Good and viscosity solutions of fully nonlinear elliptic equations

We introduce the notion of a ``good" solution of a fully nonlinear uniformly elliptic equation. It is proven that ``good" solutions are equivalent to -viscosity solutions of such equations. The main contribution of the paper is an explicit construction of elliptic equations with strong solutions that approximate any given fully nonlinear uniformly elliptic equation and its -viscosity solution. The results also extend some results about ``good" solutions of linear equations.

     

Sublimation of atomic layers from a chromium surface

We employ low-energy electron microscopy to study the kinetics of thermal etching, or sublimation, of Cr(001) at approximately 1100 K. Atomic layers are removed from the surface by spontaneous nucleation and growth of two-dimensional vacancy islands, by rotation of spiral steps, and by island decay. The growth rates of vacancy islands and the rotation frequencies of double spirals are measured as a function of temperature, and the results are correlated with activation barriers of surface processes. Mass transport between the surface and bulk is shown to be unimportant.     

Surface mass diffusion and step stiffness on an anisotropic surface; Mo(0 1 1)

Results of step fluctuation experiments for Mo(0 1 1), using low-energy electron microscopy, are re-examined using recently developed procedures that offer accurate coefficients of surface mass diffusion. By these means, surface diffusion D_s is documented at T/T_m ∼ 0.5, while the crossover to relaxation driven by bulk vacancy diffusion is inferred for T/T_m ∼ 0.6. Here, T_m is the melting temperature T_m = 2896 K. We obtain D_s = 4 × 10⁻⁴ exp(−1.13 eV/k_BT) cm²/s for the temperature interval 1080-1680 K. Possible indications of diffusion along step edges appear for T/T_m ∼ 0.4. The same measurements of step fluctuation amplitudes determine also the step stiffness, which by symmetry is anisotropic on Mo(0 1 1). It is shown that three independent procedures yield mutually consistent step stiffness anisotropies. These are (1) step fluctuation amplitudes; (2) step relaxation rate anisotropies; and (3) the observed anisotropies of islands in equilibrium on the Mo(0 1 1) surface. The magnitude of the step stiffness obtained from step edge relaxation is consistent with earlier measurements that determine diffusion from grain boundary grooving.     

Viscosity Solutions of an Infinite-Dimensional Black—Scholes—Barenblatt Equation

We study an infinite-dimensional Black—Scholes—Barenblatt equation which is a Hamilton—Jacobi—Bellman equation that is related to option pricing in the Musiela model of interest rate dynamics. We prove the existence and uniqueness of viscosity solutions of the Black—Scholes—Barenblatt equation and discuss their stochastic optimal control interpretation. We also show that in some cases the solution can be locally uniformly approximated by solutions of suitable finite-dimensional Hamilton—Jacobi—Bellman equations.     

Characterisation of structured thin films made from complex materials by photoabsorption spectromicroscopy

2 Al₃ and YBa₂Cu₃O₇/PrBa₂Cu₃O₇. To investigate devices built from these complex materials we applied element-sensitive photoemission electron microscopy (PEEM). Information about the chemical composition of the imaged sample can be obtained by PEEM via tuning the photon energy to X-ray absorption edges. To apply spectromicroscopy we acquired microscopic images using photon energies near and at the edges. Such images give the lateral distribution of a specific element. Microspectroscopy is performed by recording the intensity of the true secondary electrons in selected spots during a sweep of the photon energy. The main aim of our work was to observe oxygen-related defects and changes in the composition affecting the physical properties of the materials. Therefore, we applied both methods to micro-patterned devices using soft-X-ray synchrotron radiation and found that small local defects and chemical differences can be easily detected. Such defects and chemical differences are quite critical to the physical properties of the devices, since they simulate spurious effects thus influencing the reliability of the devices. Received: 13 March 1998/Accepted: 22 April 1998     

Adjusting the Structure of β-Cyclodextrin to Improve Complexation of Anthraquinone-Derived Drugs

β-Cyclodextrin (CD) derivatives containing an aromatic triazole ring were studied as potential carriers of the following drugs containing an anthraquinone moiety: anthraquinone-2-sulfonic acid (AQ2S); anthraquinone-2-carboxylic acid (AQ2CA); and a common anthracycline, daunorubicin (DNR). UV-Vis and voltammetry measurements were carried out to determine the solubilities and association constants of the complexes formed, and the results revealed the unique properties of the chosen CDs as effective pH-dependent drug complexing agents. The association constants of the drug complexes with the CDs containing a triazole and lipoic acid (βCDLip) or galactosamine (βCDGAL), were significantly larger than that of the native βCD. The AQ2CA and AQ2S drugs were poorly soluble, and their solubilities increased as a result of complex formation with βCDLip and βCDGAL ligands. AQ2CA and AQ2S are negatively charged at pH 7.4. Therefore, they were less prone to form an inclusion complex with the hydrophobic CD cavity than at pH 3 (characteristic of gastric juices) when protonated. The βCDTriazole and βCDGAL ligands were found to form weaker inclusion complexes with the positively charged drug DNR at an acidic pH (pH 5.5) than in a neutral medium (pH 7.4) in which the drug dissociates to its neutral, uncharged form. This pH dependence is favorable for antitumor applications.