大都市双核廊道结构空间增长过程研究——以美国华盛顿—巴尔的摩地区为例

本文以华盛顿-巴尔的摩地区200年都市化发展史为例,通过Mapinfo7.0得到两城市内、外接圆半径值①,以Logistic模型为基础计算出其半径增长速率并进行对比分析。研究表明,巴尔的摩和华盛顿城市化区的扩展表现为核心与廊道的共同增长,但二者的增长速率不具有同步增长过程;1962年前华盛顿城市化区的空间形态要优于巴尔的摩,随后则相反。传统的双核廊道结构空间增长研究多以整体为对象研究其增长过程,本文的创新特色在于通过对比分析两个城市内、外接圆半径的变化,来揭示双核廊道结构空间增长的特殊规律。

关于Bokov不等式的两点注记

1966年,E.A.Bokov建立了关于三角形高线长h_a、h_b、h_c和内接圆半径r的不等式: 1/(h_a-2r)+1/(h_b-2r)+1/(h_c-2r)≥3/r。 (1) 现就Bokov不等式笔者作两点注记: 1.

欧拉不等式的一个加强猜想的验证

设AABC的三边分别为a，b，C，外接圆和内接圆半径分别为R，r，则有不等式R≥2r．上述不等式是数学家欧拉于1765年建立．由于该不等式具有简单而不平凡的特点，所以至今仍然在几何不等式领域里保持着高水平的地位，关于它的各种加强和推广的研究一直没有间断过．文[1]提出欧拉不等式的如下加强猜想：

Further Improvement of Klamkin Inequality

In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.

关于欧拉不等式一个猜想的改进

设△ABC的三边为a，b，c，外接圆和内接圆半径分别为R，r，则有不等式R≥2r，此即为著名的欧拉不等式．文[1]提出欧拉不等式的如下加强猜想．

Inequalities for inscribed simplexes

The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex and the squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not less than the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is a tangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that the circumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship between the circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex.

R^2中凸域的等周亏格的一个上界

本文运用平面凸域的性质给出了平面上凸域D的等周亏格的一个上界。