Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis...Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way.展开更多
In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp ...In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.展开更多
The notion of radial Blaschke-Minkowski homomorphism was introduced by Schuster. In this paper, we study the radial Blaschke and radial Minkowski linear combinations, respectively, and give several inequalities under ...The notion of radial Blaschke-Minkowski homomorphism was introduced by Schuster. In this paper, we study the radial Blaschke and radial Minkowski linear combinations, respectively, and give several inequalities under the notion of radial Blaschke Minkowski homomorphism in forms of star dual.展开更多
文摘Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671119)the Shanghai Leading Academic Discipline Project (Grant No.J50101)the Shanghai University Graduate Innovation Foundation Project (GrantNo.SHUCX092003)
文摘In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.
基金Supported by the National Natural Science Foundation of China(11371224)
文摘The notion of radial Blaschke-Minkowski homomorphism was introduced by Schuster. In this paper, we study the radial Blaschke and radial Minkowski linear combinations, respectively, and give several inequalities under the notion of radial Blaschke Minkowski homomorphism in forms of star dual.
