Dzyadyk's Technique for Ordinary Differential Equations Using Hermitian Interpolating Polynomials

For the case of Hermitian interpolation, we consider the approximation-iterative method introduced by Dzyadyk. We construct a practical algorithm.     

Non-local symmetries of first-order equations

It is shown how one can transform scalar first-order ordinarydifferential equations which admit non-local symmetries of theexponential type to integrable equations admitting canonicalexponential non-local symmetries. As examples we invoke theAbel equation of the second kind, the Riccati equation and naturalgeneralizations of these. Moreover, our method describes howa double reduction of order for a second-order ordinary differentialequation which admits a two-dimensional Lie algebra of generatorsof point symmetries can be affected if the second-order equationis first reduced in order once by a symmetry which does notspan an ideal of the two-dimensional Lie algebra.     

An Overview of the Literature on the Synthetic Routes to Azolyloxadiazoles

Published data on the methods of preparation of different azoles linked directly to oxadiazoles are described systematically. This review is divided into classes based on the number of heteroatoms in the azoles connected to oxadiazole ring, and the subtitles are divided according to the type of oxadiazoles isomer.     

Luminescence recognition of different organophosphorus pesticides by the luminescent Eu(III)–pyridine-2,6-dicarboxylic acid probe

Luminescence quenching of a novel long lived Eu(III)–pyridine-2,6-dicarboxylic acid probe of 1:2 stoichiometric ratio has been studied in 0.10 volume fraction ethanol–water mixture at pH 7.5 (HEPES buffer) in the presence of the organophosphorus pesticides chlorfenvinphos (P1), malathion (P2), azinphos (P3), and paraxon ethyl (P4). The luminescence intensity of Eu(III)–(PDCA)₂ probe decreases as the concentration of the pesticide increases. It was observed that the quenching due to P3 and P4 proceeds via both diffusional and static quenching processes. Direct methods for the determination of the pesticides under investigation have been developed using the luminescence quenching of Eu(III)–pyridine-2,6-dicarboxylic acid probe in solution. The linear range for determination of the selected pesticides is 1.0–35.0 μM. The detection limits were 0.24–0.55 μM for P3, P4, and P1 and 2.5 μM for P2, respectively. The binding constants (K), and thermodynamic parameters of the OPs with Eu(III)–(PDCA)₂ were evaluated. Positive and negative values of entropy (ΔS) and enthalpy (ΔH) changes for Eu(III)–(PDCA)₂–P1 ternary complex were calculated. As the waters in this study do not contain the above mentioned OPs over the limit detectable by the method, a recovery study was carried out after the addition of the adequate amounts of the organophosphorus pesticides under investigation.     

Membrane sensors for the selective determination of thiopental.

Novel miniaturized polyurethane (PU) membrane sensors in an all-solid state graphite support were developed, electrochemically evaluated and used for the assay of thiopental drug. The thiopental (T) sensors are based on the formation of ion-association complexes of thiopental with copper(II) and cobalt(II)-bathophenanthroline (bphen) counter anions as electroactive materials dispersed in a polyurethane matrix. The sensors show a linear response for thiopental over the range of 1 x 10(-1) - 5 x 10(-5) M thiopental at 25 degrees C over the pH range 6 - 11 with anionic slopes of -28.7 and -28.3 mV decade(-1) with Cu- and Co-bphen thiopental membrane sensors, respectively. These sensors exhibit a fast response time (25 - 45 s), a low detection limit (5 x 10(-6) M), a long lifetime (7 weeks) and good stability. The selectivity coefficients for thiopental sensors relative to the number of interfering anions, were investigated. These sensors were used for the direct potentiometry of thiopental in a pharmaceutical formulation and human serum. Results with mean accuracy of 99.8 +/- 0.5% of nominal were obtained, which compare well with data obtained using spectrophotometric (UV-Vis) and British Pharmacopoeia (BP) methods.     

On the approximate solution of nonlinear Volterra-Fredholm integral equations on a complex domain by Dzyadyk’s method

In 1980–1984, V. K. Dzyadyk suggested and modified an iterative approximation method (IA-method) for numerical solution of the Cauchy problem y′=f(x,y), y(x ₀)=x₀. Particular cases of nonlinear mixed Volterra-Fredholm integral equations of the second kind arise in the mathematical simulation of the space-time development of an epidemic. This paper is concerned with the approximate solution of integral equations of this type by the Dzyadyk method on complex domains. Finally, we test this method numerically by four different examples. University of Cairo, Giza, Egypt. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 11, pp. 1519–1528, November, 1997.     

Si/SiO2 multilayers: synthesis by reactive magnetron sputtering and photoluminescence emission

This paper relates a complete study of Si/SiO₂ multilayer (ML) structures. First, we suggest an original way of synthesis based on reactive magnetron sputtering of a pure silica target. The photoluminescence spectra of these MLs consist of two Gaussian bands in the visible-near infrared spectral region. The stronger one (I band) is fixed at about 780 nm and probably due to interface states. The weaker one (Q band) is tuneable with the Si sublayer thickness and originates from a radiative recombination within the nanosized Si layers. For this latter band the peak position is a function of the Si sublayer thickness and shows a discontinuity at 30 Å. This corresponds to an Si phase change. For thicknesses above 30 Å, the sublayers are composed of nanocrystalline silicon whereas below 30 Å the sublayers are made of amorphous silicon. We develop a model based on a quantum well to which we have added an interfacial region between Si and SiO₂. It is characterised by an interfacial potential of 0.3 eV. This model depicts the simultaneous behaviour of Q and I bands for an Si sublayer thickness below 30 Å.     

Development and validation of thin-layer chromatography and high-performance thin-layer chromatography methods for the simultaneous determination of linagliptin and empagliflozin in their co-formulated dosage form

JPC – Journal of Planar Chromatography – Modern TLC - A sensitive, simple and validated thin-layer chromatography (TLC) method (method A) and a high-performance thin-layer...     

Synthesis and Antimicrobial Activity of Novel Heterocycles Utilizing 3‐(1,4‐Dioxo‐3,4‐dihydrophthalazin‐2(1H)‐yl)‐3‐oxopropanenitrile as Precursors

The reaction of 3‐(1,4‐dioxo‐3,4‐dihydrophthalazin‐2(1H)‐yl)‐3‐oxopropanenitrile 1 and salicyladehyde furnished coumarin derivatives 4 and 5 . Coupling reaction of 1 with aryl diazonium chlorides and benzene‐1,4‐bis (diazonium) chloride gave the corresponding hydrazones 6a , b and bishydrazone 9 , respectively. Hydrazones 6 underwent intramolecular cyclization upon treating with hydrazine hydrate to give 3‐aminopyrazoles 7 . Pyranyl phthalazine 13 was prepared from the reaction of 1 with ethyl 2‐cyano‐3‐ethoxyacrylate 10 . Enaminonitrile 14 was reacted with hydrazine hydrate/phenylhydrazine and hydroxylamine to afford the corresponding pyrazoles 16 and oxime 17 . The antimicrobial evaluation revealed pyrazole derivatives 7a , b and 16a , b displayed a broad spectrum activity against most strains. 3‐Aminopyrazole derivative 7b showed potent antibacterial activity against all tested microorganisms.