The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it ...The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.展开更多
Purpose:Diaspora researchers work in one country but have ancestral origins in another,either through moves during a research career(mobile diaspora researchers)or by starting research in the target country(embedded d...Purpose:Diaspora researchers work in one country but have ancestral origins in another,either through moves during a research career(mobile diaspora researchers)or by starting research in the target country(embedded diaspora researchers).Whilst mobile researchers might be tracked through affiliation changes in bibliometric databases,embedded researchers cannot.This article reports an evidence-based discussion of which countries’diaspora researchers can be partially tracked using first or last names,addressing this limitation.Design/methodology/approach:A frequency analysis of first and last names of authors of all Scopus journal articles 2001-2021 for 200 countries or regions.Findings:There are great variations in the extent to which first or last names are uniquely national,from Monserrat(no unique first names)to Thailand(81%unique last names).Nevertheless,most countries have a subset of first or last names that are relatively unique.For the 50 countries with the most researchers,authors with relatively national names are always more likely to research their name-associated country,suggesting a continued national association.Lists of researchers’first and last name frequencies and proportions are provided for 200 countries/regions.Research limitations:Only one period is tracked(2001-2021)and no attempt was made to validate the ancestral origins of any researcher.Practical implications:Simple name heuristics can be used to identify the international spread of a sample of most countries’diaspora researchers,but some manual checks of individual names are needed to weed out false matches.This can supplement mobile researcher data from bibliometric databases.Originality/value:This is the first attempt to list name associations for the authors of all countries and large regions,and to identify the countries for which diaspora researchers could be tracked by name.展开更多
为了解决复数域下基于QR分解的LLL(A.K.Lenstra,H.W.Lenstra and L.Lovász)算法中复Givens旋转矩形式不统一的问题,文章从复数域下原始LLL算法中Gram-Schmidt系数与QR分解的上三角矩阵R中元素之间的关系出发,证明了上三角矩阵R的...为了解决复数域下基于QR分解的LLL(A.K.Lenstra,H.W.Lenstra and L.Lovász)算法中复Givens旋转矩形式不统一的问题,文章从复数域下原始LLL算法中Gram-Schmidt系数与QR分解的上三角矩阵R中元素之间的关系出发,证明了上三角矩阵R的元素与Gram-Schmidt系数以及Lovász条件之间的等价的关系;从复数的指数形式出发,推导出2种适合LLL算法的复Givens旋转矩阵形式,并证明只有其中一种符合Lovász条件下复Givens旋转矩阵形式。仿真结果表明,采用基于QR分解的复数域LLL算法的MIMO系统相比采用基于Gram-Schmidt正交化LLL算法的MIMO系统具有更好的误比特率性能。展开更多
文摘The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.
文摘Purpose:Diaspora researchers work in one country but have ancestral origins in another,either through moves during a research career(mobile diaspora researchers)or by starting research in the target country(embedded diaspora researchers).Whilst mobile researchers might be tracked through affiliation changes in bibliometric databases,embedded researchers cannot.This article reports an evidence-based discussion of which countries’diaspora researchers can be partially tracked using first or last names,addressing this limitation.Design/methodology/approach:A frequency analysis of first and last names of authors of all Scopus journal articles 2001-2021 for 200 countries or regions.Findings:There are great variations in the extent to which first or last names are uniquely national,from Monserrat(no unique first names)to Thailand(81%unique last names).Nevertheless,most countries have a subset of first or last names that are relatively unique.For the 50 countries with the most researchers,authors with relatively national names are always more likely to research their name-associated country,suggesting a continued national association.Lists of researchers’first and last name frequencies and proportions are provided for 200 countries/regions.Research limitations:Only one period is tracked(2001-2021)and no attempt was made to validate the ancestral origins of any researcher.Practical implications:Simple name heuristics can be used to identify the international spread of a sample of most countries’diaspora researchers,but some manual checks of individual names are needed to weed out false matches.This can supplement mobile researcher data from bibliometric databases.Originality/value:This is the first attempt to list name associations for the authors of all countries and large regions,and to identify the countries for which diaspora researchers could be tracked by name.
文摘为了解决复数域下基于QR分解的LLL(A.K.Lenstra,H.W.Lenstra and L.Lovász)算法中复Givens旋转矩形式不统一的问题,文章从复数域下原始LLL算法中Gram-Schmidt系数与QR分解的上三角矩阵R中元素之间的关系出发,证明了上三角矩阵R的元素与Gram-Schmidt系数以及Lovász条件之间的等价的关系;从复数的指数形式出发,推导出2种适合LLL算法的复Givens旋转矩阵形式,并证明只有其中一种符合Lovász条件下复Givens旋转矩阵形式。仿真结果表明,采用基于QR分解的复数域LLL算法的MIMO系统相比采用基于Gram-Schmidt正交化LLL算法的MIMO系统具有更好的误比特率性能。
