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     

Preparation of a dual-functionalized fumed silica nanoparticle catalysis for synthesis of azaluorenone derivatives

Research on Chemical Intermediates - A dual-functional silica-based catalyst was prepared by treating fumed silica with amino-containing silane then 1,4-butane sultone. The presence of functional...     

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 experimental/numerical investigation of variations in strip speed,water shower pattern and water temperature on high-temperature strip cooling rate in hot strip mill

Journal of Thermal Analysis and Calorimetry - Hot-rolled strips are cooled on the run-out table to achieve the customer-required mechanical properties. Cooling reduces the oxidation, which can...     

Antiinfective properties of ursolic acid-loaded chitosan nanoparticles against Staphylococcus aureus

The present study aimed to synthesize ursolic acid-loaded chitosan nanoparticles (UA-Ch-NPs) as an antiinfective agent against 21 Staphylococcus aureus isolates. The UA-Ch-NPs were synthesized by a simple method and then characterized by TEM, FTIR, DLS-zeta potential, and XRD analyses. According to the characterization results, highly dispersed spherical nanoparticles with a mean diameter of 258 nm and a zeta potential of + 40.1 mV were developed. The antibacterial properties of UA-Ch-NPs were investigated and their inhibitory effect on biofilm formation was demonstrated by AFM. Finally, the expression levels of icaA and icaD were measured using real-time PCR. Results indicated that the minimum inhibitory concentration (MIC) of UA and UA-Ch-NPs against S. aureus was 64 and 32 µg/mL, respectively. The treatment of bacterial cells with UA-Ch-NPs significantly decreased the expression of icaA and icaD genes which are engaged in biofilm formation. Our results indicated that UA-Ch-NPs could be a promising material for antibacterial and antibiofilm applications.     

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...     

Engineered mesoporous ionic‐modified γ‐Fe2O3@hydroxyapatite decorated with palladium nanoparticles and its catalytic properties in water

A new mesoporous organic–inorganic nanocomposite was formulated and then used as stabilizer and support for the preparation of palladium nanoparticles (Pd NPs). The properties and structure of Pd NPs immobilized on prepared 1,4‐diazabicyclo[2.2.2]octane (DABCO) chemically tagged on mesoporous γ‐Fe₂O₃@hydroxyapatite (ionic modified (IM)‐MHA) were investigated using various techniques. The synergistic effects of the combined properties of MHA, DABCO and Pd NPs, and catalytic activity of γ‐Fe₂O₃@hydroxyapatite‐DABCO‐Pd (IM‐MHA‐Pd) were investigated for the Heck cross‐coupling reaction in aqueous media. The appropriate surface area and pore size of mesoporous IM‐MHA nanocomposite can provide a favourable hard template for immobilization of Pd NPs. The loading level of Pd in the nanocatalyst was 0.51 mmol g^?1. DABCO bonded to the MHA surface acts as a Pd NP stabilizer and can also lead to colloidal stability of the nanocomposite in aqueous solution. The results reveal that IM‐MHA‐Pd is highly efficient for coupling reactions of a wide range of aryl halides with olefins under green conditions. The superparamagnetic nature of the nanocomposite means that the catalyst to be easily separated from solution through magnetic decantation, and the catalytic activity of the recycled IM‐MHA‐Pd showed almost no appreciable loss even after six consecutive runs.