Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enros...Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.展开更多
Monitoring indoor harmful gas can obtain the infrared spectra of mixed harmful gases.Since the absorption bands of mixed gases overlap and their qualitative and quantitative analyses are not easy,feature extraction me...Monitoring indoor harmful gas can obtain the infrared spectra of mixed harmful gases.Since the absorption bands of mixed gases overlap and their qualitative and quantitative analyses are not easy,feature extraction method based on joint approximative diagonalization of eigenmatrix（JADE）is proposed.By fully mining the hidden information of original data and analyzing higher-order statistics information of the data,each substance spectrum in the mixed gas can be accurately distinguished.In addition,a multi-dimensional data quantitative analysis model of the extracted independent source is established by using support vector machine（SVM）based on regular theory.The experimental results show that the correlation coefficients of the components of mixed gases is above 0.999 1by quantitative analysis,which verifies the accuracy of this feature extraction method.展开更多
A investigation of the properties of the bound states of D^- centers confined in a parabolic quantum dot has been performed for the case with the presence of a perpendicular magnetic field. Calculations are carried ou...A investigation of the properties of the bound states of D^- centers confined in a parabolic quantum dot has been performed for the case with the presence of a perpendicular magnetic field. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. The binding energies of the ground and some bound-excited states are obtained as a function of the applied magnetic field strength. Detailed calculations of the binding energies for a number of low-lying states show that for field strength less than B = 2.1 T, the D center confined in a quantum dot possesses two bound states, for 2.1 〈 B 〈 2.4 T, there exist three bound states, etc. Further relevant characteristics of the D- center quantum dots in magnetic fields are provided.展开更多
Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute t...Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute the number of the orbits of An（R） and then compute the order of the orthogonal group determined by the special symmetric matrix. Finally we get the number of the symmetric matrices which are in the same orbit with the special symmetric matrix.展开更多
Consider the stable Steinberg group St（K） over a skew field K. An element x is called an involution if x^2 = 1. In this paper, an involution is allowed to be the identity. The authors prove that an element A of GLn...Consider the stable Steinberg group St（K） over a skew field K. An element x is called an involution if x^2 = 1. In this paper, an involution is allowed to be the identity. The authors prove that an element A of GLn（K） up to conjugation can be represented as BC, where B is lower triangular and C is simultaneously upper triangular. Furthermore. B and C can be chosen so that the elements in the main diagonal of B are β1,β2,…,βn,and of C are γ1,γ2,…,γncn,where cn∈[K^n,K^n] and ∏j=1^n βjγj=det A,it is Also proved that every element δin St（K） is a product of 10 involutions.展开更多
A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated b...A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.展开更多
Based on one year gradient wind data and the wind data of a strong typhoon observed by three meteorological towers located on the coast and at the inshore sea,the underlying surfaces of the meteorological towers were ...Based on one year gradient wind data and the wind data of a strong typhoon observed by three meteorological towers located on the coast and at the inshore sea,the underlying surfaces of the meteorological towers were classified and the roughness lengths were calculated quantitatively.On the basis of strong wind characteristic representative assessment and sample selection on the wind data of strong typhoon Hagupit,the gust factor variation characteristics of tropical cyclones under different underlying surfaces were analyzed.The observed fact and variation rule were found as follows:1) The roughness lengths under neutral atmospheric condition which were calculated using logarithmic wind profile fitting based on the observation data can describe the slight change of the underlying surface objectively.2) The gust factor of strong typhoon wind didn't have variation trends with wind speed.But the variation amplitude of the gust factor was rather large over rough underlying surface which had pronounced effect on the numerical design of structural engineering.3) The variation of the gust factor with height satisfied power law or logarithmic law.The power law fitting was more suitable for smooth underlying surface while the logarithmic fitting was better over rough underlying surface.4) The observation data also suggested that the relationship between gust factor and roughness length can be described by power or linear equation.5) The gust factor observed in this typhoon case was different from the gust factor recommended by WMO:The gust factor of the offshore wind came from rough underlying surface was higher than the value recommended by WMO while the gust factor of the onshore wind came from smooth underlying surface is less than the WMO recommended value.展开更多
文摘Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.
基金National Natural Science Foundation of China(No.61127015)
文摘Monitoring indoor harmful gas can obtain the infrared spectra of mixed harmful gases.Since the absorption bands of mixed gases overlap and their qualitative and quantitative analyses are not easy,feature extraction method based on joint approximative diagonalization of eigenmatrix（JADE）is proposed.By fully mining the hidden information of original data and analyzing higher-order statistics information of the data,each substance spectrum in the mixed gas can be accurately distinguished.In addition,a multi-dimensional data quantitative analysis model of the extracted independent source is established by using support vector machine（SVM）based on regular theory.The experimental results show that the correlation coefficients of the components of mixed gases is above 0.999 1by quantitative analysis,which verifies the accuracy of this feature extraction method.
基金supported by National Natural Science Foundation of China under Grant No. 10775035
文摘A investigation of the properties of the bound states of D^- centers confined in a parabolic quantum dot has been performed for the case with the presence of a perpendicular magnetic field. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. The binding energies of the ground and some bound-excited states are obtained as a function of the applied magnetic field strength. Detailed calculations of the binding energies for a number of low-lying states show that for field strength less than B = 2.1 T, the D center confined in a quantum dot possesses two bound states, for 2.1 〈 B 〈 2.4 T, there exist three bound states, etc. Further relevant characteristics of the D- center quantum dots in magnetic fields are provided.
基金the Key Project of Chinese Ministry of Education (03060)
文摘Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute the number of the orbits of An（R） and then compute the order of the orthogonal group determined by the special symmetric matrix. Finally we get the number of the symmetric matrices which are in the same orbit with the special symmetric matrix.
基金Project supported by the Key Project of the Ministry of Education of China (No. 03060).
文摘Consider the stable Steinberg group St（K） over a skew field K. An element x is called an involution if x^2 = 1. In this paper, an involution is allowed to be the identity. The authors prove that an element A of GLn（K） up to conjugation can be represented as BC, where B is lower triangular and C is simultaneously upper triangular. Furthermore. B and C can be chosen so that the elements in the main diagonal of B are β1,β2,…,βn,and of C are γ1,γ2,…,γncn,where cn∈[K^n,K^n] and ∏j=1^n βjγj=det A,it is Also proved that every element δin St（K） is a product of 10 involutions.
基金supported by National Natural Science Foundation of China(Grant Nos.11271035,91430213 and 11421101)
文摘A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.
基金supported by the National Natural Science Foundation of China (Grant Nos. 90715031, 40775071) the National Special Re-search Fund for Non-Profit Sector of China Ministry of Science and Tech-nology (Grant No. GYHY200806012)
文摘Based on one year gradient wind data and the wind data of a strong typhoon observed by three meteorological towers located on the coast and at the inshore sea,the underlying surfaces of the meteorological towers were classified and the roughness lengths were calculated quantitatively.On the basis of strong wind characteristic representative assessment and sample selection on the wind data of strong typhoon Hagupit,the gust factor variation characteristics of tropical cyclones under different underlying surfaces were analyzed.The observed fact and variation rule were found as follows:1) The roughness lengths under neutral atmospheric condition which were calculated using logarithmic wind profile fitting based on the observation data can describe the slight change of the underlying surface objectively.2) The gust factor of strong typhoon wind didn't have variation trends with wind speed.But the variation amplitude of the gust factor was rather large over rough underlying surface which had pronounced effect on the numerical design of structural engineering.3) The variation of the gust factor with height satisfied power law or logarithmic law.The power law fitting was more suitable for smooth underlying surface while the logarithmic fitting was better over rough underlying surface.4) The observation data also suggested that the relationship between gust factor and roughness length can be described by power or linear equation.5) The gust factor observed in this typhoon case was different from the gust factor recommended by WMO:The gust factor of the offshore wind came from rough underlying surface was higher than the value recommended by WMO while the gust factor of the onshore wind came from smooth underlying surface is less than the WMO recommended value.
