【摘要】 本文利用拓朴学的结论对利益区域是凸多面体的混料问题给出一种直接设计方法。凸多面体剖分成几个单纯形,每个单纯形与正规单纯形同胚,凸多面休上的设计问题即转化成几个正规单纯形上的设计问题。分块求最优点,经比较得到凸多面体的最优点。并且提出凸多面体的最小剖分问题:当凸多面体K的N个顶点P₁(x₁¹,x₂¹,……,x_q+1¹,P₂(x₁²,x₂²,……x_q+1²,……,P_N(x₁^N,x₂^N)……,x_q+1^N为已知时,怎样将此N个顶点进行组合,使 K=sum from i=1 to P(P_i1P_i2……P_iq+1) 且 P=min, 这里S(P_i1P_i2……P_iq+1)表示P_i1,P_i2,……,P_iq+1为顶点的单纯形。更多还原

【Abstract】 A direct design method applicable to mixture problems for which the interest region is a convex-polyhedron has been given in this note by use of a topological result. The convex-polyhedron is subdivided into several simpli-ces, each of them are homeomorphic with respect to the normal-simplex, insomuch that the design problem on convex-polyhedron may be transformed into several design problems on normal-simplex. After finding those optimal points by blocking, the optimal point on convex-polyhedron would be natually determined by means of comparison and choice. Therefore, a problem of minimal subdivision has to be suggested here for further discussion, i.e., WhenN vertices , of the convex-polyhedron K were given, N vertices shoud be so combined that andp = min,Where S(Pi1Pi2……Ouq+1) expresses the simplex, of which the vertices arepu1, pi2,……piq+1.更多还原