Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants

Numerical Algorithms - For their several attractive features from the viewpoint of the numerical computations, linear barycentric rational interpolants have been recently used to construct various...     

Copper nanoparticles supported on 2‐methoxy‐1‐phenylethanone‐functionalized MCM‐41: An efficient and recyclable catalyst for one‐pot three‐component C–S coupling reaction of aryl halides with benzyl bromide and thiourea

An environmentally friendly copper‐based catalyst supported on 2‐methoxy‐1‐phenylethanone‐functionalized MCM‐41 was prepared and characterized by Fourier transform‐infrared, transmission electron microscopy, field emission‐scanning electron microscopy, X‐ray diffraction and inductively coupled plasma techniques. The catalyst was applied for the one‐pot three‐component C–S coupling reactions of aryl halides with benzyl bromide and thiourea under aerobic conditions to afford the corresponding coupled products in good yields in water. The catalyst could be recovered and recycled five times. These results prove 2‐methoxy‐1‐phenylethanone‐functionalized MCM‐41 supported Cu (II) complex was not leached during the reaction. Also it shows the correct heterogeneous nature of the catalyst.     

The phenomenon of simplified scattering from rough surfaces to reflection in fractional space

In this paper, the scattering of incident plane waves from rough surfaces has been modeled in a fractional space. It is shown how wave scattering from a rough surface could correspond to a simple reflection problem in a fractional space. In an integer dimensional space, fluctuations of the surface result in wave scattering, while in the fractional space, these fluctuations are compensated by the geometry of space. In the fractional space, reflection is equivalent to scattering from the integer dimensional space. Comparing scattered wave functions from different self-affine rough surfaces in the framework of the Kirchhoff theory with the results from the fractional space, we see good agreement between them.     

Suppression of harmonic perturbations and bifurcation control in tracking objectives of a boiler–turbine unit in power grid

In the presence of harmonic disturbances, boiler–turbine units may demonstrate quasi-periodic behaviour due to the occurrence of various types of bifurcation. In this article, a nonlinear model of boiler–turbine unit is considered in which drum pressure, electric output and drum water level are controlled via manipulation of valve positions for fuel, steam and feed-water flow rates. For bifurcation control in tracking problem, two controllers are designed based on gain scheduling and feedback linearization (FBL). To investigate the efficiency of control strategies, three cases are considered for desired tracking objectives (a sequence of steps, ramps/steps, and a combination of them). According to the results, FBL controller works successfully in suppression of harmonic perturbations and consequently bifurcation control. As it is implemented, quasi-periodic solutions (caused by Hopf bifurcation) are vanished; leading to the appearance of periodic solutions with low amplitudes. Consequently, appropriate tracking performance with less oscillatory behaviour is observed for the drum pressure, electric output, and drum water level (desirable for the power grid). In addition, when FBL controller is used, less control efforts are predicted for the bifurcation control.     

Chemical durability of lead silicate glass in HNO3, HCl and H2SO4 aqueous acid solutions

Acid dissolution of silicate glasses with different lead contents was rigorously investigated. Aqueous solutions containing 0.5, 1, and 2 N HNO₃, HCl and H₂SO₄ were used to measure the durability of the glass probes. Scanning Electron Microscopy (SEM), Energy Dispersive Spectroscopy (EDS), Inductively Coupled Plasma (ICP), X-ray Diffraction (XRD) and weight loss analyses were used to evaluate the morphological/compositional changes of the probes, the ash deposit, and the aqueous solutions produced due to the dissolution of the glass specimens. Empirical results showed that any increase in the lead content of the probes deteriorated the durability of the glasses by accelerating the hydrolysis of the silica network. ZrO₂ and TiO₂ additions had inverse effect and improved the chemical durability and the practical life-time of the lead glasses.     

Determination of trace amounts of cadmium,copper and nickel in environmental water and food samples using GO/MgO nanocomposite as a new sorbent

A solid phase extraction method based on graphene oxide (GO) modified with magnesium oxide (MgO) nanoparticles was developed for the preconcentration and determination of trace amounts of cadmium, copper and nickel ions. The adsorbed analytes were eluted by 4.0 mL of 0.1 M (EDTA) and injected to flame atomic absorption spectrometer. The factors influencing the complex formation and extraction of these heavy metals were optimized. Studies on potential interference by various anions and cations showed the method to be highly selective. The preconcentration factor was about 11 with relative standard deviation of <4.0 for 8 replication determination. The detection limits for the Cd, Cu, Ni were found to be 0.5, 3.4 and 25 µg L^?1, respectively. The method was successfully applied for the determination of cadmium, copper and nickel in tap water, well water, sea water, rice and macaroni samples with spike recoveries ranging 93–105 %.     

Supersymmetric Solutions of PT-/non-PT-symmetric and Non-Hermitian Central Potentials via Hamiltonian Hierarchy Method

The supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian deformed Morse and Pöschl-Teller potentials are obtained by solving the Schrödinger equation. The Hamiltonian hierarchy method is used to get the real energy eigenvalues and corresponding eigenfunctions.     

On the spectral character of Toeplitz operators on planar regions

Self-adjoint Toeplitz operators on multiply connected planar regions are investigated using theta functions on the double. An explicit resolvent form for self-adjoint Toeplitz operators on a Hardy space associated with any representing measure on a -holed planar region is given via reproducing kernels in terms of theta functions on . This resolvent formula is a generalization of an analogous formula obtained by K. F. Clancey (1991) for the case of harmonic measure. Applications of this resolvent form to the spectral type of the self-adjoint Toeplitz operators are described.

     

Enhanced synchronous spectrofluorimetric determination of aflatoxin B1 in pistachio samples using multivariate analysis

The determination of aflatoxin B₁ (AFB1) in pistachio has been accomplished by normal and synchronous fluorimetry in combination with some multivariate calibration methods and derivative techniques. Extending the two-dimensional synchronous fluorescence scan to a three-dimensional total synchronous fluorescence scan was used to obtain the optimized Δλ for AFB1 in pistachio sample. The methods are based on the enhanced fluorescence of AFB1 by β-cyclodextrine in 10% (v/v) methanol-water solution. Twenty-six pistachio samples containing AFB1 in the range 0-15 ppb were used as calibration set. Eighteen combinational methods were tested to make best model for prediction of AFB1 and finally best results obtained using a method based on synchronous fluorimetry in combination with multiple linear regressions (MLR). For concentrations ranging from 0 to 15 ppb of AFB1 in 22 pistachio samples as prediction set, the values of root mean square difference (RMSD) and relative error of prediction (REP) using MLR were 0.328 and 4.453%, respectively were observed. Two naturally contaminated pistachio samples were analyzed by synchronous fluorimetry using MLR and compared with HPLC results.