Weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) for decomposition of multiway arrays: applications on certain chemical system data sets

This work focuses on the utilization of a very recently developed decomposition method, weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) which can be equivalently used on continuous functions, and, multiway arrays after appropriate unfoldings. This recursive method has been constructed on the Bivariate EMPR and the remainder term of each step therein has been expanded into EMPR from step to step until no remainder term appears in one of the consecutive steps. The resulting expansion can also be expressed in a three factor product representation whose core factor is a tridiagonal matrix. The basic difference and novelty here is the non-constant weight utilization and the applications on certain chemical system data sets to show the efficiency of the WTMEMPR truncation approximants.     

Synthesis of chalcone‐containing methacrylate‐based hydrogen bonded side chain liquid crystalline polymer and its dielectric properties

In this work, a new methacrylate‐based hydrogen bonded side chain liquid crystalline polymer having chalcone moieties (HBCP) was prepared from poly(4‐(3‐(pyridin‐4‐yl)acryloyl) phenyl methacrylate) and 11‐(4‐cyanobiphenyl‐4(‐oxy) undekan‐1‐ol (LC11)) by molecular self‐assembly processes via hydrogen bond formation between nitrogen of the HBCP and hydroxyl group of the LC11. The formation of H bond was confirmed by using Fourier transform infrared (FTIR) spectroscopy. The phase transition temperatures and liquid crystalline phases of the HBCP were examined by DSC and POM measurements. The dielectric properties of HBCP have been determined by impedance analyzer within the frequency interval of 100 Hz–15 MHz. According to Cole–Cole plot, the equivalent circuit of the LC system has been found as a capacitor in parallel with a resistor. The resonance frequency, f_r, of the R–C circuit has also been calculated as 1.59 MHz by phase angle versus frequency curve. The dielectric relaxation type of HBCP has been determined as nearly‐Debye type because the absorption coefficient, α, equals to 0.01655. From the conductivity point of view, HBCP displays dc conductivity at the low and high frequency regions that correspond to 100 Hz–12 kHz and 3.3 MHz–15 MHz, respectively. On the other hand, it has been revealed that the ac conductivity of the LC system investigated obeys Super Linear Power Law (SLPL) at the intermediate frequency domain. Copyright © 2015 John Wiley & Sons, Ltd.     

A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number

A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier–Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes a frequent requirement in the simulation of turbulent flows in complex geometries. The two‐step method is considered here; to obtain a regularization that is second order accurate in space and time, the method computes a low‐order accurate, stable, and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is stable and the accuracy in both space and time is improved after the correction step. We also perform a qualitative test to demonstrate that the method is capable of capturing qualitative features of a turbulent flow, even on a very coarse mesh. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 814–839, 2017     

Decay rates for memory‐type plate system with delay and source term

In this paper, we consider a plate equation with infinite memory in the presence of delay and source term. Under suitable conditions on the delay and source term, we establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity. Our result allows a wider class of relaxation functions and improves earlier results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

On interpolation of noncommutative symmetric Hardy spaces

We proved the noncommutative analogue of Calderón’s result for fully symmetric spaces \(E_1\) and \(E_2\) on (0, 1) and for a finite von Neumann algebra \({{\mathcal {M}}}\). We also proved the noncommutative symmetric Hardy space’s analogue of Calderón’s result for fully symmetric spaces and for finite subdiagonal subalgebras.     

Experimental and theoretical studies on molecular structures and vibrational modes of novel compounds containing silver

The two novel silver containing complexes of N-(pyridin-2-yl)pyridin-2-amine (NDPA) molecule has been synthesized and characterized by elemental analysis, FT-Raman and FT-IR (at far and mid regions) spectroscopies. The optimized geometries of the compounds were obtained by using DFT/B3LYP method with LANL2DZ basis set for the (C₁₀H₉N₃) · AgNO₃ and B3LYP method with DGDZVP basis set for the (C₁₀H₉N₃) · AgClO₄. The vibrational frequencies and their IR and Raman intensities were determined by theoretical methods. In addition, the HOMO-LUMO energies, thermochemical properties and atomic charges for the complexes were obtained in same level of theory. The experimental and theoretical results show that the silver atoms are coordinated to ligands in bidentate fashion. In addition, in the structures of complexes there are intra-molecular interactions. The oxygen atoms of nitrate and perchlorate are bonded to ligand via hydrogen bonds.     

A magnetic MoS2-Fe3O4 nanocomposite as an effective adsorbent for dispersive solid-phase microextraction of lead(II) and copper(II) prior to their determination by FAAS

Microchimica Acta - The authors describe the preparation of a nanocomposite (mag-MoS2-Fe3O4) that was prepared from molybdenum disulfide (MoS2) and magnetic Fe3O4 nanoparticles by a hydrothermal...     

Hille’s non-oscillation theorem and the decay of solutions to a class of semi-linear PDE’s

With a change of perspective in Hille’s paper on oscillation [Trans. Amer. Math. Soc. 64 (1948), 234–252], we provide optimal integral conditions for an application of the method of sub-solutions and super-solutions to investigating the existence of solutions for the semi-linear elliptic equation in the euclidean space , n ≥ 3, that decay to zero as . Received: 26 October 2006