On Semilattice Decomposition of an Abel–Grassmann’s Groupoid

In this paper, we have decomposed an AG-groupoid. Let S be an AG-groupoid with left identity and a relation γ be defined on S as: aγb if and only if there exist positive integers m and n such that bm ∈ ( Sa)S and a n ∈ ( Sb)S for all a and b in S. We have proved that S/γ is a maximal separative semilattice homomorphic image of S. Every AG-groupoid S is uniquely expressible as a semilattice Y of archimedean AG-groupoids Sα (α∈ Y ). The semilattice Y is isomorphic to S/γ and the S α (α∈ Y ) are the equivalence classes of S mod γ.     

Banana peel: A green and economical sorbent for the selective removal of Cr(VI) from industrial wastewater

This study describes the use of banana peel, a commonly produced fruit waste, for the removal of Cr(VI) from industrial wastewater. The parameters pH, contact time, initial metal ion concentration, and temperature were investigated and the conditions resulting in rapid and efficient adsorption (95% within 10 min) were determined. The binding of metal ions was found to be pH dependent with the optimal sorption occurring at pH 2. The retained species were eluted with 5 mL of 2 M H₂SO₄. To elucidate the mechanism of the process, total amounts of chromium and Cr(VI) were analyzed using flame atomic absorption and ultraviolet–visible (UV–vis) spectroscopic techniques, respectively. The Langmuir and Dubinin–Radushkevich (D–R) isotherms were used to describe the partitioning behavior for the system at different temperatures. Kinetics and thermodynamics of Cr(VI) removal by banana peel were also studied. The influence of diverse ions on the sorption behavior revealed that only Fe(II) ions (of those tested) suppressed the sorption of Cr(VI) ions to some extent. The method was applied for the removal of Cr(VI) from industrial wastewater.     

Classification of Kantowski-Sachs and Bianchi Type III Space-Times According to Their Killing Vector Fields in Teleparallel Theory of Gravitation

In this paper we classify Kantowski-Sachs and Bianchi type Ⅲ space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the telepaxallel Killing vector fields are 4 or 6, which are the same in numbers as in general relativity. In case of 4 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 6 Killing vector fields the metric functions become constants and the Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case.     

Structural and magnetic properties of nano-crystalline FeCoNiN thin films

Iron cobalt nickel nitride (FeCoNiN) thin films are prepared by sol-gel spin coating route. The structural, magnetic and surface properties of the thin films are evaluated. The crystalline nature of thin films was enhanced upon annealing, leading to increased crystallite size. The X-ray diffraction shows mixed phases with crystallite size in the range of 20–26.93 nm. Thin films show ferromagnetism at room temperature. Coercivity and saturation magnetization are in the range of 642–716 Oe and 2.5–7.5 emu/cm³ respectively. Both coercivity and saturation magnetization increased with annealing of thin films. Magnetic properties are related to the crystallinity of thin films. The increase in crystallite size results into an increase of magnetic properties. Rectangular shaped particles are seen on the surface of thin films. The same type of grains can be seen on the surface of thin films which confirmed the formation of FeCoNiN as predicted by XRD. These novel thin films might be used in memory devices and optoelectronic applications.     

Preparation of stable dispersion of graphene using copolymers: dispersity and aromaticity analysis

In this study, effectiveness of non-ionic block copolymers such as Lugalvan BNO12 and Triton X series (Triton X100 & Triton X405) has been reported for graphene dispersion in aqueous solutions. Stability of the aqueous graphene dispersions is investigated using UV–visible spectroscopy, Rheological, and Conductivity studies. Adsorption isotherms are constructed to determine the amount of polymers adsorbed on the surface of graphene by the spectroscopic analysis. Lugalvan BNO12 has been found to be adsorbed in higher amounts on the graphene surface compared to the Triton X series polymers. Thermogravimetric analysis (TGA) and Fourier Transform Infrared (FTIR) Spectroscopy investigations indicated grafting of polymers chains to the graphene surfaces. The dispersions prepared with optimum concentrations (as determined from adsorption isotherms) of polymers have shown lower viscosity and conductivity values. Lugalvan BNO12 has been found to be a better stabilizer for graphene than the Triton X series dispersants because the former contains two aromatic rings in its structure that acts as an anchoring group and helps in the stabilization of graphene dispersion in comparison to the single aromatic group in the Triton X series. The experimental results reported have shown that the aromaticity of polymeric dispersants plays significant role in the aqueous graphene dispersions. The non-ionic block copolymers that assisted dispersed graphene are potential candidates for the fabrication of various devices such as sensors, batteries, and supercapacitors applications.     

Optical soliton perturbation with full nonlinearity by extended trial function method

The extended trial function scheme is applied to retrieve soliton solutions to the perturbed nonlinear Schrödinger’s equation with ten forms of fiber nonlinearity. Bright, dark and singular soliton solutions are retrieved that appear with their respective existence criteria. Some additional forms of nonlinear waves naturally emerge as a byproduct of the integration scheme.     

Electron-induced scattering dynamics of Boron,Aluminium and Gallium trihalides in the intermediate energy domain

This article is focused on the calculation of electron-induced ionisation and total scattering cross sections by Boron, Aluminium and Gallium trihalide molecules in the intermediate energy domain. The computational formalism, spherical complex optical potential has been employed for the study of these two scattering cross sections. The ionisation cross section has been derived from the inelastic cross section using a semi-empirical method called complex scattering potential-ionisation contribution (CSP-ic) method. We have also calculated the ionisation cross section using the BEB theory with Hartree–Fock and density functional theory (DFT- ωB97XD) orbitals so that a comparison can be made with the cross sections predicted by CSP-ic method. For this theoretical study, we have also calculated polarisability and bond length of some targets which were not found in literature using DFT/B3LYP in Gaussian 09 software.     

Optimizing Image Reconstruction in SENSE Using GPU

Parallel magnetic resonance imaging (MRI) (pMRI) uses multiple receiver coils to reduce the MRI scan time. To accelerate the data acquisition process in MRI, less amount of data is acquired from the scanner which leads to artifacts in the reconstructed images. SENSitivity Encoding (SENSE) is a reconstruction algorithm in pMRI to remove aliasing artifacts from the undersampled multi coil data and recovers fully sampled images. The main limitation of SENSE is computing inverse of the encoding matrix. This work proposes the inversion of encoding matrix using Jacobi singular value decomposition (SVD) algorithm for image reconstruction on GPUs to accelerate the reconstruction process. The performance of Jacobi SVD is compared with Gauss–Jordan algorithm. The simulations are performed on two datasets (brain and cardiac) with acceleration factors 2, 4, 6 and 8. The results show that the graphics processing unit (GPU) provides a speed up to 21.6 times as compared to CPU reconstruction. Jacobi SVD algorithm performs better in terms of acceleration in reconstructions on GPUs as compared to Gauss–Jordan method. The proposed algorithm is suitable for any number of coils and acceleration factors for SENSE reconstruction on real time processing systems.     

First-principles calculations of structural,electronic, and thermodynamic properties of ZnO_(1-x)S_x alloys

In this study the pseudo-potential method is used to investigate the structural, electronic, and thermodynamic proper- ties of ZnOl_xSx semiconductor materials. The results show that the electronic properties are found to be improved when calculated by using LDA ~ U functional as compared with local density approximation （LDA）. At various concentrations the ground-state properties are determined for bulk materials ZnO, ZnS, and their tertiary alloys in cubic zinc-blende phase. From the results, a minor difference is observed between the lattice parameters from Vegard＇s law and other calculated results, which may be due to the large mismatch between lattice parameters of binary compounds ZnO and ZnS. A small deviation in the bulk modulus from linear concentration dependence is also observed for each of these alloys. The ther- modynamic properties, including the phonon contribution to Helmholtz free energy △F, phonon contribution to internal energy △E, and specific iheat at constant-volume Cv, are calculated within quasi-harmonic approximation based on the calculated phonon dispersion relations.     

Robust strategic bidding in auction-based markets

In this paper, we propose an alternative methodology for devising revenue-maximizing strategic bids under uncertainty in the competitors’ bidding strategy. We focus on markets endowed with a sealed-bid uniform-price auction with multiple divisible products. On recognizing that the bids of competitors may deviate from equilibrium and are of difficult statistical characterization, we proposed a two-stage robust optimization model with equilibrium constraints aiming to devise risk-averse strategic bids. The proposed model is a trilevel optimization problem that can be recast as a particular instance of a bilevel program with equilibrium constraints. Reformulation procedures are proposed to find a single-level equivalent formulation suitable for column-and-constraint generation (CCG) algorithm. Results show that even for the case in which an imprecision of 1% is observed on the rivals’ bids in the equilibrium point, the robust solution provides a significant risk reduction (of 79.9%) in out-of-sample tests. They also indicate that the best strategy against high levels of uncertainty on competitors’ bid approaches to a price-taker offer, i.e., bid maximum capacity at marginal cost.