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Extension of phase-isometries between the unit spheres of atomic $L_p$-spaces for $p>0$
Xujian Huang,Xihong Jin 대한수학회 2019 대한수학회보 Vol.56 No.6
In this paper, we prove that for every surjective phase-iso\-metry between the unit spheres of real atomic $L_p$-spaces for $p>0$, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.
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EXTENSION OF PHASE-ISOMETRIES BETWEEN THE UNIT SPHERES OF ATOMIC L<sub>p</sub>-SPACES FOR p > 0
Huang, Xujian,Jin, Xihong Korean Mathematical Society 2019 대한수학회보 Vol.56 No.6
In this paper, we prove that for every surjective phase-isometry between the unit spheres of real atomic $L_p$-spaces for p > 0, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.
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Xu, Jian,Cao, Lei,Feng, Yongyi,Huang, Yanlin,Wang, Yaorong,Qin, Lin,Seo, Hyo Jin Elsevier 2017 Journal of luminescence Vol.183 No.-
<P><B>Abstract</B></P> <P>In<SUB>2</SUB>Si<SUB>2</SUB>O<SUB>7</SUB> is a known indium-based scintillator with fast ultraviolet photoluminescence. Unfortunately the emission only can be detected below 200K. the poor thermal stability limits its application at room temperature. In this work, the luminescence improvement of In<SUB>2</SUB>Si<SUB>2</SUB>O<SUB>7</SUB> was realized by F<SUP>−</SUP>-ions doping in the lattices. The ceramic phosphors were via typical solid-state reaction method. The pure crystalline phase with thortveirite-type structure was confirmed by X-ray diffraction (XRD) Rietveld refinements. The photoluminescence (PL) emission and excitation spectra together with the luminescence thermal stability were tested. The fluorescence decay curves CIE emission Stokes shifts were measured. The ceramic samples could present blue luminescence with maximum wavelength at about 340nm under the excitation of UV light or high energy X-ray irradiation. The pure sample only presents luminescence below 200K, however, the F-doping can be greatly enhance the luminescence thermal stability. The F-doped In<SUB>2</SUB>Si<SUB>2</SUB>O<SUB>7</SUB> could present emission signals with fast decay lifetime of 850ns at room temperature. The luminescence transitions from the In<SUP>3+</SUP>-O<SUP>2−</SUP> charge transfer (CT) were discussed on the structure properties.</P>
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Xu, Jian,Qin, Chuanxiang,Huang, Yanlin,Wang, Yaorong,Qin, Lin,Seo, Hyo Jin Elsevier 2017 APPLIED SURFACE SCIENCE - Vol.396 No.-
<P><B>Abstract</B></P> <P>Pure and V<SUP>5+</SUP>-doped Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> (3Bi<SUB>2</SUB>O<SUB>3</SUB>·2MoO<SUB>3</SUB>) photocatalysts were synthesized through electrospinning, followed by low-temperature heat treatment. The samples developed into nanoparticles with an average size of approximately 50nm. The crystalline phases were verified via X-ray powder diffraction measurements (XRD). The surface properties of the photocatalysts were studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS) analyses. The UV–vis spectra showed that V doping in Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> shifted the optical absorption from the UV region to the visible-light wavelength region. The energy of the band gap of Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> was reduced by V doping in the lattices. The photocatalytic activities of the pure and V-doped Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> were tested through photodegradation of rhodamine B (RhB) dye solutions under visible light irradiation. Results showed that 20 mol% V-doped Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> achieved efficient photocatalytic ability. RhB could be degraded by V-doped Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> in 2h. The photocatalytic activities and mechanisms were discussed according to the characteristics of the crystal structure and the results of EIS and XPS measurements.</P> <P><B>Highlights</B></P> <P> <UL> <LI> V<SUP>5+</SUP>-doped Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> was synthesized by the electrospinning preparation. </LI> <LI> The band gap energy of Bi6Mo12O15 was greatly reduced by V-doping in the lattices. </LI> <LI> V-doped Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> shows high activity in RhB degradation under visible light. </LI> <LI> Crystal structure of Bi<SUB>6</SUB>Mo<SUB>2</SUB>O<SUB>15</SUB> is favorable for high photocatalytic capacity. </LI> </UL> </P>
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