几何学中的升维类比与发现

数学的发现与数学的论证是数学的两大重要内容,如果没有数学的发现则论证就成了无源之水,无本之木;如果没有论证,命题的真假就不得而知,则发现就失去了意义。阐述了几何学中的升维类比与发现,一是命题的发现,二是论证的思想方法的发现。     

关于一个几何命题证明的思考

数学学习的重要目的在于培养学生的数学思维能力,养成良好的数学思维品质。从不同的角度分析问题、解决问题是培养数学思维品质的一个好方法,对培养思维的灵活性、广阔性有重要意义。从3个角度出发,给出一个几何命题的证明方法。     

高师"初等几何研究"课程改革的实践与认识

针对基础教育改革的现实和高师"初等几何研究"课程存在的问题,就本课程的改革进行了探索.具体从课程体系方面:突出学生利用几何知识进行问题解决和几何建模的能力等;从教学内容方面:强调高初结合和对中学几何知识缺陷的补充等;从教学模式方面:高师数学课堂的"自主·合作·创造"模式三方面对改革的实践进行了总结.     

新FRP技术加固钢筋混凝土矩形柱改善延性的试验研究

Reinforced concrete （RC） columns lacking adequately detailed transverse reinforcement do not possess the necessary ductility to dissipate seismic energy during a major earthquake without severe strength degradation. In this paper, a new retrofit method, which utilized fiber-reinforced plastics （FRP） confinement mechanism and anchorage of embedded bars, was developed aiming to retrofit non-ductile large RC rectangular columns to prevent the damage of the plastic hinges. Carbon FRP （CFRP） sheets and glass FRP （GFRP） bars were used in this test, and five scaled RC columns were tested to examine the function of this new method for improving the ductility of columns. Responses of columns were examined before and after being retrofitted. Test results indicate that this new composite method can be very effective to improve the anti-seismic behavior of non-ductile RC columns compared with normal CFRP sheets retrofitted column.     

矩形截面纤维流场压降及细颗粒扩散捕集效率

采用格子波尔兹曼气固两相流模型模拟扩散机制下矩形纤维捕集颗粒过程,研究纤维周围流场压降和扩散捕集效率随不同纤维布置方式的变化规律。把模拟得到的值（系统压降与捕集效率）与相同体积分数的圆柱纤维所对应的理论值相比,得到相应比例系数。分析规律,并采用Levenberg-Marquardt方法对其进行处理,得到相应比例系数的拟合公式。根据已有的圆形纤维压降与扩散效率的理论公式,再结合求得的拟合公式,对不同工况下的矩形纤维系统压降和扩散捕集效率进行计算。分析结果发现：矩形纤维系统压降与放置角度和长宽比均相关;而扩散捕集效率与长宽比成正比,与放置角度基本无关。     

Sexual dimorphism in bone–muscle relationship in young adults

The purpose of this study was to analyse associations between lean soft tissue (LST), a surrogate of skeletal muscle mass and key fracture-related geometric characteristics of the proximal femur. Moreover, we examined the role that muscle played on the proximal femur geometry in response to physical activity (PA). Participants were 83 young adults. Leg LST (exposure) was assessed by dual energy X-ray absorptiometry (DXA). Proximal femur geometry was derived from a left hip DXA scan. Geometric variables (outcomes) included the femoral neck axis length (FNAL), the femoral neck width (FNW), the neck–shaft angle and FNW|FNAL (an index of robustness). PA was evaluated by accelerometry. Linear regression was used to analyse relationships. Additional exposure variables included body height and mass. In males, leg LST explained 17.4% of variation in FNAL (P < 0.001) and 15% in FNW (P = 0.015). In females, it explained 8.8% of the variance in FNAL (P = 0.020). Associations remained significant in males, but not in females, when vigorous PA was added to the models. These results suggest that public health approaches to promote PA may be particularly important in females since vigorous PA seems to convey advantages in femur geometry and consequently in bone strength.     

Knots in the Fourth Dimension

ABSTRACT

The article analyses a debate that preoccupied the Russian press in the winter of 1878/9. Writers, journalists and scientists discussed whether mathematics could explain spiritualist séance phenomena. At its core, this was an assessment of social change and a debate about the ambiguity of modern life. While spiritualists hoped to bridge the divide between science and religion, subjectivity and objectivity, their opponents feared that séance phenomena and modern mathematics undermined a rationalist world-view that was endowed with reliability and universal truth. That no agreement could be reached indicates that the post-reform public sphere had become truly pluralist and modern.     

"三线共点"的常用证明方法

从仿射几何学与射影几何学的基本方法出发,简述了"三线共点"问题的一些基本的证明方法.     

一类椭圆型方程组解的存在性

本文研究了一类依赖于正参数λ椭圆型方程组,利用变分方法得到方程组存在最小能量解且为正解。     

在解析几何教学中引入数学实验课的理论探讨

建构主义学习理论强调认知来源于学生对认知活动的自主参与,数学实验正是认知学习中可以替代具体活动的新技术。数学实验课对解析几何传统教学方式是一种有益的补充,该文将探讨如何把数学实验融入解析几何教学之中。