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Daftardar-Jafari Method for Fractional Heat-like and wave-like Equations with Variable Coefficients

Applied Mathematics 2017年第2期8卷 215-228页

作者： Waleed Al-Hayani Department of Mathematics College of Computer Science and Mathematics University of Mosul Iraq

In this paper, Daftardar-Gejji and Jafari method is applied to solve fractional heat-like and wave-like models with variable coefficients. The method is proved for a variety of problems in one, two and three dimensional spaces where analytical approximate solutions are obtained. The examples are presented to show the efficiency and simplicity of this method.

关键词： Daftardar-Jafari Method Heat-like Equations wave-like Equations Fractional Calculus

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Mixed-solvothermal Synthesis, Crystal Structure and Luminescence of a New Dinuclear Yttrium(III) Coordination Polymer with 1-D wave-like Infinite Chains

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结构化学 2018年第5期

作者：冯玉全姜兰婷邢正正王璐 College of Chemistry and Pharmacy Engineering Nanyang Normal University

A new dinuclear Y3+coordination polymer{[Y2(H2O)2(C14H8O4)3(C12H8N2)2]·3H2O}n(1, C14H8O4= 2,2΄-biphenyldicarboxylate, phen = 1,10-phenanthroline), has been obtained by means of a mixed-solvothermal method using ethylene glycol and water as solvent. The compound was characterized by elemental analysis, energy-dispersive X-ray spectroscopy (EDS), IR spectrum and single-crystal X-ray diffraction. The results reveal that 1 belongs to monoclinic system, space groupC2/cwitha= 24.249(3),b= 12.069(48),c= 22.7304(08) Å,β= 113.480(7)°,Z= 4,V= 6102(2) Å3,Dc= 1.462 g∙cm-3,F(000) = 2728,μ= 1.968 mm-1, the finalR= 0.0673,wR= 0.1508 andS= 1.085. Its structure can be regarded as a 1-Dcoordination polymer constructed by Y3+cations, 2,2΄-biphenyldicarboxylate, 1,10-phenanthroline and water molecules. The compound not only contains two kinds of organic ligands, but also exhibits interesting wave-like infinite chains and 18-MR windows with the diameter of 4.070(7)Å × 5.326(9)Å. The structure is further stabilized by means of O–H···O hydrogen bonds andπ-πstacking interactions. Furthermore, the luminescent properties (including emission spectrum, CIE chromaticity coordinate and decay curve) of 1 were also investigated in the solid-state at room temperature.

关键词： mixed-solvothermal synthesis,dinuclear Y3+coordination polymer, wave-like infinite chains,luminescent properties

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