An algorithm has been obtained for solving the packing problem of placing convex polygons with different shapes and sizes into a rectangular vessel by simulating the elastic mechanics process,it is pointed out that,ba...An algorithm has been obtained for solving the packing problem of placing convex polygons with different shapes and sizes into a rectangular vessel by simulating the elastic mechanics process,it is pointed out that,based on this algorithm,a sysem of computer-aided design can be developed for arranging two-dimensional materials.展开更多
If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a spec...If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.展开更多
In the era of big data,the ways people work,live and think have changed dramatically,and the social governance system is also being restructured.Achieving intelligent social governance has now become a national strate...In the era of big data,the ways people work,live and think have changed dramatically,and the social governance system is also being restructured.Achieving intelligent social governance has now become a national strategy.The application of big data technology to counterterrorism efforts has become a powerful weapon for all countries.However,due to the uncertainty,difficulty of interpretation and potential risk of discrimination in big data technology and algorithm models,basic human rights,freedom and even ethics are likely to be impacted and challenged.As a result,there is an urgent need to prioritize basic human rights and regulate the application of big data for counter terrorism purposes.The legislation and law enforcement regarding the use of big data to counter terrorism must be subject to constitutional and other legal reviews,so as to strike a balance between safeguarding national security and protecting basic human rights.展开更多
文摘An algorithm has been obtained for solving the packing problem of placing convex polygons with different shapes and sizes into a rectangular vessel by simulating the elastic mechanics process,it is pointed out that,based on this algorithm,a sysem of computer-aided design can be developed for arranging two-dimensional materials.
基金Supported by the Doctoral programme foundation of National Education Ministry of China
文摘If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.
文摘In the era of big data,the ways people work,live and think have changed dramatically,and the social governance system is also being restructured.Achieving intelligent social governance has now become a national strategy.The application of big data technology to counterterrorism efforts has become a powerful weapon for all countries.However,due to the uncertainty,difficulty of interpretation and potential risk of discrimination in big data technology and algorithm models,basic human rights,freedom and even ethics are likely to be impacted and challenged.As a result,there is an urgent need to prioritize basic human rights and regulate the application of big data for counter terrorism purposes.The legislation and law enforcement regarding the use of big data to counter terrorism must be subject to constitutional and other legal reviews,so as to strike a balance between safeguarding national security and protecting basic human rights.
