设 R 为任意除环,M 是 R 上全部有限矩阵的集合.如果一个从 M 到 M 的对合函数被给出,人们就可以研究相应的 Moore-Penrose 广义逆的理论.然而,人们并不清楚对合函数的具体形状.当 R 是域时 Edward T.Wong 在文[1]中有一个猜测.本文试...设 R 为任意除环,M 是 R 上全部有限矩阵的集合.如果一个从 M 到 M 的对合函数被给出,人们就可以研究相应的 Moore-Penrose 广义逆的理论.然而,人们并不清楚对合函数的具体形状.当 R 是域时 Edward T.Wong 在文[1]中有一个猜测.本文试图证明这个猜测并且确定除环上矩阵对合函数的全部形式.展开更多
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
The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],...The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.展开更多
The performances of selection cooperation are investigated over asymmetric fading channels where the source-relay and the relay-destination channels experience Nakagami-m and Rayleigh fading,respectively.Decode-and-fo...The performances of selection cooperation are investigated over asymmetric fading channels where the source-relay and the relay-destination channels experience Nakagami-m and Rayleigh fading,respectively.Decode-and-forward(DF)protocol is adopted and the Nth best relay is selected from M available relays.Probability density function(PDF)for the instantaneous signal-to-noise ratio(SNR)at the destination is derived first.Then,it is used to derive the exact expressions for outage probability and average symbol error rate(SER).The results hold for arbitrary M or N.Finally,simulations are carried out to verify the correctness of our theoretical analysis and results show that M and N almost have the same effect on the performance of outage probability and SER.展开更多
Results of thermal expansion prediction from atomic scale for metastable liquid metals are reported herein. Three pure liquid metals Ni, Fe, and Cu together with ternary Ni60Fe20Cu20 alloy are used as models. The pair...Results of thermal expansion prediction from atomic scale for metastable liquid metals are reported herein. Three pure liquid metals Ni, Fe, and Cu together with ternary Ni60Fe20Cu20 alloy are used as models. The pair distribution functions were em- ployed to monitor the atomic structure. This indicates that the simulated systems are ordered in atomic short range and disor- dered in long range. The thermal expansion coefficient was computed as functions of temperature and atom cutoff radius, which tends to maintain a constant when the cutoff radius increases to approximately 15A. In such a case, slightly more than 1000 atoms are required for liquid Ni, Cu, Fe and Ni60Fe20Cu20 alloy, that is, the macroscopic thermal expansion can be pre- dicted from the volume change of such a tiny cell. Furthermore, the expansion behaviors of the three types of atoms in liquid Ni60Fe20Cu20 alloy are revealed by the calculated partial expansion coefficient. This provides a fundamental method to predict the macroscopic thermal expansion from the atomic scale for liquid alloys, especially in the undercooled regime.展开更多
Ab-initio molecular dynamics simulation was performed to investigate the local atomic structure of Co55Ta^0B35 alloys. Pair distribution function, coordination number, HA index and Voronoi polyhedra were used to descr...Ab-initio molecular dynamics simulation was performed to investigate the local atomic structure of Co55Ta^0B35 alloys. Pair distribution function, coordination number, HA index and Voronoi polyhedra were used to describe the detailed local structure of this alloy. It was revealed Co7TalB2, Co6TalB2 and CosTa2B4 among the dominant （0 3 6 0）, （0 4 4 0）, （0 1 10 2） and （0 3 6 4） polyhedra were the basic local structure units in CossTal0B3s amorphous alloy. Furthermore, most of the dominant poly- hedra tended to have Ta atoms involved and these polyhedra may have a critical role during glass formation.展开更多
文摘设 R 为任意除环,M 是 R 上全部有限矩阵的集合.如果一个从 M 到 M 的对合函数被给出,人们就可以研究相应的 Moore-Penrose 广义逆的理论.然而,人们并不清楚对合函数的具体形状.当 R 是域时 Edward T.Wong 在文[1]中有一个猜测.本文试图证明这个猜测并且确定除环上矩阵对合函数的全部形式.
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.
文摘The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.
基金Supported by the National Natural Science Foundation of China(No.6087024)the Cultivation Fund of the Key Scientific and Technical Innovation Project(No.708059)+2 种基金Open Found of State Key Laboratory of Integrated Services Networks(No.ISN12-10)Open Research Fund of National Mobile Communications Research Laboratory(No.2012D10)the Natural Science Foundation of Shandong Province(No.ZR2011FM027)
文摘The performances of selection cooperation are investigated over asymmetric fading channels where the source-relay and the relay-destination channels experience Nakagami-m and Rayleigh fading,respectively.Decode-and-forward(DF)protocol is adopted and the Nth best relay is selected from M available relays.Probability density function(PDF)for the instantaneous signal-to-noise ratio(SNR)at the destination is derived first.Then,it is used to derive the exact expressions for outage probability and average symbol error rate(SER).The results hold for arbitrary M or N.Finally,simulations are carried out to verify the correctness of our theoretical analysis and results show that M and N almost have the same effect on the performance of outage probability and SER.
基金supported by the National Natural Science Foundation of China(Grant Nos.51474175,51271150 and 51327901)the Program for New Century Excellent Talents and NPU Foundation for Fundamental Research
文摘Results of thermal expansion prediction from atomic scale for metastable liquid metals are reported herein. Three pure liquid metals Ni, Fe, and Cu together with ternary Ni60Fe20Cu20 alloy are used as models. The pair distribution functions were em- ployed to monitor the atomic structure. This indicates that the simulated systems are ordered in atomic short range and disor- dered in long range. The thermal expansion coefficient was computed as functions of temperature and atom cutoff radius, which tends to maintain a constant when the cutoff radius increases to approximately 15A. In such a case, slightly more than 1000 atoms are required for liquid Ni, Cu, Fe and Ni60Fe20Cu20 alloy, that is, the macroscopic thermal expansion can be pre- dicted from the volume change of such a tiny cell. Furthermore, the expansion behaviors of the three types of atoms in liquid Ni60Fe20Cu20 alloy are revealed by the calculated partial expansion coefficient. This provides a fundamental method to predict the macroscopic thermal expansion from the atomic scale for liquid alloys, especially in the undercooled regime.
基金supported by the National Natural Science Foundation of China (Grant No. 51101004)the Fundamental Research Funds for the Central Universities
文摘Ab-initio molecular dynamics simulation was performed to investigate the local atomic structure of Co55Ta^0B35 alloys. Pair distribution function, coordination number, HA index and Voronoi polyhedra were used to describe the detailed local structure of this alloy. It was revealed Co7TalB2, Co6TalB2 and CosTa2B4 among the dominant （0 3 6 0）, （0 4 4 0）, （0 1 10 2） and （0 3 6 4） polyhedra were the basic local structure units in CossTal0B3s amorphous alloy. Furthermore, most of the dominant poly- hedra tended to have Ta atoms involved and these polyhedra may have a critical role during glass formation.
