Essential maps and coincidence theory

Using an elementary approach, we present new coincidence principles for general classes of maps.     

Fixed points for mappings with a contractive iterate at each point

We generalize the results of Sehgal and Guseman for mappings on a complete metric space with a contractive iterate condition at each point.     

Preparation of a Novel Polymer‐Modified Si Surface for DNA Immobilization

The design of a novel polymer‐modified overlayer composed of PPAPE and GPMS on a silicon wafer for immobilization of DNA molecules is described. After hydroxylation of Si(100) surfaces, GPMS molecules were self‐assembled onto these surfaces. PPAPE molecules were then covalently attached to the epoxy‐terminated surfaces. The incubation time and concentration of PPAPE was found to effect both layer thickness and water CA. The type of organic solvent and the pH were found to change the nature of the PPAPE‐modified surface for DNA immobilization. It is concluded that PPAPE‐modified surfaces show advantages for DNA immobilization by electrostatic interactions between DNA molecules and positively charged free amino groups of the PPAPE‐modified surfaces at the appropriate pH values.

     

An Extension of Polyak’s Theorem in a Hilbert Space

Let H be an infinite-dimensional real Hilbert space equipped with the scalar product (⋅,⋅) _H . Let us consider three linear bounded operators,

Method validation for measurement of hair nicotine level in nonsmokers

The development of strategies to address the growing worldwide burden of exposure to secondhand smoke (SHS) would be facilitated by sensitive and accurate methods for assessing SHS exposure. Hair provides a readily available matrix for assessing biomarkers of typical SHS exposure. We developed and applied an optimized analytical method using an isotope dilution gas chromatography-mass spectrometry (GC/MS) for hair nicotine measurement. The utility of this optimized method is illustrated by presenting data on SHS exposure of women and children from 31 countries. Using this isotope dilution method with spiked samples (3.3 ng/mg), we found that the greatest hair nicotine extraction efficiency was obtained with a 60 min shaking time. In the field study (n = 2400), a positive association was evident between hair nicotine concentrations from nonsmokers and higher numbers of cigarettes smoked per day in a household.     

Interfacial chemistry in internally oxidized (Cu,Mg)-alloys

(Cu,Mg) alloys are internally oxidized at different oxygen chemical potential at 900°C. Oxidation scale microstructure is studied by SEM and TEM. MgO forms as large magnesia agglomerates without any special orientation relationship and isolated cubo-octahedral topotaxial MgO precipitates, the shape of which varies with decreasing oxygen activity from octahedral to cubic. The interfaces of the cubo-octahedral precipitates are studied in detail by CTEM, HREM and EELS. At the highest oxygen activity, important rigid-body contraction/expansion across the interface is found together with a strong modification in the interfacial electronic structure (compared to the adjacent bulk phases) indicating important hybridization of O 2p and Cu 3d states. Both suggest oxide bonding. At lower oxygen activity, interfaces show increasing structural disorder in the copper phase and microfaceting or terracing of the interfacial plane; the intensity of interfacial ELNES features associated to the O 2p and Cu 3d hybridization diminishes and finally disappears with decreasing oxygen activity. Changes with oxygen chemical potential in precipitate morphology, interface atomic and electronic structure are explained by Gibbs’ adsorption/desorption of excess oxygen to the interface. Adsorption isotherms are modeled for various configurations and compared to the experimental results.     

A note on reactive equilibria in the discounted prisoner's dilemma and associated games

Necessary and sufficient conditions are derived under which the Tit-for-Tat strategy pair is a subgame perfect equilibrium in the standard discounted prisoner's dilemma. The sensitivity of the equilibrium to changes in the discount parameters is shown to be a common feature of all such nontrivial “reactive” equilibria. This appears to rule them out as reasonable solutions to the discounted prisoner's dilemma. In remarks, we indicate how these results can be extended to a fairly general class of games.     

Synthetic utilization of polynitroaromatic compounds. 2. Synthesis Of 4,6-dinitro-1,2-benzisothiazol-3-ones and 4,6-dinitro-1, 2-benzisothiazoles from 2-benzylthio-4,6-dinitrobenzamides

Cyclization of 2-benzylthio-4,6-dinitrobenzamides to 4,6-dinitro-1, 2-benzisothiazol-3-ones was achieved using SO(2)Cl(2) in CH(2)Cl(2) at room temperature. Alkylation of these heterocycles proceeded in a nonregioselective manner to yield a mixture of corresponding O- and N-alkylated products. Oxidation of 4,6-dinitro-1,2-benzisothiazoles (50% H(2)O(2) in AcOH) afforded the corresponding S-oxides and S, S-dioxides, depending on oxidation conditions. Unexpectedly, oxidation of a 3-methoxy derivative resulted in ring opening with the formation of the corresponding sulfamide. Chlorination of these 4,6-dinitro-1,2-benzisothiazol-3-ones (PCl(5)-POCl(3)) gave the expected 3-chloroisothiazoles.