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 numeric–analytic method for time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative

In this paper, the fractional variational iteration method (FVIM) was applied to obtain the approximate solutions of time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. Numerical results showed the FVIM is powerful, reliable and effective method when applied strongly nonlinear equations with modified Riemann–Liouville derivative.     

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.     

Separation of brombuterol enantiomers in capillary electrophoresis with cyclodextrin‐type chiral selectors and investigation of structure of selector‐selectand complexes using nuclear magnetic resonance spectroscopy

The major goal of this study was to determine the affinity pattern of brombuterol (BB) enantiomers toward various cyclodextrins (CD) and to evaluate the potential of NMR spectroscopy for understanding fine mechanisms of interactions between CDs and BB enantiomers. Separation of BB enantiomers was performed in a fused‐silica capillary using a phosphate buffer, pH 2.5, at the room temperature in the normal polarity mode. It was shown once again that CE in combination with NMR spectroscopy represents a very sensitive tool for studies of affinity patterns and structure of CD complexes with chiral guests. Although opposite affinity patterns of BB enantiomers were observed toward native β‐ and γ‐CDs, no significant differences between the structures of the complexes of these two CDs with BB were detected by NMR spectroscopy. In contrary to this, the opposite affinity pattern of BB enantiomers toward β‐CD and its two sulfated derivatives, heptakis (2,3‐O‐diacetyl‐6‐sulfo)‐β‐CD (HDAS‐β‐CD) and heptakis (2‐O‐methyl‐3,6‐di‐O‐sulfo)‐β‐CD (HMDS‐β‐CD) was associated with major differences in the structure of the complexes. In addition, it was shown again that HMDS‐β‐CD provides separation of enantiomers without formation of inclusion‐type complex with the chiral analyte.     

Sensitive Determination of Terbutaline Using a Platform Based on Nanoparticles of Europium Oxide and Carbon Nanotubes

This study presents a sensitive voltammetric determination of terbutaline (TER) on a platform based on carbon nanotubes (CNTs) and europium oxide nanoparticles (Eu₂O₃NPs) coated glassy carbon electrodes (GCEs). An ultrasonic bath was performed for the preparation of composite material. The material was characterized by energy dispersive X‐ray spectroscopy (EDX), X‐ray diffraction method (XRD) and scanning electron microscopy (SEM). The Eu₂O₃NPs/CNTs/GCE system was assessed for the oxidation of terbutaline (TER). A broad oxidation peak was appeared at 0.71 V using a bare GCE. However, the voltammetry of TER has been improved at a GCE coated with CNTs and a well‐defined anodic peak exhibited at 0.61 V. Furthermore, the nanoparticles of Eu₂O₃ and CNTs coated GCE has greatly improved the electrochemical behaviour of TER and a sharp peak was appeared at 0.59 V. Cyclic voltammetry at Eu₂O₃NPs/CNTs/GCE also reveals a high catalytic effect for the oxidation of TER with an oxidation peak that is distinctly enhanced compared to GCE and CNTs/GCE. Eu₂O₃ nanoparticles were utilized to enhance the surface area of GCE and then improve the sensitivity of the procedure. The response of TER was linear over a concentration range of 2.0×10^?8 M ?9.5×10^?6 M with an LOD of 3.7×10^?9 M. Square wave voltammetric analysis of tablets by Eu₂O₃NPs/CNTs/GCE yielded a recovery of 99.2 % with an RSD% of 3.2. The modified electrode (EuO₂NPs/CNTs/GCE) provides accuracy and precision to the analysis of samples.     

Poly(amidoamine) dendrimer‐coated magnetic nanoparticles for the fast purification and selective enrichment of glycopeptides and glycans

Glycosylated proteins modulate various important functions of organisms. To reveal the functions of glycoproteins, in‐depth characterization studies are necessary. Although mass spectrometry is a very efficient tool for glycoproteomic and glycomic studies, efficient sample preparation methods are required prior to analyses. In the study, poly(amidoamine) dendrimer‐coated magnetic nanoparticles were presented for the specific enrichment and fast purification of glycopeptides and glycans. The enrichment and purification performance of the developed method was evaluated both at the glycopeptide, and the glycan level using several standard glycoprotein digests and released glycan samples. The poly(amidoamine) dendrimer‐coated magnetic nanoparticles not only showed selective affinity (Immunoglobulin G/Bovine Serum Albumin, 1/10 by weight) to glycopeptides and released glycans but also good sensitivity (0.4 ng/µL for Immunoglobulin G) for glycoproteomic and glycomic applications. Thirty‐five glycopeptides of Immunoglobulin G were detected after enrichment with poly(amidoamine) dendrimer‐coated magnetic nanoparticles. In addition, 55 ¹⁸O tagged deamidated glycopeptides belonging to human plasma glycoproteome were confirmed. Finally, fifty 2‐aminobenzoic acid, and 30 procainamide‐labelled human plasma N‐glycans released from human plasma glycoproteins were determined after purifications. The results indicate that the proposed enrichment and purification method using poly(amidoamine) dendrimer‐coated magnetic nanoparticles could be simply adjusted to sample preparation methods.     

Exploration of fractal nature of WO3 nanowire aggregates

The morphology of WO₃ aggregates formed by irregular nanoparticles (D∼40 nm) and nanowires of different aspect ratios (2, 4, 6, and 10 μm nominal lengths) dispersed in commonly used polar solvents without dispersant agents is investigated using a small-angle light scattering technique and by means of fractal theory. Nanoparticles form compact spherical aggregates (D_f∼2.6), whereas 2 μm nanowires with low aspect ratio (L/D∼10) follow a slow cluster-cluster aggregation mechanism with no discernable change in fractal dimension (D_f=2.1) monitored in an extended period of 6 months, despite a notable growth in size (R_g=2.3-3.1 μm). For higher aspect ratio nanowires, scattered intensity profiles, which migrate towards the Porod regime, qualitatively obey the Lorenz-Mie theory predictions. The 10 μm nanowires with very high aspect ratio (L/D∼250) are observed to form stable dispersions in a time span of 6 days. Analytical methods based on spherical primary particle formulations predict D_f=1.9, 1.7, and 1.4 for 4, 6, and 10 μm nanowires, respectively.     

Observation of entanglement between two light beams spanning an octave in optical frequency

We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a chi;{(2)} nonlinear medium. The entangler was a nonlinear optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An interconversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wave function inseparability of 0.74(1)<1, thereby satisfying the criterion of entanglement.     

Current-voltage characteristics of Au/GaN/GaAs structure

Au/GaN/n-GaAs structure has been fabricated by the electrochemically anodic nitridation method for providing an evidence of achievement of stable electronic passivation of n-doped GaAs surface. The change of the electronic properties of the GaAs surface induced by the nitridation process has been studied by means of current-voltage (I-V) characterizations on Schottky barrier diodes (SBDs) shaped on gallium nitride/gallium arsenide structure. Au/GaN/n-GaAs Schottky diode that showed rectifying behavior with an ideality factor value of 2.06 and barrier height value of 0.73 eV obeys a metal-interfacial layer-semiconductor (MIS) configuration rather than an ideal Schottky diode due to the existence of GaN at the Au/GaAs interfacial layer. The formation of the GaN interfacial layer for the stable passivation of gallium arsenide surface is investigated through calculation of the interface state density N_ss with and without taking into account the series resistance R_s. While the interface state density calculated without taking into account R_s has increased exponentially with bias from 2.2×10¹² cm⁻² eV⁻¹ in (E_c−0.48) eV to 3.85×10¹² cm⁻² eV⁻¹ in (E_c−0.32) eV of n-GaAs, the N_ss obtained taking into account the series resistance has remained constant with a value of 2.2×10¹² cm⁻² eV⁻¹ in the same interval. This has been attributed to the passivation of the n-doped GaAs surface with the formation of the GaN interfacial layer.