Symmetric inequalities with power-exponential functions

We establish symmetric inequalities with power-exponential functions and propose a conjecture.     

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

Visible light-responsive cell scaffolds with bilayer structures for single cell separation

Collagen is a major component of the extracellular matrix, and collagen gels have been used as cell scaffolds. We previously prepared gold nanoparticle (AuNP)-embedded collagen gels (AuCol) to serve as cell scaffolds that were sensitive to visible light. We performed single cell detachment from this cell scaffold using a microscope equipped with a laser irradiation system. In the present study, we adjusted hydrogel thickness and AuNP concentration in AuCol, with a goal of improving cell detachment efficiency. Thin hydrogels became blackened after the laser irradiation, and thick hydrogels with high AuNP concentrations were not permeable to the laser light. We, therefore, prepared bilayer gels, composed of AuCol as the upper layer and intact collagen gel (Col) as the bottom layer. These bilayer gels allowed more effective cell detachment, because they were thick and optically transparent. Our results indicated that an AuCol/Col ratio of 2 enabled the highest cell detachment efficiency. Essentially, no cell damage was observed in our system, suggesting that this is a cell-friendly single cell separation system.     

Extremely Photostable Electron-Deficient Phthalocyanines that Generate High Levels of Singlet Oxygen

A robust lead-mediated synthetic procedure for the generation of phthalocyanines substituted with electron-withdrawing groups has been developed. The free-base phthalocyanine and various metal complexes were prepared without discernible degradation of the peripheral electron-withdrawing substituents. Upon irradiation with red light, some of the thus-obtained metal complexes generated high levels of singlet oxygen. In particular, a palladium complex exhibited attractive photostability upon exposure to singlet oxygen as a bleaching agent. The photostability of such complexes that may manifest concomitantly to the generation of high levels of singlet oxygen was attributed to the presence of the electron-withdrawing groups, which results in energetically low-lying highest occupied molecular orbitals.     

Adsorption of ammonia and water on functionalized edge-rich carbon nanofibers

The preparation, characterization and ammonia and water adsorption properties of edge-rich carbon nanofibers (CNFs) were studied, including platelet CNFs (PCNFs) and cup-stacked CNFs (CSCNFs). Since PCNFs and CSCNFs have many chemically active exposed edges, functionalization by oxidizing the edges was carried out by ozone stream and by nitric acid. Transmission electron microscopy, N₂ adsorption isotherms and temperature-programmed desorption analysis showed that the nitric acid treatment partly destroyed the graphite structure of the PCNFs and created acid functional groups and micropores, whereas the ozone treatment created functional groups without damaging the structure. Ammonia adsorption isotherms clarified that NH₃ adsorption on PCNFs and CSCNFs occurred mainly on oxygen-containing groups, whereas the adsorption on activated carbon fibers (ACFs) occurred on both oxygen-containing groups and the carbon surface without the functional groups, and the CSCNFs showed larger amounts of adsorbed ammonia compared to the PCNFs. Especially at a relatively low pressure range (<0.2 atm), the PCNFs/CSCNFs/ACFs showed the same ammonia adsorption mechanism; that is, the one-to-one interaction between oxygen atoms in the functional groups and hydrogen atoms in ammonia molecules. In addition, the adsorption on the ACFs appeared to occur mainly by interaction with the carbon surface at relatively high pressure (0.3–1.0 atm). Our experimental results and previous findings suggest that NH₃ adsorption on PCNFs is due mainly to NH…O hydrogen bonding between oxygen-containing groups and ammonia rather than to chemical bonding.     

Synthesis of well‐defined block copolymer composed of flexible amphiphilic poly(ethylene glycol) and hydrophobic liquid crystalline segments by living coordination polymerization of allene derivatives and its application to thin film with perpendicularly oriented cylindrical nanostructure

A block copolymer composed of a flexible polar poly(ethylene glycol) (PEG) and a less polar liquid crystalline poly(allene) segments is prepared by the living coordination polymerization of an allene derivative possessing trans‐azobenzene‐containing mesogenic substituent by the use of a π‐allylnickel macroinitiator bearing PEG segment. The thin film of the block copolymer is prepared by the spin coating of its solution onto mica or silicon wafer which proves to possess perpendicularly oriented nanocylindrical microphase separated structures as supported by the differential calorimetric, polarized optical microscopic, grazing‐incidence small‐angle X‐ray scattering, transmission electron microscope, and atomic force microscope measurements.     

Enhancement of Light Absorption Ability of Synthetic Chlorophyll Derivatives by Conjugation with a Difluoroboron Diketonate Group

The enhancement of the light absorption ability of synthetic chlorophyll derivatives is demonstrated. Chlorophyll derivatives directly conjugated with a difluoroboron 1,3‐diketonate group at the C3 position were synthesized from methyl pyropheophorbide‐d through Barbier acylmethylation of the C3‐formyl moiety, oxidation of the C3‐carbinol, and difluoroboron complexation of the diketonate. Electronic absorption spectra in a diluted solution showed that the synthetic conjugates gave an absorption band at λ=400–500 nm, with a Qy band shifted to a longer wavelength of λ≈700 nm. DFT calculations demonstrated that the absorption bands and redshifts were ascribable to the coupling of the LUMO of chlorin with that of the difluoroboron diketonate moiety. The introduction of a pyrenyl group at the C3³‐position of the conjugate afforded an additional charge‐transfer band over λ=500 nm, producing a pigment that bridged the green gap in standard chlorophylls.