Jacobi-Picard iteration method for the numerical solution of nonlinear initial value problems

In this paper, an effective numerical iterative method for solving nonlinear initial value problems (IVPs) is presented. The proposed iterative scheme, called the Jacobi-Picard iteration (JPI) method, is based on the Picard iteration technique, orthogonal shifted Jacobi polynomials, and shifted Jacobi-Gauss quadrature formula. In comparison with traditional methods, the JPI method uses an iterative formula for updating next step approximations and calculating integrals of the shifted Jacobi polynomials are performed via an exact relation. Also, a vector-matrix form of the JPI method is provided in details which reduce the CPU time. The performance of the presented method has been investigated by solving several nonlinear IVPs. Numerical results show the efficiency and the accuracy of the proposed iterative method.     

Synthesis of new phosphonato esters by reaction between triphenyl or trialkyl phosphite and acetylenic diesters in the presence of NH‐containing compounds

The reaction between triphenyl or trialkyl phosphite and acetylenic esters in the presence of some heterocyclic or aromatic NH compounds such as thiazolidine‐2,4‐dione, 2‐methyl indole, 5‐bromoisatine, 3‐nitroacetanilide, saccharin, 5,5‐dimethylhydantoin, 2‐nitroaniline, 4‐nitroaniline, benzophenon hydrazine, and anthranilic acid led to the formation of phosphonato esters in high yield. © 2011 Wiley Periodicals, Inc. Heteroatom Chem 22:630–639, 2011; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.20725     

Synthesis and antimicrobial evaluation of some new bicyclopyrazolone‐based thiopyran ring systems

A series of bicyclopyrazolones were synthesized from the condensation reaction of methyl 4‐oxotetrahydro‐2H‐thiopyran‐3‐carboxylate with hydrazine derivatives in ethanol. All synthesized products were characterized by FT‐IR, ¹H, and ¹³C NMR spectral data, elemental analyses, and mass spectrometry. The antibacterial and antifungal activities of these compounds were evaluated against Staphylococcus aureus and Bacillus subtilis as Gram‐positive bacteria, Escherichia coli and Pseudomonas aeruginosa as Gram‐negative bacteria, and the fungus Candida albicans. The results revealed that bicyclopyrazolones including an aryl or aryl sulfonyl group in the N‐2 position of the pyrazolone moiety are the most effective against all the microorganisms studied in this work.     

A Novel Bioelectrochemical Sensor Based on Immobilized Urease on the Surface of Nickel Oxide Nanoparticle and Polypyrrole Composite Modified Pt Electrode

Nickel oxide nanoparticle (NiO?NP) and polypyrrole (PPy) composite were deposited on a Pt electrode for fabrication of a urea biosensor. To develop the sensor, a thin film of PPy?NiO composite was deposited on a Pt substrate that serves as a matrix for the immobilization of enzyme. Urease was immobilized on the surface of Pt/PPy?NiO by a physical adsorption. The response of the fabricated electrode (Pt/PPy?NiO/Urs) towards urea was analyzed by chronoamperometry and cyclic voltammetry (CV) techniques. Electrochemical response of the bio‐electrode was significantly enhanced. This is due to electron transfer between Ni²⁺ and Ni³⁺ as the electro‐catalytic group and the reaction between polypyrrole and the urease‐liberated ammonium. The fabricated electrode showed reliable and demonstrated perfectly linear response (0.7–26.7 mM of urea concentration, R²= 0.993), with high sensitivity (0.153 mA mM^?1 cm^?2), low detection of limit (1.6 μM), long stability (10 weeks), and low response time (～5 s). The developed biosensor was highly selective and obtained data were repeatable and reproduced using PPy‐NiO composite loaded with immobilized urease as urea biosensors.     

Rheological and morphological properties of PA6/ECO nanocomposites

Polyamide-6/poly(epichlorohydrin - co - ethylene oxide) (PA6/ECO) nanocomposites were prepared with 6 wt.% organoclay and different ECO content from 5 to 40 wt.%, via two-step melt blending process. The effects of organoclay and rubber content on the morphological and rheological properties of samples have been studied. Samples have been characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and rheometry in small amplitude oscillatory shear. XRD results indicate that the nanoclay platelets are partially exfoliated in both PA6 and ECO phases. The higher rubber content of nanocomposite samples results in higher exfoliation degree of the nanoclay layers. SEM photomicrographs of samples show that the size of rubber droplets increases by the introducing of nanoclay. Oscillatory shear measurements show that the storage modulus of nanocomposite samples significantly increases in comparison with unfilled blends. The formation of physical network is the prime cause of such increase. Moreover, presence of nanoclay dramatically increases melt yield stress of the samples. Palierne emulsion model has been applied to predict the rheological behavior of unfilled blends. A quantitative agreement between Palierne model and those of experimental data is found for low ECO content samples.     

Study of three-component reaction of α-ketoesters and active methylenes with OH-acids to synthesize new 2-amino-4H-pyran derivatives and evaluation of their antibacterial and antioxidant activities

Research on Chemical Intermediates - Synthesis of new derivatives of 2-amino-4H-pyrans is reported via three-component reaction of α-ketoesters, active methylenes, and OH-acids in the presence...     

Switching the reactivity of dihydrothiopyran-4-one with aldehydes by aqueous organocatalysis: Baylis-Hillman, aldol, or aldol condensation reactions

An aqueous medium containing catalytic amounts of a tertiary amine was employed to direct the chemoselectivity of the reaction of aldehydes with 1a. With DBU, 2 was formed at room temperature as a rare exemplary of Baylis-Hillman reactions in heterocyclic enones. DABCO alternated the pathway toward an aldol reaction to form syn/anti mixtures of 3 with the syn isomers being the major products. With Et(3)N, aldol condensation dominated.     

Multiplicity results for elliptic problems with variable exponent and nonhomogeneous Neumann conditions

Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)‐Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

A Facile,One-Pot Synthesis of Azoic Compounds and Anthraquinone Derivatives Containing Dialkyl Phosphoryl Moieties in Multicomponent Reactions

Protonation of the reactive 1:1 intermediates produced in the reactions between triphenylphosphine and dialkyl acetylenedicarboxylates by 1-amino-anthraquinone or 1,5-diphenylcarbazone as a core dye leads to vinyl phosphonium salts, which undergo Michael addition with conjugate base of NH compounds to produce stable phosphorus ylides as novel dyes in fairly good yields. These ylides can exist in two geometrical isomers (Z) and (E) for 3, because the negative charge of the ylide moiety of these compounds are strongly conjugated with the adjacent carbonyl group. Rotation around the carbon–carbon double bond is slow in the (Z) and (E) geometrical isomers on the NMR time scale at ambient temperature. These compounds are assigned by their IR, ¹H, ¹³C NMR spectral data as well as their mass spectroscopic data.