Uniqueness for an overdetermined boundary value problem for the p-Laplacian

For set , and let be a measure with compact support. Suppose, for , there are functions and (bounded) domains , both containing the support of with the property that in (weakly) and in the complement of . If in addition is convex, then and .

     

Effect of annealing treatment on the magnetic properties of mechanochemical synthesized La0.8Pb0.2MnO3 manganites

In this paper, we have investigated the effect of annealing on structural and magnetic properties of La_0.8Pb_0.2MnO₃ (LPMO) polycrystalline samples. Mechanochemical procedure has been used to produce LPMO nanocrystalline samples from oxide precursors. From the AC susceptibility measurements we found that the magnitude of susceptibility increases and the paramagnetic–ferromagnetic (PM–FM) transition width decreases by annealing the ball milled powders. Also, reentrant spin glass (RSG) behavior has been found in high temperature annealed samples. It seems that, due to the evaporation of PbO in high temperature annealed samples, vacancies created in perovskite structure and portion of the Mn³⁺–O–Mn⁴⁺ network is broken. So the FM double-exchange interaction is weakened due to the magnetic dilution and the antiferromagnetc (AFM) phase fraction increases in high temperature annealed samples. The competition between FM double-exchange interaction and AFM super-exchange interaction produces spin frustration and is responsible for the occurrence of RSG.     

1-(对甲苯基)-2-(三对甲苯基-5-亚磷酰基)乙醛的汞(Ⅱ)配合物的X射线晶体学、光谱表征和理论计算研究

通过2-溴-1-（对甲苯基）乙醛与三（对甲苯基）膦的反应制备α-磷配体：1-（对甲苯基）-2-（三对甲苯基-5-亚磷酰基）乙醛（L）。氯化镉和溴化汞与L分别反应,生成配合物[Cd（L）Cl₂]₂（C1）和[Hg（L）（μ₂-Br）Br]₂（C2）。用IR和NMR（¹H,¹³C,³¹P）对配合物进行了表征。通过单晶X射线衍射测定了C2的结构,并在B3LYP/6-31G^*水平对C2的结构进行了DFT计算研究,以揭示C2的复合反应位点与Schiff碱等亲核基团的相互作用。     

Synthesis of magnetically modified mesoporous nanoparticles and their application in simultaneous determination of Pb(II), Cd(II) and Cu(II)

In this study, a novel adsorbent from a mesoporous family (MCM-41) coating with CoFe₂O₄ and piperazine was synthesized by a simple and easy route. Its application for simultaneous preconcentration of three heavy metals including lead, cadmium and copper in real samples followed by a flame atomic absorption spectroscopy was investigated. The central composite design was employed for investigating the most effective factors of pH, amount of adsorbent, the equilibrium time and their interactions. Under the optimum conditions, the detection limits for lead, cadmium and copper were 0.50, 0.30 and 0.25 μg L^?1, respectively, and the preconcentration factor (PF) was 33. The presented method was successfully employed for the simultaneous determination of the three mentioned heavy metals in real samples with recoveries of 90%–105%. The accuracy of the suggested methods was also investigated through spiking samples and a reasonable range for recoveries from 90.3% to 107% was acquired. The isotherm models and thermodynamic parameters have also been studied. The new adsorbent showed fast adsorption kinetics within 10 min and maximum Langmuir monolayer capacities of 238.09, 178.57 and 208.33 mg g^?1 for lead, cadmium and copper, respectively.     

High‐Efficiency Perovskite Solar Cells Enabled by Anatase TiO2 Nanopyramid Arrays with an Oriented Electric Field

One‐dimensional (1D) nanostructured oxides are proposed as excellent electron transport materials (ETMs) for perovskite solar cells (PSCs); however, experimental evidence is lacking. A facile hydrothermal approach was employed to grow highly oriented anatase TiO₂ nanopyramid arrays and demonstrate their application in PSCs. The oriented TiO₂ nanopyramid arrays afford sufficient contact area for electron extraction and increase light transmission. Moreover, the nanopyramid array/perovskite system exhibits an oriented electric field that can increase charge separation and accelerate charge transport, thereby suppressing charge recombination. The anatase TiO₂ nanopyramid array‐based PSCs deliver a champion power conversion efficiency of approximately 22.5 %, which is the highest power conversion efficiency reported to date for PSCs consisting of 1D ETMs. This work demonstrates that the rational design of 1D ETMs can achieve PSCs that perform as well as typical mesoscopic and planar PSCs.     

An ultra compact photonic crystal wavelength division demultiplexer using resonance cavities in a modified Y-branch structure

An ultra small size 4-channel wavelength division demultiplexer based on 2D photonic crystal modified Y-Branch, suitable for integration, is proposed in this paper. The output wavelengths of designed structure can be tuned for communication applications (around 1550 nm) by choosing suitable defect parameters in the corner of each resonance cavity and output waveguides. The cross section of the structure is 313.28 μm² (17.8 μm × 17.6 μm) and desirable for integration based on popular planar technology. The bandwidth of each channel is near to 1 nm and the channel spacing is approximately 3.5 nm and wavelengths of demultiplexer channels are 1548.8 nm, 1551.9 nm, 1555.4 nm and 1559.3 nm respectively. Also, the crosstalk is between −33.1855 dB and −10.4947 dB. Furthermore, the mean values of the crosstalk and quality factor are −22.54 dB and 1496.7 respectively.     

Existence of an extremal ground state energy of a nanostructured quantum dot

This paper is concerned with two rearrangement optimization problems. These problems are motivated by two eigenvalue problems which depend nonlinearly on the eigenvalues. We consider a rational and a quadratic eigenvalue problem with Dirichlet’s boundary condition and investigate two related optimization problems where the goal function is the corresponding first eigenvalue. The first eigenvalue in the rational eigenvalue problem represents the ground state energy of a nanostructured quantum dot. In both the problems, the admissible set is a rearrangement class of a given function.     

Rapid and Convenient Method for the Synthesis of Symmetrical Disulfides

Abstract

We present here the results on the use of 1,3,5-triazo-2,4,6-triphosphorine-2,2,4,4,6,6-hexachloride as an efficient promoter in the conversion of thiols to the corresponding symmetrical disulfides under solvent-free conditions. Aromatic thiols bearing electron donating and electron withdrawing groups, heteroaromatic, and alkyl thiols reacted efficiently to afford excellent yields of disulfides in short reaction times after easy work-up. Different functional groups including carboxyl, methoxy, methylthio, and halogen are tolerated.

Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfer, and Silicon and the Related Elements for the following free supplemental files: Additional figures and tables.     

1-(对甲苯基)-2-(三对甲苯基-5-亚磷酰基)乙醛的汞(Ⅱ)配合物的X射线晶体学、光谱表征和理论计算研究（英文）

通过2-溴-1-(对甲苯基)乙醛与三(对甲苯基)膦的反应制备α-磷配体:1-(对甲苯基)-2-(三对甲苯基-5-亚磷酰基)乙醛(L)。氯化镉和溴化汞与L分别反应,生成配合物[Cd(L)Cl_2]_2(C1)和[Hg(L)(μ_2-Br)Br]_2(C2)。用IR和NMR(~1H,~(13)C,~(31)P)对配合物进行了表征。通过单晶X射线衍射测定了C2的结构,并在B3LYP/6-31G~*水平对C2的结构进行了DFT计算研究,以揭示C2的复合反应位点与Schiff碱等亲核基团的相互作用。