Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not gen...Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.展开更多
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the nu...Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.展开更多
In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.
This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition f...This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.展开更多
In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in...In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.展开更多
It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obt...It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.展开更多
A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matr...A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for? . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.展开更多
“Breeding by design” for pure lines may be achieved by construction of an additive QTL-allele matrix in a germplasm panel or breeding population, but this option is not available for hybrids, where both additive and...“Breeding by design” for pure lines may be achieved by construction of an additive QTL-allele matrix in a germplasm panel or breeding population, but this option is not available for hybrids, where both additive and dominance QTL-allele matrices must be constructed. In this study, a hybrid-QTL identification approach, designated PLSRGA, using partial least squares regression(PLSR) for model fitting integrated with a genetic algorithm(GA) for variable selection based on a multi-locus, multi-allele model is described for additive and dominance QTL-allele detection in a diallel hybrid population(DHP). The PLSRGA was shown by simulation experiments to be superior to single-marker analysis and was then used for QTL-allele identification in a soybean DPH yield experiment with eight parents. Twenty-eight main-effect QTL with 138 alleles and nine QTL × environment QTL with 46 alleles were identified, with respective contributions of 61.8% and 23.5% of phenotypic variation. Main-effect additive and dominance QTL-allele matrices were established as a compact form of the DHP genetic structure. The mechanism of heterosis superior-to-parents(or superior-to-parents heterosis, SPH) was explored and might be explained by a complementary locus-set composed of OD+(showing positive over-dominance, most often), PD+(showing positive partial-to-complete dominance, less often) and HA+(showing positive homozygous additivity, occasionally) loci, depending on the parental materials. Any locus-type, whether OD+, PD + and HA+, could be the best genotype of a locus. All hybrids showed various numbers of better or best genotypes at many but not necessarily all loci, indicating further SPH improvement. Based on the additive/dominance QTL-allele matrices, the best hybrid genotype was predicted, and a hybrid improvement approach is suggested. PLSRGA is powerful for hybrid QTL-allele detection and cross-SPH improvement.展开更多
基金Supported by the National Natural Science Foundation of China（71261010）
文摘Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.
基金Supported by the Nature Science Foundation of Henan Province（2003110010）
文摘In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.
文摘This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.
文摘In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.
文摘It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.
文摘A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for? . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.
基金supported by the National Key Research and Development Program of China (2021YFF1001204,2017YFD0101500)the MOE Program of Introducing Talents of Discipline to Universities (“111”Project, B08025)+4 种基金the MOE Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT_17R55)the MARA CARS-04 Programthe Jiangsu Higher Education PAPD Programthe Fundamental Research Funds for the Central Universities (KYZZ201901)the Jiangsu JCICMCP Program。
文摘“Breeding by design” for pure lines may be achieved by construction of an additive QTL-allele matrix in a germplasm panel or breeding population, but this option is not available for hybrids, where both additive and dominance QTL-allele matrices must be constructed. In this study, a hybrid-QTL identification approach, designated PLSRGA, using partial least squares regression(PLSR) for model fitting integrated with a genetic algorithm(GA) for variable selection based on a multi-locus, multi-allele model is described for additive and dominance QTL-allele detection in a diallel hybrid population(DHP). The PLSRGA was shown by simulation experiments to be superior to single-marker analysis and was then used for QTL-allele identification in a soybean DPH yield experiment with eight parents. Twenty-eight main-effect QTL with 138 alleles and nine QTL × environment QTL with 46 alleles were identified, with respective contributions of 61.8% and 23.5% of phenotypic variation. Main-effect additive and dominance QTL-allele matrices were established as a compact form of the DHP genetic structure. The mechanism of heterosis superior-to-parents(or superior-to-parents heterosis, SPH) was explored and might be explained by a complementary locus-set composed of OD+(showing positive over-dominance, most often), PD+(showing positive partial-to-complete dominance, less often) and HA+(showing positive homozygous additivity, occasionally) loci, depending on the parental materials. Any locus-type, whether OD+, PD + and HA+, could be the best genotype of a locus. All hybrids showed various numbers of better or best genotypes at many but not necessarily all loci, indicating further SPH improvement. Based on the additive/dominance QTL-allele matrices, the best hybrid genotype was predicted, and a hybrid improvement approach is suggested. PLSRGA is powerful for hybrid QTL-allele detection and cross-SPH improvement.
