Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.     

pH-Dependent Slipping and Exfoliation of Layered Covalent Organic Framework

Layered/two-dimensional covalent organic frameworks (2D COF) are crystalline porous materials composed of light elements linked by strong covalent bonds. Interlayer force is one of the main factors directing the formation of a stacked layer structure, which plays a vital role in the stability, crystallinity, and porosity of layered COFs. The as-developed new way to modulate the interlayer force of imine-linked 2D TAPB-PDA-COF (TAPB = 1,3,5-tris(4-aminophenyl)benzene, PDA = terephthaldehyde) by only adjusting the pH of the solution. At alkaline and neutral pH, the pore size of the COF decreases from 34 Å due to the turbostratic effect. Under highly acidic conditions (pH 1), TAPB-PDA-COF shows a faster and stronger turbostratic effect, thus causing the 2D structure to exfoliate. This yields bulk quantities of an exfoliated few/single-layer 2D COF, which was well dispersed and displayed a clear Tyndall effect (TE). Furthermore, nanopipette-based electrochemical testing also confirms the slipping of layers with increase towards acidic pH. A model of pH-dependent layer slipping of TAPB-PDA-COF was proposed. This controllable pH-dependent change in the layer structure may open a new door for potential applications in controlled gas adsorption/desorption and drug loading/releasing.     

Tracking the atomic pathways of Pt3Ni-Ni(OH)2 core-shell structures at the gas-liquid interface by in-situ liquid cell TEM

Using the in-situ liquid cell transmission electron microscopy, the three-stage growth of Pt_3Ni-Ni(OH)_2 core-shell structures at the gas-liquid interfaces was clearly observed, which consists of(1) a thermodynamically driven Pt_3Ni alloy core by the monomer attachment,(2) a nickel(Ni) shell formation due to the depletion of the Pt salt precursor, and(3) the oxidation and of the Ni shell into Ni(OH)_2 flakes. We also further observed the nucleation and growth of the Ni(OH)_2 flakes on an existing layer either at the middle part or at the step edge. More interestingly, the dynamic transformation among a Pt_3Ni alloy, Ni clusters and Ni(OH)_2 flakes was also imaged even at a high electron dose rate.     

Parameterized inverse singular value problem for anti-bisymmetric matrices

In this paper, the singular value decompositions of anti-symmetric matrices and anti-bisymmetric matrices are presented, and a class of parameterized inverse singular value problem for anti-bisymmetric matrices is solved. Numerical examples which confirm our theory are presented.     

Preparation of 4-sulfonylcalix[6]arene modified Fe<Subscript>3</Subscript>O<Subscript>4</Subscript> as adsorbent for adsorption of U(VI) from aqueous solution

The 4-sulfonylcalix[6]arene modified Fe₃O₄ (MFS) was characterized by FT-IR, SEM, VSM, TGA, etc., which showed that its saturation magnetization was 64.99 emu g^?1 with the particle size 10–40 nm. The maximum adsorption efficiency by MFS for 2.5 mg L^?1 U(VI) solution amounted to 94.39%, which was higher than that by Fe₃O₄ (65.22%) under its optimum adsorption conditions. The adsorption of MFS and Fe₃O₄ were both followed the pseudo-second order model and the Langmuir isotherm model. The Gibbs free energy change and enthalpy change revealed that the adsorption of U(VI) by MFS was a spontaneous and endothermic process.     

Optical pulse shaper with integrated slab waveguide for arbitrary waveform generation using optical gradient force

Integrated optical pulse shaper opens up possibilities for realizing the ultra high-speed and ultra wide-band linear signal processing with compact size and low power consumption. We propose a silicon monolithic integrated optical pulse shaper using optical gradient force, which is based on the eight-path finite impulse response. A cantilever structure is fabricated in one arm of the Mach–Zehnder interferometer（MZI） to act as an amplitude modulator. The phase shift feature of waveguide is analyzed with the optical pump power, and five typical waveforms are demonstrated with the manipulation of optical force. Unlike other pulse shaper schemes based on thermo–optic effect or electro–optic effect, our scheme is based on a new degree of freedom manipulation, i.e., optical force, so no microelectrodes are required on the silicon chip,which can reduce the complexity of fabrication. Besides, the chip structure is suitable for commercial silicon on an insulator（SOI） wafer, which has a top silicon layer of about 220 nm in thickness.     

α‐Diamine Nickel Catalysts with Nonplanar Chelate Rings for Ethylene Polymerization

A series of novel α‐diamine nickel complexes, (ArNH‐C(Me)‐(Me)C‐NHAr)NiBr₂, 1 : Ar=2,6‐diisopropylphenyl, 2 : Ar=2,6‐dimethylphenyl, 3 : Ar=phenyl), have been synthesized and characterized. X‐ray crystallographic analysis showed that the coordination geometry of the α‐diamine nickel complexes is markedly different from conventional α‐diimine nickel complexes, and that the chelate ring (N‐C‐C‐N‐Ni) of the α‐diamine nickel complex is significantly distorted. The α‐diamine nickel catalysts also display different steric effects on ethylene polymerization in comparison to the α‐diimine nickel catalyst. Increasing the steric hindrance of the α‐diamine ligand by substitution of the o‐methyl groups with o‐isopropyl groups leads to decreased polymerization activity and molecular weight; however, catalyst thermal stability is significantly enhanced. Living polymerizations of ethylene can be successfully achieved using 1 /Et₂AlCl at 35 °C or 2 /Et₂AlCl at 0 °C. The bulky α‐diamine nickel catalyst 1 with isopropyl substituents can additionally be used to control the branching topology of the obtained polyethylene at the same level of branching density by tuning the reaction temperature and ethylene pressure.     

Terpenoids from Loxocalyx urticifolius

Two new diterpenoids, loxocalyxin A ( 1 ) and 13‐epiloxocalyxin A ( 2 ), and two new sesquiterpenoids, loxocalyxins B and C ( 3 and 4 , resp.), together with three known compounds, were isolated from the MeOH extract of the whole plant of Loxocalyx urticifolius Hemsl . The structures of the new compounds were established by means of spectroscopic analysis including one‐ and two‐dimensional NMR spectroscopy. All new structures were confirmed by X‐ray crystallographic analysis. Their absolute configurations were established.