In this paper we discuss the convergence of the directed graph-algorithm for solving a kind of optimization problems where the objective and subjective functions are all separable, and the parallel implementation proc...In this paper we discuss the convergence of the directed graph-algorithm for solving a kind of optimization problems where the objective and subjective functions are all separable, and the parallel implementation process for the directed graph -algorithm is introduced.展开更多
The inverse problem in calculus of variation is studied. By introducing a newconcept called Varialional Integral, a new method to systematically study the inverseproblem in calculus of rariations is given. Using thi...The inverse problem in calculus of variation is studied. By introducing a newconcept called Varialional Integral, a new method to systematically study the inverseproblem in calculus of rariations is given. Using this new method to the elastodynamicsand hydrodynamics of viscous fhuids some kinds of variaiional principles andgeneralized variational prineiples are obtained respectively.展开更多
Let P（z） be a polynomial of degree n which does not vanish in ｜z｜ 〈k, k≥ 1. It is known that for each 0 〈 s 〈 n and 1 ≤ R ≤ k,M（P（s）,R）≤（1/（R^s＋k^s）[{d（s）/dx（s）（1＋x^n）}x=1]（（R＋k）/（1＋k）...Let P（z） be a polynomial of degree n which does not vanish in ｜z｜ 〈k, k≥ 1. It is known that for each 0 〈 s 〈 n and 1 ≤ R ≤ k,M（P（s）,R）≤（1/（R^s＋k^s）[{d（s）/dx（s）（1＋x^n）}x=1]（（R＋k）/（1＋k）^nM（P,1）. In this paper, we obtain certain extensions and refinements of this inequality by in- volving binomial coefficients and some of the coefficients of the polynomial P（z）.展开更多
文摘In this paper we discuss the convergence of the directed graph-algorithm for solving a kind of optimization problems where the objective and subjective functions are all separable, and the parallel implementation process for the directed graph -algorithm is introduced.
文摘The inverse problem in calculus of variation is studied. By introducing a newconcept called Varialional Integral, a new method to systematically study the inverseproblem in calculus of rariations is given. Using this new method to the elastodynamicsand hydrodynamics of viscous fhuids some kinds of variaiional principles andgeneralized variational prineiples are obtained respectively.
文摘Let P（z） be a polynomial of degree n which does not vanish in ｜z｜ 〈k, k≥ 1. It is known that for each 0 〈 s 〈 n and 1 ≤ R ≤ k,M（P（s）,R）≤（1/（R^s＋k^s）[{d（s）/dx（s）（1＋x^n）}x=1]（（R＋k）/（1＋k）^nM（P,1）. In this paper, we obtain certain extensions and refinements of this inequality by in- volving binomial coefficients and some of the coefficients of the polynomial P（z）.
