Bloch-to-BMOA pullbacks on the disk

For a given holomorphic self map of the unit disk, we consider the Bloch-to- composition property (pullback property) of . Our results are cannot have the pullback property if touches the boundary too smoothly, while has the pullback property if touches the boundary rather sharply. One of these results yields an interesting consequence completely contrary to a higher dimensional result which has been known. These results resemble known results concerning the compactness of composition operators on the Hardy spaces. Some remarks in that direction are included.

     

Effect of the axial cysteine ligand on the electronic structure and reactivity of high-valent iron(IV) oxo-porphyrins (Compound I): a theoretical study

The effect of axial ligands on the reactivity of high-valent iron(IV) oxo-porphyrins (Compound I) was investigated using the B3LYP hybrid density functional method. We studied alkane hydroxylation using four models: Compound I with thiolate, imidazole, phenolate, and chloride anions as axial ligands. The first three ligands were employed as models for cysteinate, histidine, and tyrosinate, respectively. Our calculations show that anionic ligands and neutral ligands favor different electronic states for stationary points in the reaction coordinate, and the calculated energy barrier and energy of several reaction intermediates show similar values. A remarkable effect of axial ligands was found in the final product release step. Our calculations show that the thiolate ligand weakens a bond between heme and an alcohol. In contrast, the imidazole ligand significantly increases the interaction between heme and an alcohol, which causes the catalytic cycle to be less efficient.     

Scalable ambient synthesis of water‐soluble poly(β‐hydroxythio‐ether)s

Proton transfer polymerization through thiol‐epoxy “click” reaction between commercially available and hydrophilic di‐thiol and di‐epoxide monomers is carried out under ambient conditions to furnish water‐soluble polymers. The hydrophilicity of monomers permitted use of aqueous tetrahydrofuran as the reaction medium. A high polarity of this solvent system in turn allowed for using a mild catalyst such as triethylamine for a successful polymerization process. The overall simplicity of the system translated into a simple mixing of monomers and isolation of the reactive polymers in an effortless manner and on any scale required. The structure of the resulting polymers and the extent of di‐sulfide defects are studied with the help of 13C‐ and ¹H‐NMR spectroscopy. Finally, reactivity of the synthesized polymers is examined through post‐polymerization modification reaction at the backbone sulfur atoms through oxidation reaction. The practicality, modularity, further functionalizability, and water solubility aspects of the described family of new poly(β‐hydroxythio‐ether)s is anticipated to accelerate investigations into their potential utility in bio‐relevant applications. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3381–3386     

Transesterification reaction of the BaSO4‐filled PBT/poly(ethylene terephthalate) blend

For the poly(butylene terephthalate) (PBT)/poly(ethylene terephthalate) blend system, the addition of a barium sulfate (BaSO₄) particle, the surface of which was modified with a titanate coupling agent, suppressed the transesterification reaction. The polyester chain ends, considered one of the main sites of transesterification reactions, were blocked through a chemical reaction with the surface hydroxyl groups of the BaSO₄ particle; a block copolymer‐like architecture was obtained with a BaSO₄ linkage. The formation of the block copolymer‐like structure for the polyesters stuck to the BaSO₄ particle facilitated crystallization by providing a crystallization nucleus without a significant transesterification reaction, resulting in higher mechanical properties. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2589–2597, 2001     

Asymptotic Properties of Axis-Symmetric D-Solutions of the Navier–Stokes Equations

We consider asymptotic behavior of Leray’s solution which expresses axis-symmetric incompressible Navier–Stokes flow past an axis-symmetric body. When the velocity at infinity is prescribed to be nonzero constant, Leray’s solution is known to have optimum decay rate, which is in the class of physically reasonable solution. When the velocity at infinity is prescribed to be zero, the decay rate at infinity has been shown under certain restrictions such as smallness on the data. Here we find an explicit decay rate when the flow is axis-symmetric by decoupling the axial velocity and the horizontal velocities. The first author was supported by KRF-2006-312-C00466. The second author was supported by KRF-2006-531-C00009.     

The Revival Wave Induced Spontaneously in a BZ-Type Mixture

We have examined the unusual behavior of wave propagation in the BrO₃ ^- - 1,4- cyclohexanedione - ferroin reaction system. Two patterns of traveling wave have been induced spontaneously with long time lag in the reaction process. A new wave has been induced as a concentric pattern after an initially induced wave has disappeared. The initially induced wave shows an irregular spiral pattern with a high wave frequency. The two waves show very different behavior in the pattern and in other wave characteristics as well. We compared the behavior of the two waves and suggested an appropriate reaction process for unusual behavior of wave propagation in the system by considering the reaction intermediates of the organic compounds. This revised version was published online in June 2006 with corrections to the Cover Date.     

Preliminary result of an advanced tangential X-ray pinhole camera system with a duplex MWPC on KSTAR plasma

An advanced tangential X-ray pinhole camera (TXPC) has been developed for KSTAR by utilizing a 2-D duplex multi-wire proportional counter (MWPC) detector. The KSTAR MWPC employs a 2-D parallel type readout system for high temporal resolution and adopts a duplex type for the capability of electron temperature measurement via the multi-color method. This paper presents the performance test result of the developed MWPC system utilizing a Fe-55 X-ray source. As a preliminary experimental result from the 2012 KSTAR campaign, the clear presentation of sawtooth activities and its frequency change, and 2-D plasma images during the vertical disruption event are given.     

Specific interaction governing the melt intercalation of clay with poly(styrene‐co‐acrylonitrile) copolymers

In the melt intercalation of cation‐exchange clay, mixtures of montmorillonite and poly(styrene‐co‐acrylonitrile) (SAN) with various acrylonitrile contents were studied to examine the effect of specific interaction. When organic molecules with hydroxyl groups were used as intercalants for the clay, the amount of SAN penetrating the gallery of the layered structure of the clay and the corresponding increase in the gallery height occurred at a much higher rate because of the attractive specific interaction between acrylonitrile groups and polar groups on the clay surface. However, there was a limit to the increase in the gallery height, and the tendency for the gallery height to increase with the acrylonitrile group content disappeared when the acrylonitrile content was greater than 30 wt %, implying that excessive attractive interaction on the clay surfaces and polymer molecules glued the two adjacent silicate layers together; consequently, the increase in the gallery height could not be accomplished. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2430–2435, 2001     

Decay rate of solutions of Navier-Stokes equations in 3-dimensional half space

In this article, we derive the L² spatial decay rate of a weak solution of the incompressible flow in the half space. When the half space (or some other fluid region with boundary) is concerned, pressure estimate is main obstacle since we do not have enough information of the pressure on the boundary. In this paper, we give an idea which does not require any pressure information on the boundary, and we hope that our idea could be applied to other problems such as exterior domain problem.