Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Path to achieving molecular dispersion in a dense reactive mixture

A uniform dispersion of reactants is necessary to achieve a complete reaction involving multicomponents. In this study, we have examined the role of plasticizer in the reaction of two seemingly unlikely reactants: a highly crystalline hexamethylenetetramine (HMTA) and a strongly hydrogen bonded phenol formaldehyde resin. By combining information from NMR, infrared spectroscopy and differential scanning calorimetry, we were able to determine the role of specific intermolecular interactions necessary for the plasticizer to dissolve the highly crystalline HMTA and to plasticize the phenol formaldehyde resin in this crosslinking reaction. The presence of the plasticizer increased the segmental mobility, disrupted the hydrogen bonded matrix, and freed the hydroxyl units, which further increased the solubility of the HMTA. Both the endothermic and exothermic transitions are accounted for in the calorimetric data obtained. For the first time, it is possible to obtain the effective molar ratio of each component needed to complete the crosslinking reaction efficiently. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1519–1526     

Identifying anomalous Floquet edge modes via bulk-edge correspondence

Floquet engineering appears as a new protocol for designing topological states of matter,and features anomalous edge modes pinned at quasi-energy π/T with vanished topological index.We propose how to predict the anomalous edge modes via the bulk Hamiltonian in frequency space,and use Zak phase to quantitatively index the topological properties.The above methods are clarified by the example of time periodic Kitaev chain with chemical potential of harmonic driving and pulse driving,and topological phase transitions are manifested at different driving frequencies.     

Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation ■ where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_0)~tφ(x) and show T_(t_0)~tφ(x) converges uniformly to a time-periodic viscosity solution u~*(x,t) of ?_tu+H(t,x,?_xu,u)=0.     

DFT mechanistic study of the H2‐assisted chain transfer copolymerization of propylene and p‐methylstyrene catalyzed by zirconocene complex

DFT computations have been performed to investigate the mechanism of H₂‐assisted chain transfer strategy to functionalize polypropylene via Zr‐catalyzed copolymerization of propylene and p‐methylstyrene (pMS). The study unveils the following: (i) propylene prefers 1,2‐insertion over 2,1‐insertion both kinetically and thermodynamically, explaining the observed 1,2‐insertion regioselectivity for propylene insertion. (ii) The 2,1‐inserion of pMS is kinetically less favorable but thermodynamically more favorable than 1,2‐insertion. The observation of 2,1‐insertion pMS at the end of polymer chain is due to thermodynamic control and that the barrier difference between the two insertion modes become smaller as the chain length becomes longer. (iii) The pMS insertion results in much higher barriers for subsequent either propylene or pMS insertion, which causes deactivation of the catalytic system. (iv) Small H₂ can react with the deactivated [Zr]?pMS?PP_n facilely, which displace functionalized pMS?PP_n chain and regenerate [Zr]? H active catalyst to continue copolymerization. The effects of counterions are also discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 576–585     

Flame-retardant effect of cross-linked phosphazene derivatives and pentaerythritol derivatives on polypropylene

Journal of Thermal Analysis and Calorimetry - A phosphazene-based flame retardant (PBFA) was synthesized by hexachlorocyclotriphosphazene and N-aminoethylpiperazine. To improve the flame retardancy...     

A Photoactivated Cu–CeO2 Catalyst with Cu-[O]-Ce Active Species Designed through MOF Crystal Engineering

Fully utilizing solar energy for catalysis requires the integration of conversion mechanisms and therefore delicate design of catalyst structures and active species. Herein, a MOF crystal engineering method was developed to controllably synthesize a copper–ceria catalyst with well-dispersed photoactive Cu-[O]-Ce species. Using the preferential oxidation of CO as a model reaction, the catalyst showed remarkably efficient and stable photoactivated catalysis, which found practical application in feed gas treatment for fuel cell gas supply. The coexistence of photochemistry and thermochemistry effects contributes to the high efficiency. Our results demonstrate a catalyst design approach with atomic or molecular precision and a combinatorial photoactivation strategy for solar energy conversion.