Let G be a group and （A, B） be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, D^π=A^cop∝B=＋p∈GDπ^p with Dπ^p=A^cop∝Bp, is the Drinfeld double of the ...Let G be a group and （A, B） be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, D^π=A^cop∝B=＋p∈GDπ^p with Dπ^p=A^cop∝Bp, is the Drinfeld double of the pair （A, B）, and then the deformation D^π becomes a multiplier Hopf algebra. B×A can be considered as a subalgebra of M（D^π×D^π）, the image of element b×a in B×A is （1∝b）×（a∝1） in M（D^π×D^π）. Let W =∑αWα∈ M（B×A） be a π-canonical multiplier for the pair （A, B） with Wα∈M（Bα×A） for all α∈G. The image of W in M（D^π×D^π）is a π-quasitriangular structure over D^π.展开更多
An isothermal section of the Mg-Nd-Gd ternary system at 723 K was established by diffusion triple technique and electron probe microanalysis （EPMA）. Mg3Gd and Mg3Nd form a continuous solid solution （Gd,Nd）3Mg, and...An isothermal section of the Mg-Nd-Gd ternary system at 723 K was established by diffusion triple technique and electron probe microanalysis （EPMA）. Mg3Gd and Mg3Nd form a continuous solid solution （Gd,Nd）3Mg, and a continuous solid solution （Gd,Nd）Mg is also formed between MgGd and MgNd. Mg7Gd, Mg5Gd, Mg2Gd, Mg41Nd5, （Gd,Nd）3Mg and （Gd,Nd）Mg are found in the ternary system. In these intermetallic phases, Mg7Gd has been reported to be a metastable phase in previous literatures. The solubilities of Mg, Gd and Nd in all the phases were detected. Furthermore, four three-phase equilibria, α（Mg）＋Mg7Gd＋Mg41Nd5, Mg7Gd＋Mg5Gd＋Mg41Nd5, Mg5Gd＋Mg41Nd5＋（Gd,Nd）3Mg and （Gd,Nd）3Mg＋（Gd,Nd）Mg＋Mg2Gd, were identified in the isothermal section.展开更多
Through alloy sampling combined with diffusion triple technique, phase equilibria in Al-Ti-Zr ternary system at 1073 Kwere experimentally determined with electron probe microanalysis （EPMA）. Experimental results sho...Through alloy sampling combined with diffusion triple technique, phase equilibria in Al-Ti-Zr ternary system at 1073 Kwere experimentally determined with electron probe microanalysis （EPMA）. Experimental results show that there is a solid solutionβ（Ti,Zr） which dissolves Al up to 16.3% （mole fraction）. Ti and Zr can substitute each other in most Ti-Al and Al-Zr binaryintermediate phases to a certain degree while the maximum solubility of Zr in Ti3Al and TiAl reaches up to 17.9% and 4.0% （molefraction）, respectively. The isothermal section consists of 16 single-phased regions, 27 two-phased regions and 14 three-phasedregions. No ternary phase was detected.展开更多
Phase equilibria in Ti?Ni?Pt ternary system have been experimentally determined through diffusion triple technique combined with alloy samples approach.Assisted with electron probe microanalysis(EPMA)and X-ray diffrac...Phase equilibria in Ti?Ni?Pt ternary system have been experimentally determined through diffusion triple technique combined with alloy samples approach.Assisted with electron probe microanalysis(EPMA)and X-ray diffraction(XRD)techniques,isothermal sections at 1073 and 1173 K of this system were constructed and existence of ternary phase Ti2(Ni,Pt)3 was confirmed.In addition,binary compounds Ti3Pt5 and TiPt3-were found to be stable at 1073 and 1173 K,and remarkable ternary solubility in some binary compounds was detected,e.g.,solubility of Pt in TiNi can be up to about 36%(molar fraction)at 1073 K and 40%(molar fraction)at 1173 K.Furthermore,a ternary invariant transition reaction TiNi3+Ti3Pt5→Ti2(Ni,Pt)3+TiPt3+at a temperature between 1073 and 1173 K was deduced.展开更多
Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to b...Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.展开更多
基金Specialized Research Fund for the Doctoral Program of Higher Education(No20060286006)the National Natural Science Foundation of China(No10871042)
文摘Let G be a group and （A, B） be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, D^π=A^cop∝B=＋p∈GDπ^p with Dπ^p=A^cop∝Bp, is the Drinfeld double of the pair （A, B）, and then the deformation D^π becomes a multiplier Hopf algebra. B×A can be considered as a subalgebra of M（D^π×D^π）, the image of element b×a in B×A is （1∝b）×（a∝1） in M（D^π×D^π）. Let W =∑αWα∈ M（B×A） be a π-canonical multiplier for the pair （A, B） with Wα∈M（Bα×A） for all α∈G. The image of W in M（D^π×D^π）is a π-quasitriangular structure over D^π.
文摘?-(2-methylthio -4 -methyl -5 -pyrimidinyl)-2. 4 - pentadiyn- 1 -ol- (4- N. N-dimethylamino-azobenzene -4' -sulfonate) (PDABS - 1 ). ②5 -(2 -methylthio -4 -methyl -5-pyrimidinyl)- 2.4 -pentadiyn- 1 -ol - (azobenzene - 4 -sulfonate) (PDABS -2 ). ③2. 4 -hexadiyn - 1 -ol-6- (4 - N, N-dimethylamino-azobenzene-4'-sulfonate) (HDABS - 1 ), ④2. 4 -hexadiyn - 1-ol -6 - (azobenzene4-sulfonate) (HDABS-2), the four new compounds are synthesize. The structures of the new compounds have been demonstrdted by elemental analysis. IR(KBr). 1H-NMR (CD3CO/TMS),MS. Their X(3), d33. βμ and the fabrication of their polarization orientated thin film also have ben reported in this paper.
基金Projects(50731002,50971136)supported by the National Natural Science Foundation of China
文摘An isothermal section of the Mg-Nd-Gd ternary system at 723 K was established by diffusion triple technique and electron probe microanalysis （EPMA）. Mg3Gd and Mg3Nd form a continuous solid solution （Gd,Nd）3Mg, and a continuous solid solution （Gd,Nd）Mg is also formed between MgGd and MgNd. Mg7Gd, Mg5Gd, Mg2Gd, Mg41Nd5, （Gd,Nd）3Mg and （Gd,Nd）Mg are found in the ternary system. In these intermetallic phases, Mg7Gd has been reported to be a metastable phase in previous literatures. The solubilities of Mg, Gd and Nd in all the phases were detected. Furthermore, four three-phase equilibria, α（Mg）＋Mg7Gd＋Mg41Nd5, Mg7Gd＋Mg5Gd＋Mg41Nd5, Mg5Gd＋Mg41Nd5＋（Gd,Nd）3Mg and （Gd,Nd）3Mg＋（Gd,Nd）Mg＋Mg2Gd, were identified in the isothermal section.
基金Project(51171210)supported by the National Natural Science Foundation of ChinaProject(2014CB6644002)supported by the Major State Basic Research Development Program of China
文摘Through alloy sampling combined with diffusion triple technique, phase equilibria in Al-Ti-Zr ternary system at 1073 Kwere experimentally determined with electron probe microanalysis （EPMA）. Experimental results show that there is a solid solutionβ（Ti,Zr） which dissolves Al up to 16.3% （mole fraction）. Ti and Zr can substitute each other in most Ti-Al and Al-Zr binaryintermediate phases to a certain degree while the maximum solubility of Zr in Ti3Al and TiAl reaches up to 17.9% and 4.0% （molefraction）, respectively. The isothermal section consists of 16 single-phased regions, 27 two-phased regions and 14 three-phasedregions. No ternary phase was detected.
基金Project(2016YFB0701404)supported by the National Key Research and Development Program of ChinaProject(51171210)supported by the National Natural Science Foundation of China
文摘Phase equilibria in Ti?Ni?Pt ternary system have been experimentally determined through diffusion triple technique combined with alloy samples approach.Assisted with electron probe microanalysis(EPMA)and X-ray diffraction(XRD)techniques,isothermal sections at 1073 and 1173 K of this system were constructed and existence of ternary phase Ti2(Ni,Pt)3 was confirmed.In addition,binary compounds Ti3Pt5 and TiPt3-were found to be stable at 1073 and 1173 K,and remarkable ternary solubility in some binary compounds was detected,e.g.,solubility of Pt in TiNi can be up to about 36%(molar fraction)at 1073 K and 40%(molar fraction)at 1173 K.Furthermore,a ternary invariant transition reaction TiNi3+Ti3Pt5→Ti2(Ni,Pt)3+TiPt3+at a temperature between 1073 and 1173 K was deduced.
文摘Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.
