On the cycle map for torsion algebraic cycles of codimension two

Oblatum 7-XI-1990 &; 25-III-1991     

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002     

Total Colorings Of Degenerate Graphs

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. A graph G is s-degenerate for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤s. We prove that an s-degenerate graph G has a total coloring with Δ+1 colors if the maximum degree Δ of G is sufficiently large, say Δ≥4s+3. Our proof yields an efficient algorithm to find such a total coloring. We also give a lineartime algorithm to find a total coloring of a graph G with the minimum number of colors if G is a partial k-tree, that is, the tree-width of G is bounded by a fixed integer k.     

The effect of UV irradiation on the reduction of Au(III) ions adsorbed on manganese dioxide.

The effect of UV (ultraviolet) irradiation on the adsorption of Au(III) ions on manganese dioxide and their reduction to Au(0) (gold with 0 valence state) was investigated using XPS (X-ray photoelectron spectroscopy) and 197Au M?ssbauer spectroscopy. The UV irradiation accelerated the adsorption and the reduction. From the fact that the proportion of Au(0) estimated from Au 4f XPS spectra for surface analysis was significantly smaller than that from 197Au M?ssbauer spectra for bulk analysis, we deduced that Au(0) was interpenetrated to the inside of manganese dioxide (into deeper places than about 30 A) where XPS is impossible to detect. The content of surface hydroxyl groups on manganese dioxide also increased due to the UV irradiation. The relationship between the charge in the content of hydroxyl groups and the interpenetration of Au(0) is discussed.     

Enhanced skin permeation of salicylate by ion-pair formation in non-aqueous vehicle and further enhancement by ethanol and l-menthol

Enhancement of skin permeability of salicylate from non-aqueous vehicle by ion-pair formation with either alkylamines or benzylamine as model cationic ions was examined in excised guinea pig dorsal skin. Solubility of salicylate in isopropyl myristate (IPM) was increased by the addition of either alkylamines or benzylamine as counter ions. The increase was more significant in the presence of amines with longer alkyl chains. Flux of salicylate increased in the presence of these amines due to the increase in the solubility. Maximum flux was observed in the presence of n-hexylamine, which induced an 11-fold increase due to 137-fold increase in solubility. Flux and permeability coefficients of salicylate in the presence of n-butylamine, n-hexylamine, iso-octylamine and benzylamine as counter ions in IPM were larger than those of the non-ionic form of salicylic acid. Flux of 3-methylsalicylate (3-CH3 substituent) and that of 5-hydroxysalicylate (5-OH substituent) were smaller than that of salicylate in the presence of n-hexylamine. After partition to the skin surface, the ion-pair is suggested to dissociate and permeate separately according to the study using lidocaine as the counter ion. Flux of salicylate increased in the presence of benzylamine as the counter ion by the addition of 15% ethanol and 15% ethanol plus 1% l-menthol due to further improvement in the solubility as well as an increase in the permeability coefficient.     

Structural phase transitions at clean and metal-covered Si(111) surfaces investigated by RHEED spot analysis

Structural phase transitions between various kinds of superlattice structures formed on a Si(111) surface have been investigated by spot analysis of reflection high-energy electron diffraction (RHEED). Reversible transitions induced by temperature changes and irreversible ones induced by metal depositions were observed. Detailed discussions on the dynamics of the phase transitions are made by quantitative analyses of integrated spot intensity and profile. For a phase transition of 7′7  1′1 structures on a clean Si(111) surface, a hysteresis with temperature difference of 5°C. between in heating and cooling processes was found in the spot intensity change, indicating a first-order transition. Hysteresis was hardly recognized, on the other hand, for transitions of Au-induced superstructures (5×2-Au or ×-Au)  1×1-Au. The spot profiles were found to be broadened during the transition of Si(111)-×-Au  1×1-Au, which was a signature of a continuous transition, while the profiles remained unchanged during the transitions of the 7×7  1×1 and 5×2-Au  1×1-Au phases. Structural conversions induced by In adsorption on the Si(111) surface kept at constant temperatures were also analyzed. The conversions at room temperature were totally dependent on the initial substrate surface structures; the 7×7 surface did not show any structural conversion with In adsorption, while the ×-In surface successively converted to a 2×2 and a × phase with coverage increase. The structural transitions at elevated temperatures were sensitively dependent on the temperatures. Sequences of transitions among the 7×7, 4×1, ×, 1×, and ×4 were quantitatively revealed as changes in RHEED spot intensity.