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,characterization, and use of poly(vinylpyrrolidonium) hydrogen phosphate ([PVP-H]H2PO4) as a new heterogeneous catalyst for efficient synthesis of 2-amino-tetrahydro-4H-pyrans

Research on Chemical Intermediates - A novel Brønsted solid acid named poly(vinylpyrrolidonium) hydrogen phosphate ([PVP-H]H2PO4) has been prepared by using H3PO4 and poly(vinylpyrrolidone) as...     

Polyelectrolyte Nanocomposite Membranes Using Imidazole-Functionalized Nanosilica for Fuel Cell Applications

The preparation and characterization of a new type of nanocomposite polyelectrolyte membrane, based on DuPont Nafion/imidazole-modified nanosilica (Im-Si), for direct methanol fuel cell applications is described. Related to the interactions between the protonated imidazole groups, grafted on the surface of nanosilica, and negatively charged sulfonic acid groups of Nafion, new electrostatic interactions can be formed in the interface of Nafion and Im-Si which result in both lower methanol permeability and also higher proton conductivity. Physical characteristics of these manufactured nanocomposite membranes were investigated by scanning electron microscopy, thermogravimetry analysis, differential scanning calorimetry, Fourier transform infrared spectroscopy, water uptake, methanol permeability, and ion-exchange capacity, as well as proton conductivity. The Nafion/Im-Si membranes showed higher proton conductivity, lower methanol permeability and, as a consequence, higher selectivity parameter in comparison to the neat Nafion or Nafion/silica membranes. The obtained results indicated that the Nafion/Im-Si membranes could be utilized as promising polyelectrolyte membranes for direct methanol fuel cell applications.     

高效可回收聚(4-乙烯基吡啶)高氯酸催化剂用于合成双香豆素和双吲哚(英文)

Poly(4-vinylpyridinium) perchlorate has been used as an efficient solid acid catalyst for the synthesis of 3,3'-(arylmethylene)bis(4-hydroxycoumarins) and bis(indolyl)methanes, with the products being formed in excellent yields over very short reaction times under mild and environmentally friendly conditions. This catalyst can be reused several times without any appreciable loss in its activity.     

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.     

Rapid Determination of Phenolic Compounds in Water Samples: Development of a Paper‐based Nanobiosensor Modified with Functionalized Silica Nanoparticles and Potato Tissue

In this study, we present a fast, simple, low‐cost and disposable method for determination of phenolic content in water samples, using a paper based polyphenol oxidase biosensor. The propylamine functionalized silica nanoparticles was dropped onto a paper sheet. After drying at room temperature, the potato tissue extract including polyphenol oxidase was immobilized on the paper via physical and chemical adsorption. The modified paper was placed on the top of the graphite screen printed electrode. To construct of an electrochemical nanobiosensor, the electrochemical behavior of the modified electrode in different steps was investigated by cyclic voltammetry and electrochemical impedance spectroscopy methods. After being optimized the effective parameters, the changes in the biosensor electrochemical response vs. to the different concentrations of the substrate (phenol solution) were monitored by differential pulse voltammetry and amperometry methods. The linear relationships for phenol detection were obtained in the concentration ranges of 0.01–160 μM and 0.1–300 μM with a detection limit of 0.007 μM and 0.042 μM with DPV and amperometry methods, respectively. This method was successfully used in the voltammetric determination of the phenol content in the real samples, like the river water and the wastewater of wood factory.     

Succinimidinium N-sulfonic acid hydrogen sulfate as an efficient ionic liquid catalyst for the synthesis of 5-arylmethylene-pyrimidine-2,4,6-trione and pyrano[2,3-d]pyrimidinone derivatives

Research on Chemical Intermediates - Succinimidinium N-sulfonic acid hydrogen sulfate ([SuSA-H]HSO4) as a new ionic liquid is prepared and characterized using a variety of techniques, including...     

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