Arithmetic functions and the Cauchy product

It is known that under the Dirichlet product, the set of arithmetic functions in several variables becomes a unique factorization domain. A. Zaharescu and M. Zaki proved an analog of the ABC conjecture in this ring and showed that there exists a non-trivial solution to the Fermat equation $$z^n=x^n+y^n$$ ($$n\ge 3$$). It is also known that under the Cauchy product, the set of arithmetic functions becomes a unique factorization domain. In this paper, we consider the ring of arithmetic functions in several variables under the Cauchy product and prove an analog of the ABC conjecture in this ring to show that there exists a non-trivial solution to the Fermat equation $$z^n=x^n+y^n$$ ($$n\ge 3$$).     

Recyclable carbon fiber‐reinforced plastics (CFRP) containing degradable acetal linkages: Synthesis,properties, and chemical recycling

Two epoxy resins containing degradable acetal linkages were synthesized by the reaction of cresol novolak‐type phenolic resin (CN) with vinyl ethers containing a glycidyl group [cyclohexane dimethanol vinyl glycidyl ether (CHDMVG) and 4‐vinyloxybutyl glycidyl ether (VBGE). Carbon fiber‐reinforced plastics (CFRPs) were prepared by heating laminated prepreg sheets with CN‐CHDMVG resin (derived from CN and CHDMVG) and CN‐VBGE resin (derived from CN and VBGE), in which carbon fibers are impregnated with epoxy resins containing curing agents [dicyandiamide (DICY)] and curing accelerator [3‐(3,4‐dichlorophenyl)‐1,1‐dimethylurea (DCMU)]. CN‐CHDMVG‐based CFRPs and CN‐VBGE‐based CFRPs exhibited almost the same tensile strength as the conventional bisphenol‐A‐based CFRPs. CN‐CHDMVG‐based CFRPs and CN‐VBGE‐based CFRPs underwent smooth breakdown with the treatment of hydrochloric acid in tetrahydrofuran at room temperature for 24 h to regenerate strands of carbon fibers. The surface conditions of the recovered carbon fibers had little changes during degradation and recovery processes on the basis of scanning electron microscopy (SEM) and X‐ray photoelectron spectroscopy (XPS). The recovered carbon fibers exhibited almost the same tensile strength as virgin carbon fibers and hence would be reused for the production of CFRPs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1052–1059     

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??This article provides the readers with an introduction to the spectral theory of ergodic one dimensional Schrodinger operators. The theorems developed by the author are mainly discussed and their proofs are given in detail.     

A Mechanistic Dichotomy in Two-Electron Reduction of Dioxygen Catalyzed by N,N’-Dimethylated Porphyrin Isomers

Selective two-electron reduction of dioxygen (O₂) to hydrogen peroxide (H₂O₂) has been achieved by two saddle-distorted N,N’-dimethylated porphyrin isomers, an N21,N’22-dimethylated porphyrin ( anti -Me₂P ) and an N21,N’23-dimethylated porphyrin ( syn -Me₂P ) as catalysts and ferrocene derivatives as electron donors in the presence of protic acids in acetonitrile. The higher catalytic performance in an oxygen reduction reaction (ORR) was achieved by anti -Me₂P with higher turnover number (TON=250 for 30 min) than that by syn -Me₂P (TON=218 for 60 min). The reactive intermediates in the catalytic ORR were confirmed to be the corresponding isophlorins ( anti -Me₂Iph or syn -Me₂Iph ) by spectroscopic measurements. The rate-determining step in the catalytic ORRs was concluded to be proton-coupled electron-transfer reduction of O₂ with isophlorins based on kinetic analysis. The ORR rate by anti -Me₂Iph was accelerated by external protons, judging from the dependence of the observed initial rates on acid concentrations. In contrast, no acceleration of the ORR rate with syn -Me₂Iph by external protons was observed. The different mechanisms in the O₂ reduction by the two isomers should be derived from that of the arrangement of hydrogen bonding of a O₂ with inner NH protons of the isophlorins.     

Power of isotopic fine structure for unambiguous determination of metabolite elemental compositions: In silico evaluation and metabolomic application

In mass spectrometry (MS)-based metabolomics studies, reference-free identification of metabolites is still a challenging issue. Previously, we demonstrated that the elemental composition (EC) of metabolites could be unambiguously determined using isotopic fine structure, observed by ultrahigh resolution MS, which provided the relative isotopic abundance (RIA) of ¹³C, ¹⁵N, ¹⁸O, and ³⁴S. Herein, we evaluated the efficacy of the RIA for determining ECs based on the MS peaks of 20,258 known metabolites. The metabolites were simulated with a ≤25% error in the isotopic peak area to investigate how the error size effect affected the rate of unambiguous determination of the ECs. The simulation indicated that, in combination with reported constraint rules, the RIA led to unambiguous determination of the ECs for more than 90% of the tested metabolites. It was noteworthy that, in positive ion mode, the process could distinguish alkali metal-adduct ions ([M + Na]⁺ and [M + K]⁺). However, a significant degradation of the EC determination performance was observed when the method was applied to real metabolomic data (mouse liver extracts analyzed by infusion ESI), because of the influence of noise and bias on the RIA. To achieve ideal performance, as indicated in the simulation, we developed an additional method to compensate for bias on the measured ion intensities. The method improved the performance of the calculation, permitting determination of ECs for 72% of the observed peaks. The proposed method is considered a useful starting point for high-throughput identification of metabolites in metabolomic research.     

Chemical investigation of metabolites produced by an endophytic Aspergillus sp. isolated from Limonia acidissima

Endophytic fungi are considered as a good source to produce important secondary metabolites with interesting bioactivities. In a continuation of our studies towards the search for environmentally friendly bioactive compounds from Sri Lankan flora, we investigated the secondary metabolites produced by the endophytic fungi Aspergillus sp. isolated from the seeds of the popular edible fruit Limonia acidissima L. of the family Rutaceae. The pure culture of the Aspergillus sp. was grown on potato dextrose broth media. After 4 weeks fermentation, fungal media were extracted with organic solvents. Chromatographic separation of the fungal extracts over silica gel, Sephadex LH-20 and RP-HPLC furnished flavasperone (1), rubrofusarin B (2), aurasperone A (3), fonsecinone D (4) and aurasperone B (5). Compounds 1–4 showed moderate activities in brine shrimp toxicity assay. This is the first report of the ¹³C NMR data of compounds 4 and 5.     

Method development for the determination of 24S‐hydroxycholesterol in human plasma without derivatization by high‐performance liquid chromatography with tandem mass spectrometry in atmospheric pressure chemical ionization mode

We developed a highly sensitive and specific high‐performance liquid chromatography with tandem mass spectrometry method with an atmospheric pressure chemical ionization interface to determine 24S‐hydroxycholesterol, a major metabolite of cholesterol formed by cytochrome P450 family 46A1, in human plasma without any derivatization step. Phosphate buffered saline including 1% Tween 80 was used as the surrogate matrix for preparation of calibration curves and quality control samples. The saponification process to convert esterified 24S‐hydroxycholesterol to free sterols was optimized, followed by liquid–liquid extraction using hexane. Chromatographic separation of 24S‐hydroxycholesterol from other isobaric endogenous oxysterols was successfully achieved with gradient mobile phase comprised of 0.1% propionic acid and acetonitrile using L‐column2 ODS (2 μm, 2.1 mm id × 150 mm). This assay was capable of determining 24S‐hydroxycholesterol in human plasma (200 μL) ranging from 1 to 100 ng/mL with acceptable intra‐ and inter‐day precision and accuracy. The potential risk of in vitro formation of 24S‐hydroxycholesterol by oxidation from endogenous cholesterol in human plasma was found to be negligible. The stability of 24S‐hydroxycholesterol in relevant solvents and human plasma was confirmed. This method was successfully applied to quantify the plasma concentrations of 24S‐hydroxycholesterol in male and female volunteers.     

Reversed phase liquid chromatographic determination of organic acids using on-line complexation with copper(II) ion

We describe a simple and sensitive liquid chromatographic method for the analysis of organic acids using on-line complexation with copper(II) ion. Organic acids complexed with copper(II) ion were separated on a reversed-phase C18 column and detected by UV absorption at 240 nm. The copper(II) ion concentration in the mobile phase had a great influence on separation and sensitivity. A mobile phase consisting of 10 mM copper(II) sulfate in 5 mM sulfuric acid (pH 2.3) was used to separate nine organic acids (tartaric, malic, malonic, lactic, acetic, citric, maleic, succinic and fumaric acids). The detection limits of the examined organic acids calculated at S/N = 3 ranged from 0.6 to 100 μM. The detector signal was linear over three orders of magnitude of organic acid concentration. The method successfully measured organic acids in juice and vinegar samples.     

Prediction of sinkage and motion resistance of a tracked vehicle using plate penetration test

The relationship between contact pressure and sinkage must be represented by a mathematical model to estimate the sinkage and the motion resistance due to a vehicle. In this study an approximate and simple pressure-sinkage model is proposed. This model takes into account the effect of the size of the penetration plate on soil response, and includes two soil values that can be obtained by a single plate penetration test. It is submitted that the sinkage and the motion resistance of a tracked vehicle can be estimated by means of the proposed model.     

Effect of Coulomb Damping on Buckling of a Two-Rod System

This paper describes a significant influence of a slight Coulomb damping on buckling, using a simple two rods system. Coulomb damping produces equilibrium regions around the well-known stable and unstable steady states under the pitchfork bifurcation which occurs in the case without Coulomb damping. Also, the stability of the states in the equilibrium regions is examined by using the phase portrait. As a consequence, due to the slight Coulomb damping, it is theoretically clarified that the states in the equilibrium regions are locally stable, even in the neighborhood of the unstable steady states under the pitchfork bifurcation in the case without Coulomb damping, i.e., even in the neighborhood of the unstable trivial steady states in the postbuckling and the unstable nontrivial steady states under the subcritical pitchfork bifurcation. Furthermore, the experimental results are in qualitative agreement with the theoretically predicted phenomena.