Viscosity approximation methods for resolvents of accretive operators in Banach spaces

In this paper, we first prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method, which is a generalization of the results of Reich [J. Math. Anal. Appl. 75 (1980), 287–292], and Takahashi and Ueda [J. Math. Anal. Appl. 104 (1984), 546–553]. Further using this result, we consider the proximal point algorithm in a Banach space by the viscosity approximation method, and obtain a strong convergence theorem which is a generalization of the result of Kamimura and Takahashi [Set-Valued Anal. 8 (2000), 361–374]. Dedicated to the memory of Jean Leray     

Densely Packed CO2 Aids Charge,Spin, and Lattice Ordering Partially Fluctuated in a Porous Metal–Organic Framework Magnet

Partial charge fluctuations in the charge-ordered state of a material, often triggered by structural disorders and/or defects, can significantly alter its physical characteristics, such as magnetic long-range ordering. However, it is difficult to post-chemically fix such accidental partial fluctuations to reconstruct a uniform charge-ordered state. Herein, we report CO₂-aided charge ordering demonstrated in a CO₂-post-captured layered magnet, [{Ru₂(o-ClPhCO₂)₄}₂{TCNQ(OMe)₂}] ⋅ CO₂ ( 1⊃CO₂ ; o-ClPhCO₂⁻=ortho-chlorobenzoate; TNCQ(OMe)₂=2,5-dimethoxy-7,7,8,8-tetracyanoquinodimethane). Pristine porous layered magnet 1 had a partially charge-fluctuated ordered state, which provided ferrimagnetic ordering at T_C=65 K. Upon loading CO₂, 1 adsorbed one mole of CO₂, forming 1⊃CO₂ , and raising T_C to 100 K. This was because of the vanishing charge fluctuations without significantly changing the framework structure. This research illustrates the post-accessible host–guest chemistry delicately combined with charge, spin, and lattice ordering in a spongy magnet. Furthermore, it highlights how this innovative approach opens up new possibilities for technology and nanoscale magnetism manipulation.     

Theoretical Limit of the Color-Change Sensitivity of a Composite Resin Dosimeter Film Based on Spiropyran/BaFCl : Eu2+/Polystyrene

The theoretical limit of the color-change sensitivity of a composite resin dosimeter film based on 6-nitro BIPS/BaFCl : Eu²⁺/polystyrene under X-ray exposure has been estimated. Each photophysical and photochemical process occurring inside the composite resin dosimeter was quantitatively determined, and the obtained values were used to estimate the theoretical limit of the color-change sensitivity for the composite resin dosimeter. The values obtained were 70.6 % for the X-ray absorption efficiency, 13 % for the fluorescence quantum yield, 73.5 % for the UV absorption efficiency and 37.6 % for the photochemical quantum yield. Assuming that the figure-of-merit is their product, its value is estimated to be 2.5 %, which contributes to the chromaticity difference and leads to a color-change sensitivity of 100 mGy. The figure-of-merit of a structurally optimized composite dosimeter was estimated to be 1.9 times that of the dosimeter without structural optimization, which showed a sensitivity of 100 mGy. We predicted that the structurally optimized composite resin dosimeter film, which eliminates optical losses due to the structure, will be able to detect X-ray exposure doses on the order of approximately 28 mGy.