Perspectives on Advanced Mathematical Thinking

This article sets the stage for the following 3 articles. It opens with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education. It then locates the articles within 4 recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level, and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices. Finally, it points out some commonalities and differences among the 3 following articles.     

Large Scale Linear Programs and Heuristics for the Design of Survivable Telecommunication Networks

We consider the problem of providing a minimum cost multi-service network subject to one link failure scenarios. We assume our network is fully meshed and demand is satisfied by using direct or two hop-paths. We provide a large scale linear programming formulation and propose and test two effective heuristics.     

Time reversal for infinite-dimensional diffusions

Summary In this paper we analize the reversibility of the diffusion property for the solution of certain infinite-dimensional systems of stochastic differential equations. Necessary and sufficient conditions ensuring this reversibility are given. The proofs use the techniques of the stochastic calculus of variations.This work was partly done when the first author was visiting the Centre de Recerca Matemàtica at Barcelona     

Milch

Ohne Zusammenfassung     

Efficient RNase H-directed cleavage of RNA promoted by antisense DNA or 2'F-ANA constructs containing acyclic nucleotide inserts

The ability of modified antisense oligonucleotides (AONs) containing acyclic interresidue units to support RNase H-promoted cleavage of complementary RNA is described. Manipulation of the backbone and sugar geometries in these conformationally labile monomers shows great benefits in the enzymatic recognition of the nucleic acid hybrids, while highlighting the importance of local strand conformation on the hydrolytic efficiency of the enzyme more conclusively. Our results demonstrate that the duplexes support remarkably high levels of enzymatic degradation when treated with human RNase HII, making them efficient mimics of the native substrates. Furthermore, interesting linker-dependent modulation of enzymatic activity is observed during in vitro assays, suggesting a potential role for this AON class in an RNase H-dependent pathway of controlling RNA expression. Additionally, the butyl-modified 2'F-ANA AONs described in this work constitute the first examples of a nucleic acid species capable of eliciting high RNase H activity while possessing a highly flexible molecular architecture at predetermined sites along the AON.     

Rheological properties of multisticker associative polyelectrolytes in semidilute aqueous solutions

Multisticker associative polyelectrolytes of acrylamide (≈86 mol %) and sodium 2‐acrylamido‐2‐methylpropanesulfonate (≈12 mol %), hydrophobically modified with N,N‐dihexylacrylamide groups (≈2 mol %), were prepared with a micellar radical polymerization technique. This process led to multiblock polymers in which the length of the hydrophobic blocks could be controlled through variations in the surfactant‐to‐hydrophobe molar ratio, that is, the number of hydrophobes per micelle (N_H). The rheological behavior of aqueous solutions of polymers with the same molecular weight and the same composition but with two different hydrophobic block lengths (N_H = 7 or 3 monomer units per block) was investigated as a function of the polymer concentration with steady‐flow, creep, and oscillatory experiments. The critical concentration at the onset of the viscosity enhancement decreased as the length of the hydrophobic segments in the polymers increased. Also, an increase in the N_H value significantly enhanced the thickening ability of the polymers and affected the structure of the transient network. In the semidilute unentangled regime, the behavior of the polymer with long hydrophobic segments (N_H = 7) was studied in detail. The results were well explained by the sticky Rouse theory of associative polymer dynamics. Finally, the viscosity decreased with an increase in the temperature, mainly because of a lowering of the sample relaxation time. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1640–1655, 2004     

Electrochemical grafting by reduction of 4-aminoethylbenzenediazonium salt: Application to the immobilization of (bio)molecules

We propose in this study a simple and rapid way to produce stable amino-derivatized conductive surfaces for the subsequent immobilization of (bio)molecules. This was achieved through the use of (4-aminoethyl)benzenediazonium salt (AEBD), which was immobilized on glassy carbon and gold electrodes by its electrochemical reduction. The presence of terminal grafted amino functions was evidenced with XPS by analyzing N1s core level. Besides this conventional surface characterisation, an electrochemical strategy is proposed here to evidence the presence of immobilized amines, in which the chemical reactivity of amines towards 2,4,6-trinitrobenzenesulfonic acid (TNBS) is used. Surface-bound TNBS served as an electrochemical marker and was detected by cyclic voltammetry. Additionally, pre-modified gold electrodes with amino functions can be derivatized with biomolecules such as glutathione (GSH). Glutathione attachment was evidenced by studying the electrochemical behaviour of ferri/ferrocyanide redox before and after its immobilization. The functionalized electrodes were then used for the detection of copper ions in neutral aqueous solutions.     

Synthesis of Unsubstituted and 4,4′-Substituted Oligobipyridines as Ligand Strands for Helicate Self-Assembly

A general strategy for the synthesis of oligobipyridine ligands 2 – 5 containing from two to five 2,2′-bipyridine subunits, for helical metal complexes is described (sec Scheme). Both the unsubstituted parent strands ( a series) as well as their derivatives bearing fester or amide functions in the 4,4′-positions of the bipyridine moieties ( b – d series) have been obtained.