计算渠道横断面面积的一种方法

在渠道测量中,为了计算挖填土施工量,需要就每一横断面分别计算出各挖方部份面积(如图1中阴影部份Ⅰ所示)和各填方部分面积(如图1中阴影部分Ⅱ、Ⅲ所示).计算工作通常是在画出各横断面图后进行的.计算方法可采用分块法、梯形法、方格法等多种.但采用这些方法计算,做起来一般都比较繁杂.由于渠道横断面的个数通常都比较多,因而就更显得这一工作繁重了.     

The Decision Problems for Properties of Transformation Groups

In this paper the fundamental result about the decision problems for properties of FRT-groups (i. e. the groups each of which is isomorphic with a group generated by a finite number of recursive transformations) has been proved: Let p be any algebraic property for groups such that there is a FRT-group G_1 which has the property p, a FRT-group G_2 which has not the property p, and G_2 is not isomorphic with any subgroup of any FRT-group which has the property p. Then the problem of deoiding, for any given groap P genetated by a finite number of recursive transformations, whether or not the group G isomorphic with P has the property p is unsolvable.     

变换群性质的判定问题

In this paper the fundamental result about the decision problems for properties-of FRT-groups (i. e. the groups each of which is isomorphic with a group generated by a finite number of recursive transformations) has been proved: Let p be any algebraic property for groups such that there is a FRT -group G₁ which has the property p, a FRT-group G₂ which has not the property p, and G₂ is not isomorphic with any subgroup of any FRT-group which has the property p. Then the problem of deciding, for any given groap P genetated by a finite number of recursive transformations, whether or not the group G isomorphic with P has the property p is unsolvable.