Reducibility of matrix weights

In this paper, we discuss the notion of reducibility of matrix weights and introduce a real vector space \(\mathcal C_\mathbb R\) which encodes all information about the reducibility of W. In particular, a weight W reduces if and only if there is a nonscalar matrix T such that \(TW=WT^*\). Also, we prove that reducibility can be studied by looking at the commutant of the monic orthogonal polynomials or by looking at the coefficients of the corresponding three-term recursion relation. A matrix weight may not be expressible as direct sum of irreducible weights, but it is always equivalent to a direct sum of irreducible weights. We also establish that the decompositions of two equivalent weights as sums of irreducible weights have the same number of terms and that, up to a permutation, they are equivalent. We consider the algebra of right-hand-side matrix differential operators \(\mathcal D(W)\) of a reducible weight W, giving its general structure. Finally, we make a change of emphasis by considering the reducibility of polynomials, instead of reducibility of matrix weights.     

New Route to Polymeric Nanoparticles by Click Chemistry Using Bifunctional Cross-Linkers

A new route to functional polymeric nanoparticles (PNPs) of different chemical nature in the 3 to 20 nm size range is reported by combining both radical addition fragmentation chain transfer (RAFT) polymerization and “click” chemistry (CC) techniques. RAFT polymerization was employed for the synthesis of well-defined statistical copolymers with pending –Cl groups along the macromolecular chain. After transformation of the –Cl groups to –N₃ groups by treatment with sodium azide, an appropriate bifunctional cross-linker is employed to obtain PNPs under CC conditions promoting intramolecular cycloaddition (cross-linking). Following this new route, polystyrene, poly(alkyl (meth)acrylate), polymethacrylic acid, poly(sodium styrenesulfonate) and poly(N-isopropyl) NPs have been synthesized and in-deep characterized.     

Electronic and geometric properties of Au nanoparticles on Highly Ordered Pyrolytic Graphite (HOPG) studied using X-ray Photoelectron Spectroscopy (XPS) and Scanning Tunneling Microscopy (STM)

Au nanoparticles grown on mildly sputtered Highly Ordered Pyrolytic Graphite (HOPG) surfaces were studied using Scanning Tunneling Microscopy (STM) and X-ray Photoelectron Spectroscopy (XPS). The results were compared with those of Ag nanoparticles on the same substrate. By varying the defect densities of HOPG and the Au coverages, one can create Au nanoparticles in various sizes. At high Au coverages, the structures of the Au films significantly deviate from the ideal truncated octahedral form: the existence of many steps between different Au atomic layers can be observed, most likely due to a high activation barrier of the diffusion of Au atoms across the step edges. This implies that the particle growth at room temperature is strongly limited by kinetic factors. Hexagonal shapes of Au structures could be identified, indicating preferential growth of Au nanostructures along the (111) direction normal to the surface. In the case of Au, XPS studies reveal a weaker core level shift with decreasing particle size compared to the 3d level in similarly sized Ag particles. Also taking into account the Auger analysis of the Ag particles, the core level shifts of the metal nanoparticles on HOPG can be understood in terms of the metal/substrate charge transfer. Ag is (partially) positively charged, whereas Au negatively charged on HOPG. It is demonstrated that XPS can be a useful tool to study metal-support interactions, which plays an important role for heterogeneous catalysis, for example.     

Tracking customer portfolio composition: A factor analysis approach

In this paper, we address the changing composition of a customer portfolio taking into account actions undertaken by the company to adapt its service offer to market conditions and/or technological innovations. We present a specific methodology to identify clusters of customers in different periods and then compare them over time. The classification process takes into account both qualitative and quantitative aspects of the consumption levels of the services or products offered by the company. The possibility of period‐to‐period variation in the customer portfolio and the service or product offer is also considered, in order to achieve a more realistic scenario. The core of the proposed methodology is related to the family of exploratory factorial and cluster techniques. The customers are classified by using a bicriterial clustering methodology based on ‘tandem’ analysis (multiple factor analysis+cluster analysis of the main factors). The bicriterial approach allows for a compromise between customers' consumption levels (a quantitative criterion) and their consumption/non‐consumption pattern (a qualitative criterion). The evolution of the customer portfolio composition is explored through multiple correspondence analysis. This technique allows visual comparison of the position of different clusters against time and the identification of key changes in customer consumption behavior. The methodology is tested on realistic customer portfolio scenarios for a major telecommunication company. We simulate various scenarios to show the strengths of our proposal. Copyright © 2009 John Wiley & Sons, Ltd.     

Electrokinetics: insights from simulation on the microscopic scale

Electrokinetic effects, i.e. the coupled hydrodynamic and electric phenomena which occur near charged interfaces, constitute a challenge to theorists due to the variety of length and time scales involved. We discuss recent advances in the modelling of these phenomena, emphasising the interplay between the molecular specificity and the collective induced flows that emerge. We discuss the complementary simulation methodologies that have been developed either to focus on the molecular aspects of electrokinetics or on their effective properties on larger scales, as well as the proposed hybrid schemes that can incorporate both aspects. We highlight the insights that molecular studies have brought on the nature of interfacial charges and their implications for kinetic phenomena in confined fluids and also discuss advances in a number of relevant contexts.     

Lie algebras admitting a unique quadratic structure

We prove that any Lie algebra g over a field K of characteristic zero admitting a unique up to a constant quadratic structure is necessarily a simple Lie algebra. If the field K is algebraically closed, such condition is also sufficient.

Further, a real Lie algebra g admits a unique quadratic structure if and only if its complexification g^C is a simple Lie algebra over C     

Molecular dynamics assessment of doxorubicin–carbon nanotubes molecular interactions for the design of drug delivery systems

Carbon nanotubes (CNTs) constitute an interesting material for nanomedicine applications because of their unique properties, especially their ability to penetrate membranes, to transport drugs specifically and to be easily functionalized. In this work, the energies of the intermolecular interactions of single-walled CNTs and the anticancer drug doxorubicin (DOX) were determined using the AMBER 12 molecular dynamics MM/PBSA and MM/GBSA methods with the aim of better understanding how the structural parameters of the nanotube can improve the interactions with the drug and to determine which structural parameters are more important for increasing the stability of the complexes formed between the CNTs and DOX. The armchair, zigzag, and chiral nanotubes were finite hydrogen-terminated open tubes, and the DOX was encapsulated inside the tube or adsorbed on the nanotube surface. Pentagon/heptagon bumpy defects and polyethylene glycol (PEG) nanotube functionalization were also studied. The best interaction occurred when the drug was located inside the cavity of the nanotube. Armchair and zigzag nanotubes doped with nitrogen, favored interaction with the drug, whereas chiral nanotubes exhibited better drug interactions when having bumpy defects. The π-π stacking and N-H…π electrostatic interactions were important components of the attractive drug-nanotube forces, enabling significant flattening of the nanotube to favor a dual strong interaction with the encapsulated drug, with DOX–CNT equilibrium distances of 3.1–3.9 Å. These results can contribute to the modeling of new drug-nanotube delivery systems.

     

Thermodynamic study of complexation of Zn(II)/L (L− = acetate,indomethacin and diclofenac anions) by isothermal titration calorimetry

Journal of Thermal Analysis and Calorimetry - In this work, a thermodynamic study of the Zn(II)/L systems (L??=?acetate, AcO? or indomethacin anion, Indo? or...     

On the Use of Thermodynamic Cycles for the Calculation of Standard Potentials for the Oxidation of Solid Metals in Solution

The performance of a thermodynamic cycle for the calculation of the standard reduction potential (SRP) of a series of metals is examined. It is found that the introduction of simple entropic corrections substantially improves the agreement with experimental data. The accuracy of the estimations is in the range of 0.04 V, which opens the possibility to calculate the SRP for metals in non-aqueous solvents or other unusual situations.