Chains of strongly non-reflexive dual groups of integer-valued continuous functions

Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.

     

Role of Al or Eu on thermoluminescence of Al- and/or Eu-doped SiO2 crystals

Although SiO₂ crystals have been used in electroluminescence devices and thermoluminescence (TL) dosimeters, the emission mechanism of TL has not yet been clearly explained. Recently, as we could get amorphous and highly pure SiO₂ prepared by the sol-gel method, we have investigated the TL emission mechanism using Al³⁺- and/or Eu³⁺-doped SiO₂ crystalline samples prepared by the heat-treatment under much lower temperature that the melting point of SiO₂. The TL spectrum of the Eu³⁺-doped sample displayed several peaks, including two main peaks due to the electron transitions from ⁵D₂ to ⁷F₅ (ca. 570 nm) and from ⁵D₀ to ⁷F₂ (ca. 610 nm). As doping concentration increased, all the peak intensities reduced from maximum values except that due to the electron transition from ⁵D₀ to ⁷F₂. These observations are thought to result from a cross-relaxation process due to the lack of inversion symmetry at the Eu³⁺ site.     

Synthesis of optically active tetrahydrozerumbone

Tetrahydrozerumbone 2, which has a powerful balmy fragrance, has a stereogenic carbon at C2 and can be easily prepared from zerumbone 1, which is one of the most important materials that displays an NMRDOS character. Reduction of 2 gave two diastereomers 3 and 4; their optically active (>99% ee) alcohols were obtained by lipase-catalyzed stereoselective transesterification of each racemic alcohol. The enantioselectivity of tetrahydrozerumbol does not entirely depend on the hydroxyl position but on the 2-methyl position. Compounds (R)-2 and (S)-2 were obtained by Dess–Martin oxidation of the corresponding alcohols. Interestingly, (R)-2 showed a strong balmy fragrance while (S)-2 had hardly any fragrance.     

Structural development of ultra‐high strength polyethylene fibers: Transformation from kebabs to shishs through hot‐drawing process of gel‐spun fibers

Structural development of ultra‐high strength polyethylene fibers via hot‐drawing processes of as‐spun gel fibers was investigated by means of transmission electron microscopy. It is found that the shish‐kebabs developed in both the as‐spun and drawn fibers can be transformed continuously into the micro‐fibril structure composed mostly of the shish structure through the hot‐drawing process. The structure transformation involves a drastic decrease in diameter of the kebab plus the shish but almost no change in the shish diameter. This result suggests that the chains in the kebabs are incorporated into the shishs and consumed to extend the longitudinal dimension of the shishs during the drawing process. The proposed new deformation model well explains the relationship between the fiber morphology and their mechanical properties: the tensile strength and modulus of the fibers can be determined by the number of the shish in the fiber and the macroscopic diameter of the fiber, which are apriori determined at the spinning process. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1861–1872, 2010     

Room Temperature Solution ENDOR of some Super Stable Fluorocarbon Radicals

Room temperature fluorine electron nuclear double resonance (ENDOR) has been successfully observed for several superstable fluorocarbon radicals ·C(C₂F₄R)(i-C₃F₇)₂ in solution. Three radicals were employed in which CF₃, F, and O-c-C₆F₁₀SO₃C₂F₅ were introduced as R, and all the hyperfine couplings (hfcs) obtained by ENDOR were assigned with the help of ESR simulation and ab initio MO calculation. In case of ·C(i-C₃F₇)₃ large ¹³C and considerable β-fluorine couplings suggest the nonplaner arrangement for the central and three carbons at the β-position, in spite of the fact that all the methyl fluorine show the same hfc. Therefore, a rapid puckering motion along the C₃ axis together with the methyl rotation should average the hfc’s of the 18 fluorine nuclei to give the same value. When one of the CF₃ groups is substituted with an F nucleus, the five CF₃ groups give two hfc values, suggesting some dynamics still exists for the molecular frame. When a large group, O-c-C₆F₁₀SO₃C₂F₅, is substituted for CF₃, all the five CF₃ groups become nonequivalent and the ENDOR signal becomes intensive and sharp even at 290 K, indicating that the molecular frame becomes rigid. The relation between the ENDOR spectra of these systems and the intramolecular dynamics is discussed.     

Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. VI*

The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 389–400, 2001