Liquid chromatographic determination of trace levels of nitrophenols in water samples after dispersive magnetic solid phase extraction

An efficient and fast dispersive magnetic solid phase extraction method was developed using MIL‐101(Cr)/poly (mercaptobenzothiazole)@magnetite nanoparticles for the preconcentration and determination of nitrophenols in river and rain water samples. High‐performance liquid chromatography‐Ultraviolet instrument was applied for the analysis of target nitrophenols. The effect of several variables on the extraction performance was explored via design of experiment approach. Limits of detection and linear dynamic ranges were attained in the range of 0.05–0.10 µg/L and 0.2–250 µg/L, respectively. The enrichment factors were in the range of 317–363. The precision (n = 3) of dispersive magnetic solid phase extraction method was in the range of 5.3–6.8%. Eventually, the method was utilized for the analysis of target nitrophenols in river and rain water samples.     

Nano-sized local magnetic field induced by circular motion of ions and molecules in a nanotorus under gigahertz rotating electric fields

Recently, we reported molecular dynamics simulations of stable cyclotron motions of ions and water molecules in a carbon nanotorus, induced by different rotating electric fields (EFs). This study is devoted to the calculation and characterisation of the magnetic field (MF) induced by these cyclotron motions. Results show that carbon nanotorus containing ions or water molecules acts as an EF-to-MF transducer. Components of the instantaneous induced MF show large-scale oscillations superimposed by strong fluctuations arising respectively from overall circular motion and random collisions of moving species. Analysis of the space-dependencies of the induced MF components shows that the induced MF is maximum at the centre of the nanotorus. The MF induced by cyclotron motion of ions follows the orders B(Ca²⁺)?>?B(Na⁺)?≈?B(K⁺) at E?=?1.0?V/nm and B(E?=?1.0?V/nm)?>?B(E?=?0.5?V/nm)?>?B(E?=?0.1?V/nm). The time-averaged induced MF of the cyclotron motion of 81 water molecules is almost 10² times stronger than that of ions. The induced MF strength is decreased with increasing distance from nanotorus and decays effectively at about 17.3–18.1 and 15.9–18.2?nm along the z-axis of the nanotorus for ions and water molecules, respectively. The magnitude of the MF induced by cyclotron motions of water molecules and ions, respectively, decreases and increases in the nanotorus with freed carbon atoms.     

Synthesis,Hirshfeld surface analysis,luminescence and thermal properties of three first-row transition metal complexes containing 4′-hydroxy-2,2′:6′,2″-terpyridine: Application for preparation of nano metal oxides

A series of new mono- and bis-terpyridine complexes [Mn(tpyOH)Cl₂] ( 1 ), [Ni(tpyOH)₂](PF₆)₂ ( 2 ) and [Zn(tpyO)(η¹-OCOCH₃)(H₂O)]⋅3H₂O ( 4 ) containing 4′-hydroxy-2,2′:6′,2″-terpyridine (tpyOH) were synthesized and structurally characterized using elemental analysis, infrared spectroscopy and single-crystal X-ray diffraction. The reaction of MnCl₂ with tpyOH in a mixture of methanol and CH₂Cl₂ resulted in the formation of 1 . The X-ray crystal structure of 1 reveals that Mn(II) is penta-coordinated by three nitrogen atoms from tpyOH and two Cl⁻ in a slightly distorted trigonal bipyramidal geometry. Complex 2 was also prepared by the reaction of nickel(II) chloride with tpyOH in a methanolic medium in the presence of NH₄PF₆. Notably, the complex [Ni(tpyOH)(tpyO)]PF₆ ( 3 ), obtained during the crystallization of 2 from dichloromethane, was characterized using X-ray crystallography which shows that six nitrogen atoms from terpyridine ligands occupy the coordination sites around the Ni(II) centre in a distorted octahedral geometry with four longer bonds and two shorter Ni N bonds. The reaction of zinc(II) acetate with tpyOH in a mixture of methanol and CH₂Cl₂ led to the formation of 4 . The crystal structure of 4 reveals the formation of penta-coordinated Zn(II) complex containing three nitrogen atoms from tpyO, a monodentate acetate ligand and one coordinated water molecule. Hirshfeld surface analyses and two-dimensional fingerprint plots show that the main interactions are O…H/H…O contacts in 1 , 3 and 4 . The thermal decomposition reactions of 1 , 2 and 4 were studied using thermogravimetric analysis in detail due to their different structures. The solution luminescence features of 1 , 2 and 4 include high-energy intense π → π* intraligand and low-energy metal-to-ligand charge transfer transitions at room temperature. The calcination of the coordination complexes led to the formation of corresponding nano metal oxides. The products were structurally characterized using infrared spectroscopy, scanning electron microscopy and energy-dispersive X-ray spectroscopy. The average particle size using Scherrer's equation was calculated to be below 50 nm.     

Euler’s elastica-based algorithm for Parallel MRI reconstruction using SENSitivity Encoding

Optimization Letters - SENSitivity Encoding (SENSE) is an effective mathematical formulation for reconstructing under-sampled MRI data obtained in Parallel Magnetic Resonance Imaging (Parallel...     

On the global convergence rate of the gradient descent method for functions with Hölder continuous gradients

The gradient descent method minimizes an unconstrained nonlinear optimization problem with \({\mathcal {O}}(1/\sqrt{K})\), where K is the number of iterations performed by the gradient method. Traditionally, this analysis is obtained for smooth objective functions having Lipschitz continuous gradients. This paper aims to consider a more general class of nonlinear programming problems in which functions have Hölder continuous gradients. More precisely, for any function f in this class, denoted by \({{\mathcal {C}}}^{1,\nu }_L\), there is a \(\nu \in (0,1]\) and \(L>0\) such that for all \(\mathbf{x,y}\in {{\mathbb {R}}}^n\) the relation \(\Vert \nabla f(\mathbf{x})-\nabla f(\mathbf{y})\Vert \le L \Vert \mathbf{x}-\mathbf{y}\Vert ^{\nu }\) holds. We prove that the gradient descent method converges globally to a stationary point and exhibits a convergence rate of \({\mathcal {O}}(1/K^{\frac{\nu }{\nu +1}})\) when the step-size is chosen properly, i.e., less than \([\frac{\nu +1}{L}]^{\frac{1}{\nu }}\Vert \nabla f(\mathbf{x}_k)\Vert ^{\frac{1}{\nu }-1}\). Moreover, the algorithm employs \({\mathcal {O}}(1/\epsilon ^{\frac{1}{\nu }+1})\) number of calls to an oracle to find \({\bar{\mathbf{x}}}\) such that \(\Vert \nabla f({{\bar{\mathbf{x}}}})\Vert <\epsilon \).     

On the Stability of a k-Cubic Functional Equation in Intuitionistic Fuzzy n-Normed Spaces

In this paper, we investigate some stability results concerning the k-cubic functional equation f(kx + y) + f(kx?y) = kf(x + y) + kf(x?y) + 2k(k²?1)f(x) in the intuitionistic fuzzy n-normed spaces.     

Design and development of a fiber-optic immunosensor utilizing near-infrared fluorophores

The design and application of a fluorescent fiber-optic immunosensor (FFOI) are reported. The FFOI is utilized for the detection of antibody/antigen binding within the near-infrared (NIR) spectral region. The technique is developed through the combined use of fiber-optic, semiconductor laser-excitation, fluorescence detection, NIR dye, and immunochemical techniques. The antibody is immobilized on the FFOI and utilized as a recognition component for trace amounts of specific antigen. The FFOI is constructed to utilize an antibody sandwich technique. The assay involves the immobilization of the capture antibody on the sensing tip of the FFOI followed by the exposure of the immobilized sensing tip to the antigen. The antigen-coated FFOI is then introduced to a second antibody previously labeled with the NIR dye. Typical measurements are performed in about 15 min. A semiconductor laser provides the excitation (780 nm) of the immune complex. The resulting emission is detected by a silicon photodiode detector (820 nm). The intensity of the resulting fluorescence is directly proportional to the concentration of the antigen. The sensitivity of the analysis reaches 10 ng/ml and the response time is 10–15 min.     

Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

Let ${(R, \mathfrak{m})}$ be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of ${R, H _{\mathfrak{m}} ^{d} (R)}$ , has finite G _C -injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay.     

Atomic force microscopy investigation of surface roughness generated between SiO2 micro-pits in CHF3/Ar plasma

The present paper investigates the surface roughness generated by reactive ion etching (RIE) on the location between silicon dioxide (SiO₂) micro-pits structures. The micro-pit pattern on polymethyl methacrylate (PMMA) mask was created by an electron beam lithography tool. By using PMMA as a polymer resist mask layer for pattern transfer in RIE process, the carbon (C) content in etching process is increased, which leads to decrease of F/C ratio and causes domination of polymerization reactions. This leads to high surface roughness via self-organized nanostructure features generated on SiO₂ surface which was analyzed using atomic force microscopy (AFM) technique. The etching chemistry of CHF₃ plasma on PMMA masking layer and SiO₂ is analyzed to explain the polymerization. The surface root-mean-square (RMS) roughness below 1 nm was achieved by decreasing the RF power to 150 W and process pressure lower than 10 mTorr.     

Bregman operator splitting with variable stepsize for total variation image reconstruction

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form $\min\{\phi(Bu) +1/2\|Au-f\|_{2}^{2}\}$ , where ? may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a line search to achieve better efficiency. These schemes are applicable to total variation (TV)-based image reconstruction. The stepsize rule starts with a Barzilai-Borwein (BB) step, and increases the nominal step until a termination condition is satisfied. The stepsize rule is related to the scheme used in SpaRSA (Sparse Reconstruction by Separable Approximation). Global convergence of the proposed BOSVS algorithm to a solution of the optimization problem is established. BOSVS is compared with other operator splitting schemes using partially parallel magnetic resonance image reconstruction problems. The experimental results indicate that the proposed BOSVS algorithm is more efficient than the BOS algorithm and another split Bregman Barzilai-Borwein algorithm known as SBB.