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 position-space renormalization group approach to percolation

In a position-space renormalization group (PSRG) approach to percolation one calculates the probabilityR(p,b) that a finite lattice of linear sizeb percolates, wherep is the occupation probability of a site or bond. A sequence of percolation thresholdsp _c (b) is then estimated fromR(p _c ,b)=p _c (b) and extrapolated to the limitb to obtainp _c =p _c (). Recently, it was shown that for a certain spanning rule and boundary condition,R(p _c ,)=R _c is universal, and sincep _c is not universal, the validity of PSRG approaches was questioned. We suggest that the equationR(p _c ,b)=, where isany number in (0,1), provides a sequence ofp _c (b)'s thatalways converges top _c asb. Thus, there is anenvelope from any point inside of which one can converge top _c . However, the convergence is optimal if =R _c . By calculating the fractal dimension of the sample-spanning cluster atp _c , we show that the same is true aboutany critical exponent of percolation that is calculated by a PSRG method. Thus PSRG methods are still a useful tool for investigating percolation properties of disordered systems.     

Highly Efficient and Practical Syntheses of Lavendamycin Methyl Ester and Related Novel Quinolindiones

The novel 7-(N-formyl-, 7-(N-acetyl-, and 7-(N-isobutyrylamino)-2-methylquinoline-5,8-diones were synthesized in excellent overall yields in three steps via the nitration of the commercially available 8-hydroxy-2-methylquinoline followed by a reduction-acylation step and then oxidation. Acid hydrolysis of 7-(N-acetylamino)-2-methylquinoline-5,8-dione (14a) afforded the novel 7-aminoquinoline-5,8-dione 7 in excellent yields. Due to our efficient preparation of dione 14a, we now report a short and practical method for the total synthesis of the potent antitumor agent lavendamycin methyl ester (1b) with an excellent overall yield.     

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.     

Donor ligand, basal ligand and solvent effects on the equilibrium constants of triphenylphosphinecobalt(III) Schiff base complexes with phosphite ligands

The equilibrium constants and the thermodynamic parameters were spectrophotometrically measured for the 1:1 adduct formation of [Co(Salen)(PPh₃)]ClO₄.H₂O, and [Co(7,7′-Me₂Salen)(PPh₃)]ClO₄.H₂O as acceptors, with P(OR)₃ (R = methyl, ethyl, and i-propyl) as donors, in acetonitrile (CH₃CN) and dimethylformamide (DMF) as solvents at constant ionic strength (I = 0.1 M NaClO₄), and various temperatures (t = 10–50 °C). Our results revealed the following trends: stability of the cobalt(III) Schiff base complexes toward a given phosphite donor, [Co(7,7′-Me₂Salen)(PPh₃)]⁺ < [Co(Salen)(PPh₃)]⁺; binding of the donors (phosphites) toward a given cobalt(III) Schiff base complex, P(OEt)₃ > P(OMe)₃ > P(O-ⁱPr)₃; influence of solvent on the stability of a given cobalt(III) Schiff base complex toward a given phosphite donor, CH₃CN < DMF.     

Solid phase extraction of gold by sorption on octadecyl silica membrane disks modified with pentathia-15-crown-5 and determination by AAS

A simple and selective method for rapid and efficient concentration and determination of μg l⁻¹ levels of Au(III) ions in aqueous solution using octadecyl silica membrane disks modified by pentathia-15-crown-5 and flame atomic absorption spectrometry is presented. The influence of flow rates of eluent and sample solution, amount of ligand, types and least amount of eluent for elution of Au from disks were investigated. Break through volume and limit of detection of the membrane disks modified by 5 mg of the thiacrown ether was found to be 2.0 l and 1.0 μg l⁻¹, respectively. The effects of various cationic interferences on percent recovery of gold were studied. The method was successfully applied for the determinations of gold in some pharmaceutical samples and for the recovery of trace Au³⁺ ions from synthetic and water samples.     

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.

     

Synthesis and Evaluation of Biocompatible pH‐Sensitive Hydrogels as Colon‐Specific Drug Delivery Systems

Because of the growing importance of pH‐sensitive hydrogels as drug delivery systems, biocompatible copolymeric hydrogels based N‐vinyl‐2‐pyrrolidinone (NVP) and methacrylic acid (MAA) were designed and synthesized. These hydrogels were investigated for oral drug delivery. Radical copolymerizations of N‐vinyl‐2‐pyrrolidinone (NVP) and methacrylic acid (MAA) with the various ratios of cross‐linking agent were carried out at 70 °C. Azabisisobutyronitrile (AIBN) was the free‐radical initiator employed and Cubane‐1,4‐dicarboxylic acid (CDA) linked to two 2‐hydroxyethyl methacrylate (HEMA) group was the crosslinking agent (CA) used for hydrogel preparations. The hydrogels were characterized by differential scanning calorimetry and FT‐IR. Equilibrium swelling studies were carried out in enzyme‐free simulated gastric and intestinal fluids (SGF and SIF, respectively). A model drug, olsalazine [3,3′‐azobis (6‐hydroxy benzoic acid)] (OSZ) as an azo derivative of 5‐aminosalicylic acid (5‐ASA), was entrapped in these gels and the in‐vitro release profiles were established separately in both enzyme‐free SGF and SIF. The drug‐release profiles indicated that the amount of drug released depended on the degree of swelling. The swelling was modulated by the amount of crosslinking of the polymer bonded drug (PBDs) prepared. Based on the great difference in hydrolysis rates at pH 1 and 7.4, these pH‐sensitive hydrogels appear to be good candidates for colon‐specific drug delivery.