Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity

Using some nonlinear domain decomposition method, we prove the existence of branches of solutions having singular limits for some 4-dimensional semilinear elliptic problem with exponential nonlinearity.     

Integrability of det△↓u and Evolutionary Wente＇s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Structure,Thermal Behavior and Characterization of a New Hybrid Iron Fluoride FeF4(2,2'-bipyridine)(H2O)2

New crystal of FeF₄(2,2'-bipyridine)(H₂O)₂ was prepared by hydrothermal synthesis. Crystalline structure determination is performed from single crystal X-ray diffraction data. The unit cell is monoclinic space group P2₁/n, with cell parameters a=0.9046(5) nm, b=0.7502(5) nm, c=1.9539(5) nm, β=93.307(5)°, V=1.3238(12) nm³ and Z=4. The structure of FeF₄(2,2'-bipyridine)(H₂O)₂ is built up from FeF₄N₂ octahedra coordinated by two nitrogen atoms of the 2,2'-bipyridine molecules, and four fluorine atoms as well as uncoordinated H₂O molecules. Thermal analysis of the title compound showed that the decomposition introduced four steps. IR spectra confirmed the presence of 2,2'-bipyridine molecules. The optical absorption was measured at the corresponding l_max using UV-Vis diffuse reflectance spectrum.     

Integrability of det▽u and Evolutionary Wente's Problem Associated to Heat Operator

In this note,the authors resolve an evolutionary Wente's problem associated to heat equation,where the special integrability of det▽u for u∈H~1(R~2,R~2)is used.     

Synthesis,Structural Study and Phase Transitions Characterization by Thermal Analysis and Vibrational Spectroscopy of an Ammonium Rubidium Arsenate Tellurate

The Rb_2.42(NH₄)_0.58(HAsO₄)(H₂AsO4)·Te(OH)₆ crystals(denoted by RbNAsTe) crystallize in the monoclinic system, space group P2₁/n with the following parameters:a=1.3059(5) nm, b=0.6755(3) nm, c=1.6675(6) nm, β=94.126(4)°, Z=4 and V=1.46733(10) nm³. Thermal analyses(DSC, DTA and TG) confirm the presence of the phase transition and the temperature of the decomposition. The vibrational spectroscopy study at room temperature show the presence and the independence of anionic groups, cationic groups, and give more importance to the hydrogen bonds. Raman spectra were recorded in the temperature range of 298-503 K. The temperature dependence of the Raman line shift, intensity reduction and the half width detects the phase transitions and confirms their nature. So, the phase transition at 453 K corresponds to the superprotonic-ionic conduction phase transition, and those at 483 and 491 K correspond to the decomposition of our material.