Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…...Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.展开更多
Using simple unequal-thickness billet combining isothermal local loading can control the metal flow and improve the cavity fill in manufacturing process of large-scale rib-web titanium alloy component with low cost an...Using simple unequal-thickness billet combining isothermal local loading can control the metal flow and improve the cavity fill in manufacturing process of large-scale rib-web titanium alloy component with low cost and short cycle. The beveling transition pattern is well used for variable-thickness region of billet （VTRB） due to its simple and ample range of transition condition. The transition condition development in the local loading process has a significant influence on dynamic boundary of unrestricted portion of VTRB. With the help of reasonable assumptions, a mathematical model of transition condition development was established by theoretical analysis. The predicted results for local loading process of rib-web component using the established model were compared with the numerical and experimental ones, and the results indicated that the model of transition condition development is reasonable. Using the established model could deal with the dynamic boundary of unrestricted portion of VTRB well, and the model is suitable for the analysis of metal flow and cavity fill in local loading process of multi-ribs component.展开更多
Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities...Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities for the areas of the bisection planes of the dihedral angles of a simplex in nE are established.展开更多
The helicity amplitudes for the processes of e^＋e^- →J/ψ→γηc→γYY（Y： hyperon） are presented, together with the joint angular distributions for ηc decays into ∧∧,∑^0 ∑^0, and [1]-[1]＋. The sensitivities...The helicity amplitudes for the processes of e^＋e^- →J/ψ→γηc→γYY（Y： hyperon） are presented, together with the joint angular distributions for ηc decays into ∧∧,∑^0 ∑^0, and [1]-[1]＋. The sensitivities to measure the hyperon decay parameters in these decays are evaluated based on the helicity amplitudes. The prospects to test the Bell inequality in experiment using the decay of ηc→∧∧ are discussed.展开更多
In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational ineq...In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.展开更多
In this paper,a new version of the general form of the main inequality of Reich-Strebel is given.As applications,we improve the strong triangle inequality and generalize the Delta inequality in certain sense.
The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poin...The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poincar'e inequalities.展开更多
文摘Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.
基金Project (50935007) supported by the National Natural Science Foundation of ChinaProject (2010CB731701) supported by the National Basic Research Program of China
文摘Using simple unequal-thickness billet combining isothermal local loading can control the metal flow and improve the cavity fill in manufacturing process of large-scale rib-web titanium alloy component with low cost and short cycle. The beveling transition pattern is well used for variable-thickness region of billet （VTRB） due to its simple and ample range of transition condition. The transition condition development in the local loading process has a significant influence on dynamic boundary of unrestricted portion of VTRB. With the help of reasonable assumptions, a mathematical model of transition condition development was established by theoretical analysis. The predicted results for local loading process of rib-web component using the established model were compared with the numerical and experimental ones, and the results indicated that the model of transition condition development is reasonable. Using the established model could deal with the dynamic boundary of unrestricted portion of VTRB well, and the model is suitable for the analysis of metal flow and cavity fill in local loading process of multi-ribs component.
基金Funded by the Natural Science Foundation of Anhui (2004kj104).
文摘Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities for the areas of the bisection planes of the dihedral angles of a simplex in nE are established.
基金Supported by the National Natural Science Foundation of ChinaYouth Innovation Project of IHEPthe Innovation Projcct of Guangxi Graduate Eduction under Grant No. 2007106020702M54
文摘The helicity amplitudes for the processes of e^＋e^- →J/ψ→γηc→γYY（Y： hyperon） are presented, together with the joint angular distributions for ηc decays into ∧∧,∑^0 ∑^0, and [1]-[1]＋. The sensitivities to measure the hyperon decay parameters in these decays are evaluated based on the helicity amplitudes. The prospects to test the Bell inequality in experiment using the decay of ηc→∧∧ are discussed.
文摘In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.
基金supported by National Natural Science Foundation of China(Grant No.10971008)
文摘In this paper,a new version of the general form of the main inequality of Reich-Strebel is given.As applications,we improve the strong triangle inequality and generalize the Delta inequality in certain sense.
基金supported by the National Natural Science Foundation of China(No.10971148)
文摘The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poincar'e inequalities.
