On a second-order nonlinear discrete multi-point eigenvalue problem

We study the existence and non-existence of positive solutions of a system of nonlinear second-order difference equations with eigenvalues subject to multi-point boundary conditions.     

A New,Mild, and Rapid Transformation of Acylals to Bisulfites in One-Pot Synthesis by Bismuth (III) Nitrate Pentahydrate

Abstract

Direct conversion of acylals to the corresponding bisulfites can be easily performed in the presence of bismuth (III) nitrate pentahydrate in ethanol at room temperature in good yields.     

Polystyrene‐supported Pd(II) complex‐catalysed carboacylation of 2‐arylpyridines with alcohols via C─H bond activation under solvent‐free conditions

Polystyrene‐supported N ,N ‐dimethylethylenediamine Pd(II) complex C was used as an efficient catalyst for the synthesis of aromatic ketones via ortho ‐acylation of sp² C─H bonds of 2‐arylpyridines with alcohols as effective coupling partners. The alcohols were oxidized with tert ‐butyl hydroperoxide to their corresponding aldehydes in situ and efficiently coupled with 2‐arylpyridines to form aryl ketones under solvent‐free conditions. Furthermore, catalyst C could be easily recovered by simple filtration and reused for five cycles without any significant decrease in its activity.     

Synthesis and Characterization of Novel Biodegradable Di‐ and Tri‐Block Copolymers Based on Ethylene Carbonate Polymer as Hydrophobic Segment

Synthesis of novel amphiphilic biodegradable block copolymers based on ethylene carbonate is reported in this study. Polyethylene glycol monomethyl ether (MeO‐PEO) and polyethylene glycol (PEG) of varying molar masses are used as macro‐initiator for ring‐opening polymerization of ethylene carbonate in the presence of sodium stannate trihydrate as a heterogeneous transesterification catalyst. Earlier elution of block copolymer from macro‐initiator in size exclusion chromatography (SEC) indicated the successful synthesis of the block copolymers. Ratios of both types of blocks are varied systematically. Liquid chromatography at critical conditions is used for the analysis of the non‐critical individual blocks, and if there are any critical segments that are not attached to the non‐critical block. To the best of our knowledge, this is the first report on the synthesis of ethylene carbonate‐based amphiphilic block copolymers. Chromatographic critical conditions of the ethylene carbonate polymer are also reported for the first time. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 1887–1893     

MAGNESIUM HYDROGEN SULFATE POWDER CATALYZED STEREOSELECTIVE CONVERSION OF DIALKYL 2-(IMIDO-N -YL)-3-(TRIPHENYLPHOSPHORANYLIDENE)- BUTANEDIOATES TO ELECTRON-POOR (Z)-N -VINYLIMIDES IN SOLVENT-FREE CONDITIONS

Magnesium hydrogen sulfate powder was found to catalyze stereoselective conversion of dialkyl 2-(imido-N-yl)-3-(triphenylphosphorany-lidene)butanedioates to electron-poor (Z)-N-vinylimides in solvent-free conditions at 95°C 1 h in high conversions. Microwave also was found to catalyze the same reactions in the presence of magnesium hydrogen sulfate powder in solvent-free conditions in 3 min.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

1,3-Dibromo-5,5-dimethylhydantoin(DBH)/kaolin:An efficient reagent system for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes under solvent-free conditions

1,3-Dibromo-5,5-dimethylhydantoin,has been used as an efficient catalyst for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes in the presence of kaolin.All reactions are performed in the absence of solvent in relatively short reaction times in good to high yields.     

Controllability results for the two-dimensional heat equation with mixed boundary conditions using Carleman inequalities: a linear and a semilinear case

In this paper, we prove controllability results for a two-dimensional semilinear heat equation with mixed boundary conditions. It is well-known that mixed boundary conditions can present a singular behaviour of the solution. First, we will prove global Carleman estimates then we will use these inequalities to obtain controllability results.     

Necessary and sufficient optimality conditions for fractional multi-objective problems

Using a special scalarization, we give necessary optimality conditions for fractional multiobjective optimization problems. Under a generalized invexity, sufficient optimality conditions are also given. All over the article, the data are assumed to be continuous but not necessarily Lipschitz.