On the rate of convergence of solutions in free boundary problems via penalization

The rate of convergence of approximate solutions via penalization for free boundary problems are concerned. A key observation is to obtain global bounds of penalized terms which give necessary estimates on integrations by the nonlinear adjoint method by L.C. Evans.     

Switchable C- and N-bound isomers of transition-metal cyanocarbanions: synthesis and interconversions of cyclopentadienyl ruthenium complexes of phenylsulfonylacetonitrile anions

The synthesis, structure, and dynamic behavior of bistable C- and N-bound isomers of transition-metal cyanocarbanions are described. A series of C-bound cyclopentadienyl (Cp) ruthenium phosphane complexes, [Ru{CH(CN)SO2Ph}(Cp)L1L2] (3), and their N-bound isomers, [Ru+(Cp)(NCCH(-)SO2Ph)L1L2] (4), were prepared by treating [RuCl(Cp)(PR3)2] with the sodium salt of phenylsulfonylacetonitrile and performing ligand-exchange reactions with the resulting compounds. Structural characterization by X-ray diffraction indicates that the cyanocarbanion moiety of 3 has an alpha-metalated structure, whereas that of 4 has a zwitterionic, end-on structure. Heating these complexes in aprotic solvents gives rise to irreversible linkage isomerization between C- and N-bound isomers, in which the relative thermal stabilities vary greatly depending on the steric and electronic nature of the ligands. Mechanistic studies of N-to-C isomerization revealed that the reaction proceeds irreversibly in a unimolecular manner without the formation of coordinatively unsaturated species. A metal-sliding process, which occurs over the -C-C triple chemical bond N pi-conjugated surface of the cyanocarbanion moiety, was suggested by results from kinetic studies and density functional theory (DFT) calculations. C-to-N isomerizations proceed by the above-mentioned intramolecular process, with a temperature-dependent contribution from the formation and cleavage of mu2-C,N coordination dimers [{Ru{CH(CN)SO2Ph}(Cp)(PPh3)}2] (15 and 16).     

Cover Feature: Fluoroalkyl Sulfoximines for Versatile Photocatalytic Radical Fluoroalkylations (Chem. Rec. 9/2023)

Fluoroalkyl sulfoximines, which serve as electron-accepting fluoroalkyl radical sources, are easy-to-handle, solid, and bench-stable chemicals. Fluoroalkyl radicals can be generated from sulfoximine reagents using strong one-electron injectors, such as a highly reducing photoredox catalyst in the excited state. Our group has developed photocatalytic radical di- and mono-fluoromethylation and α-monofluoroalkylation of olefins with the corresponding fluoroalkyl sulfoximines. In this personal account, appropriate combinations of fluoroalkyl sulfoximines and photoredox catalysts, leading to successful radical fluoroalkylation, have been discussed.     

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127–146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator \({\mathscr{A}}\) which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator \({\mathscr{A}}\) to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.     

Pancreatic lipase-inhibiting triterpenoid saponins from fruits of Acanthopanax senticosus

Sixteen triterpenoid saponins were isolated from the fruits of Acanthopanax senticosus, including a new compound, acanthopanaxoside E (1), which was established as 3-O-beta-D-glucuronopyranosyl echinocystic acid 28-O-beta-D-glucopyranoside on the basis of various spectroscopic analyses and chemical degradation. By using a pancreatic lipase-inhibiting assay system, the crude saponin fraction showed inhibitory activity on pancreatic lipase, which is a key enzyme in lipid digestion. Among the isolated compounds, silphioside F (2), copteroside B (3), hederagenin 3-O-beta-D-glucuronopyranoside 6'-O-methyl ester (4) and gypsogenin 3-O-beta-D-glucuronopyranoside (5) showed inhibitory activity toward pancreatic lipase with IC(50) values of 0.22, 0.25, 0.26 and 0.29 mM, respectively, and the free carboxylic acid groups in position 28 within their chemical structures were required for enhancement of pancreatic lipase inhibition.     

Pancreatic lipase-inhibiting triterpenoid saponins from Gypsophila oldhamiana

Three new triterpenoid saponins, gypsosaponins A-C (1-3), were isolated from the roots of Gypsophila oldhamiana (Caryophyllaceae). Their structures were established as 3-O-beta-D-galactopyranosyl-(1-->2)-[beta-D-xylopyranosyl-(1-->3)]-beta-D-glucuronopyranosyl quillaic acid 28-O-alpha-L-arabinopyranosyl-(1-->2)-alpha-L-arabinopyranosyl-(1-->3)-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-beta-D-fucopyranoside (1), 3-O-beta-D-galactopyranosyl-(1-->2)-[beta-D-xylopyranosyl-(1-->3)]-methyl-beta-D-glucuronopyranosyl gypsogenin 28-O-beta-D-glucopyranosyl-(1-->3)-[beta-D-xylopyranosyl-(1-->4)]-alpha-L-rhamnopyranosyl-(1-->2)-beta-D-fucopyranoside (2), and 23-O-beta-D-glucopyranosyl gypsogenic acid 28-O-beta-D-glucopyranosyl-(1-->3)-[beta-D-glucopyranosyl-(1-->6)]-beta-D-glucopyranoside (3), on the basis of various spectroscopic analyses and chemical degradations. The biological activities of 1-3 were examined inhibitory activity against pancreatic lipase, which showed inhibition of 58.2%, 99.2% and 50.3% at concentration of 1 mg/ml, respectively.     

Simultaneous determination of amphoteric surfactants in detergents by capillary electrophoresis with indirect UV detection

A simple, rapid and simultaneous determination of four types of amphoteric surfactants, i.e., C8, C10, C12, C14, C16 and C18-homologues of alkyldimethylamine N-oxide (AO), alkylamidopropylamine N-oxide (APAO), alkylbetaine (Bt) and alkylamidopropylbetaine (APB), was performed by using capillary electrophoresis (CE) with indirect UV detection. To optimize the separation conditions, effects of pH of background solution (BGS), organic modifier and chromophore for indirect UV detection on the CE separation of the amphoteric compounds were investigated. Addition of 50% (v/v) acetonitrile to the BGS under a lower pH condition brought a good separation performance due to the suppression of micelle formation for the analytes and the adsorption onto the inner surface of the capillary. Under an optimal condition, the 24 amphoteric analytes were completely separated in a single run within 17min. The relative standard deviation of the migration time was ranging from 0.20 to 0.23% and the limit of detection values for AO, APAO, Bt and APB homologues were 10-20, 20, 20-50 and 50microg/mL, respectively. Furthermore, the developed method can provide a high resolution separation of the amphoteric surfactants in commercially available detergents and shampoo without any sample pretreatments.     

Time-resolved in situ ATR-IR observations of the process of sorption of water into a poly(2-methoxyethyl acrylate) film

A process of water sorption into a biocompatible polymer, poly(2-methoxyethyl acrylate) (PMEA), was investigated by time-resolved, in situ, attenuated total reflection infrared spectroscopy. Evidence for three different types of hydrated water in PMEA, that is, nonfreezing water, freezing bound water, and freezing water, were found. Each hydration structure was elucidated at the functional group level. Nonfreezing water, which never crystallizes, even at -100 degrees C, has a C=O...H-O type of hydrogen bonding interaction with the carbonyl group of PMEA. Freezing bound water, which crystallizes in a heating process below 0 degrees C, interacts with the methoxy moiety in the PMEA side chain terminal. Freezing water, which crystallizes approximately 0 degrees C, has bulk-water-like structure with an O-H...O-H hydrogen bonds network. It has been concluded from the present study that the methoxy moiety in the PMEA side chain terminal plays an important role for the excellent biocompatibility of PMEA.     

Surfactant-mixing effects on the interfacial tension and the microemulsion formation in water/supercritical CO2 system

The effects of surfactant mixing on interfacial tension and on microemulsion formation were examined for systems of air/water and water/supercritical CO2 (scCO2) interfaces and for water/scCO2 microemulsions. A fluorinated surfactant, sodium bis(1H,1H,2H,2H-heptadecafluorodecyl)-2-sulfosuccinate (8FS(EO)2), was mixed with the three hydrocarbon surfactants, Pluronic L31, Tergitol TMN-6, and decyltrimethylammonium chloride (DeTAC), at equimolar ratio. For all the cases, the interfacial tension was significantly lowered by the mixing. The positive synergistic effect suggests that the mixed surfactants tend to pack more closely on the interface than the pure constituents. It was found, however, that the microemulsion formation in scCO2 was never facilitated by the mixing, except for the case of TMN-6. This is probably due to the segregation of the surfactants into hydrocarbon-rich and fluorocarbon-rich phases on the microemulsion surface.