A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations

We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Fréchet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods.

We already derived such a theorem in [11 N. Yamamoto ( 1998 ). A numerical verification method for solutions of boundary value problems with local uniqueness by Banach's fixed-point theorem . SIAM J. Numer. Anal. 35 : 2004 – 2013 .[Crossref] , [Google Scholar]], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations.     

Reversible Sodium Metal Electrodes: Is Fluorine an Essential Interphasial Component?

Alkaline metals are an ideal negative electrode for rechargeable batteries. Forming a fluorine‐rich interphase by a fluorinated electrolyte is recognized as key to utilizing lithium metal electrodes, and the same strategy is being applied to sodium metal electrodes. However, their reversible plating/stripping reactions have yet to be achieved. Herein, we report a contrary concept of fluorine‐free electrolytes for sodium metal batteries. A sodium tetraphenylborate/monoglyme electrolyte enables reversible sodium plating/stripping at an average Coulombic efficiency of 99.85 % over 300 cycles. Importantly, the interphase is composed mainly of carbon, oxygen, and sodium elements with a negligible presence of fluorine, but it has both high stability and extremely low resistance. This work suggests a new direction for stabilizing sodium metal electrodes via fluorine‐free interphases.     

A pilot study on improving the absorptivity of a thick microperforated panel absorber

Microperforated panel (MPP) absorbers are promising as a basis for the next-generation of sound absorbing materials. MPPs are typically made of a thin metal or plastic panel. However, thin limp panels are generally not suitable as an interior finish of room walls because they do not have sufficient strength, which prevents practical application of MPPs as an interior finish of room walls. In order to overcome the lack of appropriate strength required for room walls, it is possible to make an MPP out of a thick panel. However, thick MPPs are usually not efficient because the resistance and/or reactance become too high. In this study, trial production of thick MPPs and measurement of their normal absorption coefficients were carried out. Results show that efficient absorption can be given with a thick MPP by using a tapered perforation.     

Biosynthesis of Indole Diterpene Lolitrems: Radical-Induced Cyclization of an Epoxyalcohol Affording a Characteristic Lolitremane Skeleton

Lolitrems are tremorgenic indole diterpenes that exhibit a unique 5/6 bicyclic system of the indole moiety. Although genetic analysis has indicated that the prenyltransferase LtmE and the cytochrome P450 LtmJ are involved in the construction of this unique structure, the detailed mechanism remains to be elucidated. Herein, we report the reconstitution of the biosynthetic pathway for lolitrems employing a recently established genome-editing technique for the expression host Aspergillus oryzae. Heterologous expression and bioconversion of the various intermediates revealed that LtmJ catalyzes multistep oxidation to furnish the lolitrem core. We also isolated the key reaction intermediate with an epoxyalcohol moiety. This observation allowed us to establish the mechanism of radical-induced cyclization, which was firmly supported by density functional theory calculations and a model experiment with a synthetic analogue.     

A Theoretical study on the charge and discharge states of Na-ion battery cathode material,Na1+xFePO4F

Na₂FePO₄F is a promising cathode material for a Na-ion battery because of its high electronic capacity and good cycle performance. In this work, first principle calculations combined with cluster expansion and the Monte Carlo method have been applied to analyze the charge and discharge processes of Na₂FePO₄F by examining the voltage curve and the phase diagram. As a result of the density functional theory calculation and experimental verification with structural analysis, we found that the most stable structure of Na_1.5FePO₄F has the P2₁/b11 space group, which has not been reported to date. The estimated voltage curve has two clear plateaus caused by the two-phase structure composed of P2₁/b11 Na_1.5FePO₄F and Pbcn Na₂FePO₄F or Na₁FePO₄F and separated along the c-axis direction. The phase diagram shows the stability of the phase-separated structure. Considering that Na₂FePO₄F has diffusion paths in the a- and c-axis directions, Na₂FePO₄F has both innerphase and interphase diffusion paths. We suggest that the stable two-phase structure and the diffusion paths to both the innerphase and interphases are a key for the very clear plateau. We challenge to simulate a nonequilibrium state at high rate discharge with high temperature by introducing a coordinate-dependent chemical potential. The simulation shows agreement with the experimental discharge curve on the disappearance of the two plateaus. © 2018 Wiley Periodicals, Inc.     

The structural evolution of alkoxy-derived gel during drying

The effects of drying temperature on the structural evolution of alkoxy-derived silica gel prepared using various catalysts have been investigated. The dependence of specific surface area, S_g, reflecting the structure, on the temperature of drying was remarkable for a non-catalyzed xerogel. The effect of drying temperature on the S_g of an ammonia-catalyzed xerogel was also found but was not very large. The S_g of xerogels obtained by drying at 60°C was always higher by 50% than the gels dried at 30°C without regard to the aging temperature. The S_g of xerogels from HCl-catalyzed solution was of the order of several m²/g, however, the S_g of the aerogel obtained by hypercritical drying of the wet gel from a similar solution was about 800 m²/g. These phenomena were understood on the basis of SAXS measurements on both wet gels and aerogels.     

Structural changes of poly-L-lysine in solution and lyophilized form

Two structural changes of poly-l-lysine have been studied by various spectroscopic techniques; one is a structural change of a random coil sample in solution to a mixture of alpha-helix and beta-sheet during rapid freezing in the lyophilizing process, and the other is a pressure-induced structural change from an alpha-helix to a beta-sheet structure for a lyophilized sample.     

Koshikamide B, a cytotoxic peptide lactone from a marine sponge Theonella sp

Koshikamide B (1) has been isolated from two separate collections of the marine sponge Theonella sp. as the major cytotoxic constituent. Koshikamide B is a 17-residue peptide lactone composed of six proteinogenic amino acids, two D-isomers of proteinogenic amino acids, seven N-methylated amino acids, and two unusual amino acid residues. The unusual amino acids are N(delta)-carbamoylasparagine and 2-(3-amino-2-hydroxy-5-oxopyrrolidin-2-yl)propionic acid (AHPP); the former is first found as the constituent of peptides, whereas the latter is a new amino acid residue. The N-terminus of koshikamide B is blocked by a methoxyacetyl group. The structure of koshikamide B (1) has been determined by interpretation of spectral data and analysis of chemical degradation products. Koshikamide B (1) exhibits cytotoxicity against P388 murine leukemia cells and the human colon tumor (HCT-116) cell line with an IC50 value of 0.45 and 7.5 microg/mL, respectively.     

Interlaboratory evaluation of two enzyme-linked immunosorbent assay kits for the determination of crustacean protein in processed foods

The labeling of foods containing material derived from crustaceans such as shrimp and crab is to become mandatory in Japan because of increases in the number of allergy patients. To ensure proper labeling, 2 novel sandwich enzyme-linked immunosorbent assay (ELISA) kits for the determination of crustacean protein in processed foods, the N kit (Nissui Pharmaceutical Co., Ltd, Ibaraki, Japan) and the M kit (Maruha Nichiro Holdings, Inc., Ibaraki, Japan), have been developed. Five types of model processed foods containing 10 and/or 11.9 microg/g crustacean soluble protein were prepared for interlaboratory evaluation of the performance of these kits. The N kit displayed a relatively high level of reproducibility relative standard deviation (interlaboratory precision; 4.0-8.4% RSDR) and sufficient recovery (65-86%) for all the model processed foods. The M kit displayed sufficient reproducibility (17.6-20.5% RSDR) and a reasonably high level of recovery (82-103%). The repeatability relative standard deviation (RSDr) values regarding the detection of crustacean proteins in the 5 model foods were mostly < 5.1% RSDr for the N kit and 9.9% RSDr for the M kit. In conclusion, the results of this interlaboratory evaluation suggest that both these ELISA kits would be very useful for detecting crustacean protein in processed foods.