Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative

We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the “fractional centered derivative” approach. We determine the error of the Riesz fractional derivative to the fractional centered difference. We apply the Crank–Nicolson method to a fractional diffusion equation which has the Riesz fractional derivative, and obtain that the method is unconditionally stable and convergent. Numerical results are given to demonstrate the accuracy of the Crank–Nicolson method for the fractional diffusion equation with using fractional centered difference approach.     

Effects of cosolvents cetyltrimethylammonium bromide on the thresholds for nucleation of nitrogen in aqueous solutions

The decomposition of ammonium nitrite in water creates a supersaturated solution of nitrogen. The same process occurs in water-organic solvent mixtures. Acetone, dioxane, dimethylsulfoxide (DMSO) and dimethylformamide (DMF) are the cosolvents used in this study. The limits of supersaturation of nitrogen (C _SL /mol L^–1) were determined in all of these solvent mixtures by releasing the dissolved gas sonicationally and measuring the volume of released gas. C _SL was generally increased in the presence of cosolvents. The effectiveness sequence of organic solvents was found to be as DMF SL and all of the measured quantities of this study were generally affected by micelle formation.     

Determination of Minimum Enzymatic Decolorization Time of Reactive Dye Solution by Spectroscopic & Mathematical Approach

Synthetic dyes are very important for textile dyeing,paper printing,color photography and petroleum products.Traditional methods of dye removal include biodegradation,precipitation,adsorption,chemical degradation,photo degradation,and chemical coagulation.Dye decolorization with enzymatic reaction is an important issue for several research field(chemistry,environment)In this study,minimum decolorization time of Remazol Brilliant Blue R dye with Horseradish peroxidase enzyme was calculated using with mathematical equation depending on experimental data.Dye decolorization was determined by monitoring the absorbance decrease at the specific maximum wavelength for dye.All experiments were carried out with different initial dye concentrations of Remazol Brilliant Blue R at 25 ℃ constant temperature for 30 minutes.The development of the least squares estimators for a nonlinear model brings about complications not encountered in the case of the linear model.Decolorization times for completely removal of dye were calculated according to equation.It was shown that mathematical equation was conformed exponential curve for dye degradation.     

Enzymatic Decolorization of Anthraquinone and Diazo Dyes Using Horseradish Peroxidase Enzyme Immobilized onto Various Polysulfone Supports

In this study, covalent immobilization of the horseradish peroxidase (HRP) onto various polysulfone supports was investigated. For this purpose, different polysulfones were methacrylated with methacryloyl chloride, and then, nonwoven fabric samples were coated by using solutions of these methacrylated polysulfones. Finally, support materials were immersed into aquatic solution of HRP enzyme for covalent immobilization. Structural analysis of enzyme immobilization onto various polysulfones was confirmed with Fourier transform infrared spectroscopy, atomic force microscopy, and proton nuclear magnetic resonance spectroscopy. Decolorization of textile diazo (Acid Black 1) and anthraquinone (Reactive Blue 19) dyes was investigated by UV–visible spectrophotometer. Covalently immobilized enzyme has been used seven times in freshly prepared dye solutions through 63 days. Dye decolorization performance of the immobilized systems was observed that still remained high (70 %) after reusing three times. Enzyme activities of immobilized systems were determined and compared to free enzyme activity at different conditions (pH, temperature, thermal stability, storage stability). Enzyme activities of immobilized systems and free enzyme were also investigated at the different temperatures and effects of temperature and thermal resistance for different incubation time at 50 °C. In addition, storage activity of free and immobilized enzymes was determined at 4 °C at different incubation days.     

Spectral studies of safranin-O in different surfactant solutions

The interaction of Safranin-O (SO), a cationic dye, with various surfactants viz., anionics; Sodiumdodecylsulfate (SDS) and Sodiumdodecylsulfonate (SDSo), nonionics; polyoxyethylenesorbitanmonolaurate (Tween 20) and polyoxyethylenedodecylether (Brij 35), cationic; Dodecyltrimethylammoniumbromide (DTAB) and zwitterionic; Laurylsulfobetaine (LSB) was studied spectrophotometrically as a function of surfactant concentration ranging from premicellar to postmicellar region in aqueous media in the absence and presence of cosolvents. The binding constants (K(b)) and fraction of bound SO to micelles (f), were calculated by means of Benesi-Hildebrand Equation. The binding tendency of SO to micelles followed the order as; Tween 20>Brij 35>SDS>SDSo>LSB. The presence of cosolvents, such as Methanol, Dimethylformamide (DMFA) and 1,4 Dioxan (DX) at various volume percentages, increased the CMC of both SDS and Tween 20 and at a certain concentration totally inhibited the micellization. The binding of SO to micelles decreased as the concentration of the cosolvents increased. This inhibitory effect of cosolvents on binding of SO to micelles followed the order as; Methanol>DMFA>DX.     

Purification of Acetylcholinesterase by 9-Amino-1,2,3,4-tetrahydroacridine from Human Erythrocytes

The acetylcholinesterase enzyme was purified from human erythrocyte membranes using a simple and effective method in a single step. Tacrine (9-amino-1,2,3,4-tetrahydroacridine) is a well-known drug for the treatment of Alzheimer's disease, which inhibits cholinesterase. We have developed a tacrine ligand affinity resin that is easy to synthesize, inexpensive and selective for acetylcholinesterase. The affinity resin was synthesized by coupling tacrine as the ligand and l-tyrosine as the spacer arm to CNBr-activated Sepharose 4B. Acetylcholinesterase was purified with a yield of 23.5 %, a specific activity of 9.22 EU/mg proteins and 658-fold purification using the affinity resin in a single step. During purification, the enzyme activity was measured using acetylthiocholine iodide as a substrate and 5,5′-dithiobis-(2-nitrobenzoicacid) as the chromogenic agent. The molecular weight of the enzyme was determined as about 70 kDa monomer upon disulphide reduction by sodium dodecyl sulphate polyacrylamide gel electrophoresis. K _m, V _max, optimum pH and optimum temperature for acetylcholinesterase were found by means of graphics for acetylthiocholine iodide as the substrate. The optimum pH and optimum temperature of the acetylcholinesterase were determined to be 7.4 and 25–35 °C. The Michaelis–Menten constant (K _m) for the hydrolysis of acetylthiocholine iodide was found to be 0.25 mM, and the V _max was 0.090 μmol/mL/min. Maximum binding was achieved at 2 °C with pH 7.4 and an ionic strength of approximately 0.1 M. The capacity for the optimum condition was 0.07 mg protein/g gel for acetylcholinesterase.