Compact adjoint operators and approximation properties

This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties.     

On the convergence of splittings for semidefinite linear systems

Recently, Lee et al. [Young-ju Lee, Jinbiao Wu, Jinchao Xu, Ludmil Zikatanov, On the convergence of iterative methods for semidefinite linear systems, SIAM J. Matrix Anal. Appl. 28 (2006) 634-641] introduce new criteria for the semi-convergence of general iterative methods for semidefinite linear systems based on matrix splitting. The new conditions generalize the classical notion of P-regularity introduced by Keller [H.B. Keller, On the solution of singular and semidefinite linear systems by iterations, SIAM J. Numer. Anal. 2 (1965) 281-290]. In view of their results, we consider here stipulations on a splitting A=M-N, which lead to fixed point systems such that, the iterative scheme converges to a weighted Moore-Penrose solution to the system Ax=b. Our results extend the result of Lee et al. to a more general case and we also show that it requires less restrictions on the splittings than Keller’s P-regularity condition to ensure the convergence of iterative scheme.     

Raman spectroscopic study of 2-methyl-1-propanethiol in silver sol

The surface-enhanced Raman scattering (SERS) of 2-methyl-1-propanethiol is investigated in a silver sol. As for other thiols, the molecule appears to be chemisorbed dissociatively on the silver surface by rupture of its S---H bond. At the bulk concentration sufficient for full monolayer coverage, the P_C conformer with a methyl group rans to the sulfur atom is found to be the most advantageous form on the surface. The vibrational assignments for the 2-methyl-1-propanethiol molecule are made by using the SERS data in conjunction with the previously reported normal-mode assignments for the corresponding alkyl chloride molecule, 1-chloro-2-methylpropane.     

Characterizations of Hartley Proper Efficiency in Nonconvex Vector Optimization

Journal of Global Optimization -     

Determination of impurities in tantalum by a radiochemical neutron activation analysis

A radiochemical separation method using Dowex 1×8 (200–400 mesh) has been applied to two tantalum metals of 99.9% purity. While tantalum was still retained on the resin, the elements Na, K, Cr, Mn, Fe, Co and Zn were separated with 2M HF and subsequently the elements Sc, As, Zr, Mo, Eu, W and Hf with a mixture of 0.5M HF and 3M HCl. The separation yields for all impurities was 98–100%. Elemental contents were calculated by a single comparator method using two monitors.     

Spatial stability of a homogeneous system of voids under cascade damage

We consider the microstructural evolution of a system consisting of voids and sessile interstitial clusters continuously produced by irradiation. The stability of the evolution is rigorously analyzed, assuming spatial homogeneity as represented by a mean-field formulation. It is found that, in fully annealed pure metals with a sufficiently low void growth rate, the development of a spatially homogeneous microstructure is unstable. In fact, heterogeneous development already takes place during the void nucleation stage. The characteristic scale of the developing heterogeneity and its temperature dependence are obtained from the analysis, and are found to be consistent with experimental observations. Received: 21 March 2001 / Accepted: 30 May 2001 / Published online: 30 August 2001     

Thermal stability study of conductive polyaniline/polyimide blend films on their conductivity and ESR measurement

Conductivity stability at thermal environment of conductive polyaniline‐complexes/polyimide (PANI‐complexes/PI) blends, which were doped by camphorsulfonic acid (CSA) and dodecylbenzenesulfonic acid (DBSA), respectively, were investigated by conductivity measurements, electron spin resonance (ESR) spectra, differential and scanning thermometer (DSC). In the conversion process of PANI/Polyamic acid (PAA) to PANI/PI, the blend endeavored some kinds of alteration such as decomplexation of moisture and solvent, dissociation of dopant, crosslinking of PANI chain, and the imidization of PAA chain. PANI‐DBSA/PI showed higher thermal stability of conductivity than PANI‐CSA/PI, and both samples showed nearly linear decay of conductivity with increasing temperature showing greatly enhancement of conductivity stability. When they were exposed at near or over glass transition temperature, the conductivity decay became faster. The conductivity stability at base environment was also higher for PANI‐DBSA/PI due to difficulty in accessing of hydroxyl ion to PANI, which were resulted from dopant. DBSA‐doped blends showed increased polaron mobility and concentration at relatively high temperature, which led to extremely higher conductivity and its stability at high temperature. Copyright © 2002 John Wiley & Sons, Ltd.     

HR-coated facet effect on the spectral characteristics of a three-section DBR tunable laser

High-relfection (HR)-coated facet effects on the spectral characteristics of a three-section distributed Bragg reflector (DBR) tunable laser are investigated theoretically, in which the output power emits to the DBR section. It is found that the output power to the DBR sectionP _DBR compared to the cleaved facet output powerP ₀ is nearly constant to some degree with increasing tuning current. Owing to the high-Q resonator, the HR-coated DBR laser showed a decrease in spectral linewidth. However, there is still linewidth broadening of the HR-coated DBR laser even though the rate of increase is smaller than that of the cleaved-facet DBR laser. In the case of output power emission to the DBR section, it is thought that the HR-coated effect can overcome the decrease in output power under frequency tuning, which is one of the most important drawbacks of DBR laser performance.     

Effects of solvent treatment on crystallization kinetics of poly(p-phenylene sulfide)

Isothermal melt crystallization kinetics were investigated by differential scanning calorimetry (DSC) for virgin and α-chloronaphthalene solvent-treated poly(phenylene sulfide) (PPS) systems. The overall crystallization rates were found to be much faster for the solvent-treated PPS than for the virgin neat PPS. Additionally, the Avrami crystallization plot for the solvent-treated PPS samples appeared as two straight portions with an apparent discontinuity, but as a continuous straight line for the virgin PPS system. After the treatment of solvent dissolution and subsequent drying, the residual trace α-chloronaphthalene, upon being quenched to the crystallization temperatures, initiated some localized solvent-induced nuclei-like crystals in PPS. It was the nuclei that enhanced secondary crystallization in treated PPS during the second stage, and the higher extents of secondary crystallization in the solvent-treated PPS caused the apparent discontinuous break in the Avrami plots. The causes for the difference were explained and the mechanism of the sequential primary/secondary crystallization kinetics for the solvent-treated PPS was satisfactorily described with a proposed series-parallel crystallization model. ©1995 John Wiley & Sons, Inc.     

Effect of the linear siloxane chain in cyclic silsesquioxane (CSSQ) on the mechanical/electrical property of the thin films

Several kinds of cyclic silsesquioxane (CSSQ) precursors containing linear siloxane chain were prepared to improve both the mechanical properties of their thin films and the compatibility with heptakis (2,3,6-tri-O-methyl)-β-cyclodextrin (tCD) as a porogen. The precursors were synthesized using a hydrolysis/condensation reaction with 2,4,6,8-tetramethyl-2,4,6,8-tetra (trimethoxysilylethyl) cyclotetrasiloxane (cyclic monomer) and three kinds of linear siloxane monomers. As the linear siloxane chain length increases in the CSSQ precursors, the compatibility between the CSSQ precursor and tCD molecules improved due to the chain flexibility of the precursor. Moreover, the mechanical strength of the CSSQ precursor (4ST37) containing linear tetrasiloxane was the best among the prepared precursors. The enhancement of mechanical property might also be attributed to the content of Si-OH groups as well as the chain flexibility, which could help the crosslinking reaction of Si-OH groups in the film curing process.