Infinitely many solutions for a zero mass Schodinger-Poisson-Slater problem with critical growth

In this paper, we are concerned with the following Schr\"{o}dinger-Poisson-Slater problem with critical growth: $$ -\Delta u+(u^{2}\star \frac{1}{|4\pi x|})u=\mu k(x)|u|^{p-2}u+|u|^{4}u\,\,\mbox{in}\,\,\R^{3}. $$ We use a measure representation concentration-compactness principle of Lions to prove that the $(PS)_{c}$ condition holds locally. Via a truncation technique and Krasnoselskii genus theory, we further obtain infinitely many solutions for $\mu\in(0,\mu^{\ast})$ with some $\mu^{\ast}>0$.     

Stability and bifurcation analysis of a delayed predator-prey model of prey dispersal in two-patch environments

In this paper, a class of delayed predator-prey model of prey dispersal in two-patch environments is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.     

Optical properties of conjugated polymers having linear carbon moieties

Alternate conjugated copolymers consisting of phenylene or biphenylylene unit and linear carbons unit such as cumulene and polyyne were synthesized. The optical property of these polymers was investigated by UV–Vis and fluorescence spectroscopies. Among cumulene-type polymers, the polymer having allene moiety showed a unique hypsochromic shift and intense blue fluorescence in solution, while poly(phenylenebutadiynylene)s, typical of polyyne-type linear conjugated polymers, showed fluorescence in the region from blue-green to green in high efficiency besides thermotropic liquid crystalline property. Substituent effects of the polymers on optical property as well as the band structure were evaluated on the basis of Hammet parameters, which was utilized for designing of the polymers. The poly(arylenebutadiynylenes)s were applied in polymer LED. The devices consisting of ITO/PEDOT-PSS/emitting polymer/Ca/Al realized EL emissions in the region covering RGB colors.     

An amphiphilic supramolecular polymer: Construction,self-assembly and pH-responsive behavior in water

A novel amphiphilic supramolecular polymer (ASP) with rigid linear main chain has been constructed by the co-assembly of a rigid amphiphilic monomer and cucurbit[8]uril (CB[8]) in water, driven by CB[8]-based host-guest interactions. The ASP could further self-assemble into well-defined architectures including nanotubes and 2D films, depending on its concentration. Moreover, pH-responsive behavior of the ASP was also observed.     

Adsorption of thorium(IV) from aqueous solutions by poly(cyclotriphosphazene-co-4,4′-diaminodiphenyl ether) microspheres

Journal of Radioanalytical and Nuclear Chemistry - Poly(cyclotriphosphazene-co-4,4′-diaminodiphenyl ether) microspheres (PZA) was based on hexachlorocyclotriphosphazene (HCCP) and...     

Introduction of phosphate groups into metal-organic frameworks to synthesize MIL-101(Cr)-PMIDA for selective adsorption of U(VI)

Journal of Radioanalytical and Nuclear Chemistry - Metal-organic frameworks (MOFs) MIL-101(Cr)-PMIDA with phosphate groups were prepared for the adsorption of U(VI). The morphology and structure of...     

Oxidation of aromatic sulfides with molecular oxygen: Controllable synthesis of sulfoxides or sulfones

The recent development of selective oxidation of aromatic sulfides with molecular oxygen was highlighted. The sulfoxides and sulfones could be obtained by simply switching the reaction media, i.e., bis(2-butoxyethyl)ether (BBE) or poly(ethylene glycol)dimethyl ether (PEGDME). The application of the high-boiling-point polyether as an initiator and green media can eliminate the need of large quantities of additives and volatile solvents. This strategy represents an economic and eco-friendly method that could find potential applications.