The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are establi...The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.展开更多
The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],...The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.展开更多
Based on one year gradient wind data and the wind data of a strong typhoon observed by three meteorological towers located on the coast and at the inshore sea,the underlying surfaces of the meteorological towers were ...Based on one year gradient wind data and the wind data of a strong typhoon observed by three meteorological towers located on the coast and at the inshore sea,the underlying surfaces of the meteorological towers were classified and the roughness lengths were calculated quantitatively.On the basis of strong wind characteristic representative assessment and sample selection on the wind data of strong typhoon Hagupit,the gust factor variation characteristics of tropical cyclones under different underlying surfaces were analyzed.The observed fact and variation rule were found as follows:1) The roughness lengths under neutral atmospheric condition which were calculated using logarithmic wind profile fitting based on the observation data can describe the slight change of the underlying surface objectively.2) The gust factor of strong typhoon wind didn't have variation trends with wind speed.But the variation amplitude of the gust factor was rather large over rough underlying surface which had pronounced effect on the numerical design of structural engineering.3) The variation of the gust factor with height satisfied power law or logarithmic law.The power law fitting was more suitable for smooth underlying surface while the logarithmic fitting was better over rough underlying surface.4) The observation data also suggested that the relationship between gust factor and roughness length can be described by power or linear equation.5) The gust factor observed in this typhoon case was different from the gust factor recommended by WMO:The gust factor of the offshore wind came from rough underlying surface was higher than the value recommended by WMO while the gust factor of the onshore wind came from smooth underlying surface is less than the WMO recommended value.展开更多
文摘The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.
文摘The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.
基金supported by the National Natural Science Foundation of China (Grant Nos. 90715031, 40775071) the National Special Re-search Fund for Non-Profit Sector of China Ministry of Science and Tech-nology (Grant No. GYHY200806012)
文摘Based on one year gradient wind data and the wind data of a strong typhoon observed by three meteorological towers located on the coast and at the inshore sea,the underlying surfaces of the meteorological towers were classified and the roughness lengths were calculated quantitatively.On the basis of strong wind characteristic representative assessment and sample selection on the wind data of strong typhoon Hagupit,the gust factor variation characteristics of tropical cyclones under different underlying surfaces were analyzed.The observed fact and variation rule were found as follows:1) The roughness lengths under neutral atmospheric condition which were calculated using logarithmic wind profile fitting based on the observation data can describe the slight change of the underlying surface objectively.2) The gust factor of strong typhoon wind didn't have variation trends with wind speed.But the variation amplitude of the gust factor was rather large over rough underlying surface which had pronounced effect on the numerical design of structural engineering.3) The variation of the gust factor with height satisfied power law or logarithmic law.The power law fitting was more suitable for smooth underlying surface while the logarithmic fitting was better over rough underlying surface.4) The observation data also suggested that the relationship between gust factor and roughness length can be described by power or linear equation.5) The gust factor observed in this typhoon case was different from the gust factor recommended by WMO:The gust factor of the offshore wind came from rough underlying surface was higher than the value recommended by WMO while the gust factor of the onshore wind came from smooth underlying surface is less than the WMO recommended value.
