The new synthetic route of (±)shikalkin 1 was developed. 3-(1-Hydroxy-4-methyl-3- pentenyl)-5, 8-dimethoxy-1-naphthol 8 was obtained from compound 3 in 10 steps. Then (±)shikalkin 1 was synthesized from 8 i...The new synthetic route of (±)shikalkin 1 was developed. 3-(1-Hydroxy-4-methyl-3- pentenyl)-5, 8-dimethoxy-1-naphthol 8 was obtained from compound 3 in 10 steps. Then (±)shikalkin 1 was synthesized from 8 in one step with reagents AgO/HNO3 in 1, 4-dioxane.展开更多
Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depen...Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depends on the penalty for the system of linearly constrained equations and therefore the method with variable penalties is advantageous in practice. In this paper, we extend the Kontogiorgis and Meyer method [12] by removing the monotonicity assumption on the variable penalty matrices. Moreover, we introduce a self-adaptive rule that leads the method to be more efficient and insensitive for various initial penalties. Numerical results for a class of Fermat-Weber problems show that the modified method and its self-adaptive technique are proper and necessary in practice.展开更多
基金We thank the National Natural Science Foundation of China[30069004]for financial supports
文摘The new synthetic route of (±)shikalkin 1 was developed. 3-(1-Hydroxy-4-methyl-3- pentenyl)-5, 8-dimethoxy-1-naphthol 8 was obtained from compound 3 in 10 steps. Then (±)shikalkin 1 was synthesized from 8 in one step with reagents AgO/HNO3 in 1, 4-dioxane.
基金The first author was supported the NSFC grant 10271054,the third author was supported in part by the Hong Kong Research Grants Council through a RGC-CERG Grant (HKUST6203/99E)
文摘Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depends on the penalty for the system of linearly constrained equations and therefore the method with variable penalties is advantageous in practice. In this paper, we extend the Kontogiorgis and Meyer method [12] by removing the monotonicity assumption on the variable penalty matrices. Moreover, we introduce a self-adaptive rule that leads the method to be more efficient and insensitive for various initial penalties. Numerical results for a class of Fermat-Weber problems show that the modified method and its self-adaptive technique are proper and necessary in practice.
