On Discrete Painlevé Equations Associated with the Lattice KdV Systems and the Painlevé VI Equation

A new integrable nonautonomous nonlinear ordinary difference equation is presented that can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial differential equations of Korteweg–de Vries (KdV) type. The new equation, which is referred to as generalized discrete Painlevé equation (GDP), contains various "discrete Painlevé equations" as subcases for special values/limits of the parameters, some of which have already been given in the literature. The general solution of the GDP can be expressed in terms of Painlevé VI (PVI) transcendents. In fact, continuous PVI emerges as the equation obeyed by the solutions of the discrete equation in terms of the lattice parameters rather than the lattice variables that label the lattice sites. We show that the bilinear form of PVI is embedded naturally in the lattice systems leading to the GDP. Further results include the establishment of Bäcklund and Schlesinger transformations for the GDP, the corresponding isomonodromic deformation problem, and the self-duality of its bilinear scheme.     

Methods for the synthesis of chiral sulfur heterocycles and their application in the asymmetric Baylis–Hillman reactions

Enantiomerically pure (2S,6S)-2,6-diphenyltetrahydro-2H-thiopyran, (2S)-2-phenyltetrahydro thiophene, and (2S)-2-phenyltetrahydro-2H-thiopyran were prepared in 70–72% yields and with 86–99% ee via cyclization of the corresponding dimesylate in an S_N2 cyclization reaction using sodium sulfide nonahydrate. The results on the application of various chiral sulfides in asymmetric Baylis–Hillman reactions are also described.     

Bacterial cellulose-reinforced hydroxyapatite functionalized graphene oxide: a potential osteoinductive composite

Bacterial cellulose (BC) is a nanofibrous biocompatible scaffold used in bone tissue engineering. Graphene oxide/hydroxyapatite (GOHA) composite supports the adhesion of osteoblast cells with good viability. In the present study, GOHA was prepared by the wet chemical precipitation method, and BC obtained from Acetobacter aceti was added to the aqueous suspension of GOHA to prepare GOHABC. The scanning electron microscopic image of GOHABC showed uniform adsorption of GOHA on the surface of BC. The osteoinductive potential of the GOHABC scaffold was analyzed by alkaline phosphatase (ALP) activity assay using MG-63 cells, and its biocompatibility nature was studied by using both MG-63 and NIH-3T3 cells. The ALP activity and biocompatibility studies showed that GOHABC is a potential osteoinductive material in vitro and may be tried in the future for in vivo studies.     

ZrB2/Pt/Au Ohmic contacts on bulk, single-crystal ZnO

There is a strong interest in developing thermally stable metallization schemes for ZnO and boride-based contact stacks are expected to have potential because of their thermodynamic stability. The contact characteristics on bulk single-crystal n-ZnO of a ZrB₂/Pt/Au metallization scheme deposited by sputtering are reported as a function of annealing temperature in the range 300-800°C. The contacts were rectifying for anneal temperatures <500 °C but exhibited Ohmic behavior at higher temperatures and exhibit a minimum specific contact resistivity of 9 × 10⁻³ Ω cm after 700 °C anneals. The contact stack reverts to rectifying behavior after annealing above 800 °C, coincident with a degraded surface morphology and intermixing of the Au, Pt and ZrB₂. The boride-based contacts exhibit higher thermal stability but poorer specific contact resistivity than conventional Ti/Au metal stacks on ZnO.     

On the quantization of the Kowalevskaya top

The equations of motion of a heavy top can be integrated for three different combinations of the parameters of the system. Historically, the discovery of these three integrable cases is attributed to Euler, Lagrange and Kowalevskaya, respectively. While the quantization of the first two cases can be performed in a straightforward way, the quantum integrability of the Kowalevskaya top is far from trivial. We show here how one can recover quantum integrability for this case as well.     

On the discrete form of the Fokas–Ablowitz equation

The Fokas–Ablowitz equation, quadratic in the second derivative, is obtained from Painlevé VI by a Miura transformation. We present here two different discretisations in terms of difference- and multiplicative, q-, equations.     

Integrability of the Hirota-Satsuma equations: Two tests

We examine the Hirota-Satsuma equation from the point of view of integrability. We show that the equation satisfies the Painlevé criterion, which according to the Ablowitz-Ramani-Segur conjecture makes it a candidate for integrability. Moreover we show that the two different kinds of solitons discovered by Hirota and Satsuma can be freely added, another indication of integrability.     

Engineering Chemically Exfoliated Large‐Area Two‐Dimensional MoS2 Nanolayers with Porphyrins for Improved Light Harvesting

Molybdenum disulfide (MoS₂) is a promising candidate for electronic and optoelectronic applications. However, its application in light harvesting has been limited in part due to crystal defects, often related to small crystallite sizes, which diminish charge separation and transfer. Here we demonstrate a surface‐engineering strategy for 2D MoS₂ to improve its photoelectrochemical properties. Chemically exfoliated large‐area MoS₂ thin films were interfaced with eight molecules from three porphyrin families: zinc(II)‐, gallium(III)‐, iron(III)‐centered, and metal‐free protoporphyrin IX (ZnPP, GaPP, FePP, H₂PP); metal‐free and zinc(II) tetra‐(N‐methyl‐4‐pyridyl)porphyrin (H₂T4, ZnT4); and metal‐free and zinc(II) tetraphenylporphyrin (H₂TPP, ZnTPP). We found that the photocurrents from MoS₂ films under visible‐light illumination are strongly dependent on the interfacial molecules and that the photocurrent enhancement is closely correlated with the highest occupied molecular orbital (HOMO) levels of the porphyrins, which suppress the recombination of electron–hole pairs in the photoexcited MoS₂ films. A maximum tenfold increase was observed for MoS₂ functionalized with ZnPP compared with pristine MoS₂ films, whereas ZnT4‐functionalized MoS₂ demonstrated small increases in photocurrent. The application of bias voltage on MoS₂ films can further promote photocurrent enhancements and control current directions. Our results suggest a facile route to render 2D MoS₂ films useful for potential high‐performance light‐harvesting applications.     

Preliminary investigations on the antibacterial activity of zinc oxide nanostructures

We have fabricated electroactive multilayer thin films containing ferritin protein cages. The multilayer thin films were prepared on a solid substrate by the alternate electrostatic adsorption of (apo)ferritin and poly(N-isopropylacrylamide-co-2-carboxyisopropylacrylamide) (NIPAAm-co-CIPAAm) in pH 3.5 acetate buffer solution. The assembly process was monitored using a quartz crystal microbalance. The (apo)ferritin/poly(NIPAAm-co-CIPAAm) multilayer thin films were then cross-linked using a water-soluble carbodiimide, 1-[3-(dimethylamino)propyl]-3-ethylcarbodiimide. The cross-linked films were stable under a variety of conditions. The surface morphology and thickness of the multilayer thin films were characterized by atomic force microscopy, and the ferritin iron cores were observed by scanning electron microscopy to confirm the assembly mechanism. Cyclic voltammetry measurements showed different electrochemical properties for the cross-linked ferritin and apoferritin multilayer thin films, and the effect of stability of the multilayer film on its electrochemical properties was also examined. Our method for constructing multilayer films containing protein cages is expected to be useful in building more complex functional inorganic nanostructures.