The relation between the circum-radius and the in-radius of an n-dimensional simplex in E^n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some s...The relation between the circum-radius and the in-radius of an n-dimensional simplex in E^n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.展开更多
Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional...Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional Euler equations when ω0∈L(2,1).展开更多
The formulae of the relationships between Euler angles and texture are important for the orientation distribution functions of research materials.At present,it is found that the formulae for the orthogonal and hexagon...The formulae of the relationships between Euler angles and texture are important for the orientation distribution functions of research materials.At present,it is found that the formulae for the orthogonal and hexagonal crystal structure proposed by Roe and Bunge are not in accord with the normal direction(ND)being perpendicular to the rolling direction(RD).In this paper,these formulae are deduced independently according to the notations proposed by Roe and Bunge.The results show that in addition to the coincidence with the formulae for the cubic crystal structure given by the Roe and Bunge,the other formulae are different from Roe’s and Bunge’s.The new formulae are in accord with ND,RD,and transverse direction(TD)at right angles.展开更多
基金Foundation item： Supported by the National Science Foundation of China（60671051） Supported by the Foundation of Anhui Higher School（KJ2009A45）
文摘The relation between the circum-radius and the in-radius of an n-dimensional simplex in E^n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.
基金The Beijing Natural Science Foundation (1992002) and Beijing Education Committee Foundation.
文摘Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional Euler equations when ω0∈L(2,1).
基金Sponsored by the National Natural Science Foundation of China(Grant No.51962017)。
文摘The formulae of the relationships between Euler angles and texture are important for the orientation distribution functions of research materials.At present,it is found that the formulae for the orthogonal and hexagonal crystal structure proposed by Roe and Bunge are not in accord with the normal direction(ND)being perpendicular to the rolling direction(RD).In this paper,these formulae are deduced independently according to the notations proposed by Roe and Bunge.The results show that in addition to the coincidence with the formulae for the cubic crystal structure given by the Roe and Bunge,the other formulae are different from Roe’s and Bunge’s.The new formulae are in accord with ND,RD,and transverse direction(TD)at right angles.
