Asymptotic forms of solutions of certain linear ordinary differential equations

We analyze the asymptotic behavior as x → ∞ of the product integral Π_x0^xe^A(s)ds, where A(s) is a perturbation of a diagonal matrix function by an integrable function on [x₀,∞). Our results give information concerning the asymptotic behavior of solutions of certain linear ordinary differential equations, e.g., the second order equation y″ = a(x)y.     

Reinforcement problems for elliptic equations and variational inequalities

Summary Consider the Dirichlet problem for an elliptic equation in a domain , with coefficients having discontinuity on a surface . Suppose divides into _{1 2}(₂ the inner core), the thickness of ₁ is of order of magnitude , and the modulus of ellipticity in ₁ is of order magnitude ₁. The asymptotic behavior of the solution is studied as 0, ₁ 0, provided lim (/₁) exists. Other questions of this type are studied both for elliptic equations and for elliptic variational inequalities.The second author is partially supported by National Science Foundation Grant 7406375 A01. The third author is partially supported by National Science Foundation Grant MC575-21416 A01.     

ESR lineshapes and kinetic behavior of nitroxide spin probes in micellar solutions

The ESR spectrum of the nitroxide radical 2,2,6,6-tetramethylpiperidine-N-oxide (TEMPO) has been investigated in aqueous solutions of the following surfactants:n-octylammonium bromide, sodiumn-octylsulfonate,n-decylammonium bromide,n-docecyltrimethylammonium bromide, and sodiumn-dodecylsulfate. The spectra were recorded at 25° C as function of surfactant concentration in the ranges 0–0.5m for the C₁₀ and C₁₂ compounds and 0–1.0m for the others. Analysis of the spectra using computer simulation methods yields the hyperfine coupling constanta _H and the widthW _H of the partially resolved lines in the proton hyperfine structure. Changes in these variables with surfactant concentration are interpreted from medium effects on the magnetic properties of the radical, kinetics of radical-micelle interactions, and rotational dynamics of the nitroxide probe in these solutions.