Legendre wavelet solution of neutral differential equations with proportional delays

The aim of this paper is to solve neutral differential equations with proportional delays by using Legendre wavelet method. Using orthonormal polynomials is the main advantage of this method since it enables a decrease in the computational cost and runtime. Some examples are displayed to illustrate the efficiency and accuracy of the proposed method. Numerical results are compared with various numerical methods in literature and show that the present method is very effectual in solving neutral differential equations with proportional delays. © 2019, Korean Society for Computational and Applied Mathematics

Lucas polynomial solution of nonlinear differential equations with variable delays

In this study, a novel matrix method based on Lucas series and collocation points has been used to solve nonlinear differential equations with variable delays. The application of the method converts the nonlinear equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Lucas coefficients. The method is tested on three problems to show that it allows both analytical and approximate solutions. © 2020, Hacettepe University. All rights reserved

New Dihexadecyldithiophosphate SAMs on Gold Provide Insight into the Unusual Dependence of Adsorbate Chelation on Substrate Morphology in SAMs of Dialkyldithiophosphinic Acids

We report the formation and characterization of new self-assembled monolayers (SAMs) formed from dihexadecyldithiophosphate (C16) 2DDP and compare their properties with those of SAMs formed from the structurally similar adsorbate dihexadecyldithiophosphinic acid (C 16)2DTPA. The new (C16)2DDP SAMs were characterized using X-ray photoelectron spectroscopy, reflection-absorption infrared spectroscopy, contact angle measurements, and electrochemical impedance spectroscopy. The data indicate that (C16)2DDP forms SAMs on gold films formed by e-beam evaporation in which all adsorbates chelate to gold, in contrast to (C16)2DTPA SAMs, in which 40% of the adsorbates are monodentate. The alkyl chains of the (C 16)2DDP SAM are also less densely packed and ordered than those of the (C16)2DTPA SAM. To understand these differences, we present density functional theory calculations that show that there are only minimal differences between the geometric and electronic structures of the two adsorbates and that the energetic difference between monodentate and bidentate binding of a gold(I) ion are surprisingly small for both adsorbates. This study leads to the conclusion that differences in intermolecular interactions within the SAM are the driving force for the difference in chelation between the two adsorbates. © 2013 American Chemical Society