Half twists and the cohomology of hypersurfaces

A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight , its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a Hodge substructure in the cohomology. We determine when the half twist exists and relate it to the geometry and moduli of the hypersurfaces. We use our results to prove the existence of a Kuga-Satake correspondence for certain cubic 4-folds. Received: 25 August 2000; in final form: 8 January 2001 / Published online: 18 January 2002     

A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.     

Fourth power diophantine equations in Gaussian integers

In this paper, we examine a class of fourth power diophantine equations of the form \(x^4+kx^2y^2+y^4=z^2\) and \(ax^4+by^4=cz^2\), in the Gaussian integers, where a and b are prime integers.     

Some remarks on the Hodge conjecture for abelian varieties

We show how the classical Hodge conjecture for the middle cohomology of an abelian variety is equivalent to the general Hodge conjecture for the middle cohomology of a smooth ample divisor in the abelian variety. This is best suited to abelian varieties with actions of imaginary quadratic fields.     

The influence of hydrophobic amino acid side groups on the acidity of the aromatic imidazole ring of histidine: A theoretical study

In this study we have calculated the acidity constant (pKa) of imidazole ring in Histidine‐Hydrophobic amino acid dipeptides using the quantum chemistry and continuum solvation methods. Density functional theory calculations with the large basis sets are used to determine the Gibbs free energy of deprotonate in the gas and liquid phases. Based on our results ΔG_S values are located between ?69.38 and ?18.82 kcal mol^?1 which are related to His⁺–Gly and His forms, respectively. pKa of the dipeptides in the aqueous phase was obtained from the calculated gas‐phase and solvation free energies through a thermodynamic cycle and the solvation model chemistry of Martin Karplus et al. Solvation effects are treated using a self‐consistent reaction field formalism involving polarized continuum models. According to our calculations pKa values are between 5.50 and 8.19 that are belong to His⁺–ILe and His⁺–Ala forms, respectively. Natural bond orbital analysis of dipeptides reveals that the electron delocalization in imidazole ring is the most effective factor in determination of acidity order for these compounds. Structural analysis confirmed that the orientation of carbonyl group with respect to imidazole ring is an effective factor in imidazole ring stability. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Conjugate natural convection of nanofluids inside an enclosure filled by three layers of solid,porous medium and free nanofluid using Buongiorno’s and local thermal non-equilibrium models

Journal of Thermal Analysis and Calorimetry - The natural convective heat transfer of nanofluids was addressed inside a square enclosure filled by three different layers: solid, porous medium and...     

A Promising Material for Selective Sensing Biomarker Gas Molecules

Russian Journal of Physical Chemistry A - The interaction of many biomarker gas molecules on pure, AlB-doped and GaB-doped boron nitride nanotube was studied by the density functional theory method...     

Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by designing new correlations and optimal artificial neural networks

In this paper, at the first, new correlations were proposed to predict the rheological behavior of MWCNTs–SiO₂/EG–water non-Newtonian hybrid nanofluid using different sets of experimental data for the viscosity, consistency and power law indices. Then, based on minimum prediction errors, two optimal artificial neural network models (ANNs) were considered to forecast the rheological behavior of the non-Newtonian hybrid nanofluid. One hundred and ninety-eight experimental data were employed for predicting viscosity (Model I). Two sets of forty-two experimental data also were considered to predict the consistency and power law indices (Model II). The data sets were divided to training and test sets which contained respectively 80 and 20% of data points. Comparisons between the correlations and ANN models showed that ANN models were much more accurate than proposed correlations. Moreover, it was found that the neural network is a powerful instrument in establishing the relationship between a large numbers of experimental data. Thus, this paper confirmed that the neural network is a reliable method for predicting the rheological behavior of non-Newtonian nanofluids in different models.

     

N‐Inversion in N‐phenyloxaziridine: substituent and solvent effects via density functional theory

In this work, using density functional theory, the kinetic effects of the substitution of a t‐butyl group and\or the incorporation of an oxygen atom, and both, at the aziridine ring moiety were investigated for N‐inversion in N‐phenylaziridine. Then, for N‐inversion in 3‐t‐butyl‐N‐phenyloxaziridine, the kinetic Hammett substituent effects were studied using the different para‐substituted groups on the N‐phenyl ring moiety. The natural bond orbital (NBO) study was the last case in this work. The calculations were performed in the gas phase and solution (in carbon tetrachloride and dichloromethane). The incorporation of an oxygen atom in the aziridine ring strongly weakens the N‐inversion process. In addition, while both t‐butyl substituent and solvent slightly reinforce the N‐inversion of N‐phenyloxaziridine, in N‐phenylaziridine, they decrease the N‐inversion rate to some extent. In both phases, more pronounced in solution and especially in dichloromethane, and in agreement with the NBO results, the electron‐withdrawing groups on para position of the N‐phenyl ring strongly increase the rate of N‐inversion of 3‐t‐butyl‐N‐phenyloxaziridine molecule.     

Electrocatalytic reduction of NAD+ at glassy carbon electrode modified with single-walled carbon nanotubes and Ru(III) complexes

A simple procedure was developed to prepare a glassy carbon electrode modified with carbon nanotubes and Ruthenium (III) complexes. First, 25 μl of dimethyl sulfoxide–carbon nanotubes solutions (0.4 mg/ml) was cast on the surface of the glassy carbon electrode and dried in air to form a carbon nanotube film at the electrode surface. Then, the glassy carbon/carbon nanotube-modified electrode was immersed into a Ruthenium (III) complex solution (direct deposition) for a short period of time (10–20 s for multiwalled carbon nanotubes and 20–40 s for single-walled carbon nanotubes). The cyclic voltammograms of the modified electrode in aqueous solution shows a pair of well-defined, stable, and nearly reversible redox couple, Ru(III)/Ru(II), with surface-confined characteristics. The attractive mechanical and electrical characteristics of carbon nanostructures and unique properties and reactivity of Ru complexes are combined. The transfer coefficient (α), heterogeneous electron transfer rate constants (k _s), and surface concentrations (Γ) for the glassy carbon/single-walled carbon nanotubes/Ru(III) complex-, glassy carbon/multiwalled carbon nanotubes/Ru(III) complex-, and glassy carbon/Ru(III) complex-modified electrodes were calculated using the cyclic voltammetry technique. The modified electrodes showed excellent catalytic activity, fast response time, and high sensitivity toward the reduction of nicotinamide adenine dinucleotide in phosphate buffer solutions at a pH range of 4–8. The catalytic cathodic current depends on the nicotinamide adenine dinucleotide concentration. In the presence of alcohol dehydrogenase, the modified electrode exhibited a response to addition of acetaldehyde. Therefore, the main product of nicotinamide adenine dinucleotide electroreduction at the Ru(III) complex/carbon nanotube-modified electrode was the enzymatically active NADH. The purposed sensor can be used for acetaldehyde determination.