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.     

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.     

ZIF-Induced d-Band Modification in a Bimetallic Nanocatalyst: Achieving Over 44 % Efficiency in the Ambient Nitrogen Reduction Reaction

The electrochemical nitrogen reduction reaction (NRR) offers a sustainable solution towards ammonia production but suffers poor reaction performance owing to preferential catalyst–H formation and the consequential hydrogen evolution reaction (HER). Now, the Pt/Au electrocatalyst d-band structure is electronically modified using zeolitic imidazole framework (ZIF) to achieve a Faradaic efficiency (FE) of >44 % with high ammonia yield rate of >161 μg mg_cat⁻¹ h⁻¹ under ambient conditions. The strategy lowers electrocatalyst d-band position to weaken H adsorption and concurrently creates electron-deficient sites to kinetically drive NRR by promoting catalyst–N₂ interaction. The ZIF coating on the electrocatalyst doubles as a hydrophobic layer to suppress HER, further improving FE by >44-fold compared to without ZIF (ca. 1 %). The Pt/Au-N_ZIF interaction is key to enable strong N₂ adsorption over H atom.     

An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs

We present an exact formula for the radius of robust feasibility of uncertain linear programs with a compact and convex uncertainty set. The radius of robust feasibility provides a value for the maximal ‘size’ of an uncertainty set under which robust feasibility of the uncertain linear program can be guaranteed. By considering spectrahedral uncertainty sets, we obtain numerically tractable radius formulas for commonly used uncertainty sets of robust optimization, such as ellipsoids, balls, polytopes and boxes. In these cases, we show that the radius of robust feasibility can be found by solving a linearly constrained convex quadratic program or a minimax linear program. The results are illustrated by calculating the radius of robust feasibility of uncertain linear programs for several different uncertainty sets.     

Clarke coderivatives of efficient point multifunctions in parametric vector optimization

The paper is devoted to the study of the Clarke/circatangent coderivatives of the efficient point multifunction of parametric vector optimization problems in Banach spaces. We provide inner/outer estimates for evaluating the Clarke/circatangent coderivative of this multifunction in a broad class of conventional vector optimization problems in the presence of geometrical, operator and (finite and infinite) functional constraints. Examples are given for analyzing and illustrating the obtained results.     

On a fixed-point theorem

Institute of Mathematics, Hanoi. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 30, No. 3, pp. 93–94, July–September, 1996.