Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

Experimental and Theoretical Structure Elucidation of the [2 : 1] Complex Ion of Carbo[n]helicene with n=6, 7 and 8 and Ag+

Gas-phase complexes of [n]helicenes with n=6, 7 and 8 and the silver(I) cation are generated utilizing electrospray ionization mass spectrometry (ESI-MS). Besides the well-established [1 : 1] helicene/Ag⁺-complex in which the helicene provides a tweezer-like surrounding for the Ag⁺, there is also a [2 : 1] complex formed. Density functional theory (DFT) calculations in conjunction with energy-resolved collision-induced dissociation (ER-CID) experiments reveal that the second helicene attaches via π-π stacking to the first helicene, which is part of the pre-formed [1 : 1] tweezer complex with Ag⁺. For polycyclic aromatic hydrocarbons (PAHs) of planar structure, the [2 : 1] complex with silver(I) is typically structured as an Ag⁺-bound dimer in which the Ag⁺ would bind to both PAHs as the central metal ion (PAH–Ag⁺–PAH). For helicenes, the Ag⁺-bound dimer is of similar thermochemical stability as the π-π stacked dimer, however, it is kinetically inaccessible. Coronene (Cor) is investigated in comparison to the helicenes as an essentially planar PAH. In analogy to the π-π stacked dimer of the helicenes, the Cor−Ag⁺−Cor−Cor complex is also observed. Competition experiments using [n]helicene mixtures reveal that the tweezer complexes of Ag⁺ are preferably formed with the larger helicenes, with n=6 being entirely ignored as the host for Ag⁺ in the presence of n=7 or 8.     

New Polyurethane/Docosane Microcapsules as Phase‐Change Materials for Thermal Energy Storage

Polyurethane microcapsules were prepared by mini‐emulsion interfacial polymerization for encapsulation of phase‐change material (n‐docosane) for energy storage. Three steps were followed with the aim to optimize synthesis conditions of the microcapsules. First, polyurethane microcapsules based on silicone oil core as an inert template with different silicone oil/poly(ethylene glycol)/4,4′‐diphenylmethane diisocyanate wt % ratio were synthesized. The surface morphology of the capsules was analyzed by scanning electronic microscopy (SEM) and the chemical nature of the shell was monitored by Fourier transform infrared spectroscopy (FT‐IR). Capsules with the silicone oil/poly(ethylene glycol)/4,4′‐diphenylmethane diisocyanate 10/20/20 wt % ratio showed the best morphological features and shell stability with average particle size about 4 μm, and were selected for the microencapsulation of the n‐docosane. In the second stage, half of the composition of silicone oil was replaced with n‐docosane and, finally, the whole silicone oil content was replaced with docosane following the same synthetic procedure used for silicone oil containing capsules. Thermal and cycling stability of the capsules were investigated by thermal gravimetric analysis (TGA) and the phase‐change behavior was evaluated by differential scanning calorimetry (DSC).     

Ortho‐Quinone Methides as Reactive Intermediates in Asymmetric Brønsted Acid Catalyzed Cycloadditions with Unactivated Alkenes by Exclusive Activation of the Electrophile

An efficient method for the highly enantioselective synthesis of chiral chromanes bearing multiple stereogenic centers was developed. A chiral BINOL‐based N‐triflylphosphoramide proved to be an effective catalyst for the in situ generation of ortho‐quinone methides (o‐QMs) and their subsequent cycloaddition reaction with unactivated alkenes provided chromanes with excellent diastereo‐ and enantioselectivity.     

Synthesis of Ag nanoparticles for the electrochemical detection of anticancer drug flutamide

Ag nanoparticles were synthesized on the surface of a glassy carbon electrode modified with p‐tert‐butylcalix[4]arene and p‐tert‐butylcalix[6]arene by the deposition of Ag+at an open circuit potential ...