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.     

Gas chromatography-mass spectrometry determination of the pentafluorobenzoyl derivative of methylhydrazine in false morel (Gyromitra esculenta) as a monitor for the content of the toxin gyromitrin

The main toxic compound found in false morel (Gyromitra esculenta) is acetaldehyde-N-methyl-N-formylhydrazone (gyromitrin). This paper describes a method of determining the total hydrazones content based on acid hydrolysis of gyromitrin and other related hydrazones in air-dried false morel followed by derivatisation of methylhydrazine with pentafluorobenzoyl chloride. The derivative, tris-pentafluorobenzoyl methylhydrazine (tris-PFB-MH) is analyzed by gas chromatography-mass spectrometry. The overall precision of the method is better than 10% (relative standard deviation) for 0.5 ng/microl methylhydrazine in solution. The minimum detectable concentration of methylhydrazine (tris-PFB-MH) by this method is estimated to be approximately 12 pg/microl, which is equal to 0.3 microg/g dry matter (DM) of false morel.     

On Dynamics of Brans–Dicke Theory of Gravitation

We study longstanding problem of cosmological clock in the context of Brans–Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogeneous cosmological models. Then, we show that formulation of the Brans–Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann–Robertson–Walker cosmological models.     

Flow of a non‐linear (density‐gradient‐dependent) viscous fluid with heat generation,viscous dissipation and radiation

In this paper, we study the flow of a compressible (density‐gradient‐dependent) non‐linear fluid down an inclined plane, subject to radiation boundary condition. The convective heat transfer is also considered where a source term, similar to the Arrhenius type reaction, is included. The non‐dimensional forms of the equations are solved numerically and the competing effects of conduction, dissipation, heat generation and radiation are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesis of Bisindolylindeno[1,2-b]quinoxaline and Bisindolylindeno[3,4-b]pyrazine with Poly(N,N′-dibromo-N-ethylnaphthyl-2,7-disulfonamide)

Poly(N,N′-dibromo-N-ethylnaphthyl-2,7-disulfonamide) (PBNS) as novel reagent was synthesized. Bisindolylindeno[1,2-b]quinoxaline and bisindolylindeno[3,4-b]pyrazine derivatives were synthesized in a simple and efficient method from the three-component condensation reaction of indole, indane-1,2,3-trione, and diamine aromatic compounds by PBNS under solvent-free conditions at 80 °C in good to excellent yields, short reaction times, and a simple procedure for new derivatives.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications^® for the following free supplemental resource(s): Full experimental and spectral details.]     

Synthesis and Characterization of pH‐Sensitive Positive‐charge Silica Nanoparticles for Oral Anionic Drug Delivery

The objective of this study is to utilize the pH sensitivity of modified mesoporous silica nanoparticles (MSN) for oral drug delivery. In the first time, a pH‐sensitive ionic liquid was synthesized through the quaternization of 3‐aminopropyltrimethoxysilane (3‐ATMS) with sodium monochloroacetate (SMCA). Then, silica nanoparticle was modified by this pH‐sensitive ionic liquid and converted to a pH‐sensitive positive‐charge silica nanoparticle (PCSN). The nanoparticle was characterized by FTIR and SEM. Naproxen as anionic drug molecules was entrapped in this pH‐sensitive positive‐charge silica nanoparticles (PCSN) and the in vitro release profiles were established separately in both (SGF, pH 1) and (SIF, pH 7.4).     

One Pot Synthesis of Some New Spiro[3H-Indol-3,5′(4′H)-[1,2,4] Oxadiazol]-2-Ones and Bis[Spiro[3H-Indol-3,5′(4′H)-[1,2,4] Oxadiazol]-2-Ones]

A facile preparation of the title compound by 1,3-dipolar cycloaddition reaction of benzonitrile oxides with isatin imines or isatin diimines, in excellent yield, are reported.     

A New Solvated Phosphoric Triamide, [(C6H4(3-CH3)NH)3P(O)] · (C2H5OH): A Database Analysis of N Atom Geometry in Compounds with an [N]3P(O) Fragment

Abstract

In the crystal structure of the title compound C₂₁H₂₄N₃OP · C₂H₅OH, there are three crystallographically independent phosphoric triamide molecules and three ethanol molecules. The environments of the nitrogen atoms are practically planar. The phosphorus atoms display a distorted tetrahedral environment; the maximum and minimum values of angles are observed for one O?P?N and one N?P?N angles, respectively. In this structure, the phosphoramide and ethanol molecules are linked by some different intermolecular O?H···O and N?H···O hydrogen bonds to form chains. The title solvated compound has been further characterized by IR and ³¹P{¹H}, ¹H and ¹³C NMR spectroscopy. The geometry of the nitrogen atoms in this compound is analyzed and compared with those of analogous structures deposited in the Cambridge Structural Database (CSD; Allen, Acta Cryst. 2002, B58, 380-388).