The memory of thin polymer films generated by spin coating

The European Physical Journal E - The interstitial tumor microenvironment is composed of heterogeneously organized collagen-rich porous networks as well as channel-like structures and interfaces...     

Exploring students' mathematical performance,metacognitive experiences and skills in relation to fundamental theorem of calculus

Several studies have explored students’ understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students’ understanding of the Fundamental Theorem of Calculus (FTC). In addition, students’ metacognitive experiences and skills whilst solving FTC questions have not previously been explored. This paper explored students’ mathematical performance, metacognitive experiences and metacognitive skills in relation to FTC questions by interviewing nine university and eight Year 13 students. The findings show that several students had difficulty solving questions related to the FTC and that students’ metacognitive experiences and skills could be further developed.     

Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral calculus, each subtype is exemplified. The developed dimension may enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to develop and align educational objectives, teaching activities, and assessments in integral calculus, or how metacognition and metacognitive knowledge could be used to support teaching and learning.     

On smoothing,regularization, and averaging in stochastic approximation methods for stochastic variational inequality problems

Traditionally, most stochastic approximation (SA) schemes for stochastic variational inequality (SVI) problems have required the underlying mapping to be either strongly monotone or monotone and Lipschitz continuous. In contrast, we consider SVIs with merely monotone and non-Lipschitzian maps. We develop a regularized smoothed SA (RSSA) scheme wherein the stepsize, smoothing, and regularization parameters are reduced after every iteration at a prescribed rate. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to the least norm solution in an almost sure sense, extending the results in Koshal et al. (IEEE Trans Autom Control 58(3):594–609, 2013) to the non-Lipschitzian regime. Additionally, we provide rate estimates that relate iterates to their counterparts derived from a smoothed Tikhonov trajectory associated with a deterministic problem. To derive non-asymptotic rate statements, we develop a variant of the RSSA scheme, denoted by aRSSA\(_r\), in which we employ a weighted iterate-averaging, parameterized by a scalar r where \(r = 1\) provides us with the standard averaging scheme. The main contributions are threefold: (i) when \(r<1\) and the parameter sequences are chosen appropriately, we show that the averaged sequence converges to the least norm solution almost surely and a suitably defined gap function diminishes at an approximate rate \(\mathcal{O}({1}\slash {\root 6 \of {k}})\) after k steps; (ii) when \(r<1\), and smoothing and regularization are suppressed, the gap function admits the rate \(\mathcal{O}({1}\slash {\sqrt{k}})\), thus improving the rate \(\mathcal{O}(\ln (k)/\sqrt{k})\) under standard averaging; and (iii) we develop a window-based variant of this scheme that also displays the optimal rate for \(r < 1\). Notably, we prove the superiority of the scheme with \(r < 1\) with its counterpart with \(r=1\) in terms of the constant factor of the error bound when the size of the averaging window is sufficiently large. We present the performance of the developed schemes on a stochastic Nash–Cournot game with merely monotone and non-Lipschitzian maps.     

Preparation and characterization of a novel water soluble amino chitosan (amino-CS) derivative for facilitated transport of CO<Subscript>2</Subscript>

With the goal of obtaining a water soluble polymeric carrier for preparation of fixed facilitated transport membranes, a water soluble amino containing chitosan derivative was prepared through Michael-addition reaction between chitosan and ethyl acrylate followed by amidation of the ester groups with an appropriate diamine. This derivative was characterized using ¹H-NMR spectroscopy. Then, facilitated transport membranes were prepared by casting a thin layer of chitosan derivative/poly(vinyl alcohol) blend on a porous polysolfune support; and the effect of fixed carrier’s content, feed temperature and feed pressure on the CO₂ permeance, and CO₂/CH₄ selectivity of produced membranes were studied. A facilitated transport mechanism for CO₂ through this membrane was concluded.     

Retraction Note to: N. Zamani “On graded distributive modules,”

Mathematical Notes - This article has been retracted at the request of the Editorial Board of the journal in accordance with the COPE guidelines. This article contains a significant amount of...     

Advanced Surfaces by Anchoring Thin Hydrogel Layers of Functional Polymers

Surface design and engineering is a critical tool to improve the interaction of materials with their surroundings. Immobilization of soft hydrogels is one of the attractive strategies to achieve surface modification. The goal of this review is to provide a comprehensive overview of the different strategies used for surface tethering of hydrogel layers via crosslinking immobilization of pre-fabricated functional polymers. In this strategy, crosslinkable polymers are first prepared via various polymerization techniques or post-functionalization of polymers. Afterwards, the crosslinkable polymers are attached or tethered on the surfaces of substrates using a variety of approaches including photo-crosslinking, click reactions, reversible linkages, etc. For each case, the principles of hydrogel tethering have been explained in detail with representative examples.Moreover, the potential applications of the as-modified substrates in specific cases have also been addressed and overviewed.     

A New Model for Prediction of One Electron Reduction Potential of Nitroaryl Compounds

This paper introduces a simple model for prediction of one electron reduction potential [E(RNO₂/R ^? NO₂^–)] of various nitroaryl compounds. The new method uses energy difference between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) in gas phase at the B3LYP/6‐311++G** level (ΔE_HOMO‐LUMO) and some structural parameters. It was used for 35 nitroaryl compounds including nitrobenzenes, nitrofurans, 2‐nitroimidazoles, 4‐nitroimidazoles, 5‐ninuintidazoles, nitroazaindoles, nitroacridines, and miscellaneous nitroaryl compounds. The root mean square (rms) percent deviation and the average absolute error of predictions of E(RNO₂/R ^? NO₂^–) relative to experiment were decreased from 12.4 % and 0.42 V to 3.5 % and 0.11 V, respectively, upon consideration of several structural parameters. Increment of the value of ΔE_HOMO‐LUMO and inclusion of specific polar groups can increase thermodynamic stability of these compounds.     

Synthesis of a PEG-PNIPAm thermosensitive dendritic copolymer and investigation of its self-association

A Novel thermosensitive dendritic copolymer based on polyethylene glycol(PEG) and poly(Nisopropylacrylamide)(PNIPAm) with a cloud point(CP) around 36 ?C was successfully synthesized by preparation of a dendritic polyol and followed by atom transfer radical polymerization(ATRP) of N-isopropylacrylamide. The dendritic copolymer was characterized using gel-permeation chromatography(GPC), FTIR and 1H-NMR spectroscopy. The selfassociation behavior of the copolymer in aqueous medium was investigated by dynamic light scattering(DLS) and transmission electron microscopy(TEM). These investigations confirmed that the dendritic copolymer showed different association behaviors at various temperatures.     

Effect of source strength on dislocation pileups in the presence of stress gradients

The behaviour of a dislocation pileup with a finite-strength source is investigated in the presence of various stress gradients within a continuum model where a free-dislocation region exists around the source. Expressions for dislocation density and stress field within the pileup are derived for the situation where there are first and second spatial gradients in applied stress. For a pileup configuration under an applied stress, yielding occurs when the force acting on the leading dislocations at the pileup tips reaches the obstacle strength, and at the same time, it is required that the source be at the threshold stress for dislocation production. A numerical methodology is presented to solve the underlying equations that represent the yielding conditions. The yield stress calculated for a pileup configuration is found to depend on stress gradients, obstacle spacing and source/obstacle strengths. It increases with increasing the first stress gradient, yet dependent on the second stress gradient. Furthermore, while the dependency of yield stress on the obstacle spacing intensifies with increasing the first stress gradient, it diminishes with an increase of second stress gradient. Therefore, the second stress gradient, as a newly introduced parameter, can provide a new physical insight into the size-dependent plasticity phenomena at small length scales.