Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.     

Synthesis of Thio Analogues of Quinolone Antibacterials

A facile and rapid synthesis of thio compounds, analogues to ciprofloxacin, and norfloxacin is described.     

Invariant Pseudolinearity with Applications

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions, and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs, and η-pseudolinear programs.     

Growth of large La2−xSrxCuO4 single crystals using tilting-mirror-type infrared heating image furnace

Large single crystals of La_2−xSr_xCuO₄ (LSCO) high-T_c superconductors were grown by the infrared heating floating zone (IR-FZ) method using a tilting-mirror-type image furnace. The maximum diameter of the LSCO crystals increased to 10 mm in the tilting-mirror-type image furnace from 6 mm in the conventional image furnace. CuO rich feeds were required for the crystal growth using the tilting-mirror-type image furnace to compensate for the lack of CuO caused by the significant evaporation of CuO during the growth. The evaporation of CuO was affected by the tilting angle of the mirrors of the image furnace and by feed diameter. The optimized growth conditions were as follows: mirror tilting angle, 20°; feed diameter, 10 mm∅; and feed composition 50.7 mol% CuO.     

Acidified,Wet, Silica-Supported Tetrabutylammonium Periodate: A Convenient and Mild Reagent for Conversion of Thioamides to Their Corresponding Amides Under Solvent-Free Conditions

A series of thioamides are transformed to their corresponding oxo analogues in good to excellent yields with acidified, wet, silica-supported tetrabutylammonium periodate under solvent-free conditions.     

Porous shape memory polymers: Design and applications

Porous shape memory polymers (SMPs) exhibit geometric and volumetric shape change when actuated by an external stimulus and can be fabricated as foams, scaffolds, meshes, and other polymeric substrates that possess porous three-dimensional macrostructures. These materials have applications in multiple industries such as textiles, biomedical devices, tissue engineering, and aerospace. This review article examines recent developments in porous SMPs, with a focus on fabrication methods, methods of characterization, modes of actuation, and applications. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1300–1318     

Highly active polymeric organocatalyst: Chiral ionic polymers prepared from 10,11‐didehydrogenated cinchonidinium salt

Since few examples of 10,11‐didehydrogenated (3‐ethynyl) cinchona alkaloids have been utilized as organocatalysts in asymmetric reaction, we synthesized 10,11‐didehydrogenated cinchonidine. The 3‐vinyl group of cinchonidine was transformed into a 3‐ethynyl functionality. Based on the resulting 10,11‐didehydrogenated cinchonidine, the corresponding quaternary ammonium salt and its dimers were prepared. The ion‐exchange reaction between the quaternary ammonium salt and sodium sulfonate produced the quaternary ammonium sulfonate as a stable ionic compound. Chiral ionic polymers were then synthesized by the ion‐exchange polymerization of the 10,11‐didehydrogenated cinchonidinium salt dimer and a disulfonate. The chiral ionic polymers were found to be capable of efficiently catalyzing the asymmetric alkylation of N‐(diphenylmethylene)glycine tert‐butyl ester. The enantioselectivities obtained with the polymeric catalysts were higher than those obtained with the corresponding monomeric catalyst. Dimers of 10,11‐didehydrogenated cinchonidinium salts were prepared. Treatment of the dimer with disodium disulfonate gave the chiral ionic polymers, which showed high catalytic activity in asymmetric benzylation of N‐(diphenylmethylen)glycine tert‐butyl ester. The polymeric catalysts were reused several times without the loss of catalytic activity. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 621–627     

Residual determination and risk assessment of buprofezin in plum (Prunus domestica) grown in open‐field conditions following the application of three different formulations

This study was conducted to characterize the residual level and perform a risk assessment on buprofezin formulated as an emulsifiable concentrate, wettable powder, and suspension concentrate over various treatment schedules in plum (Prunus domestica). The samples were extracted with an AOAC quick, easy, cheap, effective, rugged, and safe, ‘QuEChERS’, method after major modifications. As intrinsic interferences were observed in blank plum samples following dispersive‐solid phase extraction (consisting of primary secondary amine and C₁₈ sorbents), amino cartridges were used for solid‐phase extraction. Analysis was carried out using liquid chromatography with diode array detection and confirmed by liquid chromatography–tandem mass spectrometry. The method showed excellent linearity with determination coefficient (R² = 1) and satisfactory recoveries (at two spiking levels, 0.5 and 2.5 mg/kg) between 90.98 and 94.74% with relative standard deviation (RSD) ≤8%. The limit of quantification (0.05 mg/kg) was considerably lower than the maximum residue limit (2 mg/kg) set by the Codex Alimentarius. Absolute residue levels for emulsifiable concentrates were highest, perhaps owing to the dilution rate and adjuvant. Notably, all formulation residues were lower than the maximum residue limit, and safety data proved that the fruits are safe for consumers. Copyright © 2016 John Wiley & Sons, Ltd.     

Reactivity Ratios and Sequence Distribution Characterization by Quantitative 13C NMR for RAFT Synthesis of Styrene‐Acrylonitrile Copolymers

The kinetics and reactivity ratios of styrene‐acrylonitrile (SA) copolymerization have been studied extensively in bulk and in a variety of solution media using conventional free radical polymerizations (FRPs). Due to the significant difference in the two reactivity ratios for this monomer pair, at certain feed ratios the copolymers display composition drift with conversion due to monomer depletion. In this study, the kinetics of SA copolymerization using Reversible Addition‐Fragmentation Chain Transfer (RAFT) has been studied in bulk at 80 °C. The reactivity ratios for the terminal model were calculated from the comonomer sequence distributions for the RAFT process at low conversion for nine different compositions and found to be in the same range as those reported for conventional FRP of SA. The changes in the composition and sequence distribution with conversion were studied for three feed compositions. The copolymers show compositional drift with conversion, except at the azeotropic composition, and match the predictions from the reactivity ratios obtained at low conversion. From quantitative ¹³C NMR the triad distributions of these copolymers were estimated and found to match the predicted triad distributions as conversion increased. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 919–927     

TRANSITION METAL,NON-METAL CARBONYL CLUSTRS AS SUPPORTS FOR UNUSUAL ACETYLIDE REACTIVITY

Group 16 elements serve as useful bridging and stabilising single atom ligands in mixed-metal carbonyl complexes and impart unusual reactivity on coordinated acetylenic moieties. Reactions of [Fe ₃ (CO) ₉ (μ ₃ -E) ₂ ] (E = S, or Se) with mononuclear acetylide complexes, [CpM(CO)_3-x(CCR)] (M = Mo or W, x = 0, R = Ph; M = Fe, x = 1, R = Ph or ferrocenyl) under facile conditions yield complexes featuring acetylide coupling, acetylide-flip and formation of oxo and acetylide-bridged complexes. In presence of free acetylenes, unusual ligand systems arising from C─S bond formation are observed and under certain conditions, formation of quinones by coupling of acetylenes with carbon monoxide is facilitated.