Cardinal characteristics at κ in a small u(κ) model

We provide a model where $\mathfrak{u}(\kappa )<2^{\kappa }$ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties.     

Uniform Convergence for Approximate Traveling Waves in Linear Reaction–Diffusion–Hyperbolic Systems

In this paper we study linear reaction–hyperbolic systems of the form , (i = 1, 2, ..., n) for x > 0, t > 0 coupled to a diffusion equation for p ₀ = p ₀(x, y, θ, t) with “near-equilibrium” initial and boundary data. This problem arises in a model of transport of neurofilaments in axons. The matrix (k _ij ) is assumed to have a unique null vector with positive components summed to 1 and the v _j are arbitrary velocities such that . We prove that as the solution converges to a traveling wave with velocity v and a spreading front, and that the convergence rate in the uniform norm is , for any small positive α.     

A neutral redox-switchable [2]rotaxane

A limited range of redox-active, rotaxane-based, molecular switches exist, despite numerous potential applications for them as components of nanoscale devices. We have designed and synthesised a neutral, redox-active [2]rotaxane, which incorporates an electron-deficient pyromellitic diimide (PmI)-containing ring encircling two electron-rich recognition sites in the form of dioxynaphthalene (DNP) and tetrathiafulvalene (TTF) units positioned along the rod section of its dumbbell component. Molecular modeling using MacroModel guided the design of the mechanically interlocked molecular switch. The binding affinities in CH(2)Cl(2) at 298 K between the free ring and two electron-rich guests--one (K(a) = 5.8 × 10(2) M(-1)) containing a DNP unit and the other (K(a) = 6.3 × 10(3) M(-1)) containing a TTF unit--are strong: the one order of magnitude difference in their affinities favouring the TTF unit suggested to us the feasibility of integrating these three building blocks into a bistable [2]rotaxane switch. The [2]rotaxane was obtained in 34% yield by relying on neutral donor-acceptor templation and a double copper-catalysed azide-alkyne cycloaddition (CuAAC). Cyclic voltammetry (CV) and spectroelectrochemistry (SEC) were employed to stimulate and observe switching by this neutral bistable rotaxane in solution at 298 K, while (1)H NMR spectroscopy was enlisted to investigate switching upon chemical oxidation. The neutral [2]rotaxane is a chemically robust and functional switch with potential for applications in device settings.     

Vibrational relaxation in the group IVA trimethylmetal chlorides

The temperature dependence of the polarized and depolarized Raman spectra of the ν₂, ν₄, ν₆ and ν₇ modes were measured for t-butyl chloride and the analogous group IVA trimethylmetal chrlorides (silicon, germanium and tin). Analysis of the lineshapes revealed that isotropic second moments and vibrational relaxation times for a given mode remained approximately constant through the series. This tranferability of relaxation parameters between molecules extended to modulation times calculated from the Kubo formalism. The above results are in contrast to earlier studies on molecules of dissimilar structure. They provide some preliminary evidence that the mechanism of vibrational relaxation may be the same for equivalent modes in members of the series.     

A filtration problem in a porous medium with variable permeability

Sunto Un problema di frontiera libera (moto di un fluido attraverso una diga in terra non omogenea) è ricondotto allo studio di una disequazione variazionale. Si danno condizioni sul coefficiente di permeabilità sufficienti ad assicurare che la parte bagnata della diga è un sottografico.

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Entrata in Redazione il 30 giugno 1976.

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This paper is partially supported by National Science Foundation Grant MPS 72-04959 A02, and by C.N.R. of Italy through L.A.N. of Pavia.     

The study of solute—solute forces by NMR relaxation

By calculation it is found that the enhancement of the NMR relaxation rate of ⁷Li⁺ by Mn²⁺ or Ni²⁺ in aqueous solution is measurably different for two models which are consistent with other magnetic relaxation and thermodynamic data for the solutions.