和第二充分条件,本文讨论最小二乘法的估计参数方法和数学分析的极值理论的方法是等价的.     

The relationship between math anxiety and math achievement in young children is mediated through working memory,not by number sense,and it is not direct

Math anxiety is considered a predictor of math achievement, although the cognitive mechanism whereby math anxiety impairs math achievement is unclear. The paper presents the results of cross-sectional (N = 241) and longitudinal (N = 369) studies conducted among early school-aged children on the cognitive mechanism whereby math anxiety impairs math achievement. The following hypotheses were tested: (1) math anxiety directly affects math achievement; (2) in accordance with processing efficiency and attentional cognitive theories, math anxiety indirectly affects math achievement through working memory; (3) in accordance with the cognitive deficit model, math anxiety indirectly affects math achievement through number sense. The results mostly confirm the mediating role of working memory and undermine the mediating role of number sense and the direct path in the relationship between math anxiety and math achievement. Because previous studies undertaken in adults show the direct path from math anxiety to math achievement and the role of symbolic number processing in explaining the relationship between the two, the methodological and developmental aspects of the obtained results are discussed in the paper.     

海原县农村中小学教师地缘结构变迁研究

通过对宁夏海原县中小学教师地缘结构五十多年变化的田野统计、推理计算及访谈发现,受国家及国家西部地区政治、经济、人口、教育等政策因素以及西部农村地区教育发展内在力量影响,五十多年来,海原县本县籍农村中小学师资数量、比重保持持续增长态势,其本县籍教师数量、比值由历史最低发展到历史最高值,而其外县、外省籍教师数量、比重由历史最高值下降到历史最低点.因此,为有效发挥外县、外省籍教师在西部农村学校的功能和教育影响力,需要从政治、经济、教育等方面有针对性调整国家西部农村地区教师地缘结构政策.     

Number line estimation from kindergarten to grade 2: A longitudinal study

A bulk of evidence supports the association of number line estimations using Arabic digits and dots with math learning. Surprisingly few studies have been conducted to explore the relationship between estimations using number words and mathematics. The present study expands previous findings by investigating estimations in three formats (Arabic digits, dots and number), adding language as predictor and by focusing at timed and untimed math learning. A sample of 132 children was followed from kindergarten till grade 2. Results reveal variability in estimation accuracy and errors declining with age and instruction in all children. In addition, our findings suggest that Arabic numerals have a more linear distribution than number words. Moreover, our findings suggest that language explains variation in kindergarten but not in evolution and, more in particular, untimed math achievement can be predicted by number line estimation. Implications for assessment, prediction of math learning and instruction are discussed.     

求解DCMST问题的模糊离散粒子群优化算法

提出了一种求解度约束最小生成树问题(DCMST)的模糊离散粒子群优化算法(PSO),粒子编码采用Prüfer数编码机制,并引入模糊矩阵产生Prüfer数,迭代过程中加入归一化运算对位置矩阵进行修正,利用最大数法进行解模糊化。通过仿真实验验证了算法的有效性。     

一类亚纯函数系数的高阶齐次线性微分方程解的性质

在J．K．Langley给出的高阶齐次线性微分方程复振荡的结果的基础上,考虑具有控制系数和系数仅有有限个极点的高阶线性齐次微分方程,研究亚纯系数齐次线性微分方程亚纯解的零点收敛指数,得到了这类方程的线性无关超越解的最少个数和零点收敛指数为有穷的解的最多个数。     

Toward a Two‐Factor Theory of One Type of Mathematics Disabilities

A two‐factor theory is proposed in an attempt to explain the difficulty that children with math disabilities have in mastering the basic number facts. The theory is based on the premise that weak cognitive representations lead to poorer retrieval of information from long‐term memory. Two groups of children with disabilities are discussed: those with math disabilities alone (MD) and those with co‐morbid math and reading disabilities (MD/RD). It is proposed that weak phonological processing abilities underlie the learning difficulties of MD/RD children, and that weak number sense is a causal factor in the math‐fact learning difficulties of MD only and some MD/RD children.     

Predicting First‐Grade Math Achievement from Developmental Number Sense Trajectories

Number sense development was tracked from the beginning of kindergarten through the middle of first grade, over six time points. Children (n= 277) were then assessed on general math achievement at the end of first grade. Number sense performance in kindergarten, as well as number sense growth, accounted for 66 percent of the variance in first‐grade math achievement. Background characteristics of income status, gender, age, and reading ability did not add explanatory variance over and above growth in number sense. Even at the beginning of kindergarten, number sense was highly correlated with end of first‐grade math achievement (r= 0.70). Clarifying the observed slope effect, general growth mixture modeling showed that children who started kindergarten with low number sense but made moderate gains by the middle of kindergarten had higher first‐grade math achievement than children who started out with similarly low number sense with flat growth. The majority of children in the low/flat growth class were from low‐income families. The findings indicate that screening early number sense development is useful for identifying children who will face later math difficulties or disabilities.