On the Number of Discrete Eigenvalues of a Discrete Schrödinger Operator with a Finitely Supported Potential

On the d-dimensional lattice \({\mathbb{Z}^d}\) and the r-regular tree \({T^r}\), an exact expression for the number of discrete eigenvalues of a discrete Laplacian with a finitely supported potential is described in terms of the support and the intensities of the potential on each case. In particular, the number of eigenvalues less than the infimum of the essential spectrum is bounded by the number of negative intensities.     

Bis(dipyrrinato)metal(ii) coordination polymers: crystallization,exfoliation into single wires,and electric conversion ability

One-dimensional coordination polymers (1D-CPs) tend either to dissociate into constitutive ligands and metals readily in solution, or to aggregate randomly and amorphously, which prevents them from widespread application. In the present research, 1D-CPs comprising bridging dipyrrin ligands and divalent metal ions (Zn²⁺, Ni²⁺, and Cu²⁺) are synthesized. A liquid/liquid interfacial reaction gives rise to single crystals suitable for X-ray diffraction analysis: A dichloromethane solution of the ligand is layered with aqueous metal(ii) acetate, such that the coordination reaction proceeds at the liquid/liquid interface. Isolated single fibers of the zinc coordination polymer may be exfoliated from the single crystal or bulk solid upon ultrasonication. Atomic force microscopy (AFM) detects the isolated fibers with lengths of more than several μm. The exfoliated 1D-CP wires feature good processability, realizing a conjugate with single-wall carbon nanotubes (SWCNTs), and a thin film on a transparent SnO₂ electrode. The processed materials show electric conversion ability: For example, the modified SnO₂ electrode serves as a photoanode for a photoelectric conversion system. The designability and tunability of the present 1D-CPs is demonstrated by a ligand modification, affording a luminescent property and an extension of the photoelectric conversion response to longer wavelengths.     

Simple Surfactant Concentration‐Dependent Shape Control of Polyhedral Fe3O4 Nanoparticles and Their Magnetic Properties

The shape and size of monodisperse Fe₃O₄ nanoparticles (NPs) are controlled using a chemical solution synthesis in the presence of the surfactant cetylpyridinium chloride (CPC). Cubic Fe₃O₄ NPs surrounded by six {100} planes are obtained in the absence of CPC. Increasing the CPC content during synthesis causes the shape of the resulting Fe₃O₄ NPs to change from cubic to truncated cubic, cuboctahedral, truncated octahedral, and finally octahedral. During this evolution, the predominantly exposed planes of the Fe₃O₄ NPs vary from {100} to {111}. The shape control results from the synergistic effect of the pyridinium cations, chloride anions, and long‐chain alkyl groups of CPC, which is confirmed by comparison with NPs synthesized in the presence of various related cationic surfactants. The size of the cubic Fe₃O₄ NPs can be tuned from 50 to 200 nm, by changing the concentration of oleic acid in the reaction solution. The Fe₃O₄ NPs exhibit shape‐dependent saturation magnetization, remanent magnetization, and coercivity.     

Development of dispersive XAFS system for analysis of time‐resolved spatial distribution of electrode reaction

Apparatus for a technique based on the dispersive optics of X‐ray absorption fine structure (XAFS) has been developed at beamline BL‐5 of the Synchrotron Radiation Center of Ritsumeikan University. The vertical axis of the cross section of the synchrotron light is used to disperse the X‐ray energy using a cylindrical polychromator and the horizontal axis is used for the spatially resolved analysis with a pixel array detector. The vertically dispersive XAFS (VDXAFS) instrument was designed to analyze the dynamic changeover of the inhomogeneous electrode reaction of secondary batteries. The line‐shaped X‐ray beam is transmitted through the electrode sample, and then the dispersed transmitted X‐rays are detected by a two‐dimensional detector. An array of XAFS spectra in the linear footprint of the transmitted X‐ray on the sample is obtained with the time resolution of the repetition frequency of the detector. Sequential measurements of the space‐resolved XAFS data are possible with the VDXAFS instrument. The time and spatial resolutions of the VDXAFS instrument depend on the flux density of the available X‐ray beam and the size of the light source, and they were estimated as 1 s and 100 µm, respectively. The electrode reaction of the LiFePO₄ lithium ion battery was analyzed during the constant current charging process and during the charging process after potential jumping.     

Highly diastereoselective synthesis of tetrahydrobenzofuran derivatives by palladium-catalyzed reaction of propargylic esters with substituted β-dicarbonyl compounds

Reactions of propargylic esters with 2-substituted cyclohexane-1,3-diones and 2-oxocyclohexanecarboxylic esters in the presence of palladium catalyst are described. Substituted tetrahydrobenzofuran derivatives having a quaternary carbon stereocenter were synthesized in a highly diastereoselective manner.     

Substrate‐induced formation of a recognition structure in a four‐polypeptide–lipid monolayer system

Poly(γ‐methyl L ‐glutamate)s with Ser, His, Asp, and Glu residues at the amino terminal as the serine protease catalytic site were prepared. The number‐average degree of polymerization of the polypeptides was 51. A dipalmitoylphosphatidylcholine monolayer containing the polypeptides was formed at the air–water interface and was transferred onto gold‐deposited glass plates. The binding of N‐acetyltyrosine ethyl ester, a typical substrate of the serine protease, to the monolayer was characterized by surface plasmon resonance measurements. The four‐polypeptide–lipid monolayer system conditioned on an aqueous solution containing the substrate N‐acetyltyrosine ethyl ester exhibited Langmuir‐type binding of the substrate. Its binding constant of 6.1 × 10⁴ M⁻¹ was about 20 times larger than that observed for a monolayer prepared on pure water. The behavior may have arisen from a substrate‐induced rearrangement of the four kinds of polypeptides in the monolayer, forming a substrate‐binding structure similar to that found in serine protease. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2186–2191, 2000     

Effect of ultraviolet light irradiation on gas permeability in polyimide membranes. 1. Irradiation with low pressure mercury lamp on photosensitive and nonphotosensitive membranes

Two types of polyimide membranes; one crosslinkable and the other noncrosslinkable using ultraviolet light irradiation (UV irradiation), were prepared and investigated concerning the effect of UV irradiation on their gas permeabilities and selectivities. Permeability and diffusion coefficients for O₂, N₂, H₂, and CO₂ were determined using the vacuum pressure and time lag method. Sorption properties for carbon dioxide were carried out to evaluate the changes in the free volume in the membranes due to the irradiation. In both membranes, permeability coefficients for all gases used in this study decreased and permselectivity, particularly for H₂ over N₂, increased with increasing UV irradiation time without a significant decrease in the flux of H₂. The coefficients depended on the membrane thickness, suggesting asymmetrical changes in both membranes due to UV irradiation. It was suggested by an attenuated total reflection (ATR) FTIR method and analysis of the gas sorption properties of the membranes that the physical changes due to UV irradiation at the irradiated side in both membranes significantly affected their gas permeation properties compared with the chemical changes, especially the crosslinking in the crosslinkable type. © 1997 John Wiley & Sons, Inc. J. Polym Sci B: Polym Phys 35: 2259–2269, 1997