The positive definiteness of elasticity tensors plays an important role in the elasticity theory.In this paper,we consider the bi-block symmetric tensors,which contain elasticity tensors as a subclass.First,we define ...The positive definiteness of elasticity tensors plays an important role in the elasticity theory.In this paper,we consider the bi-block symmetric tensors,which contain elasticity tensors as a subclass.First,we define the bi-block M-eigenvalue of a bi-block symmetric tensor,and show that a bi-block symmetric tensor is bi-block positive(semi)definite if and only if its smallest bi-block M-eigenvalue is(nonnegative)positive.Then,we discuss the distribution of bi-block M-eigenvalues,by which we get a sufficient condition for judging bi-block positive(semi)definiteness of the bi-block symmetric tensor involved.Particularly,we show that several classes of bi-block symmetric tensors are bi-block positive definite or bi-block positive semidefinite,including bi-block(strictly)diagonally dominant symmetric tensors and bi-block symmetric(B)B0-tensors.These give easily checkable sufficient conditions for judging bi-block positive(semi)definiteness of a bi-block symmetric tensor.As a byproduct,we also obtain two easily checkable sufficient conditions for the strong ellipticity of elasticity tensors.展开更多
研究了分子链中含有聚甲基丙烯酸(PMAA)链段的两亲性嵌段共聚物PS b PMAA和双亲水性嵌段共聚物PVP b PMAA,PVA b PMAA的溶液性质.结果显示,这些共聚物溶液都表现出明显的聚电解质溶液的性质,并且随着分子链中PMAA链段长度的增加,共聚物...研究了分子链中含有聚甲基丙烯酸(PMAA)链段的两亲性嵌段共聚物PS b PMAA和双亲水性嵌段共聚物PVP b PMAA,PVA b PMAA的溶液性质.结果显示,这些共聚物溶液都表现出明显的聚电解质溶液的性质,并且随着分子链中PMAA链段长度的增加,共聚物溶液的聚电解质溶液特征也随之增强,表明这些共聚物都是高分子电解质,其溶液粘度取决于其中MAA单元的比例.展开更多
基金The first author’s work was supported by the National Natural Science Foundation of China(Grant No.11871051).
文摘The positive definiteness of elasticity tensors plays an important role in the elasticity theory.In this paper,we consider the bi-block symmetric tensors,which contain elasticity tensors as a subclass.First,we define the bi-block M-eigenvalue of a bi-block symmetric tensor,and show that a bi-block symmetric tensor is bi-block positive(semi)definite if and only if its smallest bi-block M-eigenvalue is(nonnegative)positive.Then,we discuss the distribution of bi-block M-eigenvalues,by which we get a sufficient condition for judging bi-block positive(semi)definiteness of the bi-block symmetric tensor involved.Particularly,we show that several classes of bi-block symmetric tensors are bi-block positive definite or bi-block positive semidefinite,including bi-block(strictly)diagonally dominant symmetric tensors and bi-block symmetric(B)B0-tensors.These give easily checkable sufficient conditions for judging bi-block positive(semi)definiteness of a bi-block symmetric tensor.As a byproduct,we also obtain two easily checkable sufficient conditions for the strong ellipticity of elasticity tensors.
文摘研究了分子链中含有聚甲基丙烯酸(PMAA)链段的两亲性嵌段共聚物PS b PMAA和双亲水性嵌段共聚物PVP b PMAA,PVA b PMAA的溶液性质.结果显示,这些共聚物溶液都表现出明显的聚电解质溶液的性质,并且随着分子链中PMAA链段长度的增加,共聚物溶液的聚电解质溶液特征也随之增强,表明这些共聚物都是高分子电解质,其溶液粘度取决于其中MAA单元的比例.