Recent progress and future challenges in the supramolecular polymerization of metal-containing monomers

The self-assembly of discrete molecular entities into functional nanomaterials has become a major research area in the past decades. The library of investigated compounds has diversified significantly, while the field as a whole has matured. The incorporation of metal ions in the molecular design of the (supra-)molecular building blocks greatly expands the potential applications, while also offering a promising approach to control molecular recognition and attractive and/or repulsive intermolecular binding events. Hence, supramolecular polymerization of metal-containing monomers has emerged as a major research focus in the field. In this perspective article, we highlight recent significant advances in supramolecular polymerization of metal-containing monomers and discuss their implications for future research. Additionally, we also outline some major challenges that metallosupramolecular chemists (will) have to face to produce metallosupramolecular polymers (MSPs) with advanced applications and functionalities.

In this perspective article, we highlight recent significant advances in the self-assembly of metal-containing monomers and discuss their implications for future research.     

Identification of photocatalytic degradation products of non-ionic polyethoxylated surfactants in wastewaters by solid-phase extraction followed by liquid chromatography-mass spectrometric detection

The photodegradation of non-ionic surfactants (nonylphenol- and alcohol-polyethoxylates, NPEO_x and C_nEO_x) was investigated in different waters with and without a photoinducter (Fe(III)). Deionized water and industrial effluent spiked at 0.5 mg/L with C₁₀EO₆ and NPEO₉ were irradiated using a xenon arc lamp. Aliquots of the test solutions were taken at different time intervals and were preconcentrated using solid phase extraction (SPE) with C₁₈ cartridges. Liquid chromatography-atmospheric pressure chemical ionization-mass spectrometry (LC-APCI-MS) was used to identify the chemical species generated from phototransformation of non-ionic surfactants. 2 ) and nonylphenol ethoxy acetic acid (NPE₂C). Much smaller amounts of degradation products of NPEO₉ having only the alkyl chain carboxylated were also formed in the photocatalysis experiment. The identified C₁₀EO₆ photoproducts included fatty alcohols and acids. Polyethylene glycols (PEGs) were also formed as the consequence of the central scission of C₁₀EO₆ and the deethoxylation of NPEO₉. The photodegradation in wastewater samples was more efficient than in deionized water being the half-life (t_1/2) of C₁₀EO₆, 48 h and 29 h in deionized water and wastewater, respectively, and for NPEO₉, 17 h and 14 h in deionized water and wastewater, respectively. When induced photodegradation was undertaken, the t_1/2 for NPEO₉ was 21 min and 29 min in deionized water and wastewater, respectively. Disappearance of parent compounds was observed after 120 h from the beginning of the photodegradation experiment, or after 210 min of irradiation for the photocatalysis. Received: 27 September 2000 / Revised: 11 January 2001 / Accepted: 14 January 2001     

Femtosecond laser ablation profile near an interface: Analysis based on the correlation with superficial properties of individual materials

Femtosecond laser ablation of materials is turning to be an important tool for micromachining as well as for selective removal of biological tissues. In a great number of applications, laser ablation has to process through interfaces separating media of different properties. The investigation of the ablation behavior within materials and passing through interfaces is the main aim of this study. Especially, the analysis of the discontinuity in the ablation profile close to interfaces between distinct materials can reveal some of the phenomena involved in the formation of an ablated microcavity geometry. We have used a method that correlates the ablation cross sectional area with the local laser intensity. The effective intensity ablation properties were obtained from surface ablation data of distinct materials. The application of this method allows the prediction of the occurrence of a size discontinuity in the ablation geometry at the interface of distinct media, a fact which becomes important when planning applications in different media.     

Convergence properties of Hartree–Fock SCF molecular calculations

Hartree-Fock equations are viewed as nonlinear algebraic equations that can be solved iteratively. Provided we assume the existence of a solution, valuable properties of convergence may be assessed. The close connection between convergence of the SCF procedure and stability properties of the solution is shown from a nonapproximate standpoint. The convergence features of level-shifting convergence-forcing techniques are analyzed. The connection between this nonlinear algebraic approach and the related gap equation is displayed and the example of the restricted Hartree-Fock hydrogen molecule is discussed.     

On the Propagation of Regularity and Decay of Solutions to the k-Generalized Korteweg-de Vries Equation

We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u ₀ ∈ H ^3/4+ (?) whose restriction belongs to H ^l ((b, ∞)) for some l ∈ ?⁺ and b ∈ ? we prove that the restriction of the corresponding solution u(·, t) belongs to H ^l ((β, ∞)) for any β ∈ ? and any t ∈ (0, T). Thus, this type of regularity propagates with infinite speed to its left as time evolves.     

The finite <Emphasis Type=Italic>p</Emphasis>-groups with <Emphasis Type=Italic>p</Emphasis> conjugacy classes of non-normal subgroups

Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. The finite groups for which ν(G) ≤ 2 were determined by Dedekind and by Schmidt in the early times of group theory. On the other hand, if G is a finite p-group, La Haye and Rhemtulla have proved that either ν(G) ≤ 1 or ν(G) ≥ p. In this note, we determine all finite p-groups satisfying ν(G) = p for p > 2.     

Early error detection: an action-research experience teaching vector calculus

This paper describes an action-research experience carried out with second year students at the School of Engineering of the National University of Entre Ríos, Argentina. Vector calculus students played an active role in their own learning process. They were required to present weekly reports, in both oral and written forms, on the topics studied, instead of merely sitting and watching as the teacher solved problems on the blackboard. The students were also asked to perform computer assignments, and their learning process was continuously monitored. Among many benefits, this methodology has allowed students and teachers to identify errors and misconceptions that might have gone unnoticed under a more passive approach.     

Completeness in the set of wavelets

We study the completeness properties of the set of wavelets in . It is well-known that this set is not closed in the unit ball of . However, if one considers the metric inherited as a subspace (in the Fourier transform side) of , we do obtain a complete metric space.

     

Global existence and blow-up for the generalized sixth-order Boussinesq equation

In this paper we prove local well-posedness in L²(R)$L^2\left(\mathbb{R}\right)$ and H¹(R)$H^1\left(\mathbb{R}\right)$ for the generalized sixth-order Boussinesq equation _utt=_uxx+β_uxxxx+_uxxxxxx+_(|u|αu)xx$u_{tt}=u_{xx}+\beta u_{xxxx}+u_{xxxxxx}+{\left({\left|u\right|}^{\alpha }u\right)}_{xx}$. Our proof relies in the oscillatory integrals estimates introduced by Kenig et al. (1991) [14]. We also show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive the sufficient conditions for the blow-up of the solution to the problem.