In this note, for any pair of natural numbers (n,k), n≥3, k≥1, and 2k<n, we construct an infinite family of irreducible polynomials of degree n, with integer coefficients, that has exactly ...In this note, for any pair of natural numbers (n,k), n≥3, k≥1, and 2k<n, we construct an infinite family of irreducible polynomials of degree n, with integer coefficients, that has exactly n-2k?complex non-real roots if n is even and has exactly n-2k-1?complex non-real roots if n is odd. Our work generalizes a technical result of R. Bauer, presented in the classical monograph “Basic Algebra” of N. Jacobson. It is used there to construct polynomials with Galois groups, the symmetric group. Bauer’s result covers the case k=1?and n odd prime.展开更多
Plant root systems serve as a natural reinforcing material,significantly improving soil stability.Furthermore,the tensile strength of soil is crucial in mitigating the formation of cracks.Consequently,this study aims ...Plant root systems serve as a natural reinforcing material,significantly improving soil stability.Furthermore,the tensile strength of soil is crucial in mitigating the formation of cracks.Consequently,this study aims to investigate the influence of plant roots on the tensile strength of soil.For this investigation,Amorpha fruticose was selected due to its large root diameter and the ease of root extraction.Indoor tensile tests were conducted on individual roots and root-soil complexes under three varying factors.The results indicate a power law relationship between root diameter and tensile strength.Increased root content and dry density notably enhance the tensile strength of the root-soil complex while roots mitigate damage associated with soil brittleness.When root content increases from 0 to 10,the maximum enhancement in tensile strength of the root-soil complex reaches 42.3 kPa.The tensile strength of the root-soil complex at a dry density of 1.7 g/cm^(3)is four to five times greater than that of the complex at a dry density of 1.4 g/cm^(3).Moreover,as moisture content increases,the tensile strength of the root-soil complex initially rises before declining,with an increase range of 7.7-35.8 kPa.These findings provide a scientific basis for understanding the role of vegetation roots in soil tensile strength and for guiding slope reinforcement strategies.展开更多
Studies on natural variation are an important tool to unravel the genetic basis of quantitative traits in plants. Despite the significant roles of phytohormones in plant development, including root architecture, hardl...Studies on natural variation are an important tool to unravel the genetic basis of quantitative traits in plants. Despite the significant roles of phytohormones in plant development, including root architecture, hardly any studies have been done to investigate natural variation in endogenous hormone levels in plants. Therefore, in the present study a range of hormones were quantified in root extracts of thirteen Arabidopsis thaliana accessions using a ultra performance liquid chromatography triple quadrupole mass spectrometer. Root system architecture of the set of accessions was quantified, using a new parameter （mature root unit） for complex root systems, and correlated with the phytohormone data. Significant variations in phytohormone levels among the accessions were detected, but were remarkably small, namely less than three-fold difference between extremes. For cytokinins, relatively larger variations were found for ribosides and glucosides, as compared to the free bases. For root phenotyping, length-related traits--lateral root length and total root length--showed larger variations than lateral root number-related ones. For root architecture, antagonistic interactions between hormones, for example, indole-3-acetic acid to trans-zeatin were detected in correlation analysis. These findings provide conclusive evidence for the presence of natural variation in phytohormone levels in Arabidopsis roots, suggesting that quantitative genetic analyses are feasible.展开更多
This paper considers three algorithms for the extraction of square roots of complex integers {called Gaussians} using arithmetic based on complex modulus p + iq. These algorithms are almost twice as fast as the analog...This paper considers three algorithms for the extraction of square roots of complex integers {called Gaussians} using arithmetic based on complex modulus p + iq. These algorithms are almost twice as fast as the analogous algorithms extracting square roots of either real or complex integers in arithmetic based on modulus p, where is a real prime. A cryptographic system based on these algorithms is provided in this paper. A procedure reducing the computational complexity is described as well. Main results are explained in several numeric illustrations.展开更多
文摘In this note, for any pair of natural numbers (n,k), n≥3, k≥1, and 2k<n, we construct an infinite family of irreducible polynomials of degree n, with integer coefficients, that has exactly n-2k?complex non-real roots if n is even and has exactly n-2k-1?complex non-real roots if n is odd. Our work generalizes a technical result of R. Bauer, presented in the classical monograph “Basic Algebra” of N. Jacobson. It is used there to construct polynomials with Galois groups, the symmetric group. Bauer’s result covers the case k=1?and n odd prime.
基金The authors would like to acknowledge financial support from the Joint Funds of the National Nature Science Foundation of China(No.U22A20232)Supported by Open Project Funding of Key Laboratory of Intelligent Health Perception and Ecological Restoration of Rivers and Lakes,Ministry of Education(HGKFZ07)+2 种基金the National Natural Science Foundation of China(No.51978249)Innovation Research Team Project of the Hubei Provincial Department of Science and Technology(JCZRQT202500027)the International Collaborative Research Fund for Young Scholars in the Innovation Demonstration Base of Ecological Environment Geotechnical and Ecological Restoration of Rivers and Lakes.
文摘Plant root systems serve as a natural reinforcing material,significantly improving soil stability.Furthermore,the tensile strength of soil is crucial in mitigating the formation of cracks.Consequently,this study aims to investigate the influence of plant roots on the tensile strength of soil.For this investigation,Amorpha fruticose was selected due to its large root diameter and the ease of root extraction.Indoor tensile tests were conducted on individual roots and root-soil complexes under three varying factors.The results indicate a power law relationship between root diameter and tensile strength.Increased root content and dry density notably enhance the tensile strength of the root-soil complex while roots mitigate damage associated with soil brittleness.When root content increases from 0 to 10,the maximum enhancement in tensile strength of the root-soil complex reaches 42.3 kPa.The tensile strength of the root-soil complex at a dry density of 1.7 g/cm^(3)is four to five times greater than that of the complex at a dry density of 1.4 g/cm^(3).Moreover,as moisture content increases,the tensile strength of the root-soil complex initially rises before declining,with an increase range of 7.7-35.8 kPa.These findings provide a scientific basis for understanding the role of vegetation roots in soil tensile strength and for guiding slope reinforcement strategies.
文摘Studies on natural variation are an important tool to unravel the genetic basis of quantitative traits in plants. Despite the significant roles of phytohormones in plant development, including root architecture, hardly any studies have been done to investigate natural variation in endogenous hormone levels in plants. Therefore, in the present study a range of hormones were quantified in root extracts of thirteen Arabidopsis thaliana accessions using a ultra performance liquid chromatography triple quadrupole mass spectrometer. Root system architecture of the set of accessions was quantified, using a new parameter （mature root unit） for complex root systems, and correlated with the phytohormone data. Significant variations in phytohormone levels among the accessions were detected, but were remarkably small, namely less than three-fold difference between extremes. For cytokinins, relatively larger variations were found for ribosides and glucosides, as compared to the free bases. For root phenotyping, length-related traits--lateral root length and total root length--showed larger variations than lateral root number-related ones. For root architecture, antagonistic interactions between hormones, for example, indole-3-acetic acid to trans-zeatin were detected in correlation analysis. These findings provide conclusive evidence for the presence of natural variation in phytohormone levels in Arabidopsis roots, suggesting that quantitative genetic analyses are feasible.
文摘This paper considers three algorithms for the extraction of square roots of complex integers {called Gaussians} using arithmetic based on complex modulus p + iq. These algorithms are almost twice as fast as the analogous algorithms extracting square roots of either real or complex integers in arithmetic based on modulus p, where is a real prime. A cryptographic system based on these algorithms is provided in this paper. A procedure reducing the computational complexity is described as well. Main results are explained in several numeric illustrations.
