Fixed points of nonexpansive mappings in spaces of continuous functions

Let be a compact metrizable space and let be the Banach space of all real continuous functions defined on with the maximum norm. It is known that fails to have the weak fixed point property for nonexpansive mappings (w-FPP) when contains a perfect set. However the space , where and is the first infinite ordinal number, enjoys the w-FPP, and so also satisfies this property if . It is unknown if has the w-FPP when is a scattered set such that . In this paper we prove that certain subspaces of , with , satisfy the w-FPP. To prove this result we introduce the notion of -almost weak orthogonality and we prove that an -almost weakly orthogonal closed subspace of enjoys the w-FPP. We show an example of an -almost weakly orthogonal subspace of which is not contained in for any .

     

Analytical study of pottery from Soutpansberg

Potsherds from north and south of the Soutpansberg mountain range in Transvaal were analyzed by PIXE to establish possible trade patterns between the two regions, over the last thousand years. Correspondence analysis based on the content of 12 elements made it possible to distinguish pottery from the two regions, irrespective of where they were found. A model combining elemental and stylistic analysis was developed to explain both the physical movement of pots and the diffusion of ideas.     

Theoretical study of structural features of endo,exo double bonds and side chain in 14α‐demethylation of lanosterol

The 14α‐demethylation of biosynthetic reactions is carried out exclusively by lanosta‐8,24‐dien‐3β‐ol (lanosterol). Theoretical calculations were done to determine the importance of this structure with the Hartree–Fock scheme. It was modeled on structures similar to lanosterol with variations on the endo between C8? C9 (lanosta‐7,24‐dien‐3β‐ol and lanosta‐6,24‐dien‐3β‐ol) as compared with the exo between C24? C25 (Lanosta‐8‐en‐3β‐ol) and the size of the side chain (27‐norlanosta‐8‐en‐3β‐ol, 26,27‐dinorlanosta‐8‐en‐3β‐ol, 25,26,27‐trinorlanosta‐8‐en‐3β‐ol, 24,25,26,27‐tetranorlanosta‐8‐en‐3β‐ol, 23,24,25,26,27‐pentanorlanosta‐8‐en‐3β‐ol, 22,23,24,25,26,27‐hexanorlanosta‐8‐en‐3β‐ol). Energetic, electronic, and orbital evidence was found. The theoretical data were analyzed and were found to be important for the 14α‐demethylation, the presence of HOMO on the region C8? C9 and C14? C14¹, a negative charge on the outgoing methyl C14¹. This atomic charge varies with the size of the side chain, and with the modification of the endo and exo double bonds. The conformation of the structure of the steroid is also related to its reactivity. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Accessible and Cost-Effective Method of PDMS Microdevices Fabrication Using a Reusable Photopolymer Mold

This work describes a novel and cost-effective method of polydimethylsiloxane (PDMS) microchips fabrication by using a printing plate photopolymer called Flexcel as a master mold (Fmold). This method has demonstrated the ability to generate multiple devices from a single master, reaching a minimum channel size of 25 μm, structures height ranging from 53 to 1500 μm and achieving dimensions of 1270 × 2062 mm², which are larger than those obtained by the known techniques to date. Scanning electron microscopy, atomic force microscopy, and profilometry techniques have been employed to characterize the Fmold and PDMS replicas. The results showed high replication fidelity of Fmold to the PDMS replica. Furthermore, it was proved the reusability of the Fmold. In our study, up to 50 PDMS replicas have been fabricated without apparent degradation of the mold. The feasibility of the resulting PDMS replica was effectively demonstrated using a microfluidic device for enhanced oil recovery analysis. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1433–1442     

Relative tendency of carbonyl compounds to form enamines

Equilibria between carbonyl compounds and their enamines (from O-TBDPS-derived prolinol) have been examined by NMR spectroscopy in DMSO-d(6). By comparing the exchange reactions between pairs (enamine A + carbonyl B → carbonyl A + enamine B), a quite general scale of the tendency of carbonyl groups to form enamines has been established. Aldehydes quickly give enamines that are relatively more stable than those of ketones, but there are exceptions to this expected rule; for example, 1,3-dihydroxyacetone acetals or 3,5-dioxacyclohexanones (2-phenyl-1,3-dioxan-5-one and 2,2-dimethyl-1,3-dioxan-5-one) show a greater tendency to afford enamines than many α-substituted aldehydes.     

Co-doped ZnO nanoparticles synthesized by an adapted sol–gel method: effects on the structural,optical, photocatalytic and antibacterial properties

Pure and Co-doped ZnO nanoparticles were synthesized with different cobalt levels (1–10 mol%) via adapted sol–gel method using water as solvent and characterized by X-ray diffraction, transmission electron microscopy, Raman spectroscopy and photoacoustic absorption spectroscopy. The results showed that all the samples have hexagonal wurtzite structure, with no evidence of any secondary phases until 10 mol% of the dopant. The average crystallite size of the samples was in the range of 25–50 nm, do not showing significant differences with the increase of the dopant level. However, the band gap energy of the nanoparticles decreases from 2.98 eV (pure ZnO) to 1.95 eV (10 mol% of Co). The photocatalytic activity of the samples was evaluated on the removal of methylene blue under visible light irradiation, which revealed an efficiency reduction by Co-doping ZnO. The antibacterial property was carried out indicating activity of the prepared samples against gram-positive bacteria.     

Formic Acid: A Low-Cost,Mild, Ecofriendly,and Highly Efficient Catalyst for the Rapid Synthesis of β-Enaminones

β-Enaminones have been synthesized by the condensation reaction of β-diketones with various anilines in the presence of a catalytic amount of formic acid, mild and highly efficient acid catalyst in methanol. These condensation reactions proceed smoothly in short reaction times with near-quantitative yields.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Temporal decay of the catalytic oxidation of methane over palladium supported on silica

The temporal decay of the oxidation of methane(CH4-O2reaction)over palladium supported on silica is determined experimentally at different temperatures,comparing the results with those of various classical models which show the behavior of the adsorbed phase as the cause of the phenomenon.This effect is visualized through Monte Carlo simulations of the CH4-O2reaction on a mixed lattice whose partial poisoning,due to the configuration of the OH groups on the surface of the adsorbate,is translated into a gradual decay of the reaction’s activity.     

Size distribution evolution equations in space-competing domain growth systems

A model of microstructure development for phase transformations driven by nucleation and growth is presented. The model is based on a set of Fokker-Planck-like equations which allows us to compute the particle grain density distribution at any time during the transformation, provided that the nucleation and growth dependences on time and/or grain radius are known. The model is applicable to any kind of nucleation and growth protocols fulfilling the Johnson–Mehl–Avrami–Kolmogorov conditions, namely spatially random nucleation and isotropic growth. Comparison with stochastic (Monte Carlo) simulations is presented, giving quantitative agreement in all cases. This work shows the relationship between kinetic parameters and microstructure evolution as well as the accuracy of the developed model.