We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots.It is well known that suc...We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots.It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients.Those polynomials in the coefficients are called discriminants for multiplicities.It is also known that discriminants can be obtained using repeated parametric greatest common divisors.The resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so on.In this paper,we give a new type of discriminant that is not based on repeated greatest common divisors.The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.展开更多
We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with i<j and j≠k,k≠...We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with i<j and j≠k,k≠i.D_(2)vanishes if and only if f has at least one root which is equal to the average of two other roots.We show that D_(2)can be expressed as the resultant of f and a determinant formed with the derivatives of f,establishing a new relation between the roots and the coefficients of f.We prove several notable properties and present an application of D_(2).展开更多
Aims Intercropping legumes and non-legumes may affect the root growth of both components in the mixture,and the non-legume is known to be strongly favored by increasing nitrogen(N)supply.the knowledge of how root syst...Aims Intercropping legumes and non-legumes may affect the root growth of both components in the mixture,and the non-legume is known to be strongly favored by increasing nitrogen(N)supply.the knowledge of how root systems affect the growth of the individual species is useful for understanding the interactions in intercrops as well as for planning cover cropping strategies.the aim of this work was(i)to determine if different levels of N in the topsoil influence root depth(rD)and intensity of barley and vetch as sole crops or as an inter-cropped mixture and(ii)to test if the choice of a mixture or the N availability in the topsoil will influence the N uptake by deep roots.Methods In this study,we combined rhizotron studies with root extraction and species identification by microscopy with studies of growth,N uptake and 15N uptake from deeper soil layers,for studying the root interactions of root growth and N foraging for barley(Hordeum vul-gare l.)and vetch(Vicia sativa l.),frequently grown in mixtures as cover crops.N was added at 0(N0),50(N1)and 150(N2)kg N ha−1.the roots discrimination relying on the anatomical and morphologi-cal differences observed between dicots and monocots proved to be a reliable method providing valuable data for the analysis.Important Findingsthe intercrop and the barley attained slightly higher root intensity(rI)and rD than the vetch,with values around 150 crosses m−1 and 1.4 m,respectively,compared to 50 crosses m−1 and 0.9 m for the vetch.at deep soil layers,intercropping showed slightly larger rI values compared to the sole-cropped barley.the barley and the intercropping had larger root length density(r D)values(200-600 m m−3)than the vetch(25-130)at 0.8-1.2 m depth.the topsoil N supply did not show a clear effect on the rI,rD or r D;however,increasing topsoil N favored the proliferation of vetch roots in the intercropping at deep soil layers,with the barley:vetch root ratio ranging from 25 at N0 to 5 at N2.the N uptake of the barley was enhanced in the intercropping at the expense of the vetch(from~100 mg plant−1 to 200).the intercropped barley roots took up more labeled nitrogen(0.6 mg 15N plant−1)than the sole-cropped barley roots(0.3 mg 15N plant−1)from deep layers.展开更多
In Wireless Sensor Networks(WSN),attacks mostly aim in limiting or eliminating the capability of the network to do its normal function.Detecting this misbehaviour is a demanding issue.And so far the prevailing researc...In Wireless Sensor Networks(WSN),attacks mostly aim in limiting or eliminating the capability of the network to do its normal function.Detecting this misbehaviour is a demanding issue.And so far the prevailing research methods show poor performance.AQN3 centred efficient Intrusion Detection Systems(IDS)is proposed in WSN to ameliorate the performance.The proposed system encompasses Data Gathering(DG)in WSN as well as Intrusion Detection(ID)phases.In DG,the Sensor Nodes(SN)is formed as clusters in the WSN and the Distance-based Fruit Fly Fuzzy c-means(DFFF)algorithm chooses the Cluster Head(CH).Then,the data is amassed by the discovered path.Next,it is tested with the trained IDS.The IDS encompasses‘3’steps:pre-processing,matrix reduction,and classification.In pre-processing,the data is organized in a clear format.Then,attributes are presented on the matrix format and the ELDA(entropybased linear discriminant analysis)lessens the matrix values.Next,the output as of the matrix reduction is inputted to the QN3 classifier,which classifies the denial-of-services(DoS),Remotes to Local(R2L),Users to Root(U2R),and probes into attacked or Normal data.In an experimental estimation,the proposed algorithm’s performance is contrasted with the prevailing algorithms.The proposed work attains an enhanced outcome than the prevailing methods.展开更多
基金supported by U.S.National Science Foundations(Grant Nos.2212461 and 1813340)supported by National Natural Science Foundation of China(Grant Nos.12261010 and 11801101)。
文摘We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots.It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients.Those polynomials in the coefficients are called discriminants for multiplicities.It is also known that discriminants can be obtained using repeated parametric greatest common divisors.The resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so on.In this paper,we give a new type of discriminant that is not based on repeated greatest common divisors.The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.
基金supported by National Natural Science Foundation of China(Grant Nos.61702025 and 11801101)the Special Fund for Guangxi Bagui Scholar Project+1 种基金Guangxi Science and Technology Program(Grant No.2017AD23056)the Startup Foundation for Advanced Talents in Guangxi University for Nationalities(Grant No.2015MDQD018)。
文摘We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with i<j and j≠k,k≠i.D_(2)vanishes if and only if f has at least one root which is equal to the average of two other roots.We show that D_(2)can be expressed as the resultant of f and a determinant formed with the derivatives of f,establishing a new relation between the roots and the coefficients of f.We prove several notable properties and present an application of D_(2).
基金The Spanish CICYT(project AGL 2011-24732)financed the student and professor exchange and partly the research.
文摘Aims Intercropping legumes and non-legumes may affect the root growth of both components in the mixture,and the non-legume is known to be strongly favored by increasing nitrogen(N)supply.the knowledge of how root systems affect the growth of the individual species is useful for understanding the interactions in intercrops as well as for planning cover cropping strategies.the aim of this work was(i)to determine if different levels of N in the topsoil influence root depth(rD)and intensity of barley and vetch as sole crops or as an inter-cropped mixture and(ii)to test if the choice of a mixture or the N availability in the topsoil will influence the N uptake by deep roots.Methods In this study,we combined rhizotron studies with root extraction and species identification by microscopy with studies of growth,N uptake and 15N uptake from deeper soil layers,for studying the root interactions of root growth and N foraging for barley(Hordeum vul-gare l.)and vetch(Vicia sativa l.),frequently grown in mixtures as cover crops.N was added at 0(N0),50(N1)and 150(N2)kg N ha−1.the roots discrimination relying on the anatomical and morphologi-cal differences observed between dicots and monocots proved to be a reliable method providing valuable data for the analysis.Important Findingsthe intercrop and the barley attained slightly higher root intensity(rI)and rD than the vetch,with values around 150 crosses m−1 and 1.4 m,respectively,compared to 50 crosses m−1 and 0.9 m for the vetch.at deep soil layers,intercropping showed slightly larger rI values compared to the sole-cropped barley.the barley and the intercropping had larger root length density(r D)values(200-600 m m−3)than the vetch(25-130)at 0.8-1.2 m depth.the topsoil N supply did not show a clear effect on the rI,rD or r D;however,increasing topsoil N favored the proliferation of vetch roots in the intercropping at deep soil layers,with the barley:vetch root ratio ranging from 25 at N0 to 5 at N2.the N uptake of the barley was enhanced in the intercropping at the expense of the vetch(from~100 mg plant−1 to 200).the intercropped barley roots took up more labeled nitrogen(0.6 mg 15N plant−1)than the sole-cropped barley roots(0.3 mg 15N plant−1)from deep layers.
文摘In Wireless Sensor Networks(WSN),attacks mostly aim in limiting or eliminating the capability of the network to do its normal function.Detecting this misbehaviour is a demanding issue.And so far the prevailing research methods show poor performance.AQN3 centred efficient Intrusion Detection Systems(IDS)is proposed in WSN to ameliorate the performance.The proposed system encompasses Data Gathering(DG)in WSN as well as Intrusion Detection(ID)phases.In DG,the Sensor Nodes(SN)is formed as clusters in the WSN and the Distance-based Fruit Fly Fuzzy c-means(DFFF)algorithm chooses the Cluster Head(CH).Then,the data is amassed by the discovered path.Next,it is tested with the trained IDS.The IDS encompasses‘3’steps:pre-processing,matrix reduction,and classification.In pre-processing,the data is organized in a clear format.Then,attributes are presented on the matrix format and the ELDA(entropybased linear discriminant analysis)lessens the matrix values.Next,the output as of the matrix reduction is inputted to the QN3 classifier,which classifies the denial-of-services(DoS),Remotes to Local(R2L),Users to Root(U2R),and probes into attacked or Normal data.In an experimental estimation,the proposed algorithm’s performance is contrasted with the prevailing algorithms.The proposed work attains an enhanced outcome than the prevailing methods.
