Extremal quasimodular forms for low-level congruence subgroups

In this paper, we study “extremal” quasimodular forms of depth 1 for the Hecke subgroups of level 2, 3, and 4, and relations to modular differential equations and Atkin?s orthogonal polynomials.     

Representation of Multicomponent Liquid-Liquid Equilibria for Aqueous and Organic Solutions Using a Modified UNIQUAC Model

A modified form of the UNIQUAC model is presented to accurately reproducebinary phase equilibria and ternary and quaternary liquid-liquid equilibria ofaqueous and organic solutions. The model gives a good representation in thereproduction of binary coexistence curves over a wide temperature range usingtemperature-dependent parameters and of binary vapor-liquid equilibria usingtwo binary energy parameters, and in the correlation of ternary and quaternaryliquid-liquid equilibria using ternary and quaternary parameters, in addition tobinary parameters. The quaternary calculated results are compared with thoseobtained from the modified Wilson and extended UNIQUAC models.     

Explanation of Human Skin Color by Multiple Linear Regression Analysis Based on the Modified Lambert-Beer Law

Quantitative analysis of human skin color is needed in the medical and cosmetic fields. Because of the strong light scattering by biological tissues, however, analysis of skin color has not yet been fully successful. Human skin color is dominated by the colors of blood and melanin which are modified by scattering. Exposure of human skin to hot water or UV-ray changes its color because the absorbance spectrum of reflection from the human skin, and the changes in the absorbance spectra of reflection reflect the absorbance spectra of blood and melanin which are the absorption spectrum distorted by scattering. By applying the modified Lambert-Beer law, the absorbance spectrum of reflection from human skin can be expressed proportional to those distorted absorbance spectra of blood and melanin. Multiple linear regression analysis is successfully used to reproduce the absorbance spectrum of reflection from human skin from the distorted absorbance spectra of blood and melanin.     

[2+2] photodimerization of 1-aryl-4-pyridylbutadienes through cation–π interactions

Irradiation of 1-aryl-4-pyridylbutadienes in the presence of 1 equiv of HCl produced syn and anti head-to-tail dimers, among a number of possible dimers, whereas irradiation in the absence of HCl gave a complex mixture. This indicated that the acid serves as a catalyst for the regio- and stereoselective [2+2] photodimerization of 1-aryl-4-pyridylbutadienes through cation–π interactions between the pyridinium and aromatic rings. The produced synHT dimers underwent Cope rearrangement to produce cyclooctadienes, and they were in equilibrium at a ratio of 85:15 in CDCl₃.     

Synthesis of l-α-phosphatidyl-d-myo-inositol 3,5-bisphosphate from d-glucose

Efficient synthesis of l-α-phosphatidyl-d-myo-inositol 3,5-bisphosphate was achieved from 1,2,5,6-diisopropylidene-d-glucose by utilizing ring-closing metathesis and catalytic OsO₄ dihydroxylation.     

All-solid-state Fluoride Ion-selective Electrode using LaF3 Single Crystal with Poly(3,4-ethylenedioxythiophene) as Solid Contact Layer

An all-solid-state fluoride ion-selective electrode (ISE) was prepared using LaF₃ single crystal with poly(3,4-ethylenedioxythiophene (PEDOT) as the solid contact layer. In contrast to polymer-based ISEs, crystalline membrane-based ISEs have not been used for all-solid-state device, thereby prohibiting the integration of ISEs on a chip. The all-solid-state fluoride ISE developed in this study exhibited superior sensitivity (−56.0±0.9 mV/dec) and selectivity compared to those of conventional inner filling solution ISE. The effects of PEDOT as a solid contact layer were analyzed using chronopotentiometry and electrochemical impedance spectroscopy, which revealed that PEDOT promoted electrode stability. The all-solid-state device can miniaturize the fluoride ISE and facilitate environmental, industrial, agricultural, and physiological monitoring.