Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

Synthesis and Systematic Structural Analysis of Cationic Half-Sandwich Ruthenium Chalcogenocarbonyl Complexes

Although the chemistry of transition-metal complexes with carbonyl (CO) and thiocarbonyl (CS) ligands has been well developed, their heavier analogues, namely selenocarbonyl (CSe) and tellurocarbonyl (CTe) complexes remain scarce. The limited availability of such CSe and CTe complexes has so far hampered our understanding of the differences between such chalcogenocarbonyl (CE: E=O, S, Se, Te) ligands. Herein, we report the synthesis and properties of a series of cationic half-sandwich ruthenium CE complexes of the type [CpRu(CE)(H₂IMes)(CNCH₂Ts)][BAr^F₄] (Cp=η⁵-C₅H₅⁻; H₂IMes=1,3-dimesitylimidazolin-2-ylidene; Ar^F=3,5-(CF₃)₂C₆H₃). A combination of X-ray diffraction analyses, NMR spectroscopic analyses, and DFT calculations revealed an increasing π-accepting ability of the CE ligands in the order O<S<Se<Te. A variable-temperature NMR analysis of the thus obtained chiral-at-metal CE complexes indicated high stereochemical stability.     

The stress field of a sliding inclusion

This paper discusses the stress fields when a spheroidal inclusion, free to slip along its interface, is subjected to a constant nonshear eigenstrain, and when an elastic body containing the inhomogeneity is under all-around tension or uniaxial tension at infinity. In each case the stress field in the inclusion or the inhomogeneity is not constant, contrary to Eshelby's solution. When sliding takes place, the stress increases locally compared with the perfect bonding case, but the elastic energy decreases due to the relaxation. The relative displacement (slip) along the interface is also evaluated.     

Complexation Constants of Lanthanide Ions with Poly(Methacrylic Acid) and its Copolymers

Complexation of some lanthanide ions with poly(methacrylic acid) and its copolymers was studied by potentiometric titration. Poly [methacrylic acid-co-oligo(ethylene oxide)methacrylate] and poly(methacrylic acid-co-acrylamide) formed tris-carboxylate coordinate lanthanide complexes with large overall complexation constants, while poly-(methacrylic acid)s and copolymer with higher content of the methacrylic acid residue formed bis-coordinate ones. It was concluded that the comonomer residues in the copolymer chains decreased the steric hindrance for the complexation and/or acted as co-coordinating groups of the carboxylic group to lanthanide ions. Very large positive and favorable entropy changes were observed for the complexation with poly(methacrylic acid) and its copolymers. This contribution of thermodynamic parameters to the complexation was contrary to that for the analogous monomeric methacrylic acid complex and is assumed to be induced by dehydration of the polymers through the lanthanide ion complexation.     

Synthesis and Magnetic Property of Polyacetylene Bearing πConjugated Bis(Diphenylene)Phenylallyl Radical

Abstract

m- and p Bis(diphenylene)propenylphenylacetylene (m-, p-8) were synthesized and polymerized with WCI₆, MoCl₅, and Rh catalyst, yielding solvent-soluble poly(phenylacetylene)s bearing a π-conjugated bis(di-phenylene)propenyl groups (m-, p-7a). The polymers gave their polyanion derivatives, which were electrolytically and chemically oxidized to yield the corresponding polyradicals (m-, p-7b). The polyradicals were chemically very stable due to the resonance stabilization of an unpaired electron whose spin concentration could be increased up to ca. 2 × 10²³ spins per molar monomer unit. ESR spectroscopy suggested an antiferro-magnetic interaction between unpaired electrons.     

Approaches to Artificial Macromolecular Oxygen Carriers

Construction of artificial oxygen carriers by use of iron or cobalt complexes bound to synthetic polymers was attempted. Radical copolymerization of porphyrin vinyl monomers with styrene gave the metalloporphyrins covalently bonded to a polymer chain at low concentration. For these metalloporphyrin polymers, irreversible oxidation via dimerization was prevented in aprotic solvents and reversible oxygenation was observed. The chemical environment around the oxygen-binding site was presumed to play an important role on the stability of oxygenated complex as in the case of the tetraamide groups on the porphyrin plane. When ethylenebis(salicylideniminato)cobalt chelate coordinated to a polymer-ligand, it formed a stable oxygenated complex at room temperature. Rotational motion of the chelate was decreased markedly by the polymer chain to enhance the coordinate bond between the metal ion and the bound oxygen molecule. Furthermore, the iron porphyrin with bulky substituents was oxygenated even in homogeneous aqueous solutions by combining it with the rigid, hydrophobic domain of a water-soluble block copolymer.     

Solution‐processable colorless polyimides derived from hydrogenated pyromellitic dianhydride with controlled steric structure

This work presents novel colorless polyimides (PIs) derived from 1R,2S,4S,5R‐cyclohexanetetracarboxylic dianhydride (H″‐PMDA). Isomer effects were also discussed by comparing with PI systems derived from conventional hydrogenated pyromellitic dianhydride, that is, 1S,2R,4S,5R‐cyclohexanetetracarboxylic dianhydride (H‐PMDA). H″‐PMDA was much more reactive with various diamines than H‐PMDA, and the former led to PI precursors with much higher molecular weights. The results can be explained from the quite different steric structures of these isomers. The thermally imidized H″‐PMDA‐based films were colorless regardless of diamines because of inhibited charge‐transfer interaction. In particular, the H″‐PMDA/4,4′‐oxydianiline system simultaneously achieved a very high T_g exceeding 300 °C, high toughness (elongation at break > 70%), and good solution processability. In contrast, the H‐PMDA‐based counterparts were essentially insoluble. The outstanding solubility of the former probably results from disturbed chain stacking by its nonplanar steric structure. An advantage of chemical imidization process is also proposed. In some cases, a copolymerization approach with an aromatic tetracarboxylic dianhydride was effective to improve the thermal expansion property. The results suggest that the H″‐PMDA‐based PI systems can be promising candidates for novel high‐temperature plastic substrate materials in electronic paper displays. A potential application as optical compensation film materials in liquid crystal displays (LCD) is also proposed in this work. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Oxygen-Binding Profile of the Iron Porphyrin Complex Embedded in Polymerized Liposome: Effect of the Polymerized Liposome on the Stability and the Oxygen-Binding Ability of the Iron Porphyrin Complex

5,10,15,20-Tetra(α,α,α,α, -o-(2′, 2′-dimethyl-20′-(2′ α-trimethylammonioethyl)phosphonatoxyeicosanamido)phenyl)porphinatoiron(II) (lipidheme) complex embedded in polymerized liposome was prepared by polymerizing l-(9-(p-vinylbenzoyl)nonanoyl)-2-O-octadecyl-rac-glycero-3-phosphocholine in the presence of lipid-heme under ultraviolet irradiation. The polymerization proceeded rapidly, and the reduction of the hemin to the heme occurred spontaneously during the polymerization. The lipid-heme complex embedded in the polymerized liposome bound molecular oxygen reversibly under physiological conditions (pH 7, 37°C) and was chemically, physically, and mechanically stable during storage for a long period and even in a high-speed flow system. The oxygen-binding affinity was not affected by the type of medium due to the effect of the rigid polymerized liposome.     

Ion Tunneling in Polymeric Solid Electrolytes for Batery and Electrochromic Display in the Dry State

Polymeric solid electrolytes which show bi-or single-ionic tunneling were prepared, and their unique ion conduction was applied for the design of some devices. Poly [(oligooxyethylene) methacrylatel] /MX hybrids and poly [(oligooxyethylene) methacrylate-co-methacrylic acid alkali metal salts] were prepared as typical models of those tunneling systems. These showed ionic conductivities above 10^?5 and 10^?7 S/cm at room temperature, respectively. An all-solid-state electrochromic display and a dry battery were prepared with these polymeric solid electrolytes. The all-solid-state electrochromic display showed excellent coloring and bleaching response by 1–3 V. The all-solid-state battery showed V _oc = 3.1 V stability for over 2 weeks. Their characteristics as well as their mechanism are also reported.