The core inverse for a complex matrix was introduced by O.M.Baksalary and G.Trenkler.D.S.Rakic,N.C.Dincic and D.S.Djordjevc generalized the core inverse of a complex matrix to the case of an element in a ring.They als...The core inverse for a complex matrix was introduced by O.M.Baksalary and G.Trenkler.D.S.Rakic,N.C.Dincic and D.S.Djordjevc generalized the core inverse of a complex matrix to the case of an element in a ring.They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible.It is natural to ask when a group invertible element is core invertible.In this paper,we will answer this question.Let R be a ring with involution,we will use three equations to characterize the core inverse of an element.That is,let a,b∈R.Then a∈R with a=b if and only if(ab)^(*)=ab,ba^(2)=a,and ab^(2)=b.Finally,we investigate the additive property of two core invertible elements.Moreover,the formulae of the sum of two core invertible elements are presented.展开更多
Under hydrothermal environment,we synthesized lanthanide ions doped sodium yttrium fluoride(NaYF4:Er,Tm@NaYF4:Ce,Tb) luminescent microcrystals via an epitaxial growth technique.The structure and morphology of these mi...Under hydrothermal environment,we synthesized lanthanide ions doped sodium yttrium fluoride(NaYF4:Er,Tm@NaYF4:Ce,Tb) luminescent microcrystals via an epitaxial growth technique.The structure and morphology of these microcrystals were examined by SEM,TEM,EDS and XRD measurements.These particles show dual-mode emissions with red upconversion(UC) and green down conversion(DC) as single particles level.The mean length and diameter of these microparticles increase from 0.43 to2.26 μm and from 1.33 to 1.86 μm,respectively.Most interestingly,the photoluminescence properties of NaYF4:Er,Tm@NaYF4:Ce,Tb phosphor crystals are highly dependent on the crystallite size.The microcrystals fluoresce emit dual-mode emissions when they are solid or dispersed in solvents.Benefiting its intensive fluorescence and uniform morphology,these materials hold great potential for security and anti-counterfeiting applications.展开更多
Three-Dimensional(3D)swirling flow structures,generated by a counter-rotating dualstage swirler in a confined chamber with a confinement ratio of 1.53,were experimentally investigated at Re=2.3×10^(5)using Tomogr...Three-Dimensional(3D)swirling flow structures,generated by a counter-rotating dualstage swirler in a confined chamber with a confinement ratio of 1.53,were experimentally investigated at Re=2.3×10^(5)using Tomographic Particle Image Velocimetry(Tomo-PIV)and planar Particle Image Velocimetry(PIV).Based on the analysis of the 3D time-averaged swirling flow structures and 3D Proper Orthogonal Decomposition(POD)of the Tomo-PIV data,typical coherent flow structures,including the Corner Recirculation Zone(CRZ),Central Recirculation Zone(CTRZ),and Lip Recirculation Zone(LRZ),were extracted.The counter-rotating dual-stage swirler with a Venturi flare generates the independence process of vortex breakdown from the main stage and pilot stage,leading to the formation of an LRZ and a smaller CTRZ near the nozzle outlet.The confinement squeezes the CRZ to the corner and causes a reverse rotation flow to limit the shape of the CTRZ.A large-scale flow structure caused by the main stage features an explosive breakup,flapping,and Precessing Vortex Core(PVC).The explosive breakup mode dominates the swirling flow structures owing to the expansion and construction of the main jet,whereas the flapping mode is related to the wake perturbation.Confinement limits the expansion of PVC and causes it to contract after the impacting area.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11201063,11371089)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)+1 种基金the Jiangsu Planned Projects for Postdoctoral Research Funds(No.1501048B)the Natural Science Foundation of Jiangsu Province(No.BK20141327).
文摘The core inverse for a complex matrix was introduced by O.M.Baksalary and G.Trenkler.D.S.Rakic,N.C.Dincic and D.S.Djordjevc generalized the core inverse of a complex matrix to the case of an element in a ring.They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible.It is natural to ask when a group invertible element is core invertible.In this paper,we will answer this question.Let R be a ring with involution,we will use three equations to characterize the core inverse of an element.That is,let a,b∈R.Then a∈R with a=b if and only if(ab)^(*)=ab,ba^(2)=a,and ab^(2)=b.Finally,we investigate the additive property of two core invertible elements.Moreover,the formulae of the sum of two core invertible elements are presented.
基金Project supported by the National Natural Science Foundation of China (21271074,51372091)the Teamwork Projects funded by the Guangdong Natural Science Foundation (S2013030012842)+1 种基金Guangdong Provincial Science&Technology Project (2015B090903074)Guangzhou Science&Technology Project (201605030005)。
文摘Under hydrothermal environment,we synthesized lanthanide ions doped sodium yttrium fluoride(NaYF4:Er,Tm@NaYF4:Ce,Tb) luminescent microcrystals via an epitaxial growth technique.The structure and morphology of these microcrystals were examined by SEM,TEM,EDS and XRD measurements.These particles show dual-mode emissions with red upconversion(UC) and green down conversion(DC) as single particles level.The mean length and diameter of these microparticles increase from 0.43 to2.26 μm and from 1.33 to 1.86 μm,respectively.Most interestingly,the photoluminescence properties of NaYF4:Er,Tm@NaYF4:Ce,Tb phosphor crystals are highly dependent on the crystallite size.The microcrystals fluoresce emit dual-mode emissions when they are solid or dispersed in solvents.Benefiting its intensive fluorescence and uniform morphology,these materials hold great potential for security and anti-counterfeiting applications.
基金supported by the National Natural Science Foundation of China(Nos.12232002,12072017,12002199,and 11721202)。
文摘Three-Dimensional(3D)swirling flow structures,generated by a counter-rotating dualstage swirler in a confined chamber with a confinement ratio of 1.53,were experimentally investigated at Re=2.3×10^(5)using Tomographic Particle Image Velocimetry(Tomo-PIV)and planar Particle Image Velocimetry(PIV).Based on the analysis of the 3D time-averaged swirling flow structures and 3D Proper Orthogonal Decomposition(POD)of the Tomo-PIV data,typical coherent flow structures,including the Corner Recirculation Zone(CRZ),Central Recirculation Zone(CTRZ),and Lip Recirculation Zone(LRZ),were extracted.The counter-rotating dual-stage swirler with a Venturi flare generates the independence process of vortex breakdown from the main stage and pilot stage,leading to the formation of an LRZ and a smaller CTRZ near the nozzle outlet.The confinement squeezes the CRZ to the corner and causes a reverse rotation flow to limit the shape of the CTRZ.A large-scale flow structure caused by the main stage features an explosive breakup,flapping,and Precessing Vortex Core(PVC).The explosive breakup mode dominates the swirling flow structures owing to the expansion and construction of the main jet,whereas the flapping mode is related to the wake perturbation.Confinement limits the expansion of PVC and causes it to contract after the impacting area.
