Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item sp...Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.展开更多
In this paper,we consider infinite sums of the reciprocals of the Fibonacci numbers.Then applying the floor function to the reciprocals of this sums,we obtain a new identity involving the Fibonacci numbers.
If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers...If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers with primes, during the prime factorization, may be viewed as being the outcome of a parallel system which functions properly if and only if Euler’s formula of the product of the reciprocals of the primes is true. An exact formula for the number of primes less than or equal to an arbitrary bound is given. This formula may be implemented using Wolfram’s computer package Mathematica.展开更多
Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonic...Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonics PN（x） of order≤N and a constant C〉0 such that where ω（f,δ）L^p=sup 0〈t≤δ‖St（f）-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω（f,N^-1）L^p,St（f,μ）=1/｜S^q-2｜Sin^2λt ∫-μμ’=t f（μ＇）dμ＇ is a translation operator.展开更多
The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accur...The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where ?is the set of perfect powers of prime numbers.展开更多
By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the inf...By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.展开更多
As the end products of cellular regulatory processes,metabolites provide the link between genotypes and phenotypes.Althoughmetabolites have been widely applied for functional gene detection and phenotype prediction in...As the end products of cellular regulatory processes,metabolites provide the link between genotypes and phenotypes.Althoughmetabolites have been widely applied for functional gene detection and phenotype prediction in maize,there is little research focusing on the genetic information of metabolites per se.Here,we performed genetic analyses for the kernel metabolites of 11 parental inbred lines of six representative maize varieties,including Zhongdan 2,Danyu 13,Yedan 13,Zhengdan 958,Xianyu 355,and Suyu 16,as well as their 26 reciprocal hybrids.We identified a total of 208 metabolites in maize kernels using untargeted metabolite profiling technology.Both cluster analysis and principal component analysis indicated that kernel metabolites could distinguish hybrids from their parents.Analysis of variance further revealed that 163 metabolites exhibited significant differences between parents and hybrids,and 40 metabolites showed significant differences between reciprocal crosses.We also investigated the genetic effects and heterosis for each metabolite.By taking all hybrids into consideration,about two-thirds of all metabolites displayed overdominant with 36.8%and 31%of them displaying positive overdominant and negative overdominant,respectively.Besides,27.5%and 20.4%of all hybrid combinations showed significant mid-parent heterosis and over-parent heterosis,respectively.Our findings revealed that kernel metabolites exhibited the diversity of relationship between maize hybrids and their parental lines.Additionally,we identified 25 significant metabolicmarkers related to 11 agronomic traits using the LASSO method.Seven metabolic markers were associated with more than one trait simultaneously.These results provide a genetic basis for further utilization of metabolites in the genetic improvement of maize.展开更多
This paper examines reflexivization and reciprocality in Kalabari with particular attention to the forms,functions and structures of reflexive and reciprocal constructions(the nominal sub-type)in the language.The pape...This paper examines reflexivization and reciprocality in Kalabari with particular attention to the forms,functions and structures of reflexive and reciprocal constructions(the nominal sub-type)in the language.The paper adopts the binding theory as a framework in analysing the data.The data were gathered through interaction and introspection.The findings reveal that reflexives and reciprocals in Kalabari require a compatible clause-mate antecedent due to the strong anaphoric relationship between reflexive and reciprocal markers and their antecedents respectively.The findings further reveal that the form of Kalabari reflexives consists of-ḇù(-self)and the appropriate form of the pronoun in the language.The paper also reveals that the Kalabari language makes a tripartite distinction for number,person and gender,and the form of the reflexive does not change;only the pronoun changes,while reciprocals consist of a reduplicated form jụmọjụmọ,jápụjápụand jéin jéin.In terms of the structure,findings reveal that reflexives and reciprocals come before the verb of the clause in which they occur.The finding further reveals that reflexives in the language perform both non-emphatic and emphatic functions,while reciprocal relates to human and non-human reference of mutuality.Tonal inflection also makes a distinction in 1st person singular and 2nd person singular reflexives.It is therefore recommended that more studies be done to ascertain the form,function and structure of the verbal and possessive sub-type of reflexive and reciprocal constructions in the language.展开更多
追踪研究当中,交叉滞后模型可以探究多变量之间往复式影响,潜增长模型可以探究个体增长趋势。对两类模型进行整合,例如同时关注往复式影响与个体增长趋势,同时可以定义测量误差、随机截距等变异成分,衍生出随机截距交叉滞后模型、特质−...追踪研究当中,交叉滞后模型可以探究多变量之间往复式影响,潜增长模型可以探究个体增长趋势。对两类模型进行整合,例如同时关注往复式影响与个体增长趋势,同时可以定义测量误差、随机截距等变异成分,衍生出随机截距交叉滞后模型、特质−状态−误差模型、自回归潜增长模型、结构化残差潜增长模型等。以交叉滞后模型和潜增长模型分别作为基础模型,从个体间/个体内变异分解的角度对上述各类模型梳理,整合出此类模型的分析框架,并拓展建立“因子结构化潜增长模型(factor latent curve model with structured reciprocals)”作为统合框架。通过实证研究(早期儿童的追踪研究−幼儿园版,ECLS-K),建立21049名儿童的阅读和数学能力的往复式影响与增长趋势。研究发现,分离了稳定特质的模型拟合最优。研究也对模型建模思路和模型选择提供了建议。展开更多
文摘Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.
基金Supported by the National Natural Science Foundation of China (Grant No.11071194)
文摘In this paper,we consider infinite sums of the reciprocals of the Fibonacci numbers.Then applying the floor function to the reciprocals of this sums,we obtain a new identity involving the Fibonacci numbers.
文摘If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers with primes, during the prime factorization, may be viewed as being the outcome of a parallel system which functions properly if and only if Euler’s formula of the product of the reciprocals of the primes is true. An exact formula for the number of primes less than or equal to an arbitrary bound is given. This formula may be implemented using Wolfram’s computer package Mathematica.
基金Supported by the National Natural Science Foundation of China （No.10371024）, the Natural Science of Zhejiang Province （No. Y604003） and the Doctor Foundation of Ningbo City （No.2004A620017）.
文摘Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonics PN（x） of order≤N and a constant C〉0 such that where ω（f,δ）L^p=sup 0〈t≤δ‖St（f）-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω（f,N^-1）L^p,St（f,μ）=1/｜S^q-2｜Sin^2λt ∫-μμ’=t f（μ＇）dμ＇ is a translation operator.
文摘The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where ?is the set of perfect powers of prime numbers.
基金Supported by the NNSF of China(10771093)Supported by the NSF of Henan Province(0511010300)
文摘By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.
基金supported by grants from the National Natural Science Foundation of China(31801028,41801013,31902101)the National Key Research and Development Program of China(2016YFD0100303)+2 种基金Natural Science Foundation of Jiangsu Province(BK20180939)Qing Lan Project of Yangzhou Universitythe Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘As the end products of cellular regulatory processes,metabolites provide the link between genotypes and phenotypes.Althoughmetabolites have been widely applied for functional gene detection and phenotype prediction in maize,there is little research focusing on the genetic information of metabolites per se.Here,we performed genetic analyses for the kernel metabolites of 11 parental inbred lines of six representative maize varieties,including Zhongdan 2,Danyu 13,Yedan 13,Zhengdan 958,Xianyu 355,and Suyu 16,as well as their 26 reciprocal hybrids.We identified a total of 208 metabolites in maize kernels using untargeted metabolite profiling technology.Both cluster analysis and principal component analysis indicated that kernel metabolites could distinguish hybrids from their parents.Analysis of variance further revealed that 163 metabolites exhibited significant differences between parents and hybrids,and 40 metabolites showed significant differences between reciprocal crosses.We also investigated the genetic effects and heterosis for each metabolite.By taking all hybrids into consideration,about two-thirds of all metabolites displayed overdominant with 36.8%and 31%of them displaying positive overdominant and negative overdominant,respectively.Besides,27.5%and 20.4%of all hybrid combinations showed significant mid-parent heterosis and over-parent heterosis,respectively.Our findings revealed that kernel metabolites exhibited the diversity of relationship between maize hybrids and their parental lines.Additionally,we identified 25 significant metabolicmarkers related to 11 agronomic traits using the LASSO method.Seven metabolic markers were associated with more than one trait simultaneously.These results provide a genetic basis for further utilization of metabolites in the genetic improvement of maize.
文摘This paper examines reflexivization and reciprocality in Kalabari with particular attention to the forms,functions and structures of reflexive and reciprocal constructions(the nominal sub-type)in the language.The paper adopts the binding theory as a framework in analysing the data.The data were gathered through interaction and introspection.The findings reveal that reflexives and reciprocals in Kalabari require a compatible clause-mate antecedent due to the strong anaphoric relationship between reflexive and reciprocal markers and their antecedents respectively.The findings further reveal that the form of Kalabari reflexives consists of-ḇù(-self)and the appropriate form of the pronoun in the language.The paper also reveals that the Kalabari language makes a tripartite distinction for number,person and gender,and the form of the reflexive does not change;only the pronoun changes,while reciprocals consist of a reduplicated form jụmọjụmọ,jápụjápụand jéin jéin.In terms of the structure,findings reveal that reflexives and reciprocals come before the verb of the clause in which they occur.The finding further reveals that reflexives in the language perform both non-emphatic and emphatic functions,while reciprocal relates to human and non-human reference of mutuality.Tonal inflection also makes a distinction in 1st person singular and 2nd person singular reflexives.It is therefore recommended that more studies be done to ascertain the form,function and structure of the verbal and possessive sub-type of reflexive and reciprocal constructions in the language.
文摘追踪研究当中,交叉滞后模型可以探究多变量之间往复式影响,潜增长模型可以探究个体增长趋势。对两类模型进行整合,例如同时关注往复式影响与个体增长趋势,同时可以定义测量误差、随机截距等变异成分,衍生出随机截距交叉滞后模型、特质−状态−误差模型、自回归潜增长模型、结构化残差潜增长模型等。以交叉滞后模型和潜增长模型分别作为基础模型,从个体间/个体内变异分解的角度对上述各类模型梳理,整合出此类模型的分析框架,并拓展建立“因子结构化潜增长模型(factor latent curve model with structured reciprocals)”作为统合框架。通过实证研究(早期儿童的追踪研究−幼儿园版,ECLS-K),建立21049名儿童的阅读和数学能力的往复式影响与增长趋势。研究发现,分离了稳定特质的模型拟合最优。研究也对模型建模思路和模型选择提供了建议。
