Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

Conformations of luteoskyrin and rugulosin in solution

The pigments Luteoskyrin (Ls) and Rugulosin (Rg) might adopt a priori two extreme conformations, a planar and an angular one. To determine the predominant conformation in solution, the nature of the lowest energy transition of the chromophores and the presence of intramolecular H-bonding have been investigated. The solvent effects on electronic absorption and CD spectra indicated the π-π* nature of the lowest energy transition. Treatments of the electronic absorption results according to McRae and Kosower relations, IR absorption and PMR spectra suggested the presence of strong intra-molecular H-bonds. From these results it was concluded that Ls and Rg adopted in a variety of solvents the most planar conformation.     

Boundedness of the wavelet integral operator on weighted function spaces

The purpose of this paper is to study the boundedness of the wavelet integral operator on the Besov, BMO, and H ¹ spaces. Furthermore, for the basic wavelet with compact support, the boundedness of the wavelet transform on the weighted Besov spaces and on the weighted BMO spaces associated with a tempered weight function is also established.     

Isolating Reactions at the Picoliter Scale: Parallel Control of Reaction Kinetics at the Liquid–Liquid Interface

Miniaturized liquid–liquid interfacial reactors offer enhanced surface area and rapid confinement of compounds of opposite solubility, yet they are unable to provide in situ reaction monitoring at a molecular level at the interface. A picoreactor operative at the liquid–liquid interface is described, comprising plasmonic colloidosomes containing Ag octahedra strategically assembled at the water‐in‐decane emulsion interface. The plasmonic colloidosomes isolate ultrasmall amounts of solutions (<200 pL), allowing parallel monitoring of multiple reactions simultaneously. Using the surface‐enhanced Raman spectroscopy (SERS) technique, in situ monitoring of the interfacial protonation of dimethyl yellow (p‐dimethylaminoazobenzene (DY)) is performed, revealing an apparent rate constant of 0.09 min^?1 for the first‐order reaction. The presence of isomeric products with similar physical properties is resolved, which would otherwise be indiscernible by other analytical methods.     

Use of a simple surface-active initiator in controlled/living free-radical miniemulsion polymerization under AGET and ARGET ATRP conditions

This communication describes the first example of the efficient use of a simple amphiphilic molecule as both a surfactant and an initiator in the miniemulsion polymerization of methyl methacrylate under AGET and ARGET ATRP conditions.     

Electrochemical Reduction of Carbon Dioxide to Methanol on Hierarchical Pd/SnO2 Nanosheets with Abundant Pd–O–Sn Interfaces

Electrochemical conversion of CO₂ into fuels using electricity generated from renewable sources helps to create an artificial carbon cycle. However, the low efficiency and poor stability hinder the practical use of most conventional electrocatalysts. In this work, a 2D hierarchical Pd/SnO₂ structure, ultrathin Pd nanosheets partially capped by SnO₂ nanoparticles, is designed to enable multi‐electron transfer for selective electroreduction of CO₂ into CH₃OH. Such a structure design not only enhances the adsorption of CO₂ on SnO₂, but also weakens the binding strength of CO on Pd due to the as‐built Pd–O–Sn interfaces, which is demonstrated to be critical to improve the electrocatalytic selectivity and stability of Pd catalysts. This work provides a new strategy to improve electrochemical performance of metal‐based catalysts by creating metal oxide interfaces for selective electroreduction of CO₂.     

Isolated and Proper Efficiencies in Semi-Infinite Vector Optimization Problems

This paper deals with a nonsmooth semi-infinite multiobjective/vector optimization problem (SIMOP, for short). We first establish necessary and sufficient conditions for (local) strongly isolated solutions and (local) positively properly efficient solutions of an SIMOP. Then, we propose a dual problem to the SIMOP under consideration and examine weak and strong duality relations between them.     

Chemical Constituents of the Leaves of Artocarpus integer

Chemistry of Natural Compounds -