LetλG(z)|dz|be the hyperbolic metric on a simply connected proper domain G■C containing the origin,and let‖·‖j be the Banach norms of C^nj for j=1,2,…,k.This note is to prove that if f is a normalized biholo...LetλG(z)|dz|be the hyperbolic metric on a simply connected proper domain G■C containing the origin,and let‖·‖j be the Banach norms of C^nj for j=1,2,…,k.This note is to prove that if f is a normalized biholomorphic convex function on G,thenΦN,1/p1,…,1/pk(f)(z)=F1/p1,…,1/pk(z)=f(z1),(f'(z1))^1/p1z,…,(f'(z1))^1/pkw)is a normalized biholomorphic convex mapping on ?N={(z1,z,…,w)∈C×C^n1×…×C^nk:‖z‖^p11+…+‖w‖^pkk<1/λG(z1)},where N=1+n1+…+nk and the branch is chosen such that (f'(z1))^1/pj|z1=0=1, j=1, …, k.Applying to the Roper-Suffridge extension operator,we obtain a new convex mappings construction of an unbounded domain and a refinement of convex mappings construction on a Reinhardt domain,respectively.展开更多
Let A be a Banach algebra with unit e and a,b,c∈A,Mc=(a c 0 b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a Banach algebra are proposed.A generalized Drazin spectrum of is d...Let A be a Banach algebra with unit e and a,b,c∈A,Mc=(a c 0 b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a Banach algebra are proposed.A generalized Drazin spectrum of is defined byσ_(gD)(α)={λ∈C:α-λe is not generalized Drazin invertible}.It is shown thatσ_(gD)(a)∪σ_(gD)(b)=σ_(gD)(M_(C))∪W_(2),where W_(g) is a union of certain holes σ_(gD) and W_(g)■σ_(gD)(a)∩σ_(gD)(b),or more finely.In addition,some properties of generalized Drazin spectrum of elements in a Banach algebra are studied.展开更多
60NiTi alloy is highly promising for aerospace bearings and mechanisms.Shock load that is inevitably generated during launching process brings about an quick loading process and transient load duration,and may further...60NiTi alloy is highly promising for aerospace bearings and mechanisms.Shock load that is inevitably generated during launching process brings about an quick loading process and transient load duration,and may further results in an unnoticed but detrimental creep deformation.On this account,the nanoindentation creep behavior of solution-treated 60NiTi alloy at room temperature and the corresponding influencing mechanism were studied.The results show that creep displacement was dominated by strain rate at the very beginning of holding stage.Strain rate and flow stress at the very beginning of holding stage were increased with an increased loading rate but declined with increasing holding load or with simultaneously increasing loading rate and holding load.The underlying mechanisms were provided as nucleation and absorption of geometrically necessary dislocations(GNDs)associated with strain gradient plasticity theory rather than the model based on the consumption of creep deformation at loading stage.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.:71904075)the National Ministry of Education Humanities and Social Science Research Planning Fund Project(Grant No.:21YJAZH001)the Research Foundation of Shenzhen Hospital,Southern Medical University(Grant No.:LCJH202001,22H3ATF03).
基金partially supported by the National Natural Science Foundation of China(11671362,11571105)Beijing Municipal Natural Science Foundation(1182008)the Scientific Research Funds of Huaqiao University
文摘LetλG(z)|dz|be the hyperbolic metric on a simply connected proper domain G■C containing the origin,and let‖·‖j be the Banach norms of C^nj for j=1,2,…,k.This note is to prove that if f is a normalized biholomorphic convex function on G,thenΦN,1/p1,…,1/pk(f)(z)=F1/p1,…,1/pk(z)=f(z1),(f'(z1))^1/p1z,…,(f'(z1))^1/pkw)is a normalized biholomorphic convex mapping on ?N={(z1,z,…,w)∈C×C^n1×…×C^nk:‖z‖^p11+…+‖w‖^pkk<1/λG(z1)},where N=1+n1+…+nk and the branch is chosen such that (f'(z1))^1/pj|z1=0=1, j=1, …, k.Applying to the Roper-Suffridge extension operator,we obtain a new convex mappings construction of an unbounded domain and a refinement of convex mappings construction on a Reinhardt domain,respectively.
文摘Let A be a Banach algebra with unit e and a,b,c∈A,Mc=(a c 0 b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a Banach algebra are proposed.A generalized Drazin spectrum of is defined byσ_(gD)(α)={λ∈C:α-λe is not generalized Drazin invertible}.It is shown thatσ_(gD)(a)∪σ_(gD)(b)=σ_(gD)(M_(C))∪W_(2),where W_(g) is a union of certain holes σ_(gD) and W_(g)■σ_(gD)(a)∩σ_(gD)(b),or more finely.In addition,some properties of generalized Drazin spectrum of elements in a Banach algebra are studied.
基金financially supported by the Fundamental Research Funds for the Central Universities(xzy022019015)the National Natural Science Foundation of China(51675409)。
文摘60NiTi alloy is highly promising for aerospace bearings and mechanisms.Shock load that is inevitably generated during launching process brings about an quick loading process and transient load duration,and may further results in an unnoticed but detrimental creep deformation.On this account,the nanoindentation creep behavior of solution-treated 60NiTi alloy at room temperature and the corresponding influencing mechanism were studied.The results show that creep displacement was dominated by strain rate at the very beginning of holding stage.Strain rate and flow stress at the very beginning of holding stage were increased with an increased loading rate but declined with increasing holding load or with simultaneously increasing loading rate and holding load.The underlying mechanisms were provided as nucleation and absorption of geometrically necessary dislocations(GNDs)associated with strain gradient plasticity theory rather than the model based on the consumption of creep deformation at loading stage.
