We consider the Poisson integral u = P＊μ on the half-space R＋^N＋1 （ N 〉 1 ） （or on the unit ball of the complex plane） of some singular measureμ. If μ is an s-measure （0 〈 s 〈 N）, then some sharp estima...We consider the Poisson integral u = P＊μ on the half-space R＋^N＋1 （ N 〉 1 ） （or on the unit ball of the complex plane） of some singular measureμ. If μ is an s-measure （0 〈 s 〈 N）, then some sharp estimates of the integration of the harmonic function u near the boundary are given. In particular, we show that fpr p〉1,∫R^Nu^p（x,y）dx- y^-τ （y〉0,τ =（N-s）（p-1） ） （Given for p〉1, RN f 〉 0 and g 〉 0, ＂ f-g ＂ will mean that there exist constants C1 and C2, such that C1f ≤ g ≤ CEf ）.展开更多
The uniform and extension distribution of the optimal solution are very important criterion for the quality evaluation of the multi-objective programming problem. A genetic algorithm based on agent and individual dens...The uniform and extension distribution of the optimal solution are very important criterion for the quality evaluation of the multi-objective programming problem. A genetic algorithm based on agent and individual density is used to solve the multi-objective optimization problem. In the selection process, each agent is selected according to the individual density distance in its neighborhood, and the crossover operator adopts the simulated binary crossover method. The self-learning behavior only applies to the individuals with the highest energy in current population. A few classical multi-objective function optimization examples were used tested and two evaluation indexes U-measure and S-measure are used to test the performance of the algorithm. The experimental results show that the algorithm can obtain uniformity and widespread distribution Pareto solutions.展开更多
基金Supported by the National Natural Science Foundation of China (10671150)
文摘We consider the Poisson integral u = P＊μ on the half-space R＋^N＋1 （ N 〉 1 ） （or on the unit ball of the complex plane） of some singular measureμ. If μ is an s-measure （0 〈 s 〈 N）, then some sharp estimates of the integration of the harmonic function u near the boundary are given. In particular, we show that fpr p〉1,∫R^Nu^p（x,y）dx- y^-τ （y〉0,τ =（N-s）（p-1） ） （Given for p〉1, RN f 〉 0 and g 〉 0, ＂ f-g ＂ will mean that there exist constants C1 and C2, such that C1f ≤ g ≤ CEf ）.
文摘The uniform and extension distribution of the optimal solution are very important criterion for the quality evaluation of the multi-objective programming problem. A genetic algorithm based on agent and individual density is used to solve the multi-objective optimization problem. In the selection process, each agent is selected according to the individual density distance in its neighborhood, and the crossover operator adopts the simulated binary crossover method. The self-learning behavior only applies to the individuals with the highest energy in current population. A few classical multi-objective function optimization examples were used tested and two evaluation indexes U-measure and S-measure are used to test the performance of the algorithm. The experimental results show that the algorithm can obtain uniformity and widespread distribution Pareto solutions.
