Lateral roots play essential roles in drought tolerance in maize(Zea mays L.). However, the genetic basis for the variation in the number of lateral roots in maize remains elusive. Here, we identified a major quantita...Lateral roots play essential roles in drought tolerance in maize(Zea mays L.). However, the genetic basis for the variation in the number of lateral roots in maize remains elusive. Here, we identified a major quantitative trait locus(QTL),q LRT5-1, controlling lateral root number using a recombinant inbred population from a cross between the maize lines Zong3(with many lateral roots) and 87-1(with few lateral roots).Fine-mapping and functional analysis determined that the candidate gene for qLRT5-1,ZmLRT, expresses the primary transcript for the microRNA miR166a. ZmLRT was highly expressed in root tips and lateral root primordia,and knockout and overexpression of ZmLRT increased and decreased lateral root number,respectively. Compared with 87-1, the ZmLRT gene model of Zong3 lacked the second and third exons and contained a 14 bp deletion at the junction between the first exon and intron,which altered the splicing site. In addition,ZmLRT expression was significantly lower in Zong3 than in 87-1, which might be attributed to the insertions of a transposon and over large DNA fragments in the Zong3 ZmLRT promoter region. These mutations decreased the abundance of mature miR166a in Zong3, resulting in increased lateral roots at the seedling stage.Furthermore, miR166a post-transcriptionally repressed five development-related class-Ⅲ homeodomain-leucine zipper genes. Moreover,knockout of ZmLRT enhanced drought tolerance of maize seedlings. Our study furthers our understanding of the genetic basis of lateral root number variation in maize and highlights ZmLRT as a target for improving drought tolerance in maize.展开更多
The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infini...The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.展开更多
Dry seeding is a resource-saving rice establishment method. With an equivalent yield, dry seeded flooded rice （DSR） has been considered as a replacement for traditional transplanted flooded rice （TFR）. However, th...Dry seeding is a resource-saving rice establishment method. With an equivalent yield, dry seeded flooded rice （DSR） has been considered as a replacement for traditional transplanted flooded rice （TFR）. However, the differences in leaf and root senescence during grain filling between DSR and TFR were seldom identified. In this study, the root length, root tip number and leaf senescence of rice varieties Huanghuazhan and Yangliangyou 6 during ripening were compared between DSR and TFR. Results showed that top three leaves in DSR had the characteristics of relatively lower SPAD value, lower N content and premature leaf senescence. In addition, both the total root length and total root tip number of DSR were significantly lower than those of TFR. In conclusion, premature and quick leaf senescence was related with inadequate root length and root tip number during ripening, which might result from the deficiency of nitrogen supply in DSR. Techniques on improving leaf nitrogen status and delaying the leaf senescence during grain-filling in DSR should be developed in future researches.展开更多
Free air CO2 enrichment(FACE) and nitrogen(N) have marked effects on rice root growth,and numerical simulation can explain these effects. To further define the effects of FACE on root growth of rice, an experiment was...Free air CO2 enrichment(FACE) and nitrogen(N) have marked effects on rice root growth,and numerical simulation can explain these effects. To further define the effects of FACE on root growth of rice, an experiment was performed, using the hybrid indica cultivar Xianyou63. The effects of increasing atmospheric CO2 concentration [CO2], 200 μmol mol-1higher than ambient, on the growth of rice adventitious roots were evaluated, with two levels of N: low(LN, 125 kg ha-1) and normal(NN, 250 kg ha-1). The results showed a significant increase in both adventitious root number(ARN) and adventitious root length(ARL) under FACE treatment. The application of nitrogen also increased ARN and ARL, but these increases were smaller than that under FACE treatment. On the basis of the FACE experiment, numerical models for rice adventitious root number and length were constructed with time as the driving factor. The models illustrated the dynamic development of rice adventitious root number and length after transplanting, regulated either by atmospheric [CO2] or by N application.The simulation result was supported by statistical tests comparing experimental data from different years, and the model yields realistic predictions of root growth. These results suggest that the models have strong predictive potential under conditions of atmospheric [CO2] rises in the future.展开更多
Digital roots of numbers have several interesting properties, most of which are well-known. In this paper, our goal is to prove some lesser known results concerning the digital roots of powers of numbers in an arithme...Digital roots of numbers have several interesting properties, most of which are well-known. In this paper, our goal is to prove some lesser known results concerning the digital roots of powers of numbers in an arithmetic progression. We will also state some theorems concerning the digital roots of Fermat numbers and star numbers. We will conclude our paper by an interesting application.展开更多
In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed poin...In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.展开更多
基金financially supported by the National Key Research and Development Program of China (Grant No. 2016YFD0100801)the National Transgenic Key Project of the Ministry of Agriculture of China (Grant No. 2016ZX08009002)the Natural Science Foundation of Shandong Province (Grant No. ZR2018PC017)。
文摘Lateral roots play essential roles in drought tolerance in maize(Zea mays L.). However, the genetic basis for the variation in the number of lateral roots in maize remains elusive. Here, we identified a major quantitative trait locus(QTL),q LRT5-1, controlling lateral root number using a recombinant inbred population from a cross between the maize lines Zong3(with many lateral roots) and 87-1(with few lateral roots).Fine-mapping and functional analysis determined that the candidate gene for qLRT5-1,ZmLRT, expresses the primary transcript for the microRNA miR166a. ZmLRT was highly expressed in root tips and lateral root primordia,and knockout and overexpression of ZmLRT increased and decreased lateral root number,respectively. Compared with 87-1, the ZmLRT gene model of Zong3 lacked the second and third exons and contained a 14 bp deletion at the junction between the first exon and intron,which altered the splicing site. In addition,ZmLRT expression was significantly lower in Zong3 than in 87-1, which might be attributed to the insertions of a transposon and over large DNA fragments in the Zong3 ZmLRT promoter region. These mutations decreased the abundance of mature miR166a in Zong3, resulting in increased lateral roots at the seedling stage.Furthermore, miR166a post-transcriptionally repressed five development-related class-Ⅲ homeodomain-leucine zipper genes. Moreover,knockout of ZmLRT enhanced drought tolerance of maize seedlings. Our study furthers our understanding of the genetic basis of lateral root number variation in maize and highlights ZmLRT as a target for improving drought tolerance in maize.
文摘The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.
基金supported by the National Natural Science Foundation of China(Grant No.31371571)the National High Technology Research and Development Program of China(863 Program)(Grant No.2014AA10A605)the Fundamental Research Funds for the Central Universities(Grant No.2662017JC001)
文摘Dry seeding is a resource-saving rice establishment method. With an equivalent yield, dry seeded flooded rice （DSR） has been considered as a replacement for traditional transplanted flooded rice （TFR）. However, the differences in leaf and root senescence during grain filling between DSR and TFR were seldom identified. In this study, the root length, root tip number and leaf senescence of rice varieties Huanghuazhan and Yangliangyou 6 during ripening were compared between DSR and TFR. Results showed that top three leaves in DSR had the characteristics of relatively lower SPAD value, lower N content and premature leaf senescence. In addition, both the total root length and total root tip number of DSR were significantly lower than those of TFR. In conclusion, premature and quick leaf senescence was related with inadequate root length and root tip number during ripening, which might result from the deficiency of nitrogen supply in DSR. Techniques on improving leaf nitrogen status and delaying the leaf senescence during grain-filling in DSR should be developed in future researches.
基金funded by the National Natural Science Foundation of China(No.30270777)the Key Direction Research of Knowledge Innovation in Chinese Academy of Science(No.KZCX3-SW-440)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Free air CO2 enrichment(FACE) and nitrogen(N) have marked effects on rice root growth,and numerical simulation can explain these effects. To further define the effects of FACE on root growth of rice, an experiment was performed, using the hybrid indica cultivar Xianyou63. The effects of increasing atmospheric CO2 concentration [CO2], 200 μmol mol-1higher than ambient, on the growth of rice adventitious roots were evaluated, with two levels of N: low(LN, 125 kg ha-1) and normal(NN, 250 kg ha-1). The results showed a significant increase in both adventitious root number(ARN) and adventitious root length(ARL) under FACE treatment. The application of nitrogen also increased ARN and ARL, but these increases were smaller than that under FACE treatment. On the basis of the FACE experiment, numerical models for rice adventitious root number and length were constructed with time as the driving factor. The models illustrated the dynamic development of rice adventitious root number and length after transplanting, regulated either by atmospheric [CO2] or by N application.The simulation result was supported by statistical tests comparing experimental data from different years, and the model yields realistic predictions of root growth. These results suggest that the models have strong predictive potential under conditions of atmospheric [CO2] rises in the future.
文摘Digital roots of numbers have several interesting properties, most of which are well-known. In this paper, our goal is to prove some lesser known results concerning the digital roots of powers of numbers in an arithmetic progression. We will also state some theorems concerning the digital roots of Fermat numbers and star numbers. We will conclude our paper by an interesting application.
文摘In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.
