Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

Error Concealment Based on Semantic Prioritization with Hardware‐Based Face Tracking

With video compression standards such as MPEG‐4, a transmission error happens in a video‐packet basis, rather than in a macroblock basis. In this context, we propose a semantic error prioritization method that determines the size of a video packet based on the importance of its contents. A video packet length is made to be short for an important area such as a facial area in order to reduce the possibility of error accumulation. To facilitate the semantic error prioritization, an efficient hardware algorithm for face tracking is proposed. The increase of hardware complexity is minimal because a motion estimation engine is efficiently re‐used for face tracking. Experimental results demonstrate that the facial area is well protected with the proposed scheme.     

Kinetics of phenyl radical reactions with propane,n‐butane,n‐hexane,and n‐octane: Reactivity of C6H5 toward the secondary C?H bond of alkanes

The kinetics of C₆H₅ reactions with n‐C_nH_2n+2 (n = 3, 4, 6, 8) have been studied by the pulsed laser photolysis/mass spectrometric method using C₆H₅COCH₃ as the phenyl precursor at temperatures between 494 and 1051 K. The rate constants were determined by kinetic modeling of the absolute yields of C₆H₆ at each temperature. Another major product C₆H₅CH₃ formed by the recombination of C₆H₅ and CH₃ could also be quantitatively modeled using the known rate constant for the reaction. A weighted least‐squares analysis of the four sets of data gave k (C₃H₈) = (1.96 ± 0.15) × 10¹¹ exp[?(1938 ± 56)/T], and k (n‐C₄H₁₀) = (2.65 ± 0.23) × 10¹¹ exp[?(1950 ± 55)/T] k (n‐C₆H₁₄) = (4.56 ± 0.21) × 10¹¹ exp[?(1735 ± 55)/T], and k (n?C₈H₁₈) = (4.31 ± 0.39) × 10¹¹ exp[?(1415 ± 65)T] cm³ mol^?1 s^?1 for the temperature range studied. For the butane and hexane reactions, we have also applied the CRDS technique to extend our temperature range down to 297 K; the results obtained by the decay of C₆H₅ with CRDS agree fully with those determined by absolute product yield measurements with PLP/MS. Weighted least‐squares analyses of these two sets of data gave rise to k (n?C₄H₁₀) = (2.70 ± 0.15) × 10¹¹ exp[?(1880 ± 127)/T] and k (n?C₆H₁₄) = (4.81 ± 0.30) × 10¹¹ exp[?(1780 ± 133)/T] cm³ mol^?1 s^?1 for the temperature range 297‐‐1046 K. From the absolute rate constants for the two larger molecular reactions (C₆H₅ + n‐C₆H₁₄ and n‐C₈H₁₈), we derived the rate constant for H‐abstraction from a secondary C? H bond, k_s?CH = (4.19 ± 0.24) × 10¹⁰ exp[?(1770 ± 48)/T] cm³ mol^?1 s^?1. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 49–56, 2004     

Measurements of coupling and reflection characteristics of butt-joints in passive waveguide integrated laser diodes

Amplified spontaneous emission (ASE) spectra of passive waveguide integrated lasers have been studied to estimate the coupling efficiency and the reflectivity at the butt-joints between active and passive waveguides. A new method has been proposed for the analysis of ASE to extract the coupling efficiency and reflectivity at the butt-joints. This method was applied experimentally to estimate the coupling and reflection of the passive waveguide integrated lasers with different amounts of vertical misalignments of active and passive waveguides.     

A study of solid-state rhodium(III) sulfates

Solid-state rhodium(III) sulfates and their aqueous solutions were examined by IR and electronic absorption spectroscopy, thermogravimetry, X-ray powder diffraction analysis, and ¹⁰³Rh and ¹⁷O NMR spectroscopy. A study of the spontaneous aquation of freshly prepared solutions showed that this process results in an equilibrium between the subsystems of monomeric and oligomeric complexes. It was found that solid-state rhodium(III) sulfates vary in phase composition, basically consisting of dimeric and trimeric complexes.     

Hierarchically Ordered Polymer Films by Templated Organization of Aqueous Droplets

Hierarchically ordered structures facilitate the incorporation of diverse functions simultaneously. The present report introduces a simple and novel strategy for producing hierarchically ordered polymeric films. Hierarchical ordering of aqueous droplets on a polymer solution is realized by the imposition of physical confinement via various shaped gratings. After drying of the solution, well‐ordered hierarchical structures were fabricated in the remaining polymer film. The size of the grating structure and the lattice size of spontaneous hexagonally packed aqueous pores comprise two different length scales, thereby offering multiscale ordering. Interfacial wetting of the polymer solution to the grating surface was crucial in terms of obtaining a highly ordered structure that can be tuned by dissolving a small amount of surfactant in the polymer solution. The present novel approach provides a new opportunity for lithography‐free fabrication of complex hierarchical structures.