Computing eigenelements of boundary value problems with fractional derivatives

Variational iteration method has been successfully implemented to handle linear and nonlinear differential equations. The main property of the method is its flexibility and ability to solve nonlinear equations accurately and conveniently. In this paper, first, a general framework of the variational iteration method is presented for analytic treatment of differential equations of fractional order where the fractional derivatives are described in Caputo sense. Second, the new framework is used to compute approximate eigenvalues and the corresponding eigenfunctions for boundary value problems with fractional derivatives. Numerical examples are tested to show the pertinent features of this method. This approach provides a new way to investigate eigenvalue problems with fractional order derivatives.     

Antioxidant secondary metabolites from Geranium lasiopus Boiss. & Heldr

Chromatographic studies on the EtOAc soluble portion of the MeOH extract of Geranium lasiopus led to the isolation of eight flavonoids (kaempferol (1), quercetin (2), quercetin 3-O-β-glucopyranoside (3), quercetin 3-O-β-galactopyranoside (4), kaempferol 3-O-α-rhamnopyranosyl-(1?→?6)-β-glucopyranoside (5), quercetin 3-O-α-rhamnopyranosyl-(1?→?6)-β-glucopyranoside (6), kaempferol 3-O-α-rhamnopyranosyl-(1?→?2)-β-glucopyranoside (7) and quercetin 3-O-α-rhamnopyranosyl-(1?→?2)-β-glucopyranoside (8)), two simple phenolic compounds (gallic acid (9) and its methyl ester (10)) and a hydrolysable tannin (pusilagin (11)). The structures of the compounds were elucidated by 1- and 2-dimensional NMR techniques ((1)H, (13)C, COSY, HMBC, HMQC) and ESI-TOF-MS spectrometry. Inhibitory effects on H(2)O(2)-induced lipid peroxidation in human red blood cells of the different extracts of G. lasiopus, as well as isolated compounds, were investigated. All tested compounds showed comparable or higher activity than that of ascorbic acid and trolox.     

Performance improvement of spectral amplitude coding-optical code division multiple access systems using NAND detection with enhanced double weight code

The bit-error rate (BER) performance of the spectral amplitude coding-optical code division multiple access (SACOCDMA) system has been investigated by using NAND subtraction detection technique with enhanced double weight (EDW) code. The EDW code is the enhanced version of double weight (DW) code family where the code weight is any odd number and greater than one with ideal cross-correlation. In order to evaluate the performance of the system, we used mathematical analysis extensively along with the simulation experiment. The evaluation results obtained using the NAND subtraction detection technique was compared with those obtained using the complementary detection technique for the same number of active users. The comparison results revealed that the BER performance of the system using NAND subtraction detection technique has greatly been improved as compared to the complementary technique.     

Performance analysis of spectral-amplitude-coding optical CDMA systems with new subtract exclusive OR detection (SED) using vectors combinatorial (VC) code

This paper investigates the performance of vector combinatorial (VC) code for spectral amplitude coding optical code-division multiple-access (SAC-OCDMA) system using a newly proposed subtract exclusive OR detection (SED) technique. VC code is constructed using Euclidean vector and algebraic ways. One of the important properties of this code is that the maximum cross correlation is one, which means that multi-user interference (MUI) and phase induced intensity noise (PIIN) are reduced. The weight for the VC code can be any positive integer number. The system performance was evaluated by comparing the theoretical studies using related equations and simulation results taken from the commercial optical systems, “VPI? TransmissionMaker 7.1”. Significant improvement in system performances has been observed when the proposed SED technique employing VC code was applied compared to other codes that utilize conventional balance detection techniques for spectral amplitude coding.     

Synthesis of D-mannitol substituted ether-linked bis-1,2,3-triazoles as models of gemini surfactants

Readily available and low cost D-mannitol was converted into 1,2,5,6-di-O-isopropylidene-D-mannitol (1) in the presence of acetone and zinc chloride. Williamson etherfication of 1 with propargyl bromide afforded the bisalkyne 2 in a very good yield. 1,3-Dipolar cycloaddition of 2 with four different alkyl azides using click conditions gave four novel bistriazoles 3a-d. Removal of the acetal groups of 3a-d afforded the deprotected bistriazoles 4a-d in excellent yields. Products 3 and 4 represent models of gemini surfactants.     

Mn (II) and Zn (II) complexes of a benzimidazole ligand having undecyl chains: Crystal structures,photophysical and thermal properties

A new tridentate benzimidazole ligand (L‐C¹¹) containing undecyl chains and its Mn (II) and Zn (II) complexes were synthesised and characterized by spectroscopic and analytical methods. Molecular structures of complexes [Mn(L‐C¹¹)Cl₂] and [Zn(L‐C¹¹)Cl₂] were evaluated by X‐ray diffraction studies. The X‐ray data showed metal ions in both complexes are five‐coordinate with distorted square pyramidal geometry around the metal centres. The undecyl chains in the structure of the complexes are aligned in an interdigitated manner (head to tail) forming a non‐polar domain. The aggregation properties of the ligand and its complexes were investigated by UV–Vis. absorption and emission spectroscopies in DMF‐water mixtures. The emission spectral data revealed that the compounds showed aggregation induced quenching (AIQ) in DMF‐water solutions. Moreover, thermal properties of the compounds were investigated by TG, DTG and DSC analysis.     

On an inventory model for deteriorating items and time-varying demand

In this paper, we present an optimal procedure for finding the replenishment schedule for the inventory system in which items deteriorate over time and demand rates are increasing over a known and finite planning horizon.     

Numerical approach to differential equations of fractional order

In this paper, the variational iteration method and the Adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. This paper presents a numerical comparison between the two methods for solving systems of fractional differential equations. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.     

On the electronic structure of transition metal complexes. I. An INDO-MO investigation of some octahedral complex ions

Molecular-orbital calculations within the INDO framework are reported for the hexafluoro, hexachloro, and hexaaquo metallate (II) ions of the first transition series. The parameterization scheme and choice of orbital exponents have been detailed. The results indicate that the method in its present form gives fairly satisfactory predictions of molecular properties.     

Synthesis and conductivity of poly acene quinone radical polymers

Polymers with conductivities from 8.6 × 10⁰ to 7.3 × 10^?6 (ω cm)^?1 at 2–12 kbar were prepared by zinc-chloride-catalyzed condensation of polycyclic aromatic hydrocarbons, heterocycles, and quinones with pyromellitic dianhydride, tetrabromophthalic anhydride, and tetrachlorophthalic anhydride at 450°C. These materials are stable in air and exhibit strong electroactive character without addition of oxidizing or reducing agents (dopants).