The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each q...The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.展开更多
We estimate the correction of relativistic center-of-mass vector on electric polarizability of an equal-mass quark-antiquark system numerically. Effect on the system confined by different interactive potentials is ana...We estimate the correction of relativistic center-of-mass vector on electric polarizability of an equal-mass quark-antiquark system numerically. Effect on the system confined by different interactive potentials is analysed. A great improvement for the electric polarizability of pion meson is obtained.展开更多
We investigate the behavior of the vacuum polarization of the gauge-boson Ⅱ and the wave-function renormalization factor of the fermion A in QEDs, using the coupled Dyson-Schwinger equations for the gauge-boson and f...We investigate the behavior of the vacuum polarization of the gauge-boson Ⅱ and the wave-function renormalization factor of the fermion A in QEDs, using the coupled Dyson-Schwinger equations for the gauge-boson and fermion propagator. Using several different ansatze for the fermion-gauge-boson vertex, we find that the wave-function renormalization factor .4 and especially the vacuum polarization Ⅱ have different behaviors in the dynamical chiral symmetry breaking phase and in the chiral symmetric phase and hence in the phenomenological applications of QED3 one should choose different forms of gauge-boson propagator for these two phases. We also find that when adopting a specific ansatze of the fermion-gauge-boson vertex （ansatze （3）） the vacuum polarization function equals its one-loop perturbative result in the chiral symmetric phase. This fact suggests that in QEDs the Wigner vacuum corresponds to the perturbative vacuum.展开更多
The potential energy curves （PECs） of three low-lying electronic states （X^3∑, a^1△, and a^3△） of SO radical have been studied by ab initio quantum chemical method. The calcula- tions were carried out with the ...The potential energy curves （PECs） of three low-lying electronic states （X^3∑, a^1△, and a^3△） of SO radical have been studied by ab initio quantum chemical method. The calcula- tions were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration in- teraction （MRCI） approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification （MRCI＋Q）. These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.展开更多
Comparing the relativistic and nonrelativistic frame works, we study the effect of the relativistic center-of-mass vector on the electric polarizability of a compound system.
Let R be an abelian ring (all idempotents of R lie in the center of R), and A be an idempotent matrix over R. The following statements are proved: (a). A is equivalent to a diagonal matrix if and only if A is similar ...Let R be an abelian ring (all idempotents of R lie in the center of R), and A be an idempotent matrix over R. The following statements are proved: (a). A is equivalent to a diagonal matrix if and only if A is similar to a diagonal matrix. (b). If R is an APT (abelian projectively trivial) ring, then A can be uniquely diagonalized as diag{el, ..., en} and ei divides ei+1. (c). R is an APT ring if and only if R/I is an APT ring, where I is a nilpotent ideal of R. By (a), we prove that a separative abelian regular ring is an APT ring.展开更多
This paper focuses on the variability in entrainment rate in individual cumulus clouds using the entrainment rate estimated on the scale of 5 m in 186 shallow cumulus clouds from eight aircraft flights, using in situ ...This paper focuses on the variability in entrainment rate in individual cumulus clouds using the entrainment rate estimated on the scale of 5 m in 186 shallow cumulus clouds from eight aircraft flights, using in situ observations from the RACORO field campaign （the routine atmospheric radiation measurement aerial facility clouds with low optical water depths optical radiative observations） over the atmospheric radiation measurement Southern Great Plains site, USA. The result shows that the mean entrainment rate of all the 186 clouds systematically decreases from the cloud edge to the cloud center. Further analysis of the fluctuation of entrainment rate shows that the probability density function of entrainment rate in each flight can be fitted by the lognormal, gamma, or Weibull distributions virtually equally well, with the Weibull dis- tribution being the best. The parameter ＂standard devia- tion＂ in the lognormal distribution is weakly negatively correlated, and the other parameters in the three distribu- tions are positively correlated with relative humidity in the entrained dry air and dilution effect, respectively. Entrainment rate is negatively correlated with droplet concentration, droplet size, and liquid water content, but positively correlated with relative dispersion. The effect of entrainment rate on the spectral shape of cloud droplet size distribution is examined and linked to the systems theory on the cloud droplet size distribution.展开更多
Peroxy radicals （ROx） concentrations were measured by Peroxy Radical Chemical Amplifier （PERCA） technique during the field campaign RISFEX 2003 （RiShifi Fall Experiment 2003）, which was performed in September 20...Peroxy radicals （ROx） concentrations were measured by Peroxy Radical Chemical Amplifier （PERCA） technique during the field campaign RISFEX 2003 （RiShifi Fall Experiment 2003）, which was performed in September 2003 at Rishiri island （45.07 N, 141.12 E, and 35 m asl） in the sea of Japan. The concentrations of nighttime ROx radicals had temporal variations around an average of 7.9±5.8 （1σ） pptv and showed a positive correlation with the summed mixing ratio of four monoterpene species. Model calculations suggested that local nighttime ROx radicals were dominated by the reactions of monoterpene with ozone （03） and nitrate radical （NO3）, contributing ca. 76% and 19%, respectively. The comparisons between the observed ROx and ones modeled had implied that the current model may be overestimated the yields of peroxy radicals from the reactions of monoterpenes with ozone and an important source of peroxy radicals was possibly missed. Abnormal high concentrations of observed ROx radicals were found during high relative humidity （RH） period （especially 〉 95%）, and the possible explanation was that the humidity correction of ROx radicals under high RH conditions may be inaccurate and overestimates ROx concen-展开更多
文摘The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.
基金国家自然科学基金，the Institute of Theoretical Physics，中国科学院知识创新工程项目
文摘We estimate the correction of relativistic center-of-mass vector on electric polarizability of an equal-mass quark-antiquark system numerically. Effect on the system confined by different interactive potentials is analysed. A great improvement for the electric polarizability of pion meson is obtained.
基金The project supported in part by National Natural Science Foundation of China under Grant Nos, 10175033 and 10135030 and the Research Fund for the Doctoral Program of Higher Education under Grant No. 20030284009
文摘We investigate the behavior of the vacuum polarization of the gauge-boson Ⅱ and the wave-function renormalization factor of the fermion A in QEDs, using the coupled Dyson-Schwinger equations for the gauge-boson and fermion propagator. Using several different ansatze for the fermion-gauge-boson vertex, we find that the wave-function renormalization factor .4 and especially the vacuum polarization Ⅱ have different behaviors in the dynamical chiral symmetry breaking phase and in the chiral symmetric phase and hence in the phenomenological applications of QED3 one should choose different forms of gauge-boson propagator for these two phases. We also find that when adopting a specific ansatze of the fermion-gauge-boson vertex （ansatze （3）） the vacuum polarization function equals its one-loop perturbative result in the chiral symmetric phase. This fact suggests that in QEDs the Wigner vacuum corresponds to the perturbative vacuum.
文摘The potential energy curves （PECs） of three low-lying electronic states （X^3∑, a^1△, and a^3△） of SO radical have been studied by ab initio quantum chemical method. The calcula- tions were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration in- teraction （MRCI） approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification （MRCI＋Q）. These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.
基金The project supported by National Natural Science Foundation of China under Grant No.10075056CAS Knowledge Innovation Project No.KC2-SW-N02 of the Institute of Theoretical Physics
文摘Comparing the relativistic and nonrelativistic frame works, we study the effect of the relativistic center-of-mass vector on the electric polarizability of a compound system.
文摘Let R be an abelian ring (all idempotents of R lie in the center of R), and A be an idempotent matrix over R. The following statements are proved: (a). A is equivalent to a diagonal matrix if and only if A is similar to a diagonal matrix. (b). If R is an APT (abelian projectively trivial) ring, then A can be uniquely diagonalized as diag{el, ..., en} and ei divides ei+1. (c). R is an APT ring if and only if R/I is an APT ring, where I is a nilpotent ideal of R. By (a), we prove that a separative abelian regular ring is an APT ring.
基金supported by the National Natural Science Foundation of China(41305120,91337215)the Research Foundation for Environmental Protection of Jiangsu Province(2013042)+9 种基金the Natural Science Foundation of Jiangsu Province,China(BK20130988)the Specialized Research Foundation for the Doctoral Program of Higher Education(20133228120002)the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,China(13KJB170014)China Meteorological Administration Special Public Welfare Research Foundation(GYHY201406007)the Open Funding from State Key Laboratory of Severe Weather(2013LASW-B06)the Open Funding from Key Laboratory of Meteorological Disaster of Ministry of Education,China(KLME1305)the Qing Lan Projecta Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe US Department of Energy’s(DOE)Earth System Modeling(ESM)program via the FASTER project(www.bnl.gov/faster)Atmospheric System Research(ASR)Program
文摘This paper focuses on the variability in entrainment rate in individual cumulus clouds using the entrainment rate estimated on the scale of 5 m in 186 shallow cumulus clouds from eight aircraft flights, using in situ observations from the RACORO field campaign （the routine atmospheric radiation measurement aerial facility clouds with low optical water depths optical radiative observations） over the atmospheric radiation measurement Southern Great Plains site, USA. The result shows that the mean entrainment rate of all the 186 clouds systematically decreases from the cloud edge to the cloud center. Further analysis of the fluctuation of entrainment rate shows that the probability density function of entrainment rate in each flight can be fitted by the lognormal, gamma, or Weibull distributions virtually equally well, with the Weibull dis- tribution being the best. The parameter ＂standard devia- tion＂ in the lognormal distribution is weakly negatively correlated, and the other parameters in the three distribu- tions are positively correlated with relative humidity in the entrained dry air and dilution effect, respectively. Entrainment rate is negatively correlated with droplet concentration, droplet size, and liquid water content, but positively correlated with relative dispersion. The effect of entrainment rate on the spectral shape of cloud droplet size distribution is examined and linked to the systems theory on the cloud droplet size distribution.
基金supported by the Special Funds in Marine Public Service Project of State Oceanic Administration (201005025)National High-Tech Research and Development Plan (863) of China (2007AA092101)the International Scientific and Technological Cooperation Projects(2009DFB20610)
文摘Peroxy radicals （ROx） concentrations were measured by Peroxy Radical Chemical Amplifier （PERCA） technique during the field campaign RISFEX 2003 （RiShifi Fall Experiment 2003）, which was performed in September 2003 at Rishiri island （45.07 N, 141.12 E, and 35 m asl） in the sea of Japan. The concentrations of nighttime ROx radicals had temporal variations around an average of 7.9±5.8 （1σ） pptv and showed a positive correlation with the summed mixing ratio of four monoterpene species. Model calculations suggested that local nighttime ROx radicals were dominated by the reactions of monoterpene with ozone （03） and nitrate radical （NO3）, contributing ca. 76% and 19%, respectively. The comparisons between the observed ROx and ones modeled had implied that the current model may be overestimated the yields of peroxy radicals from the reactions of monoterpenes with ozone and an important source of peroxy radicals was possibly missed. Abnormal high concentrations of observed ROx radicals were found during high relative humidity （RH） period （especially 〉 95%）, and the possible explanation was that the humidity correction of ROx radicals under high RH conditions may be inaccurate and overestimates ROx concen-
