Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems

In this paper, Homotopy Analysis Method (HAM) is applied to numerically approximate the eigenvalues of the fractional Sturm-Liouville problems. The eigenvalues are not unique. These multiple solutions, i.e., eigenvalues, can be calculated by starting the HAM algorithm with one and the same initial guess and linear operator L\mathcal{L}. It can be seen in this paper that the auxiliary parameter (^h/_2p),\hbar, which controls the convergence of the HAM approximate series solutions, has another important application. This important application is predicting and calculating multiple solutions.     

A meshless method based on the dual reciprocity method for one‐dimensional stochastic partial differential equations

This article describes a new meshless method based on the dual reciprocity method (DRM) for the numerical solution of one‐dimensional stochastic heat and advection–diffusion equations. First, the time derivative is approximated by the time–stepping method to transforming the original stochastic partial differential equations (SPDEs) into elliptic SPDEs. The resulting elliptic SPDEs have been approximated with the new method, which is a combination of radial basis functions (RBFs) method and the DRM method. We have used inverse multiquadrics (IMQ) and generalized IMQ (GIMQ) RBFs, to approximate functions in the presented method. The noise term has been approximated at the source points, at each time step. The developed formulation is verified in two test problems with investigating the convergence and accuracy of numerical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 292–306, 2016     

Compared EC-AFM Analysis of Laser-Induced Graphene and Graphite Electrodes in Sulfuric Acid Electrolyte

Flexible and economic sensor devices are the focus of increasing interest for their potential and wide applications in medicine, food analysis, pollution, water quality, etc. In these areas, the possibility of using stable, reproducible, and pocket devices can simplify the acquisition of data. Among recent prototypes, sensors based on laser-induced graphene (LIGE) on Kapton represent a feasible choice. In particular, LIGE devices are also exploited as electrodes for sensing in liquids. Despite a characterization with electrochemical (EC) methods in the literature, a closer comparison with traditional graphite electrodes is still missing. In this study, we combine atomic force microscopy with an EC cell (EC-AFM) to study, in situ, electrode oxidation reactions when LIGE or other graphite samples are used as anodes inside an acid electrolyte. This investigation shows the quality and performance of the LIGE electrode with respect to other samples. Finally, an ex situ Raman spectroscopy analysis allows a detailed chemical analysis of the employed electrodes.     

Finding strong defining hyperplanes of PPS using multiplier form

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In this paper, we deal with the problem of finding the strong defining hyperplanes of the PPS. These hyperplanes are equations that form efficient surfaces. It is well known that the optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and, therefore, may have alternate optima for the multiplier form. Every optimal solution of the multiplier form yields a hyperplane which is supporting at the PPS. We will show that the hyperplane which corresponds to an extreme optimal solution of the multiplier form (in evaluating an efficient DMU), and whose components corresponding to inputs and outputs are non zero is a strong defining hyperplane of the PPS. This will be discussed in details in this paper. These hyperplanes are useful in sensitivity and stability analysis, the status of returns to scale of a DMU, incorporating performance into the efficient frontier analysis, and so on. Using numerical examples, we will demonstrate how to use the results.     

Solid phase extraction�Cinductively coupled plasma spectrometry for adsorption of Co(II) and Ni(II) from radioactive wastewaters by natural and modified zeolites

Natural and modified clinoptilolite as low-cost adsorbents have been used for adsorption of Co(II) and Ni(II) from nuclear wastewaters both in batch and continuous experiments. Zeolite X was also synthesized and its ability towards the selected cations was examined. Kinetic and thermodynamic behaviors for the process were investigated and adsorption equilibrium was interpreted in term of Langmuir and Freundlich equations. The effect of various parameters including the initial concentration, temperature, ionic strength and pH of solution were examined to achieve the optimized conditions. The clinoptilolite was shown good sorption potential for Co(II) and Ni(II) ions at pH values 4?C6. Based on desorption studies, nearly 74 and 85% of adsorbed Co(II) and Ni(II) were removed from clinoptilolite by HCl. The Na⁺ and NH₄ ⁺ forms of clinoptilolite were the best modified forms for the removal of investigated cations. It is concluded that the selectivity of clinoptilolite is higher for Co(II) than Ni(II). The synthesized zeolite showed more ability to remove cobalt and nickel ions from aqueous solution than the natural clinoptilolite. The microwave irradiation was found to be more rapid and effective for ion exchange compared to conventional ion exchange process.     

Experimental and theoretical characterization of N,N′-bis(2,4-dihydroxybenzylidene)-1,2-diaminobenzene schiff base and its Cu(II) complex

A new Schiff base ligand N,N′-bis(2,4-dihydroxybenzylidene)-1,2-diaminobenzene [=H₂L] and its Cu(II) complex [Cu(L)] are synthesized and characterized by IR, UV-Vis, NMR, mass spectrometry and elemental analysis. Also, the computational prediction of optimized geometries, IR spectra and NMR chemical shifts is performed using the density functional theory (DFT) method. The DFT optimized geometry of the ligand is not planar, so the three benzene rings are located in separate planes. The phenolic protons are engaged in the intramolecular hydrogen-bonding interactions. In the optimized geometry of the square comlex, dianionic L^2? acts as a tetradentate ligand, which occupies four coordination positions in the N, N, O^?, O^? manner. The consistency between the calculated and experimental results confirms the validity of the optimized structures for the H₂L ligand and its Cu complex.     

Optimal uniform error estimates for moving least‐squares collocation with application to option pricing under jump‐diffusion processes

In this study, we derive optimal uniform error bounds for moving least‐squares (MLS) mesh‐free point collocation (also called finite point method) when applied to solve second‐order elliptic partial integro‐differential equations (PIDEs). In the special case of elliptic partial differential equations (PDEs), we show that our estimate improves the results of Cheng and Cheng (Appl. Numer. Math. 58 (2008), no. 6, 884–898) both in terms of the used error norm (here the uniform norm and there the discrete vector norm) and the obtained order of convergence. We then present optimal convergence rate estimates for second‐order elliptic PIDEs. We proceed by some numerical experiments dealing with elliptic PDEs that confirm the obtained theoretical results. The article concludes with numerical approximation of the linear parabolic PIDE arising from European option pricing problem under Merton's and Kou's jump‐diffusion models. The presented computational results (including the computation of option Greeks) and comparisons with other competing approaches suggest that the MLS collocation scheme is an efficient and reliable numerical method to solve elliptic and parabolic PIDEs arising from applied areas such as financial engineering.     

Spin-valley Hall conductivity of doped ferromagnetic silicene under strain

The spin-valley Hall conductivity(SHC-VHC) of two-dimensional material ferromagnetic graphene's silicon analog,silicene, is investigated in the presence of strain within the Kubo formalism in the context of the Kane–Mele Hamiltonian.The Dirac cone approximation has been used to investigate the dynamics of carriers under the strain along the armchair(AC) direction. In particular, we study the effect of external static electric field on these conductivities under the strain.In the presence of the strain, the carriers have a larger effective mass and the transport decreases. Our findings show that SHC changes with respect to the direction of the applied electric field symmetrically while VHC increases independently.Furthermore, the reflection symmetry of the structure has been broken with the electric field and a phase transition occurs to topological insulator for strained ferromagnetic silicene. A critical strain is found in the presence of the electric field around 45%. SHC(VHC) decreases(increases) for strains smaller than this value symmetrically while it increases(decreases) for strains larger than one.     

Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.