The construction of operational matrix of fractional derivatives using B-spline functions

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper.     

Chemical composition of the essential oil of aerial parts of Haussknechtia elymaitica Boiss. from Iran: a good natural source for trans-asaron

The chemical composition of the essential oil of Haussknechtia elymaitica Boiss. was investigated by capillary GC and GC/MS for the first time. Twelve components were identified which accounting for 99.7% of the oil composition. The major compounds were trans-asarone (59.9%), trans-methyl isoeugenol (22.4%), α-zingiberene (7.96%), β-sesquiphellandrene (4.7%) and β-bisabolene (4.3%). The first three compounds considered as the main components of the essential oil were isolated and characterised by spectroscopic techniques.     

A new flavonoid and other constituents from Centaurea nicaeensis All. var. walliana M

A new flavone glucoside, apigenin 4'-(6″-methylglucuronide) (1), together with six known compounds, cirsilineol, jaceosidin, melitensin, apigenin, apigenin 7-(6″-methylglucuronide) and prunasin, were isolated from the ethanolic extract of the aerial parts of Centaurea nicaeensis All. var. walliana M. (Asteraceae) collected from Souk-Ahras, eastern Algeria. The structures were established by spectral analysis, mainly HRESI-MS, UV and 2D-NMR experiments (COSY, HSQC and HMBC).     

Electrochemical determination of tyrosine in the presence of uric acid at a carbon paste electrode modified with multi-walled carbon nanotubes enhanced by sodium dodecyl sulfate

Tyrosine (Tyr) was quantitated with high sensitivity and selectivity in the presence of uric acid (UA) using a carbon paste electrode modified with multi-walled carbon nanotubes. Tyr and UA were catalytically oxidized with diffusion-controlled characteristics. They were determined simultaneously by differential pulse voltammetry with a potential difference of 350 mV. The electrocatalytic currents increase linearly with Tyr and UA concentrations 4×10^?7?1×10^?4 M and 3×10^?7?2×10^?4 M. Their detection limits were 1×10^?7 and 5.1×10^?8 M respectively. In the presence of sodium dodecyl sulfate the Tyr detection limit improved from 1×10^?7 to 6.9×10^?8 M. The electrode was successfully used to quantitate Tyr and UA in serum.      

Synthesis, X-ray structure, electrochemistry, and theoretical studies of palladium(II) complex with a tetradentate bis(quinoline-2-carboxamide) ligand

The title complex [Pd(Me₂bqb)] (1), [Me₂bqb^2?C?=?1,2-bis(quinoline-2-carboxamide)-4,5-dimethyl-benzene dianion], has been synthesized and characterized by elemental analyses and spectroscopic methods, and the crystal and molecular structure of [Pd(Me₂bqb)] has been determined by X-ray crystallography. The complex exhibits distorted square-planar PdN4 coordination geometry with two short and two long Pd?CN bonds (Pd?CN ~1.957 and ~2.095 ?, respectively). In addition to the molecular geometry from X-ray experiment, theoretical studies have been carried out on the structure of the complex at the density functional theory (DFT-B3LYP) level in conjunction with effective core potential basis set (LANL2DZ) for Pd atom and 6-311++G(d,p) basis set for N, O, C and H atoms. Electrochemical studies in CH₂Cl₂ solution revealed A reversible redox process corresponding to the Pd^II/Pd^III couple with E _1/2 at 0.924?V (vs. SCE).     

Chemical composition and biological activity of essential oil from Pulicaria undulata from Yemen

The chemical composition of the essential oil obtained from the leaves of Pulicaria undulata Gamal Ed Din (syn P. orientalis sensu Schwartz and P. jaubertii Gamal Ed Din) was analyzed by GC-MS. Major compounds of P. undulata oil were the oxygenated monoterpenenes, carvotanacetone (91.4%) and 2,5-dimethoxy-p-cymene (2.6.%). The antimicrobial activity of the essential oil was evaluated against six microorganisms, Escherichia coli Pseudomonas aeruginosa, Staphylococcus aureus, methicillin-resistant S. aureus, Bacillus subtilis, and Candida albicans, using disc diffusion and broth microdilution methods. The oil showed the strongest bactericidal activity against Staphylococcus aureus and methicillin-resistant S. aureus, as well as Candida albicans. The essential oil showed moderate cytotoxic activity against MCF-7 breast tumor cells, with an IC50 of 64.6 +/- 13.7 microg/mL. Bioautographic assays were used to evaluate the acetylcholinesterase inhibitory effect as well as antifungal activity of the oil against Cladosporium cucumerinum.     

Tunable broadband plasmonic perfect absorber at visible frequency

Metamaterials and plasmonics as a new pioneering field in photonics joins the features of photonics and electronics by coupling photons to conduction electrons of a metal as surface plasmons (SP). This concept has been implemented for a variety of applications including negative index of refraction, magnetism at visible frequency, cloaking devices amongst others. In the present work, we used plasmonic hybrid material in order to design and fabricate a broad-band perfect plasmonic metamaterial absorber in a stack of metal and Copper-PTFE (Polytetrafluoroethylene) nanocomposite showing an average absorbance of 97.5?% in the whole visible spectrum. Our experimental results showed that the absorption peak of the stacks can be tuned upon varying the thickness and type of the spacer layer due to the sensitivity of plasmon resonance to its environment. To the best of our knowledge, this is the first report of a plasmonic metamaterial absorber based on copper with absorption around 100?% in the entire visible and near-Infrared (NIR).     

Organic-Assisted Nano-Sized Antimony Telluride Prepared by Co-Precipitation Reductive Route

Nano-sized antimony telluride is of much interest for improving the thermoelectric figure of merit. In the present work, organic-assisted antimony telluride nanorods were successfully fabricated by a simple hydrothermal method. The products were characterized by means of X-ray diffraction, scanning electron microscope, and transmission electron microscope. The results show that the typical antimony telluride synthesized by co-precipitation reductive route is rodlike in shape with about 35 nm in thickness and 300 nm in edge length.     

Interaction of cations with 2′‐deoxythymidine nucleoside and analysis of the nature and strength of cation bonds

Binding of Mg²⁺, Ca²⁺, Zn²⁺, and Cu⁺ metal ions with 2′‐deoxythymidine (dT) nucleoside was studied using a density functional theory method and a 6‐311++G(d,p) basis set. This work demonstrated that the interaction of dT with these cations is tri‐coordinated η (O2, O4′, O5′). Among the four types of cations, Zn²⁺ cation exhibited the most tendency to interact with the dT. Cations via their interaction with dT can affect the N‐glycosidic bond length, the values of pseudorotation of the sugar ring, the orientation of the base unit with respect to the sugar ring, and the acidity of the O5′H, O3′H, and N3H groups in the dT nucleoside. Natural bond orbital analysis was performed to calculate the charge transfer and natural population analysis of the complexes. Quantum theory of atoms in molecules was also applied to determine the nature of interactions. It was shown that in dT–Mg²⁺ and dT–Ca²⁺ complexes, the bonds are electrostatic (closed‐shell) interactions, although they are partially covalent and partially electrostatic interactions in dT–Zn²⁺ and dT–Cu⁺ complexes. Copyright © 2011 John Wiley & Sons, Ltd.