Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations

In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method.     

On solvability of differential equations with the Riesz fractional derivative

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy-type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well-known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory.     

On the decomposition of λK into regular tournaments of order 5

An RTD[5,λ; v] is a decomposition of the complete symmetric directed multigraph, denoted by λK, into regular tournaments of order 5. In this article we show that an RTD[5,λ; v] exists if and only if (v?1)λ ≡ 0 (mod 2) and v(v?1)λ ≡ 0 (mod 10), except for the impossible case (v,λ) = (15,1). Furthermore, we show that for each v ≡ 1,5 (mod 20), v ≠ 5, there exists a B[5,2; v] which is not RT₅-directable. © 1994 John Wiley & Sons, Inc.     

Wet carbon-based solid acid/NaNO_3 as a mild and efficient reagent for nitration of aromatic compound under solvent free conditions

Nitro aromatic compound can be obtained in high yields via nitration of aromatic compound with wet carbon-based solid acid and NaNO_3 under solvent free oxidation at room temperature.     

Solvent extraction of mercury using Alamine 304

Summary A study has been undertaken to develop a solvent extraction system for mercury using Alamine 304 in aqueous chloride medium. The parameters investigated included reagent concentration, acid concentration, pH, aqueous to organic phase ratio, and rate of extraction and stripping. The study shows that mercury can be extracted rapidly and efficiently from aqueous chloride solutions. A number of aqueous stripping reagents removed more than 90% of the mercury from the organic phase with only one equilibrium. These include HNO₃, NaOH and EDTA.

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Extraktion von Quecksilber mit Alamin 304

Zusammenfassung Die Extraktion von Quecksilber aus der wäßrigen Lösung des Chlorids mit Alamin 304 wurde untersucht. Die Konzentration des Reagens, der Säure, das pH, das Verhältnis der wäßrigen zur organischen Phase sowie das Extraktionsverhältnis wurden geprüft. Die Extraktion verläuft rasch und wirkungsvoll. Eine Reihe wäßriger Reagenzien entzieht mehr als 90% des Quecksilbers aus der organischen Phase. Dazu gehören Salpetersäure, Natronlauge und EDTA.

     

Zein film as a novel natural biopolymer membrane in electrochemical detections

Permselective modifier films are very important in preparing highly sensitive electrochemical sensors. In this work, for the first time, the behavior of gold and glassy carbon electrodes coated with biocompatible zein film as a permselective membrane for the electrochemical detection of various compounds has been investigated. For this purpose, several electroactive cationic (methylene blue, brilliant green, and thionine) and anionic (potassium ferricyanide, alizarin red S, and riboflavin-5’-phosphate) compounds have been used as model. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) showed that zein membranes prepared from casting solution containing 1% zein in ethanol/water have porous structures with high nanometric roughness. The capacitance values of electrical double layers of electrodes modified with zein film were very high for hydrophilic ions in comparison with hydrophobic ions. Point of zero charge pH (pH_pzc) of zein membrane was 4.8. The results of cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) as well as pH_pzc study indicated that zein permselective membrane acts as ion exchanger film for selected cationic compounds with fast electrochemical kinetics responses in aqueous solution (pH=7). This behavior was confirmed by circulating solutions containing model compounds from homemade continuous cell equipped with polyamide membranes modified with zein film.

Graphical Abstract

     

The role of charge distribution on the antimalarial activity of artemisinin analogues

In this work the calculated nuclear quadrupole coupling constants (NQCC; chi) of 17O in artemisinin and some of its derivatives and the effects of charge density due to the nature of ligands on NQCC of 17O were investigated. All calculations were performed at the HF/3-21G level using the Gaussian 98 program. The results show that the O-O linkage has a characteristic role in the antimalarial activity of artemisinin. In addition, various substitutions on C4 change the charge density on these oxygens and consequently change the pharmaceutical effect of artemisinin. Our results suggest that due to a larger charge density on O1, the heme iron approaches the endoperoxide moiety at the O1 position with preference to the O2 position.     

Ion pairing, H-bonding, and π–π interactions in copper(II) complex-organo-networks derived from a proton-transfer compound of the 1,10-phenanthroline-2,9-dicarboxylic acid

The one-pot reaction between the novel proton transfer compound (pydaH₂)²⁺(phendc)²⁻, LH₂, and Cu(II) afforded the compounds (pydaH)₂[Cu(phendc)₂]·10H₂O, 1, and (pydaH)₂[Cu(phendc)(phendcH)]₂·5H₂O, 2, where pyda=2,6-diaminopyridine, and phendcH₂=1,10-phenanthroline-2,9-dicarboxylic acid. The single crystal X-ray diffraction analysis of 1 and 2 revealed that these are two novel self-assembled 3D Cu(II) complex-organo-networks, in which (pydaH)⁺ ions and [Cu(phendc)₂]²⁻ or complex units are held together by ion pairing, H-bonding, and π–π interactions. Magnetic measurements over the temperature range 1.8–310 K revealed no significant magnetic coupling between Cu(II) centers in 1 or 2.     

Quaternized amino functionalized cross-linked polyacrylamide as a new solid-liquid phase transfer catalyst in reduction of carbonyl compounds with NaBH4

Poly[N-(2-aminoethyl)acrylamido]trimethyl ammonium chloride resin was developed as a new polymeric phase transfer catalyst. This quaternized polyacrylamide catalyzed the chemoselective reduction of aldehydes and ketones by NaBH₄ to give corresponding alcohols in high yields under mild conditions.     

A robust-adaptive fuzzy coverage control for robotic swarms

In this paper, a decentralized adaptive control scheme for multi-robot coverage is proposed. This control method is designed based on centroidal Voronoi configuration integrated with robust adaptive fuzzy control techniques. We consider simple single integrator mobile robots used for covering dynamical environments, where an adaptive fuzzy logic system is used to approximate the unknown parts of control law. A robust coverage criterion is used to attenuate the adaptive fuzzy approximation error and measurement noises to a prescribed level. Therefore, the robots motion is forced to obey solutions of a coverage optimization problem. The advantages of the proposed controller can be listed as robustness to external disturbances, computation uncertainties, and measurement noises, while applicability on dynamical environments. A Lyapunov-function based proof is given of robust stability, i.e. convergence to the optimal positions with bounded error. Finally, simulation results are demonstrated for a swarm coverage problem simultaneous with tracking mobile intruders.