辛差分格式的阶条件和高阶格式的构造

哈密尔顿系统具有很多本质的性质，如保面积、保能量和动量等，而最重要的是自治哈密尔顿系统相流的辛性质，这为保相面积和相体积提供了保证，因此我们希望差分格式在被用来求哈密尔顿系统的数值解时能保持这种辛性质。在文献［１─３］中，冯康等人发展了哈密尔顿系统辛差分格式的一整套理论。本文主要考虑辛ＲＫＮ方法及显式辛格式的阶条件，并给出一些高阶辛ＲＫＮ格式，还提出一种利用低阶格式构造高阶格式的方法。此方法对辛格式和非辛格式均适用。限于篇幅，本文略去大部分定理的证明并尽可能简化说明。     

谈"单积一口清"的训练技巧

学习"单积一口清"是乘、除算的基础,但练好它并非易事.文章从练习"单积一口清"的时间科学安排和练习步骤出发,对如何练好"单积一口清"进行阐述.     

Diagnosing Teachers’ Understandings of Rational Numbers: Building a Multidimensional Test Within the Diagnostic Classification Framework

We report a multidimensional test that examines middle grades teachers’ understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers’ and students’ reasoning in this content area. We administered the test to a national sample of 990 in‐service middle grades teachers and analyzed the item responses using the log‐linear cognitive diagnosis model. We report the diagnostic quality of the test at the item level, mastery classifications for teachers, and attribute relationships. Our results demonstrate that, when a test is grounded in research on cognition and is designed to be multidimensional from the onset, it is possible to use diagnostic classification models to detect distinct patterns of attribute mastery.     

基于改进Ganny算子的SAR图像边缘检测

Canny算子法是边缘检测的重要方法之一。本文从SAR图像乘性噪声的特点出发,通过增加前处理和更改核函数对Canny算子进行了改进,扩展了Canny算子在SAR图像边缘检测中的应用。仿真结果表明该算法提取的边缘丰富,同时又抑制了噪声。     

局部k连通（k道路连通）空间

给出局部连通性与局部道路连通性的定义及等价刻画,研究它们的基本性质,证明它们是拓扑不变性、开遗传性、可商性;最后证明它们是有限可积但不是任意可积,并给出局部连通性可数可积的充要条件．     

Fractions as the Coordination of Multiplicatively Related Quantities: A Cross-Sectional Study of Children's Thinking

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared) in their solutions to equal sharing problems and to see to what extent this coordination was multiplicative. A secondary goal was to document children's solutions for equal sharing problems in which the quantities had a common factor (other than 1). Data consisted of problem-solving interviews with students in 1st, 3rd, 4th, and 5th grades (n=112). We found two major categories of strategies: (a) Parts Quantities strategies and (b) Ratio Quantities strategies. Parts quantities involved children's partitions of continuous units expressed in terms of the number of pieces that would be created. Ratio quantities involved children's creation of associated sets of discrete quantities. Within these strategies, children drew upon a range of relationships among fractions, ratio, multiplication, and division to mentally or physically manipulate quantities of sharers and things to produce exhaustive and equal partitions of the items. Additionally, we observed that problems that included number combinations with common factors elicited a wider range of whole-number knowledge and operations in children's strategies and therefore appeared to support richer interconnections than problems with relatively prime or more basic number combinations.     

真理想存在性的一个判定方法

本文主要通过极大理想空间与乘法线性泛函的核空间的关系,给出了真理想存在性的一个判别方法.     

Multiplicative Measurements of a Trait Anxiety Scale as Predictors of Burnout

The purpose of the present study was to investigate whether combining the two dimensions of anxiety (i.e., intensity and direction) by using a multiplicative model would strengthen the prediction of burnout. Collegiate athletes (N = 157) completed the Athlete Burnout Questionnaire as well as a trait version of the Competitive State Anxiety Inventory-2D. Three separate hierarchical regression analyses with four blocks were conducted to predict each one of the burnout subscales from anxiety intensity and direction while controlling for gender. The multiplicative variable for cognitive anxiety was a significant predictor of reduced sense of accomplishment (p < .01). Self-confidence was the only directional scale that predicted reduced sense of accomplishment, emotional/physical exhaustion, and devaluation (p < .01). In addition, gender was found to predict overall burnout in all three subscales as a control variable (p < .05). Conclusions and applied implications are drawn based on the results.     

环上乘法导子的可加性

设R是任意的一个结合环,δ是环R上的一个乘法导子,若环R满足Martindale条件,则环R上的乘法导子δ是可加的。     

求一类优化问题全局解的线性化方法

对广泛应用于金融及经济等实际问题中的一类带有多乘积约束的线性规划问题提出一种全局优化算法.利用对数的性质和线性化技术,建立了问题的等价问题的松弛线性规划,并通过对可行域的细分以及一系列求解过程的讨论,从理论上证明了算法收敛到问题的全局最优解,并用数值结果验证了方法的可行性.