An inverse problem of identifying the coefficient of parabolic equation

This paper studies an inverse problem of identifying the coefficient of parabolic equation when the final observation is given, which has important application in a large fields of applied science. Based on the optimal control framework, the existence and necessary condition of the minimum for the control functional are established. Since the optimal control problem is nonconvex, one may not expect a unique solution. However, in this paper the solution is proved to be locally unique. After the necessary condition is transformed into an elliptic bilateral variational inequality, an algorithm and some numerical experiments are proposed in the paper. The numerical results show that the algorithm designed in this paper is stable and that the coefficient is recovered very well.     

Nonlinear dynamical stability of gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice

We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice. Honeycomb lattices possess a unique band structure, the first and second bands intersect at a set of so-called Dirac points. Deformation can result in the merging and disappearance of the Dirac points, and support the gap solitons. We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures being in-phase or out-of-phase. We also investigate the linear stabilities and nonlinear stabilities of these gap solitons. These results have applications of the localized structures in nonlinear optics, and may helpful for exploiting topological properties of a deformed lattice.     

Discharge characteristic of very high frequency capacitively coupled argon plasma

The discharge characteristics of capacitively coupled argon plasmas driven by very high frequency discharge are studied. The mean electron temperature and electron density are calculated by using the Ar spectral lines at different values of power(20 W–70 W) and four different frequencies(13.56 MHz, 40.68 MHz, 94.92 MHz, and 100 MHz). The mean electron temperature decreases with the increase of power at a fixed frequency. The mean electron temperature varies nonlinearly with frequency increasing at constant power. At 40.68 MHz, the mean electron temperature is the largest. The electron density increases with the increase of power at a fixed frequency. In the cases of driving frequencies of 94.92 MHz and 100 MHz, the obtained electron temperatures are almost the same, so are the electron densities. Particle-in-cell/MonteCarlo collision(PIC/MCC) method developed within the Vsim 8.0 simulation package is used to simulate the electron density, the potential distribution, and the electron energy probability function(EEPF) under the experimental condition.The sheath width increases with the power increasing. The EEPF of 13.56 MHz and 40.68 MHz are both bi-Maxwellian with a large population of low-energy electrons. The EEPF of 94.92 MHz and 100 MHz are almost the same and both are nearly Maxwellian.     

Electrocatalytic oxidation of methanol at platinum electrode modified with Eu-Fe cyanide-bridged binuclear complexes

<正>The electrocatalytic oxidation of methanol at the platinum electrode modified with Eu-Fe cyanide-bridged binuclear complexes (Eu-Fe film) was investigated for the first time by cyclic voltammetry.Compared with the bare platinum electrode,the results showed that the modified electrode had excellent electrocatalytic activity for the oxidation of methanol;the oxidation peak potential shifted more negatively and the peak current increased about twenty times.The electrooxidation of methanol at the modified electrode with Eu-Fe cyanide-bridged binuclear complexes material exhibited the better tolerance capacity to poison of intermediate species;the peak current was proportional to the concentration of methanol in the range of 0.5-2.0mol/L (R~2 = 0.9991,n =7),which was a comparatively wider linear range.Moreover,based on the linear relationship between the peak current and the square root of scan rate,electrocatalytic oxidation process of methanol was confirmed to be a diffusion control process.Furthermore,according to the counting of electron transfer number(n_α) in the rate-limiting step and the slope of linear equation between acidity of electrolyte and the oxidation peak potential(E_p),the possible mechanism of the electrooxidation of methanol at the modified electrode was primarily discussed.     

One-pot three-component synthesis of α-aminonitriles using potassium hexacyanoferrate(II) as an eco-friendly cyanide source

An efficient and environmentally friendly method has been developed for the synthesis of α-aminonitriles via one-pot three-component condensation of carbonyl compounds, amines, and potassium hexacyanoferrate(II) in the presence of benzoyl chloride as a promoter. This protocol has the features of use of eco-friendly cyanide source, high yield, and simple work-up procedure.     

The electrochemical reduction reaction of dissolved oxygen on Q235 carbon steel in alkaline solution containing chloride ions

Cyclic voltammetry, electrochemical impedance spectroscopy, and rotating disk electrode voltammetry have been used to study the effect of chloride ions on the dissolved oxygen reduction reaction (ORR) on Q235 carbon steel electrode in a 0.02 M calcium hydroxide (Ca(OH)₂) solutions imitating the liquid phase in concrete pores. The results indicate that the cathodic process on Q235 carbon steel electrode in oxygen-saturated 0.02 M Ca(OH)₂ with different concentrations of chloride ions contain three reactions except hydrogen evolution: dissolved oxygen reduction, the reduction of Fe(III) to Fe(II), and then the reduction of Fe(II) to Fe. The peak potential of ORR shifts to the positive direction as the chloride ion concentration increases. The oxygen molecule adsorption can be inhibited by the chloride ion adsorption, and the rate of ORR decreases as the concentration of chloride ions increases. The mechanism of ORR is changed from 2e⁻ and 4e⁻ reactions, occurring simultaneously, to quietly 4e⁻ reaction with the increasing chloride ion concentration.     

Synthesis,crystal structures and photoluminescence of 7-(N,N′-diethylamino)-3-phenylcoumarin derivatives

Two new coumarin derivatives, 7-(N,N′-diethylamino)-3-(4-hydroxyphenyl)-coumarin and 7-(N,N′-diethylamino)-3-(4-bromophenyl)-coumarin, were synthesized successfully. Their structures were verified by single crystal X-ray crystallography. The UV–vis absorption and fluorescence of the compounds were discussed. The compounds exhibit strong blue emission under ultraviolet light excitation. The molecular structures, the lowest energy transitions and the UV–vis spectra of 7-(N,N′-diethylamino)-3-(4-hydroxyphenyl)-coumarin and 7-(N,N′-diethylamino)-3-(4-bromophenyl)-coumarin have been studied with density functional theory (DFT) and time-dependent density functional theory (TD-DFT) at B3LYP/6-31G(d) level.     

Ionization potentials, electron affinities, resonance excitation energies, oscillator strengths, and ionic radii of element Uus (Z = 117) and astatine

Multiconfiguration Dirac-Fock (MCDF) method was employed to calculate the first five ionization potentials, electron affinities, resonance excitation energies, oscillator strengths, and radii for the element Uus and its homologue At. Main valence correlation effects were taken into account. The Breit interaction and QED effects were also estimated. The uncertainties of calculated IPs, EAs, and IR for Uus and At were reduced through an extrapolation procedure. The good consistency with available experimental and other theoretical values demonstrates the validity of the present results. These theoretical data therefore can be used to predict some unknown physicochemical properties of element Uus, Astatine, and their compounds.     

聚对苯二甲酰对苯二胺纤维的热老化行为与机理研究

在250～400℃空气中对自由状态下对位芳纶进行等温热老化处理,采用万能材料试验机、红外光谱法、广角X射线衍射法、声速法和特性黏数法表征了老化过程中力学性能和结构的变化.结果表明,在老化初期,由于分子链的解取向,强度随时间快速下降;随后的热分解使强度随老化时间继续降低,符合二级反应动力学模型,其热老化表观活化能为32.4kJ/mol.老化样品的强度随温度升高显著下降,但高于350℃时热交联反应变得明显,同时结晶度增大和结晶结构完善,使强度的损失速率减小.老化样品的模量随老化温度的升高而增大,低于350℃时,非晶态分子链的解取向占优,模量较未热老化样品低;升高至350℃时,结晶结构完善占优,表现在第二类晶格畸变参数降低、表观微晶尺寸增大,特别是微晶横向融合使a,b轴方向尺寸显著增大,模量明显高于未老化样品.