Given two disjoint 3-dimensional convex polytopes P and Q and a straight direction along Which P moves in translation, this paper presents a linear algorithm for determining Whether P collides with Q, and the possible...Given two disjoint 3-dimensional convex polytopes P and Q and a straight direction along Which P moves in translation, this paper presents a linear algorithm for determining Whether P collides with Q, and the possible collision positions on P and Q. This result is achieved by using the hierarchicat representation of polytopes, of which the preprocessing time is linear with space.展开更多
To study the Schneider＇s projection problem, Lutwak, Yang and Zhang recently introduced a new .affine invariant functional U（P） for convex polytopes in R^n. In the paper, we obtain the analytic expression of the af...To study the Schneider＇s projection problem, Lutwak, Yang and Zhang recently introduced a new .affine invariant functional U（P） for convex polytopes in R^n. In the paper, we obtain the analytic expression of the affine-invariant U（P） defined on a specific subclass of origin-symmetric convex polytopes in Rn and give an application of U（P） to the Lp-Minkowski problem.展开更多
In this paper,the problems of robust stability and stabilization,for the first time,are studied for delayed fractional-order linear systems with convex polytopic uncertainties.The authors derive some sufficient condit...In this paper,the problems of robust stability and stabilization,for the first time,are studied for delayed fractional-order linear systems with convex polytopic uncertainties.The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem.All the results are obtained in terms of linear matrix inequalities that are numerically tractable.The proposed results are quite general and improve those given in the literature since many factors,such as discrete and distributed delays,convex polytopic uncertainties,global stability and stabilizability,are considered.Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.展开更多
In this paper, we generalize the conception of characteristic function in toric topology and construct many new smooth manifolds by using it. As an application, we classify the Moment-Angle manifolds and the partial q...In this paper, we generalize the conception of characteristic function in toric topology and construct many new smooth manifolds by using it. As an application, we classify the Moment-Angle manifolds and the partial quotients manifolds of them over a polygon. In the appendix we give a simple new proof for Orlik-Raymond＇s theorem in terms of characteristic function which gives the classification for quasitoric manifolds of dimension 4.展开更多
The authors give several new criteria to judge whether a simple convex polytope in a Euclidean space is combinatorially equivalent to a product of simplices. These criteria are mixtures of combinatorial, geometrical a...The authors give several new criteria to judge whether a simple convex polytope in a Euclidean space is combinatorially equivalent to a product of simplices. These criteria are mixtures of combinatorial, geometrical and topological conditions that are inspired by the ideas from toric topology. In addition, they give a shorter proof of a well known criterion on this subject.展开更多
文摘Given two disjoint 3-dimensional convex polytopes P and Q and a straight direction along Which P moves in translation, this paper presents a linear algorithm for determining Whether P collides with Q, and the possible collision positions on P and Q. This result is achieved by using the hierarchicat representation of polytopes, of which the preprocessing time is linear with space.
基金Project supported by the National Natural Science Foundation of China (No.10671119)
文摘To study the Schneider＇s projection problem, Lutwak, Yang and Zhang recently introduced a new .affine invariant functional U（P） for convex polytopes in R^n. In the paper, we obtain the analytic expression of the affine-invariant U（P） defined on a specific subclass of origin-symmetric convex polytopes in Rn and give an application of U（P） to the Lp-Minkowski problem.
基金partly supported by the National Natural Science Foundation of China(12061006)the Science and Technology Project of Education Department of Jiangxi Province(GJJ180414)+1 种基金East China University of Technology Research Foundation for Advanced Talents(DHBK2018050)The second author is supported by the National Natural Science Foundation of China(71762001)。
文摘In this paper,we demonstrate the existence part of the discrete Orlicz-Minkowski problem for p-capacity when 1<p<2.
基金supported by Ministry of Education and Training of Vietnam(B2020-TNA)。
文摘In this paper,the problems of robust stability and stabilization,for the first time,are studied for delayed fractional-order linear systems with convex polytopic uncertainties.The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem.All the results are obtained in terms of linear matrix inequalities that are numerically tractable.The proposed results are quite general and improve those given in the literature since many factors,such as discrete and distributed delays,convex polytopic uncertainties,global stability and stabilizability,are considered.Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.
文摘In this paper, we generalize the conception of characteristic function in toric topology and construct many new smooth manifolds by using it. As an application, we classify the Moment-Angle manifolds and the partial quotients manifolds of them over a polygon. In the appendix we give a simple new proof for Orlik-Raymond＇s theorem in terms of characteristic function which gives the classification for quasitoric manifolds of dimension 4.
基金supported by the National Natural Science Foundation of China(No.11871266)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The authors give several new criteria to judge whether a simple convex polytope in a Euclidean space is combinatorially equivalent to a product of simplices. These criteria are mixtures of combinatorial, geometrical and topological conditions that are inspired by the ideas from toric topology. In addition, they give a shorter proof of a well known criterion on this subject.
