On a generalization of the extended best polynomial approximation operator in Orlicz–Lorentz spaces

In this paper, we consider the best polynomial approximation operator defined on an Orlicz–Lorentz space ${\mathrm{\Lambda }}_{w,\varphi }$, and its extension to ${\mathrm{\Lambda }}_{w,{\varphi }^{\prime }}$, where w is a non-negative continuous weight function and ${\varphi }^{\prime }$ is the derivative of ϕ, which is not required to be an Orlicz function. Our work generalizes a recent result in this field on an Orlicz–Lorentz space generated by an Orlicz function. In addition, we establish some properties and estimates for any extended best polynomial approximation.     

Migration and Precipitation of Platinum in Anion-Exchange Membrane Fuel Cells

Despite the recent progress in increasing the power generation of Anion-exchange membrane fuel cells (AEMFCs), their durability is still far lower than that of Proton exchange membrane fuel cells (PEMFCs). Using the complementary techniques of X-ray micro-computed tomography (CT), Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray (EDX) spectroscopy, we have identified Pt ion migration as an important factor to explain the decay in performance of AEMFCs. In alkaline media Pt⁺² ions are easily formed which then either undergo dissolution into the carbon support or migrate to the membrane. In contrast to PEMFCs, where hydrogen cross over reduces the ions forming a vertical “Pt line” within the membrane, the ions in the AEM are trapped by charged groups within the membrane, leading to disintegration of the membrane and failure. Diffusion of the metal components is still observed when the Pt/C of the cathode is substituted with a FeCo−N−C catalyst, but in this case the Fe and Co ions are not trapped within the membrane, but rather migrate into the anode, thereby increasing the stability of the membrane.     

Gauss-Prym maps on Enriques surfaces

We prove that the kth Gaussian map ${\gamma }_H^k$ is surjective on a polarized unnodal Enriques surface $(S,H)$ with $\phi (H)>2k+4$. In particular, as a consequence, when $\phi (H)>4(k+2)$, we obtain the surjectivity of the kth Gauss-Prym map ${\gamma }_{{\omega }_C\otimes \alpha }^k$, with $\alpha :={\omega }_{{S|}_C}$, on smooth hyperplane sections $C\in |H|$. In case $k=1$, it is sufficient to ask $\phi (H)>6$.     

Taylor's inequalities in Orlicz–Sobolev type spaces

In this paper, we obtain inequalities involving the Taylor polynomial and weak derivatives of a function in an Orlicz–Sobolev type space. Moreover, we show that any such function can be expanded in a finite Taylor series almost everywhere. As a consequence, we prove that the coefficients of any extended best polynomial $L^{\mathrm{\Phi }}$-approximation of a function on a ball almost everywhere converge to the weak derivatives of such a function when the radius tends to 0. Lastly, we get a mean convergence result of such coefficients.     

PANI-CSA: An Easy Method to Avoid ITO Photolithography in PLED Manufacturing

In order to optimize polymer light emitting diode (PLED) performances, devices with holes injected through an Indium Tin Oxide (ITO) / Polyaniline (PANI) electrode into the polymer are much more efficient than devices fabricated with the anode made only by ITO. We demonstrated that by using doped PANI as hole injection layer in a polymer light emitting diode the manufacturing process can become simpler. Indeed, the pattern of conductive layer can be produced without ITO photolithography by UV exposition. As hole transporter layer, Poly(N-vinylcarbazole) (PVK) was spin coated over the doped PANI layer and a layer of tris (8-hydroxy) quinoline aluminum (Alq₃) was then thermally evaporated so as to form the electron transport layer. To complete the device structure, Aluminum contacts were deposited onto the organic layers by vacuum evaporation at low pressure. The layers were characterized by X-ray small-angle diffraction, IR Raman and UV-Vis spectroscopies. Devices without PANI and with PANI as HIL were studied.     

Modulating Thermal Properties of Polymers through Crystal Engineering

Crystal engineering has exclusively focused on the development of advanced materials based on small organic molecules. We now demonstrate how the cocrystallization of a polymer yields a material with significantly enhanced thermal stability but equivalent mechanical flexibility. Isomorphous replacement of one of the cocrystal components enables the formation of solid solutions with melting points that can be readily fine-tuned over a usefully wide temperature range. The results of this study credibly extend the scope of crystal engineering and cocrystallization from small molecules to polymers.     

Supramolecular Capsule Catalysis Enables the Exploration of Terpenoid Chemical Space Untapped by Nature

Terpenes represent the largest and the most diverse class of natural compounds. This is remarkable as the whole variety is accessed from just a handful of highly conserved linear precursors. Modification of the cyclization precursors would enable a dramatic expansion of the accessible chemical space. However, natural enzymes do not enable us to tap into this potential, as they do not tolerate larger deviations from the prototypical substrate structure. Herein we report that supramolecular capsule catalysis enables facile access to diverse and novel terpenoid skeletons that formally can be traced back to C3-phenyl, benzyl, and homoprenyl derivatives of farnesol. Novel skeletons related to the presilphiperfolane core structure, as well as novel neoclovene derivatives were accessed efficiently in only four synthetic steps. Importantly, the products obtained carry functional groups that may be readily derivatized further.