Look-ahead in the two-sided reduction to compact band forms for symmetric eigenvalue problems and the SVD

Numerical Algorithms - We address the reduction to compact band forms, via unitary similarity transformations, for the solution of symmetric eigenvalue problems and the computation of the singular...     

Novel Approach of Evaluating Polymer Nanocomposite Structure by Measurements of the Freezing‐Point Depression

Summary: A novel experimental approach based on the freezing‐point depression of a solvent in a swollen gel has been developed to characterize the structure of nanocomposites. A higher depression in the freezing point has been related with an exfoliated nanocomposite. This increased depression not only depends on the formation of a tighter network but also on the decrease of the size of the solvent cages where the nucleation takes place.

The nucleation process of unfilled and organoclay‐filled natural rubber with the same crosslinking density.     

Triazine‐Carbon Nanotubes: New Platforms for the Design of Flavin Receptors

The synthesis of functionalised carbon nanotubes as receptors for riboflavin (RBF) is reported. Carbon nanotubes, both single‐walled and multi‐walled, have been functionalised with 1,3,5‐triazines and p‐tolyl chains by aryl radical addition under microwave irradiation and the derivatives have been fully characterised by using a range of techniques. The interactions between riboflavin and the hybrids were analysed by using fluorescence and UV/Vis spectroscopic techniques. The results show that the attached functional groups minimise the π‐π stacking interactions between riboflavin and the nanotube walls. Comparison of p‐tolyl groups with the triazine groups shows that the latter have stronger interactions with riboflavin because of the presence of hydrogen bonds. Moreover, the triazine derivatives follow the Stern–Volmer relationship and show a high association constant with riboflavin. In this way, artificial receptors in catalytic processes could be designed through specific control of the interaction between functionalised carbon nanotubes and riboflavin.     

Puiseux Expansions and Nonisolated Points in Algebraic Varieties

We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given truncated Puiseux series vector centered at the point ensuring that it is not isolated. In addition, in the case that the set of all common solutions of the system has dimension 1, we obtain further conditions specifying to what extent the given vector of truncated Puiseux series coincides with the initial part of a parametrization of a curve of solutions passing through the point.     

Understanding the reaction between muonium atoms and hydrogen molecules: zero point energy,tunnelling, and vibrational adiabaticity

The advent of very precise measurements of rate coefficients in reactions of muonium (Mu), the lightest hydrogen isotope, with H₂ in its ground and first vibrational state and of kinetic isotope effects with respect to heavier isotopes has triggered a renewed interests in the field of muonic chemistry. The aim of the present article is to review the most recent results about the dynamics and mechanism of the reaction Mu+H₂ to shed light on the importance of quantum effects such as tunnelling, the preservation of the zero point energy, and the vibrational adiabaticity. In addition to accurate quantum mechanical (QM) calculations, quasiclassical trajectories (QCT) have been run in order to check the reliability of this method for this isotopic variant. It has been found that the reaction with H₂(v=0) is dominated by the high zero point energy (ZPE) of the products and that tunnelling is largely irrelevant. Accordingly, both QCT calculations that preserve the products’ ZPE as well as those based on the Ring Polymer Molecular Dynamics methodology can reproduce the QM rate coefficients. However, when the hydrogen molecule is vibrationally excited, QCT calculations fail completely in the prediction of the huge vibrational enhancement of the reactivity. This failure is attributed to tunnelling, which plays a decisive role breaking the vibrational adiabaticity when v=1. By means of the analysis of the results, it can be concluded that the tunnelling takes place through the ν₁=1 collinear barrier. Somehow, the tunnelling that is missing in the Mu+H₂(v=0) reaction is found in Mu+H₂(v=1).     

Synthesis,characterization, and influence of synthesis parameters on particle sizes of a new microgel family

Poly(p‐nitrophenylacrylate‐co‐methacrylamide) and poly(p‐Nitrophenylacrylate‐co‐N,N′‐isopropylacrylamide) reactive microgels were synthesized by precipitation polymerization. The process was followed qualitatively by infrared spectroscopy (ATR‐FTIR) and microgels composition was determined by nuclear magnetic resonance (¹H NMR). Scanning electron microscopy of obtained colloidal particles showed strictly spherical morphologies with a moderate polydispersity. The average hydrodynamic particle diameter and particle size distributions were measured by quasi‐elastic light scattering and the particle size distributions obtained ranged from 100 to 600 nm. Several synthetic parameters affect the particle size of these materials and thus, indirectly, their properties and future applications. In this article, we report the influence of different polymerization reaction conditions in the final microgel dimensions. For example, we observed that the different solvent‐comonomer affinity induced a significant change in swollen particle size of the copolymeric microgels. On the other hand, the crosslinking density limited the particle sizes, but an excess of crosslinker content in the reaction mixture resulted in the opposite effect. Finally, we also studied the influence of initiator content in the mean particle size. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3833–3842, 2007