Influence of the sulfonate countercation on the thermal stability of nafion perfluorosulfonate membranes

We report a strong dependence of the thermal stability of Nafion® perfluorosulfonate ionomer on the nature of the counterion associated with the fixed sulfonate site. These results were obtained using thermal gravimetric analysis on a series of alkali metal and alkyl ammonium cation-exchanged Nafion films. We have found that the temperature of decomposition of Nafion is inversely dependent on the size of the exchanged cation; i.e., Nafion films show improved thermal stability as the size of the counter cation decreases. We attribute this inverse relationship of thermal stability with counterion size to an initial decomposition reaction which is strongly influenced by the strength of the sulfonate-coun-terion interaction. © 1993 John Wiley & Sons, Inc.     

Large Water-Soluble Cyclophanes with Convergent Intracavity Functionality

New tricyclic spacers, readily available through fourfold Mannich reaction of substituted dibenzyl ketones, were introduced into a series of ten H₂O-soluble cyclophanes with spacious preorganized cavity binding sites. These spacers provide H₂O-solubility with amine or crown-ether functionality remote from the cyclophane cavity while directing functional groups such as keto or OH groups in a precise geometrical array inside the cavity. The cyclophanes were designed to include organic substrates via a combination of apolar and specific polar functional group interactions. The X-ray crystal-structure analysis of the tritopic receptor 18 with one potential neutral-molecule and two cation-binding sites showed a large rectangular open cavity with dimensions of roughly 9 × 14 Å and a spacing of 9.7 Å between the O-atoms of two convergent C?O groups. Despite the binding-site preorganization, cyclophanes incorporating two of the new spacers did not show any substrate binding in aqueous solutions. The failure of these systems to function as receptors is mainly due to steric hindrance to important cyclophane aromatic ring-guest interactions. Also, the favorable solvation of the intracavity functionality may prevent the formation of complexes. Hybrid receptors constructed from the novel spacers and diphenylmethane units were found to bind flat aromatic substrates as well as bulky [4.2]paracyclophanes. The observed large differences in stability (ΔΔG°> 2 kcal mol^?1) of the complexes formed by three structurally closely related hybrid receptors with convergent C?O, OH or CH₂ groups and 6-hydroxynaphthalene-2-carbonitrile as guest can be explained by a strong solvation effect of the convergent functional groups on apolar inclusion complexation.     

A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.     

The many proofs of an identity on the norm of oblique projections

Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P ²=P, which is neither null nor the identity, it holds that ||P|| = ||I –P||. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.     

Extended Rees algebras and mixed multiplicities

Partially supported by the general research fund at the University of Kansas     

Initial-boundary value problems for incomplete singular perturbations of hyperbolic systems

The general problem studied has as a prototype the full non-linear Navier-Stokes equations for a slightly viscous compressible fluid including the heat transfer. The boundaries are of inflow-outflow type, i.e. non-characteristic, and the boundary conditions are the most general ones with any order of derivatives. It is assumed that the uniform Lopatinsky condition is satisfied. The goal is to prove uniform existence and boundedness of solution as the viscosity tends to zero and to justify the boundary layer asymptotics. The paper consists of two parts. In Part I the linear problem is studied. Here, uniform lower and higher order tangential estimates are derived and the existence of a solution is proved. The higher order estimates depend on the smoothness of coefficients; however this smoothness does not exceed the smoothness of the solution. In Part II the quasilinear problem is studied. It is assumed that for zero viscosity the overall initial-boundary value problem has a smooth solutionu ₀ in a time interval 0≦t≦T ₀. As a result the boundary laye, is weak and is uniformlyC ¹ bounded. This makes the linear theory applicable. an iteration scheme is set and proved to converge to the viscous solution. The convergence takes place for small viscosity and over the original time interval 0≦t≦T ₀.