Bonferroni inequalities are significant in application for optimal allocation in tradable emission and other scary resources. Kounias and Sotirakglou improved Bonferroni inequalities, they give the lower and upper bou...Bonferroni inequalities are significant in application for optimal allocation in tradable emission and other scary resources. Kounias and Sotirakglou improved Bonferroni inequalities, they give the lower and upper bounds for Bonferroni inequalities in the form of P（Ui=1^nAi）,but they did not discuss the optimal of lower and upper bounds for P（Ui=1^nAi）.In this paper, we give the method to obtain the optimum lower and upper bounds for Bonferroai inequalities in the form of ∑i=1^m（-1）^i＋1 aiSi for P（Ui=1^nAi）under the condition tha Q（r）≥（≤）0,The optimality of Kounias Sotirakglou bounds is also studied.展开更多
Let M=(111-1).In this paper,an optimal upper bound estimateof the modules of Fourier transforms of M-refinable distributions is obtained by theintroduction of cycle related to M.
基金National Science Foundation of China (NO:7027302170573073)
文摘Bonferroni inequalities are significant in application for optimal allocation in tradable emission and other scary resources. Kounias and Sotirakglou improved Bonferroni inequalities, they give the lower and upper bounds for Bonferroni inequalities in the form of P（Ui=1^nAi）,but they did not discuss the optimal of lower and upper bounds for P（Ui=1^nAi）.In this paper, we give the method to obtain the optimum lower and upper bounds for Bonferroai inequalities in the form of ∑i=1^m（-1）^i＋1 aiSi for P（Ui=1^nAi）under the condition tha Q（r）≥（≤）0,The optimality of Kounias Sotirakglou bounds is also studied.
基金Supported by the Natural Science Foundation of Beijing(1013005)the Educational Committee Foundation of Beijing(01KJ-019)
文摘Let M=(111-1).In this paper,an optimal upper bound estimateof the modules of Fourier transforms of M-refinable distributions is obtained by theintroduction of cycle related to M.
