This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is ...This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is presented.展开更多
A unified theoretical method is established to determine the charge-compensated C3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 crystals by simulating the electron paramagnetic resonance(EPR)parameters and Stark energy le...A unified theoretical method is established to determine the charge-compensated C3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 crystals by simulating the electron paramagnetic resonance(EPR)parameters and Stark energy levels.The potential(Er^(3+)–F^(−)–O_(4)^(2−))and(Er^(3+)-F_(7)^(−)-O_(4)^(2−))structures for theC3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 crystals are checked by diagonalizing 364×364 complete energy matrices in the scheme of superposition model.Our studies indicate that the C3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 may be ascribed to the local(Er^(3+)-F^(−)-O_(4)^(2−))structure,where the upper ligand ion F−undergoes an off-center displacement by∆Z≈0.3˚A for CdF2 and∆Z≈0.29˚A for the CaF2 along the C3 axis.Meanwhile,a local compressed distortion of the(ErFO4)6−cluster is expected to be∆R≈0.07˚A for CdF2:Er3+and∆R≈0.079˚A for CaF2:Er3+.The considerable g-factor anisotropy for Er3+ions in each of both crystals is explained reasonably by the obtained local parameters.Furthermore,our studies show that a stronger covalent effect exists in the C3v(Ⅱ)center for Er3+in CaF2 or CaF2,which may be due to the stronger electrostatic interaction and closer distance between the central Er3+ion and ligand O2−with the(Er^(3+)-F^(−)-O_(4)^(2−))structure.展开更多
Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S, if and only...Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S, if and only if S is the strong semilattice of L-right cancellative planks; also if and only if S is a spined product of a right-e wlpp semigroup and a left normal band.展开更多
基金Supported by the Natural Science Foundation of Shaanxi Province（2007A12） Supported by the Scientific Research Foundation of Shaanxi Educational Committee（11JK0507）
文摘This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is presented.
基金Project supported by the National Natural Science Foundation of China(Grant No.1170513)the Natural Science Foundation of Shaanxi Province,China(Grant No.Z20200051)+1 种基金the Foundation of the Education Department of Shaanxi Provincial Government,China(Grant No.16JK1461)the Scientific Research Foundation of Xi’an University of Architecture and Technology,China(Grant No.QN1729).
文摘A unified theoretical method is established to determine the charge-compensated C3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 crystals by simulating the electron paramagnetic resonance(EPR)parameters and Stark energy levels.The potential(Er^(3+)–F^(−)–O_(4)^(2−))and(Er^(3+)-F_(7)^(−)-O_(4)^(2−))structures for theC3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 crystals are checked by diagonalizing 364×364 complete energy matrices in the scheme of superposition model.Our studies indicate that the C3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 may be ascribed to the local(Er^(3+)-F^(−)-O_(4)^(2−))structure,where the upper ligand ion F−undergoes an off-center displacement by∆Z≈0.3˚A for CdF2 and∆Z≈0.29˚A for the CaF2 along the C3 axis.Meanwhile,a local compressed distortion of the(ErFO4)6−cluster is expected to be∆R≈0.07˚A for CdF2:Er3+and∆R≈0.079˚A for CaF2:Er3+.The considerable g-factor anisotropy for Er3+ions in each of both crystals is explained reasonably by the obtained local parameters.Furthermore,our studies show that a stronger covalent effect exists in the C3v(Ⅱ)center for Er3+in CaF2 or CaF2,which may be due to the stronger electrostatic interaction and closer distance between the central Er3+ion and ligand O2−with the(Er^(3+)-F^(−)-O_(4)^(2−))structure.
基金The NSF(11471255)of Chinathe Scientific Research Project(15JK1411)of Education Department of Shaanxi Provincial Governmentthe Scientific Research Project(17KY02)of College
文摘Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S, if and only if S is the strong semilattice of L-right cancellative planks; also if and only if S is a spined product of a right-e wlpp semigroup and a left normal band.
