Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectiv...Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following： 1. If T is {a,b,c}-ntype mapping, then inf{ ｜｜ T（x）-x｜｜ ：x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞｜｜T（xn） - Xn｜｜ = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn （x）}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13].展开更多
The emergent light distribution of a new type of contact laser scalpel is measured in three different states using a light sensor. The relationship between the angle and the light intensity is analyzed. The results sh...The emergent light distribution of a new type of contact laser scalpel is measured in three different states using a light sensor. The relationship between the angle and the light intensity is analyzed. The results show that the strongest light is emitted from two sides and the front of the scalpel. The light from the front mainly plays a role of cutting. The light from two sides contributes to stanch the wound so as to remain a clear visual field during the surgery. It also helps to increase the cutting efficiency.展开更多
Multi-sphere clumps are commonly used to simulate non-spherical particles in discrete element method simulations.It is of interest whether the degree of local non-convexity λ affects the mechanical behaviour of granu...Multi-sphere clumps are commonly used to simulate non-spherical particles in discrete element method simulations.It is of interest whether the degree of local non-convexity λ affects the mechanical behaviour of granular materials with the same non-convexity η.A series of discrete-element-method biaxial shear tests are conducted on rough particle packings with rη=0.075 and different λ values(ranging from 0.134 to 0.770).The microscale results show that the contact type changes with an increase in λ.However,the critical strength is independent of λ.The evaluation of the contributions of different contact types to the critical shear strength and a detailed analysis of the anisotropies help clarify the microscopic mechanisms that result in the independence of the critical shear strength from λ.展开更多
文摘Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following： 1. If T is {a,b,c}-ntype mapping, then inf{ ｜｜ T（x）-x｜｜ ：x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞｜｜T（xn） - Xn｜｜ = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn （x）}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13].
基金supported by the National"973"Program of China(No.2005CB724302)the National Science Fund for Distinguished Young Scholars from the National Natural Science Foundation of China(No.60588101)+1 种基金the 111 Project from the Ministry of Education of China(B08020)the Shanghai Commission of Science and Technology(No.05DZ22318,05DZ22325,04DZ05114,and 064119540).
文摘The emergent light distribution of a new type of contact laser scalpel is measured in three different states using a light sensor. The relationship between the angle and the light intensity is analyzed. The results show that the strongest light is emitted from two sides and the front of the scalpel. The light from the front mainly plays a role of cutting. The light from two sides contributes to stanch the wound so as to remain a clear visual field during the surgery. It also helps to increase the cutting efficiency.
基金financially supported by the National Natural Science Foundation of China,China(No.51809292,51478481 and 51508141)Postdoctoral Fund of Central South University,China(No.205455)Beijing Municipal Science and Technology Project:Research and Application of Design and Construction Technology of Railway Engineering Traveling the Rift Valley,China(No.Z181100003918005).
文摘Multi-sphere clumps are commonly used to simulate non-spherical particles in discrete element method simulations.It is of interest whether the degree of local non-convexity λ affects the mechanical behaviour of granular materials with the same non-convexity η.A series of discrete-element-method biaxial shear tests are conducted on rough particle packings with rη=0.075 and different λ values(ranging from 0.134 to 0.770).The microscale results show that the contact type changes with an increase in λ.However,the critical strength is independent of λ.The evaluation of the contributions of different contact types to the critical shear strength and a detailed analysis of the anisotropies help clarify the microscopic mechanisms that result in the independence of the critical shear strength from λ.
