Extensions of Heinz-Kato-Furuta inequality

We give an extension of Lin's recent improvement of a generalized Schwarz inequality, which is based on the Heinz-Kato-Furuta inequality. As a consequence, we can sharpen the Heinz-Kato-Furuta inequality.

     

A complement to monotonicity of generalized Furuta-type operator functions

Let A?B?0 with A>0, t∈[0,1] and p?1. Then we shall show that

     

On the Polar Decomposition of the Product of Two Operators and Its Applications

Let T = U|T| and S = V|S| be the polar decompositions. In this paper, we shall obtain the polar decomposition of TS as TS = UWV|TS|, where |T||S^*| = W||T||S^*|| is the polar decomposition. Next, we shall show that TS = UV|TS| is the polar decomposition if and only if |T| commutes with |S^*|. Lastly, we shall apply this result to binormal and centered operators. We shall obtain characterizations of these operator classes from the viewpoint of the polar decomposition.     

Fourier transform infrared study on the sorption of water to various kinds of polymer thin films

The state of sorbed water and the sorbing processes of water to various polymer thin films were studied with Fourier transform infrared (FTIR) spectroscopy. To prepare the polymer films, we used poly(ethylene glycol)s of different molecular weights and various kinds of vinyl polymers, such as poly(2‐methoxyethyl acrylate). The O? H stretching band of water sorbed in the films increased gradually on contact with water vapor at 50% relative humidity and leveled off. When O? H stretching bands of water sorbed to polymer films were compared, the peak positions and profiles of water sorbed to the polymeric materials with the same hydrogen‐bonding site were similar. A hybrid density‐functional method supported the assignment of the peaks. Furthermore, the diffusion coefficient (D) of water vapor in the polymer films was estimated by time‐resolved measurements of the sorbed water at the very initial stage (0–830 s). It was clearly shown that the D values of water vapor in the polymer materials with a strong hydrogen‐bonding site were smaller than those in hydrophobic polymers. The usefulness of the FTIR technique to investigate water sorption to polymer materials was definitely demonstrated. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2175–2182, 2001     

One-point extensions of Markov processes by darning

This paper is a continuation of the works by Fukushima–Tanaka (Ann Inst Henri Poincaré Probab Stat 41: 419–459, 2005) and Chen–Fukushima–Ying (Stochastic Analysis and Application, p.153–196. The Abel Symposium, Springer, Heidelberg) on the study of one-point extendability of a pair of standard Markov processes in weak duality. In this paper, general conditions to ensure such an extension are given. In the symmetric case, characterizations of the one-point extensions are given in terms of their Dirichlet forms and in terms of their L ²-infinitesimal generators. In particular, a generalized notion of flux is introduced and is used to characterize functions in the domain of the L ²-infinitesimal generator of the extended process. An important role in our investigation is played by the α-order approaching probability u _α . The research of Z.-Q. Chen is supported in part by NSF Grant DMS-0600206. The research of M. Fukushima is supported in part by Grant-in-Aid for Scientific Research of MEXT No.19540125.     

Role of the in‐plane orientation of polyimide films in graphitization

Poly(amide acid) labeled with perylenetetracarboxydiimide (PEDI) was prepared from 3,3′,4,4′‐biphenyltetracarboxylic dianhydride (BPDA), p‐phenylenediamine (PDA), and diamino‐PEDI. Poly(amide acid) was then reacted with sodium hydride and various kinds of alkyl iodides for transformation into various poly(amide ester)s. The cast films were imidized while fixed on glass substrates to give BPDA/PDA polyimide films. The degree of in‐plane molecular orientation (f) of the polyimides and their precursors, poly(amide acid) and poly(amide ester)s, were determined via measurements of the visible dichroic absorption at an incidence angle for a rodlike dye (PEDI) bound to the main chain. All precursor films showed relatively low degrees of in‐plane orientation. After imidization of the precursors fixed on glasses, however, striking spontaneous in‐plane orientation behavior was observed. The f value for polyimide film from a poly(amide acid) precursor was as high as 0.7–0.8. The f value for polyimide film from a methyl ester precursor, however, was lowered to 0.4–0.5, but it increased with the increasing size of the alkyl groups. Good correlations of the in‐plane orientation of the polyimide films with the tensile modulus of the films and the in‐plane orientation of the graphitized films were observed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3011–3019, 2001     

Construction and structural analysis of mono- and heterobimetallic bis(titanate) molecular cages

To explore the utility of bis(dihydroxynaphthalene) ligands for the construction of supramolecular structures, we demonstrated the preparation of cage-shaped complexes by combining these ligands with hexacoordinate titanium(IV). The reaction of biphenylenebis(dihydroxynaphthalene) with TiO(acac)₂ proceeded in the presence of N-methylmorpholine in DMF and an M₂L₃-type cage was obtained by self-organization. As an extension of this work, the preparation of heterobimetallic molecular cages was examined by using combinations of titanium(IV), palladium(II) or platinum(II), and pyridyldihydroxynaphthalenes. Ti(IV)/Pd(II) cages were prepared in one pot by treatment of the pyridyldihydroxynaphthalene ligands with TiO(acac)₂ followed by PdCl₂(MeCN)₂. In the preparation of Ti(IV)/Pt(II) cages, platinum(II)-bridged bis(dihydroxynaphthalene) ligands were isolated in advance from the reaction of pyridyldihydroxynaphthalene ligand precursors with K₂PtCl₄, which were then deprotected and reacted with TiO(acac)₂ in the same conditions as those for biphenylenebis(dihydroxynaphthalene). The precise structures of the Ti(IV)/Pd(II) and Ti(IV)/Pt(II) heterobimetallic cages were fully elucidated by X-ray crystallographic analysis.     

Auger electron spectroscopic analysis of corrosion products formed on A3003 aluminum alloy in model fresh water with different Zn2+ concentration

The corrosion morphology and composition of corrosion products of A3003 formed in model fresh water with different Zn²⁺ concentrations were investigated by immersion tests combined with surface observations and analysis using an Auger electron spectroscope (AES). The cross-sectional AES observations showed that the thickness of the corrosion product layer formed on A3003 decreases with increases in the Zn²⁺ concentration of the model fresh water. A cross-sectional AES point analysis suggested that the corrosion products formed on the A3003 in the Zn²⁺ containing model fresh water (Zn²⁺ > 0.1 mM) have a multilayered structure and that the inner of Zn-rich layer would have high corrosion protective properties.