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.     

(Co)cyclic (Co)homology of Bialgebroids: An Approach via (Co)monads

For a (co)monad T _l on a category , an object X in , and a functor , there is a (co)simplex in . The aim of this paper is to find criteria for para-(co)cyclicity of Z ^*. Our construction is built on a distributive law of T _l with a second (co)monad T _r on , a natural transformation , and a morphism in . The (symmetrical) relations i and w need to satisfy are categorical versions of Kaygun’s axioms of a transposition map. Motivation comes from the observation that a (co)ring T over an algebra R determines a distributive law of two (co)monads and on the category of R-bimodules. The functor Π can be chosen such that is the cyclic R-module tensor product. A natural transformation is given by the flip map and a morphism is constructed whenever T is a (co)module algebra or coring of an R-bialgebroid. The notion of a stable anti-Yetter-Drinfel’d module over certain bialgebroids, the so-called  ×  _R -Hopf algebras, is introduced. In the particular example when T is a module coring of a  ×  _R -Hopf algebra and X is a stable anti-Yetter-Drinfel’d -module, the para-cyclic object Z _* is shown to project to a cyclic structure on . For a -Galois extension , a stable anti-Yetter-Drinfel’d -module T _S is constructed, such that the cyclic objects and are isomorphic. This extends a theorem by Jara and Ştefan for Hopf Galois extensions. As an application, we compute Hochschild and cyclic homologies of a groupoid with coefficients in a stable anti-Yetter-Drinfel’d module, by tracing it back to the group case. In particular, we obtain explicit expressions for (coinciding relative and ordinary) Hochschild and cyclic homologies of a groupoid. The latter extends results of Burghelea on cyclic homology of groups.     

Measurement of L X-ray fluorescence cross sections and relative intensities for some elements in the atomic range 78 ≤ Z ≤ 92

The L X-ray fluorescence cross sections (σ_Ll, σ_Lα, σ_Lη, σ_Lβ, σ_Lβ6, σ_Lβ2,₄, σ_Lβ1,₃, σ_Lβ9,10, σ_Lγ, σ_Lγ1, σ_Lγ2,3, σ_Lγ4 and σ_Lγ5) and relative intensities (I_Lα, I_Ll, I_Lη, I_Lβ, I_Lβ6, I_Lβ2,4, I_Lβ1,3, I_Lβ9,10, I_Lγ, I_Lγ1, I_Lγ2,3, I_Lγ4 and I_Lγ5) for some elements in the atomic range 78 ≤ Z ≤ 92 have been measured at 59.54 keV photons energies from an Am-241 point source. The L X-rays emitted by samples have been counted by a Si(Li) detector. The L X-ray fluorescence cross sections and relative intensities have been also calculated theoretically by using atomic parameters. The measured values have been compared with the theoretical values.     

Accurate,sensitive determination of omega-6 and omega-3 polyunsaturated fatty acids in human plasma,urine samples

Quantitative determination of omega-6 and omega-3 polyunsaturated fatty acids in human plasma and urine with high accuracy and precision provides significant information to monitor the underlying etiology of several diseases. In this regard, liquid chromatography-mass spectrometry is a good choice owing to its great selectivity and sensitivity. Additionally, the hybrid quadrupole–time of flight–mass spectrometer systems provides easy identification of target compounds with superior mass measurements. In this study, an analytical method has been developed for simple, accurate and simultaneous determination of linoleic acid, arachidonic acid, docosahexaenoic acid and eicosapentaenoic acid in a short chromatographic analysis period. The developed method is suitable for the quantitative detection of these four compounds with detection limits ranging between 1.1–3.0 ng ml⁻¹ and its applicability was assessed in human urine and plasma samples. As a result, acceptable accuracy (between 83 and 111%) and good precision (<6%) were obtained for target compounds using matrix matching calibration strategy.     

Synthesis,characterization, and cytotoxic activity studies of new N4O complexes derived from 2-({3-[2-morpholinoethylamino]-N3-([pyridine-2-yl]methyl) propylimino} methyl)phenol

A new unsymmetrical five-coordinate Schiff base ligand (HL) with an N₄O donor set ( 2 ) has been prepared by condensation of N1-(2-morpholinoethyl)-N1-([pyridine-2-yl]methyl)propane-1,3-diamine with 2-hydroxy-benzaldehyde. Metal complexes [ML]ⁿ⁺ (M = Zn²⁺, Cd²⁺, Mn²⁺, Cu²⁺, Ni²⁺, Ag⁺, Fe³⁺, and Co²⁺ ( 3–10 ) were synthesized by the reaction of the ligand and metal salts in ethanol. The resulting products were characterized by elemental analyses, infrared, ¹H and ¹³C nuclear magnetic resonance spectra (in the case of Cd and Zn complexes), UV–Vis, electrospray ionization-mass spectrometric, and conductivity measurements. The structure of the complexes [ZnL](ClO₄) ( 3 ), [CdL](ClO₄) ( 4 ), and [CuL](ClO₄) ( 7 ) has been determined by single-crystal X-ray diffraction analysis. The metal complexes were determined to have a distorted trigonal bipyramidal (Zn and Cd) or a distorted square pyramidal (Cu) geometry. The cytotoxic potential of each compound (1–10) against MCF-7 and MDA-MB-231 (breast cancer cells), PC-3 (prostate cancer cells), and WI-38 human normal lung fibroblast cells was evaluated using the MTT (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyl tetrazolium bromide) assay. Compounds 1, 2, and 10 did not display any activity toward any cell line tested. None of the compounds except compound 8 was cytotoxic toward PC-3. Compounds 4 and 8 showed the highest cytotoxic activity against the MCF-7 and MDA-MB-231 cell lines. Because compounds 3, 6, and 9 have similar half-maximal inhibitory concentration values against cancer cells and normal cells, these compounds displayed poor selectivity between cancer and normal cells. More importantly, it was observed that compound 5 acts differently toward different types of cell lines. For example, it displays lower cytotoxicity against the WI-38 normal cell line than it does against the MDA-MB-231 cell line.