A Comparison Between James and von Neumann–Jordan Constants

In this paper, we compare James and von Neumann–Jordan constants of normed spaces under certain conditions. It is shown that if a normed space with James constant \(\sqrt{2}\) is three- or more dimensional, or is a \(\pi /2\)-rotation-invariant two-dimensional space, then its von Neumann–Jordan constant is less than or equal to \(4-2\sqrt{2}\).     

Molecular Structure and Mutual Recognition Between Host and Guest Molecules Found in the Crystal Structures of Oxacalix[4]arenes Complexed with Xylene Isomers

The crystal structures of two complexes of oxacalix[4]arene derivatives {p-isopropyl-dihomooxacalix[4]arene (IOC-4)and p-tert-butyldihomooxacalix[4]arene(BOC-4)} with xylene isomers have been determined byX-ray diffraction method. Furthermore, in order toestimate the strength of the mutual interactionsbetween host (IOC-4 and BOC-4) and guest (o-, m-and p-xylene), the heat of complex formation forthe IOC-4 : xylene complexes was calculated using a molecularorbital method, and a differential scanningcalorimetric investigation was performed forthe BOC-4 : xylene complexes.     

Sorption of carbon dioxide in fluorinated poyimides

Sorption isotherms of CO₂ for ten fluorinated polyimides measured at 35°C and up to about 25 atm are analyzed according to the dual-mode sorption model. Sorption properties for these polyimides are compared with those for other glassy Polymers including unfluorinated polyimides. The glassy polymers with higher glass transition temperatures T_g tend to show greater CO₂ sorption. Introduction of a ? C (CF₃)₂? linkage into the repeat unit of the main chain increases the sorption by 20–80%. For glassy polymers, including the fluorinated and unfluorinated polyimides, the Langmuir affinity constant b and Henry's law solubility constant k_D are correlated with the content of functional (carbonyl or sulfonyl) groups [FG], and composite parameter reflecting the magnitude of both [FG] and free-space fraction V_F, respectively, with some exceptions. The Langmuir capacity constant C′_H is correlated with T_g, but there are two correlation lines; one for unfluorinated polyimides and a different one for other glassy polymers including fluorinated polyimides. The slope of the former group is smaller probably because of smaller differences in thermal probably because of smaller differences in thermal expansion coefficients in rubbery and glassy states. Most fluorinated polyimides show greater solubility of CO₂ than unfluorinated polyimides and other glassy polymers, because of their larger C′_H and k_D. © 1993 John Wiley & Sons, Inc.     

Optimal portfolios with asymptotic criteria

This paper is concerned with a portfolio optimization model for a long planning horizon. We first argue that in this case the asymptotic growth rate and the asymptotic variance are better measures of performance than the usual mean and variance of return. We next propose an efficient algorithm for calculating the asymptotic frontier, i.e., the efficient frontier relative to the new criteria. Finally, we illustrate our methods and compare the difference between our model and the classical mean-variance-model by using historical data based on the 1064 stocks of the Tokyo Stock Exchange.     

Nilpotent subgroups of the group of self-homotopy equivalences

In this paper, we study subgroups of self-homotopy equivalences associated to generalized homology theories. We generalize Dror-Zabrodsky’s nilpotency theorem on the group of self-homotopy equivalences. Dedicated to Professor Akio Hattori on his sixtieth birthday The first-named author was partially supported by Grant-in-Aid for the Science Research of the Ministry of Education, 02740012.     

Side-chain liquid crystalline homo- and copolymethacrylates with a carbonate linkage between the benzylideneaniline mesogen and ethylene chain

New liquid crystalline (LC) homo- and copolymethacrylates having a carbonate linkage between a benzylideneaniline mesogen and ethylene chain in the side chain were prepared by free radical polymerization of methacrylate derivatives comprising 4-cyano- and/or 4-methoxybenzylide-neaniline units using AIBN as an initiator. The structures of the polymers were characterized by FTIR, ¹HNMR, and elemental analyses. The LC properties were evaluated by differential scanning calorimetry (DSC), polarizing microscopic observation of textures and X-ray diffraction. These measurements showed that all the homo- and copolymers form nematic phases. The isotropization temperatures on composition exhibited a negative deviation from a linear relationship between them predicted by the Schroeder-Van Laar equation. This phenomenon might be caused mainly by an unusual geometry arising from a smaller bond angle in the carbonate linkage.     

Electric Fields on FSM-16 Surface

The surface of mesoporous silicate, FSM-16, was investigated by infrared spectroscopy (IR) using methane and carbon monoxide as molecular probe. The appearance of 1-peak of adsorbed CH4 indicated the presence of electric field (1.4 × 105 esu) which is attributed to a weakly polarized free silanol site (site-1). The site was located at the void of oxygen framework in FSM-16 pore wall. In addition, the presence of site-2 without any electric field was found by IR spectra of adsorbed CO. The latter site was assigned to a interacted silanol groups and/or a Si–O–Si site.     

[2,3]-Wittig sigmatropic rearrangement of crotyl propargyl ether system. An emerging tool for control of acyclic stereochemistry

The [2,3]-Wittig rearrangement of properly designated (E)- and (Z)-crotyl propargyl ether system has been shown to exhibit a remarkably high degree of threo- and erythro -selection, respectively, and the stereochemical outcomes are discussed on mechanistic grounds. Some useful transformations of the rearrangement product are also described within the context of the formal total synthesis of (±)-oudemansin. Further, the high level of diastereoselection is maintained in the reaction of the α-methylcrotyl counterparts, together with the exclusive formation of the (E)-olefinic bond.     

Preparation of Transparent, Partially-Crystallized BaTiO3 Monolithic Xerogels by Sol-Gel Processing

Transparent, partially-crystallized nanostructured barium titanate (BaTiO3) monolithic xerogels (dried at 90°C) have been successfully synthesized via hydrolysis of Ba, Ti alkoxide precursor solutions in a concentration range of 1.0 mol/l with addition of water with a molar ratio of H2O/Ba 6.3. Transparent monolithic xerogels obtained from a precursor solution of 1.0 mol/l remained transparent even after firing at 500°C in oxygen, although the degree of their transparency was considerably decreased. Firing at temperatures above 500°C yielded translucent ceramics of BaTiO3, and ultimately, firing above 600°C resulted in normal opaque ceramic bodies. Those obtained from a more concentrated precursor solution of 1.2 mol/l were, on the other hand, still transparent after firing at 600°C in oxygen, and turned opaque at 700°C. The results demonstrate that the materials retained their transparency even after pyrolysis of organic compounds involving exothermic oxidation at temperatures in the range of 200 to 400°C. The densification behavior of transparent BaTiO3 monolithic xerogels obtained was found to be excellent; for example, those derived from a 1.0 mol/l precursor solution could be sintered to form monolithic BaTiO3 ceramics with a relative sintered density of about 94% and an average grain size of 1 m by firing at 1100°C for 2 h in oxygen.