Stability,periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory

By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation where A ,B ,D > 0,u _?1,u ₀>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytic invariant curves for an iterative equation related to dissipative standard map

In this paper, we study existence of invariant curves of an iterative equation which is from dissipative standard map. By constructing an invertible analytic solution g (x ) of an auxiliary equation of the form invertible analytic solutions of the form g (λ g  ^? 1(x )) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < |λ | < 1, we focus on those λ on the unit circle S ¹, that is, |λ | = 1. We discuss not only those λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition. Copyright © 2016 John Wiley & Sons, Ltd.     

Enhanced Fluorescence Imaging and Photodynamic Cancer Therapy Using Hollow Mesoporous Nanocontainers

Here we show that “off‐on” type of photodynamic therapy agents could be developed using hollow mesoporous silica nanoparticles (HMSNPs), which can be used not only for enhancing delivery of photosensitizers to cancer cells but also for enabling switchable optical properties of the photosensitizers. Fluorescence and singlet oxygen generation of the photosensitizer‐loaded HMSNP are turned off in its native state. In vitro cell studies showed that this HMSNP‐based “off‐on” agent may have potential utility in selective fluorescence detection and photodynamic therapy of cancers.     

Double-Layered Plasmonic–Magnetic Vesicles by Self-Assembly of Janus Amphiphilic Gold–Iron(II,III) Oxide Nanoparticles

Janus nanoparticles (JNPs) offer unique features, including the precisely controlled distribution of compositions, surface charges, dipole moments, modular and combined functionalities, which enable excellent applications that are unavailable to their symmetrical counterparts. Assemblies of NPs exhibit coupled optical, electronic and magnetic properties that are different from single NPs. Herein, we report a new class of double-layered plasmonic–magnetic vesicle assembled from Janus amphiphilic Au-Fe₃O₄ NPs grafted with polymer brushes of different hydrophilicity on Au and Fe₃O₄ surfaces separately. Like liposomes, the vesicle shell is composed of two layers of Au-Fe₃O₄ NPs in opposite direction, and the orientation of Au or Fe₃O₄ in the shell can be well controlled by exploiting the amphiphilic property of the two types of polymers.     

Controlled Release of Hepatocyte Growth Factor from MPEG‐b‐(PCL‐ran‐PLLA) Diblock Copolymer for Improved Vocal Fold Regeneration

An in situ‐forming gel system comprised of diblock copolymer formed from polyethylene glycol (PEG) and polycaprolactone (PCL) {MPEG‐b‐(PCL‐ran‐PLLA)} could be used in controlled drug delivery for tissue remodeling. The purpose of this study is to demonstrate favorable vocal folds (VF) regeneration by using MPEG‐b‐(PCL‐ran‐PLLA) diblock copolymers (C97L3; CL/LA ratio 97:3) incorporating hepatocyte growth factor (HGF). Gradual release of HGF from C97L3 is detected and biochemical properties of released HGF are maintained. A scar is made with microscissors on both VFs in 32 rabbits, followed by injection of HGF‐only, C97L3‐only, or HGF‐C97L3 composite gel in the left side VF, while the right side VF is left untreated. In vivo fluorescence live imaging system demonstrates that C97L3 enables the sustained release of injected HGF in the scarred VF for 12 weeks. The histological analysis shows increased glycosaminoglycan including hyaluronic acid accumulation and decreased collagen deposition. Videokymographic analysis shows more favorable vibrations of HGF‐C97L3 treated VF mucosa, compared to other treatment groups. In conclusion, the controlled HGF release helps to regulate extracellular matrix synthesis, and leads to the eventual functional improvement of the scarred VF.

     

Mean flow properties for equatorially trapped internal water wave–current interactions

The aim of this paper is to provide an analysis of the mean flow velocities, and the related mass transport induced by equatorially trapped internal water waves with a constant underlying current.     

Calderón problem for connections

In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9 Dos Santos Ferreira, D., Kenig, C., Salo, M., Uhlmann, G. (2009). Limiting Carleman weights and anisotropic inverse problems. Invent. Math. 178:119–171.[Crossref], [Web of Science ®] , [Google Scholar]] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11 Dos Santos Ferreira, D., Kurylev, Y., Lassas, M., Salo, M. (2016). The Calderón problem in transversally anisotropic geometries. J. Eur. Math. Soc., 18:2579–2626.[Crossref], [Web of Science ®] , [Google Scholar]]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy.