Deterministic relief dielectric structures to realize phase modulation of surface-plasmon polaritons

We propose a modified effective-refractive-index model for the design of relief dielectric structures on a metal surface to realize phase modulation of surface-plasmon polaritons (SPPs). In this model, the length of the dielectric structure is optimized to reach phase shifting between the SPP waves transmitted through dielectric structure and those directly propagated with the consideration of SPP losses. Specifically, a one-dimensional dielectric Fresnel zone plate is designed by employing the proposed model to demonstrate phase modulation of SPPs for the highest focusing efficiency.     

Curved fronts in the Belousov–Zhabotinskii reaction–diffusion systems in R2

In this paper we consider a diffusion system with the Belousov–Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in ${\mathbb{R}}^2$ by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in ${\mathbb{R}}^2$.     

{Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces

Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)"(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$.     

Krasnoselskii‐type fixed point theorems with applications to Hammerstein integral equations in spaces

In this paper, we study fixed point theorems and new variants of some nonlinear altenatives of Krasnoselskii type in Banach spaces by using measures of weak noncompactness. Then we give an application to solve a nonlinear Hammerstein integral equation in L¹ spaces.     

The complete continuity properties for the positive projective tensor product of atomic Banach lattices

Let E be an atomic Banach lattice and X be a separable Banach lattice. In this paper we show that ${E \hat{\otimes}_{|\pi|} X,}$ the positive projective tensor product of E and X, has the complete continuity property (respectively, the analytic complete continuity property) if and only if both E and X have the same property. We also discuss the inheritance of type I- and type II-complete continuity properties by ${E \hat{\otimes}_{|\pi|} X}$ from E and X.     

Structure Switching and Modulation of the Magnetic Properties in Diarylethene‐Bridged Metallosupramolecular Compounds by Controlled Coordination‐Driven Self‐Assembly

We report three self‐assembled iron complexes that comprised an anti‐parallel open form (o‐ L _anti), a parallel open form (o‐ L _syn), and a closed form (c‐ L ) of diarylethene conformers. Under kinetic control, Fe^II₂(o‐ L _anti)₃ was isolated, which exhibited a dinuclear structure with diamagnetic properties. Under light‐irradiation control, Fe^II₂(c‐ L )₃ was prepared and exhibited paramagnetism and spin‐crossover behaviour. Under thermodynamic control and in the presence of indispensable [Fe^III(Tp*)(CN)₃]^?, Fe^II₂(o‐ L _anti)₃ and Fe^II₂(c‐ L )₃ transformed into tetranuclear Fe^III₂Fe^II₂(o‐ L _syn)₂, which exhibited complete spin‐crossover behaviour at T_1/2=353 K.     

Encapsulating Perovskite Quantum Dots in Iron‐Based Metal–Organic Frameworks (MOFs) for Efficient Photocatalytic CO2 Reduction

Improving the stability of lead halide perovskite quantum dots (QDs) in a system containing water is the key for their practical application in artificial photosynthesis. Herein, we encapsulate low‐cost CH₃NH₃PbI₃ (MAPbI₃) perovskite QDs in the pores of earth‐abundant Fe‐porphyrin based metal organic framework (MOF) PCN‐221(Fe_x) by a sequential deposition route, to construct a series of composite photocatalysts of MAPbI₃@PCN‐221(Fe_x) (x=0–1). Protected by the MOF the composite photocatalysts exhibit much improved stability in reaction systems containing water. The close contact of QDs to the Fe catalytic site in the MOF, allows the photogenerated electrons in the QDs to transfer rapidly the Fe catalytic sites to enhance the photocatalytic activity for CO₂ reduction. Using water as an electron source, MAPbI₃@PCN‐221(Fe_0.2) exhibits a record‐high total yield of 1559 μmol g^?1 for photocatalytic CO₂ reduction to CO (34 %) and CH₄ (66 %), 38 times higher than that of PCN‐221(Fe_0.2) in the absence of perovskite QDs.