To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventiona...To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventional condition that some function value increases monotonically, but also the condition that all feasible variables remain feasible after basis change in Phase-1. That is, taking a purely combinatorial approach to achieving feasibility. This enables us to get rid of ratio test in pivoting, reducing computational cost per iteration to a large extent. Numerical results on a group of problems are encouraging.展开更多
An account of the total synthesis of(±)-,(+)-heliespirone A and(±)-,(-)-heliespirone C is presented.In the first-generation total synthesis,we found rac-24a could be easily transformed to rac-heliespirones A...An account of the total synthesis of(±)-,(+)-heliespirone A and(±)-,(-)-heliespirone C is presented.In the first-generation total synthesis,we found rac-24a could be easily transformed to rac-heliespirones A&C in a biomimic way.Taking the disappointing diastereoselectivity of prenylation from 3 to 4,the nonselective dihydroxylation from 4 to 5 and the lenthy route in strategy A into account,we designed a different synthetic plan targeting a highly enantioselective,concise and protective-group free synthesis of heliespirones A&C.The palladium-catalyzed Michael addition and Sharpless AD played the key roles in the formation of optical lactone V,which could be easily transformed to compound I through two additional steps and the succedent operations were the same as those in the first-generation total synthesis.Our synthetic efforts indicated the bio-generation of heliespirones A&C from 24a should be a real process in nature.展开更多
文摘To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventional condition that some function value increases monotonically, but also the condition that all feasible variables remain feasible after basis change in Phase-1. That is, taking a purely combinatorial approach to achieving feasibility. This enables us to get rid of ratio test in pivoting, reducing computational cost per iteration to a large extent. Numerical results on a group of problems are encouraging.
基金the financial support from the National Natural Science Foundation of China(20702032&20872098)the Ministry of Education of China(NCET-08-0365,IRT0846)National Basic Research Program of China(973 Program,2010CB833200)
文摘An account of the total synthesis of(±)-,(+)-heliespirone A and(±)-,(-)-heliespirone C is presented.In the first-generation total synthesis,we found rac-24a could be easily transformed to rac-heliespirones A&C in a biomimic way.Taking the disappointing diastereoselectivity of prenylation from 3 to 4,the nonselective dihydroxylation from 4 to 5 and the lenthy route in strategy A into account,we designed a different synthetic plan targeting a highly enantioselective,concise and protective-group free synthesis of heliespirones A&C.The palladium-catalyzed Michael addition and Sharpless AD played the key roles in the formation of optical lactone V,which could be easily transformed to compound I through two additional steps and the succedent operations were the same as those in the first-generation total synthesis.Our synthetic efforts indicated the bio-generation of heliespirones A&C from 24a should be a real process in nature.
