多元函数条件极值充分条件的探讨

本文从无条件极值的充分条件出发,通过消去等二阶导数和偏导数,得到了两类适用的多元函数条件极值的充分条件:在条件下函数u=f(x,y_1,…,y_n)的条件极值和在条件下函数u=f(x,y,z)的条件极值的充分条件。     

Vast laminated diatom mat deposits from the west low-latitude Pacific Ocean in the last glacial period

Diatoms are one of the predominant contributors to global carbon fixation by accounting for over 40% of total oceanic primary production and dominate export production. They play a significant role in marine biogeochemistry cycle. The diatom mat deposits are results of vast diatoms bloom. By analysis of diatom mats in 136°00′--140°00′E, 15°00′--21°00′N, Eastern Philippines Sea, we identified the species of the diatoms as giant Ethmodiscus rex （Wallich） Hendey. AMS 14C dating shows that the sediments rich in diatom mats occurred during 16000--28600 a B.P., which means the bloom mainly occurred during the last glacial period, while there are no diatom mat deposits in other layers. Preliminary analysis indicates that Antarctic Intermediate Water （AAIW） expanded northward and brought silicate-rich water into the area, namely, silicon leakage processes caused the bloom of diatoms. In addition, the increase of iron input is one of the main reasons for the diatom bloom.     

Improving analytic hierarchy process applied to fire risk analysis of public building

The structure importance in Fault Tree Analysis (FTA) reflects how important Basic Events are to Top Event. Attribute at alternative level in Analytic Hierarchy Process (AHP) also reflect its importance to general goal. Based on the coherence of these two methods, an improved AHP is put forward. Using this improved method, how important the attribute is to the fire safety of public building can be analyzed more credibly because of the reduction of subjective judgment. Olympic venues are very important public buildings in China. The fire safety evaluation of them will be a big issue to engineers. Improved AHP is a useful tool to the safety evaluation to these Olympic venues, and it will guide the evaluation in other areas. Support by the National Natural Science Foundation of China (Grant No. 50536030), National Project of Scientific and Technical Supporting Programs funded by Ministry of Science & Technology of China (Grant No. 2006BAK06B02) and China Postdoctoral Science Foundation (Grant No. 20070410220)