Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method

In this paper, an improved Legendre collocation method is presented for a class of integro-differential equations which involves a population model. This improvement is made by using the residual function of the operator equation. The error differential equation, gained by residual function, has been solved by the Legendre collocation method (LCM). By summing the approximate solution of the error differential equation with the approximate solution of the problem, a better approximate solution is obtained. We give the illustrative examples to demonstrate the efficiency of the method. Also we compare our results with the results of the known some methods. In addition, an application of the population model is made.     

A numerical approximation for Volterra’s population growth model with fractional order

This paper presents a numerical scheme for approximate solutions of the fractional Volterra’s model for population growth of a species in a closed system. In fact, the Bessel collocation method is extended by using the time-fractional derivative in the Caputo sense to give solutions for the mentioned model problem. In this extended of the method, a generalization of the Bessel functions of the first kind is used and its matrix form is constructed. And then, the matrix form based on the collocation points is formed for the each term of this model problem. Hence, the method converts the model problem into a system of nonlinear algebraic equations. We give some numerical applications to show efficiency and accuracy of the method. In applications, the reliability of the technique is demonstrated by the error function based on accuracy of the approximate solution.     

Axler–Zheng Type Theorem on a Class of Domains in {\mathbb{C}^n}

We prove a version of Axler–Zheng’s Theorem on smooth bounded pseudoconvex domains in ${\mathbb{C}^n}$ on which the ${\overline{\partial}}$ -Neumann operator is compact.     

An exponential matrix method for solving systems of linear differential equations

This paper presents an exponential matrix method for the solutions of systems of high‐order linear differential equations with variable coefficients. The problem is considered with the mixed conditions. On the basis of the method, the matrix forms of exponential functions and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown coefficients are determined and thus the approximate solutions are obtained. Also, an error estimation based on the residual functions is presented for the method. The approximate solutions are improved by using this error estimation. To demonstrate the efficiency of the method, some numerical examples are given and the comparisons are made with the results of other methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Asymptotic formulations of the eigenvalues and eigenfunctions for a boundary value problem

In this work, a discontinuous boundary‐value problem with retarded argument that contains a spectral parameter in the transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. Copyright © 2012 John Wiley & Sons, Ltd.     

Anti-diabetic Properties of Calcium Channel Blockers: Inhibition Effects on Aldose Reductase Enzyme Activity

Applied Biochemistry and Biotechnology - Aldose reductase (AR) belongs to NADPH-dependent oxidoreductases and converts glucose to sorbitol in the polyol pathway. AR inhibition is essential to...     

Optimization of Microwave-Assisted Extraction (MAE) for the Isolation of Antioxidants from Basil (Ocimum basilicum L.) by Response Surface Methodology (RSM)

Abstract

The recovery of antioxidants from basil (Ocimum basilicum L.) was modeled with the aid of response surface methodology (RSM) using microwave-assisted extraction (MAE). Face-centered central design (FCCD) was employed to optimize the MAE operational parameters including the extraction time (1 to 7?min), extraction temperature (30 to 120?°C), solid-to-solvent ratio (0.1 to 0.4), and solvent concentration (20 to 80% ethanol, v/v), and to obtain the best possible combinations of these parameters for a high antioxidant yield from basil. The total antioxidant capacity (TAC) was expressed in trolox (TR) equivalents per gram of dried sample (DS). Three of the operational parameters (temperature, extraction time and solvent concentration) were shown to have significant effect on the extraction efficiency of antioxidants in basil extracts (p?<?0.05). The solvent concentration was shown to be the most significant factor on antioxidant yield obtained by MAE. There was a close relationship between experimental and predicted values using the proposed method. This optimized MAE method shows an application potential for the efficient extraction of antioxidants from basil in the food and pharmaceutical industries.     

Synthesis and characterization of epoxy resins containing imine group and their curing processes with aromatic diamine

The epoxy resins containing imine bonding were prepared from hydroxyl substituted Schiff base monomers in two steps. At the first step, hydroxyl substituted Schiff base monomers were synthesized via condensation reaction. At the second step, epoxy resins were synthesized from the reaction between Schiff base monomers and epichlorohydrine (EPC). Then curing processes of epoxy resins were achieved by p-phenylenediamine compound. The structures of resulting compounds were confirmed by FT-IR, UV-Vis and ¹H-NMR. TG-DTA and DSC measurements were performed for thermal characterizations of the compounds. Chemical resistances of the cured epoxy-amine systems were determined for coating applications in acidic, alkaline and organic solvents. HCl (10%, aqueous solution), NaOH (10%, aqueous solution), DMSO, DMF, N-methylpyrrolidone, ethanol, THF and acetone were used for corrosion tests. Chemical resistance data of the synthesized epoxy resins demonstrated that they have good chemical resistance against various acid, alkaline and common organic solvents. Surface morphologies of epoxy resin and the cured epoxy resin were determined with scanning electron microscopy (SEM) measurements. Also, optical band gap (E_g) values of Schiff base monomers and epoxy resins were calculated from UV-Vis measurements.     

The mixed ligand complexes of Co(II), Ni(II), Cu(II) and Zn(II) with coumarilic acid/1,10-phenanthroline

Journal of Thermal Analysis and Calorimetry - The coumarilate (coum?) and 1,10-phenanthroline (phen) mixed ligand complexes of Co(II) (1), Ni(II) (2) Cu(II) (3) and Zn(II) (4) were...     

A rapid and sensitive reversed phase‐HPLC method for simultaneous determination of ibuprofen and paracetamol in drug samples and their behaviors in simulated gastric conditions

Paracetamol is a widely used drug for fever and pain relief. Ibuprofen is a common nonsteroidal anti‐inflammatory drug. In this study, a sensitive and accurate reversed phase high performance liquid chromatography method was developed for the simultaneous determination of ibuprofen and paracetamol. The chromatographic separation was achieved on a Phenomenex C18 (250 mm, 4.6 mm, 5 μm) column. Fifty milli molar phosphate buffer (pH 7.5) and methanol were used as mobile phase in a gradient elution mode. The retention times of paracetamol and ibuprofen were 5.7 and 10.4 min, respectively. The linearity of the developed method was established in the range of 0.25 – 250 mg/L with a correlation coefficient of 0.9998 for both analytes. The limit of detection/quantification values were found to be 0.06/0.19 and 0.08/0.26 mg/L for ibuprofen and paracetamol, respectively. The method was successfully applied in drug samples in the form of tablets and suspensions. The calculated concentrations matched with the claimed values on their prospectuses. The drug samples were studied under simulated gastric conditions to determine the behaviors of the analytes in the human body. The obtained results showed no change in the retention time of the analyte peak shapes throughout the 210 minutes.