A green one-pot three-component synthesis of α-aminophosphonates under solvent-free conditions and ultrasonic irradiation using Fe3O4@SiO2-imid-PMAn as magnetic catalyst

An efficient and environment friendly process for the synthesis of α-aminophosphonates has been devised. Through a one-pot three-component condensation of various aldehydes, amines, and triethyl phosphite in the presence of Fe₃O₄@SiO₂-imid-PMAⁿ nanoparticles as magnetic catalysts under solvent-free conditions and ultrasonic irradiation, α-aminophosphonates were obtained with excellent yields. The reactions under solvent-free conditions at room temperature are compared with the ultrasonic-assisted reactions. This new procedure has notable advantages such as short reaction time, excellent yields, easy purification, and the absence of any tedious workup or purification. The aforementioned catalyst could be easily recovered by an external magnetic field and can be reused for six consecutive reaction cycles without significant loss of activity. In addition, SEM and DLS of the catalyst after the reaction cycle were investigated.     

One-pot synthesis of multisubstituted imidazoles catalyzed by Dendrimer-PWA<Superscript>n</Superscript> nanoparticles under solvent-free conditions and ultrasonic irradiation

An efficient, green and eco-friendly protocol has been developed for the synthesis of 2,4,5-trisubstituted and 1,2,4,5-tetrasubstituted imidazoles via one-pot condensation reaction using Dendrimer-PWAⁿ as catalyst under solvent-free conditions or ultrasonic irradiation in excellent yields. The reactions under conventional heating conditions were compared with the ultrasonic-assisted reactions. The operational simplicity, practicability and applicability of this protocol to various substrates make it an interesting alternative to previous procedures. The present methodology offers several advantages such as excellent yields, short reaction times, a cleaner reaction, and the absence of any tedious work-up or purification. The catalyst is easily separated from the products by filtration and also exhibits remarkable reusable activity. SEM, BET and DLS of the catalyst were also investigated after each reaction cycle.     

Electrocatalytic determination of penicillamine using multiwall carbon nanotubes paste electrode and chlorpromazine as a mediator

In this study, we describe the application of carbon paste electrode modified with multiwall carbon nanotubes as a voltammetric sensor for determination of penicillamine (PA) in the presence of chlorpromazine as a mediator. This modified electrode showed very efficient electrocatalytic activity for the anodic oxidation of PA. The peak current of linear sweep voltammograms of PA increased linearly with it’s concentration in the range of 0.5–500 μM PA. The detection limit for PA was 0.2 μM. The RSDs for 1.0 and 10.0 μM PA were 1.1 and 1.7%, respectively. The proposed sensor was successfully applied for the determination of PA in human urine and tablet.     

Reverse phase HPLC determination of sunitinib malate using UV detector,its isomerisation study,method development and validation

Sunitinib malate, as an anticancer compound and a multi-targeted tyrosine-kinase inhibitor for treatment of glioma, was comprehensively studied by using different liquid chromatography methods. Since sunitinib malate shows Z-E isomerism, various reverse phase high performance liquid chromatography (RP-HPLC) programs were designed to access quantitative determination and good separation of Z-E stereoisomers. Moreover, some impurities including N-oxide and impurity B were to be separated from the main isomer with acceptable resolution. In the present work, different RP-HPLC programs were developed in which the type of mobile phase, flow rate, pH, and temperature were optimized to reach the best analysis conditions and control the rate of Z to E conversion. In addition, the effect of some operational parameters during the solution preparation including initial concentration of the analyte, temperature, pH, and type of solvent on the stability of Z isomer were investigated. The opted conditions for quantitative analysis were C8-Hector column as stationary phase, methanol as solvent, ammonium acetate buffer containing triethylamine as mobile phase, the pH of mobile phase of 8.5, the flow rate of 1.0 mL/min, and detection at 425 nm. In this situation the peaks of E and Z isomers were at 16.3 and 19.7 min. Full validation of the designed method was done based on ICH guidelines.     

A new relaxed HSS preconditioner for saddle point problems

We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues distribution of the preconditioned matrix are presented. The preconditioned system is solved by a Krylov subspace method like restarted GMRES. Finally, some numerical experiments on test problems arisen from finite element discretization of the Stokes problem are given to show the effectiveness of the preconditioner.     

Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces

The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2?) with respect to non-homogeneous term g(x) ∈ L ₂ ^n/2 (B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H _2,0 ^1,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem.     

Existence of μ−pseudo almost periodic solutions to some evolution equations

In this article, a new approach for pseudo almost periodic solution under the measure theory, under Acquistpace‐Terreni conditions. We make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of μ‐pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations. For illustration, we propose some application to a nonautonomous heat equation. Copyright © 2017 John Wiley & Sons, Ltd.     

Maximum Order of Triangle‐Free Graphs with a Given Rank

The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle‐free graphs with a given rank and characterize all such graphs achieving the maximum order.