The evolutions of nano-twins and martensitic transformation in 316L austenitic stainless steel during large tensile deformation were studied by electron backscatter diffraction(EBSD)technology and transmission electro...The evolutions of nano-twins and martensitic transformation in 316L austenitic stainless steel during large tensile deformation were studied by electron backscatter diffraction(EBSD)technology and transmission electron microscopy(TEM)in detail.The results show that due to the low stacking fault energy of the steel,phase transformation induced plasticity(TRIP)and twinning induced plasticity(TWIP)coexist during the tensile deformation.The deformation firstly induces the formation of deformation twins,and dislocation pile-up is caused by the reduction of the dislocation mean free path(MFP)or grain refinement due to the twin boundaries,which further induces the martensitic transformation.With the increase of tensile deformation,a large number of nano-twins andα’-martensite appear,and the width of nano-twins decreases gradually,meanwhile the frequency of the intersecting deformation twins increases.The martensitic transformation can be divided into two types:γ-austenite→α’-martensite andγ-austenite→ε-martensite.α’-martensite is mainly distributed near the twin boundaries,especially at the intersection of twins,whileε-martensite and stacking faults exist in the form of transition products between the twins and the matrix.展开更多
In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an exist...In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.展开更多
We give more efficient criteria to characterise prime ideal or primary ideal. Further, we obtain the necessary and sufficient conditions that an ideal is prime or primary in real field from the Grobner bases directly.
Let D = （V, E） be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD（v）, is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu,...Let D = （V, E） be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD（v）, is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD（V1） ≤ exPD（V2） …≤ exPD（Vn）. Then exPD（Vk） is called the k- point exponent of D and is denoted by exPD （k）, 1≤ k ≤ n. In this paper we define e（n, k） ：= max{expD （k） ｜ D ∈ PD（n, 2）} and E（n, k） ：= {exPD（k）｜ D ∈ PD（n, 2）}, where PD（n, 2） is the set of all primitive digraphs of order n with girth 2. We completely determine e（n, k） and E（n, k） for all n, k with n ≥ 3 and 1 ≤ k ≤ n.展开更多
基金supported by the Natural Science Foundation of Shaanxi Province,China(No.2021JM-061).
文摘The evolutions of nano-twins and martensitic transformation in 316L austenitic stainless steel during large tensile deformation were studied by electron backscatter diffraction(EBSD)technology and transmission electron microscopy(TEM)in detail.The results show that due to the low stacking fault energy of the steel,phase transformation induced plasticity(TRIP)and twinning induced plasticity(TWIP)coexist during the tensile deformation.The deformation firstly induces the formation of deformation twins,and dislocation pile-up is caused by the reduction of the dislocation mean free path(MFP)or grain refinement due to the twin boundaries,which further induces the martensitic transformation.With the increase of tensile deformation,a large number of nano-twins andα’-martensite appear,and the width of nano-twins decreases gradually,meanwhile the frequency of the intersecting deformation twins increases.The martensitic transformation can be divided into two types:γ-austenite→α’-martensite andγ-austenite→ε-martensite.α’-martensite is mainly distributed near the twin boundaries,especially at the intersection of twins,whileε-martensite and stacking faults exist in the form of transition products between the twins and the matrix.
基金Supported by the National Natural Science Foundation of China (No. 10771058)the Hunan Provincial Natural Science Foundation (No. 09JJ6013)
文摘In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.
基金Supported by the National Natural Science Foundation of China (No. 11071062)Hunan provincial Natural Science Foundation of China (No. 10JJ3065)+1 种基金Scientific Research Fund of Hunan province education Department (No. 10A033)Hunan Provincial Degree and Education of Graduate Student Foundation (No. JG2009A017)
文摘We give more efficient criteria to characterise prime ideal or primary ideal. Further, we obtain the necessary and sufficient conditions that an ideal is prime or primary in real field from the Grobner bases directly.
基金Supported by the National Natural Science Foundation of China(No.10771061,No.10771058)SRF of Hunan Provincial Education Department(No.07C267).
文摘Let D = （V, E） be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD（v）, is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD（V1） ≤ exPD（V2） …≤ exPD（Vn）. Then exPD（Vk） is called the k- point exponent of D and is denoted by exPD （k）, 1≤ k ≤ n. In this paper we define e（n, k） ：= max{expD （k） ｜ D ∈ PD（n, 2）} and E（n, k） ：= {exPD（k）｜ D ∈ PD（n, 2）}, where PD（n, 2） is the set of all primitive digraphs of order n with girth 2. We completely determine e（n, k） and E（n, k） for all n, k with n ≥ 3 and 1 ≤ k ≤ n.
