Conceptual mathematics: An application to education

This paper presents an alternative proposal concerning the teaching of mathematics. The present paper can be placed within the broader framework of the teaching of mathematics, but also within the more specific framework of category theory (CT). In other words, new ways will be investigated in which CT can be best developed within the broader framework of the teaching of mathematics. Following the research at the end of this paper, the outcome of this investigation is that CT can successfully be used as a background for the foundation and teaching of mathematics.     

Orbital magnetism: pros and cons for enhancing the cluster magnetism

The discrepancy seen in the experimental and theoretical results on the magnetic moment of a small magnetic cluster has been attributed to the contribution arising from orbital magnetism. In this Letter we show that the magnetic states with large orbital magnetic moment are not always energetically favorable; they could, however, be realizable by coating the cluster or deposing it on appropriate substrates. More importantly, our work shows that the crucial factors that determine the cluster magnetism are found to be the intrinsic, and consequently, the extrinsic properties of the constituent atoms of the cluster.     

Dynamical response of the sinusoidally perturbed electrodissolution/passivation of iron in sulfuric acid solutions: Entrainment,spike generation,and quasiperiodicity

The iron/sulfuric acid (Fe/2 M H(2)SO(4)) system exhibits periodic current oscillations of relaxation type within the potential transition region formed between the active and passive states of the iron electrode when it is polarized in the 2 M sulfuric acid solution. In the present work the dynamical response of the Fe/2 M H(2)SO(4) electrochemical oscillator is investigated when the applied potential at the iron electrode is sinusoidally perturbed. The behavior of the periodically perturbed Fe/2 M H(2)SO(4) oscillator differs significantly from the response of other forced oscillators, as the potential amplitude E(p) and the frequency ratio omega(p)/omega(0) vary. The omega(p) and omega(0) are the angular frequencies of the perturbed applied potential and the unperturbed oscillator, respectively. A special feature of its response is the appearance of a number of spikes, generated within the passive section of a periodic oscillatory cycle for omega(p)/omega(0)<2.9, for periods of the autonomous oscillator T(0) greater, similar 3 s. The number of the generated spikes depends on the amplitude and frequency of the perturbed applied potential as well as on the period of the autonomous oscillator. Spikes are not generated for omega(p)/omega(0)=1 and the system is harmonically entrained by the forcing frequency. However, when the system is subharmonically entrained for omega(p)/omega(0) close to 2, spike generation does occur. By increasing the perturbation frequency for omega(p)/omega(0) greater, similar 2.9 and T(0) greater, similar 3 s, or by decreasing the autonomous period for T(0)<3 s and all the omega(p)/omega(0)<2.9 ratios, the spike generation pattern, is replaced by a quasiperiodic pattern. The dynamical response of the perturbed Fe/2 M H(2)SO(4) electrochemical oscillator is characterized by using time-delay reconstructions of the attractors, Poincare maps, and Fourier power spectra.     

Understanding the unique reactivity patterns of nickel/JoSPOphos manifold in the nickel-catalyzed enantioselective C–H cyclization of imidazoles

The 3d transition metal-catalyzed enantioselective C–H functionalization provides a sustainable strategy for the construction of chiral molecules. A better understanding of the catalytic nature of the reactions and the factors controlling the enantioselectivity is important for rational design of more efficient systems. Herein, the mechanisms of Ni-catalyzed enantioselective C–H cyclization of imidazoles are investigated by density functional theory (DFT) calculations. Both the π-allyl nickel(ii)-promoted σ-complex-assisted metathesis (σ-CAM) and the nickel(0)-catalyzed oxidative addition (OA) mechanisms are disfavored. In addition to the typically proposed ligand-to-ligand hydrogen transfer (LLHT) mechanism, the reaction can also proceed via an unconventional σ-CAM mechanism that involves hydrogen transfer from the JoSPOphos ligand to the alkene through P–H oxidative addition/migratory insertion, C(sp²)–H activation via σ-CAM, and C–C reductive elimination. Importantly, computational results based on this new mechanism can indeed reproduce the experimentally observed enantioselectivities. Further, the catalytic activity of the π-allyl nickel(ii) complex can be rationalized by the regeneration of the active nickel(0) catalyst via a stepwise hydrogen transfer, which was confirmed by experimental studies. The calculations reveal several significant roles of the secondary phosphine oxide (SPO) unit in JoSPOphos during the reaction. The improved mechanistic understanding will enable design of novel enantioselective C–H transformations.

Several unique reactivity patterns of the Ni/JoSPOphos manifold, including facile hydrogen transfer via the two-step oxidative addition/migratory insertion and C(sp²)–H activation via an unconventional σ-CAM mechanism, were disclosed in this work.     

On the adsorption of cetyldimethylbenzylammonium chloride at the mercury/electrolyte solution interface

The adsorption of cetyldimethylbenzylammonium chloride (CDBACl) on the hanging mercury electrode is studied in various supporting electrolytes at various temperatures from 1 to 50 degrees C. A condensed film with low capacitance is formed at negative potentials at transition temperatures below approximately 40 degrees C. The decrease of the temperature favors the film formation, and increases the width of the capacitance pit, while its value remains practically constant. Hysteresis phenomena are also observed during different scan directions. Capacitance-time curves at the potentials where the film is formed show in some cases a nucleation and growth mechanism with induction time and studied by the Avrami formulation. At high temperatures an increase of the capacitance with time is observed depending on the CDBACl concentration and slightly on the electrolyte used, and is attributed to the formation of hemimicelles. At high negative potentials a second narrow region with lower capacitance values is observed. This is easily observed at very high temperatures, while it is absent at lower temperatures. It depends upon the concentration of CDBACl and the electrolyte used. The results are different from those obtained for the adsorption of cetyltrimethylammonium bromide on mercury, indicating the importance of interaction between the hydrophobic chains.     

Large enhancement of the nonlinear optical response of reduced fullerene derivatives

The third-order nonlinear optical properties of fulleropyrrolidine and its salt as well as their reduced forms are investigated. Upon reduction, the response increases by up to, and sometimes more than, three orders of magnitude, giving values comparable to the largest ever reported. Calculations and experiments provide a coherent picture for the nonlinear optical properties of these new materials.     

Reductive-holistic cycle: A model for the study of the didactic procedure

The concept ofreality level may be useful as a catalyst among several systems in the area of knowledge. This concept is leading us to ask, if we can make a reduction from a reality level to another, that is to the problem ofreductionism. Relative to it is the problem ofholism. At the end these concepts are connected to the category theory and adjoint functors. Within the framework of this aspect we set up a model for the study of the didactic procedure. This model is a feedback system between two reality levels or categories, these of the teacher and of the student. So, the article seeks to enhance and improve the teaching of mathematics by its attempt to understand both student's and teacher's knowledge in the same terms.     

Tight-Binding Molecular Dynamics Study of Heteronuclear Systems: Application to Si m Ge n Clusters

The structural properties of Si _m Ge _n clusters are investigated using both the tight-binding molecular dynamics (TBMD) and the ab initio simple and triple-coupled clusters [CCSD(T)] as well as the MP2/6–311G* methods. The TBMD scheme uses a minimal parameter basis and is formulated for heteroatomic systems. Excellent agreement is obtained between these methods, indicating transferability for the TBMD formulation.