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.
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 criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.
H-tensor plays an important role in identifying positive definiteness of even order real symmetric tensors.In this paper,some definitions and theorems related to H-tensors are introducedfirstly.Secondly,some new criteria...H-tensor plays an important role in identifying positive definiteness of even order real symmetric tensors.In this paper,some definitions and theorems related to H-tensors are introducedfirstly.Secondly,some new criteria for identifying nonsingular H-tensors are proposed,moreover,a new theorem for identifying positive definiteness of even order real symmetric tensors is obtained.Finally,some numerical examples are given to illustrate our results.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
Based on the quark-gluon contents of nucleon and strongly believing that the force mediators,Pomeronand its counterpart in the conventional approach of Regge theory,for high energy diffractive process would be the ten...Based on the quark-gluon contents of nucleon and strongly believing that the force mediators,Pomeronand its counterpart in the conventional approach of Regge theory,for high energy diffractive process would be the tensorglueball and Odderon respectively,we discuss photo-production of vector meson φ off the deuteron at energy less than 3GeV in the QCD inspired model in which the quark gluon degrees of freedom and glueball,Odderon exchange are takeninto account.A calculation is performed for γ + D →φ + D,and the theoretical predictions of the differential crosssection dσ^(γD)) /dt,are presented and compared with available experimental data.Our QCD inspired model reproducesdata quite well in the whole range of the experimental measurements up to |t| ■0.4 GeV.Our results can be used toextract γn→φn data,which cannot be measured in experiment.展开更多
The H-tensor is a new developed concept in tensor analysis and it is an extension of the M-tensor.In this paper,we present some criteria for identifying nonsingular H-tensors and give two numerical examples.
H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In partic...H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.展开更多
Let G= （V,A） be adigraph and k ≥ 1 an integer. For u,v ∈ V, we say that the vertex u distance k-dominate v if the distance from u to v at most k. A set D of vertices in G is a distance k-dominating set if each ver...Let G= （V,A） be adigraph and k ≥ 1 an integer. For u,v ∈ V, we say that the vertex u distance k-dominate v if the distance from u to v at most k. A set D of vertices in G is a distance k-dominating set if each vertex of V ／ D is distance k-dominated by some vertex of D. The distance k-domination number of G, denoted by γk（G）, is the minimum cardinality of a distance k-dominating set of G. Generalized de Bruijn digraphs GB（n, d） and generalized Kautz digraphs Gg（n, d） are good candidates for interconnection k networks. Denote △k ：=（∑j^k=0 d^j）^-1. F. Tian and J. Xu showed that [n△k] ≤ γk（GB（n,d）） ≤ [n/d^k] and [n△k] ≤ γk（GK（n,d）） ≤ [n/d^k]. In this paper, we prove that every generalized de Bruijn digraph GB（n, d） has the distance k- domination number [n△k] or [n△k] ＋ 1, and the distance k-domination number of every generalized Kautz digraph GK（n, d） bounded above by [n/ （d^k-1 ＋d^k）]. Additionally, we present various sufficient conditions for γk（GB（n, d）） = [n△k] and γk（GK（n, d）） = [n△k].展开更多
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.
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.
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.
基金supported by the National Natural Science Foundations of China(Grant No.31600299)The Natural Science Foundation of Shaanxi province(Grant No.2020JM-622).
文摘H-tensor plays an important role in identifying positive definiteness of even order real symmetric tensors.In this paper,some definitions and theorems related to H-tensors are introducedfirstly.Secondly,some new criteria for identifying nonsingular H-tensors are proposed,moreover,a new theorem for identifying positive definiteness of even order real symmetric tensors is obtained.Finally,some numerical examples are given to illustrate our results.
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.
基金Supported by National Natural Science Foundation of China under Grant Nos.10647002 and 10565001
文摘Based on the quark-gluon contents of nucleon and strongly believing that the force mediators,Pomeronand its counterpart in the conventional approach of Regge theory,for high energy diffractive process would be the tensorglueball and Odderon respectively,we discuss photo-production of vector meson φ off the deuteron at energy less than 3GeV in the QCD inspired model in which the quark gluon degrees of freedom and glueball,Odderon exchange are takeninto account.A calculation is performed for γ + D →φ + D,and the theoretical predictions of the differential crosssection dσ^(γD)) /dt,are presented and compared with available experimental data.Our QCD inspired model reproducesdata quite well in the whole range of the experimental measurements up to |t| ■0.4 GeV.Our results can be used toextract γn→φn data,which cannot be measured in experiment.
基金This work was supported by the National Nature Science Foundation of China(Grants no.11771275)the Science and Technology Program of Shandong Universities(no.J16LI04).
文摘The H-tensor is a new developed concept in tensor analysis and it is an extension of the M-tensor.In this paper,we present some criteria for identifying nonsingular H-tensors and give two numerical examples.
基金Acknowledgements The authors would like to give their sincere thanks to the anonymous referees for their valuable suggestions and helpful comments, which help improve the presen- tation of the paper. This work was supported by the National Natural Science Foundation of China （Grant No. 61572283）.
文摘H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11471210, 11571222, 11601262）.
文摘Let G= （V,A） be adigraph and k ≥ 1 an integer. For u,v ∈ V, we say that the vertex u distance k-dominate v if the distance from u to v at most k. A set D of vertices in G is a distance k-dominating set if each vertex of V ／ D is distance k-dominated by some vertex of D. The distance k-domination number of G, denoted by γk（G）, is the minimum cardinality of a distance k-dominating set of G. Generalized de Bruijn digraphs GB（n, d） and generalized Kautz digraphs Gg（n, d） are good candidates for interconnection k networks. Denote △k ：=（∑j^k=0 d^j）^-1. F. Tian and J. Xu showed that [n△k] ≤ γk（GB（n,d）） ≤ [n/d^k] and [n△k] ≤ γk（GK（n,d）） ≤ [n/d^k]. In this paper, we prove that every generalized de Bruijn digraph GB（n, d） has the distance k- domination number [n△k] or [n△k] ＋ 1, and the distance k-domination number of every generalized Kautz digraph GK（n, d） bounded above by [n/ （d^k-1 ＋d^k）]. Additionally, we present various sufficient conditions for γk（GB（n, d）） = [n△k] and γk（GK（n, d）） = [n△k].
