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The aim of this paper is to introduce a new two-variable polynomials defined via Hermite polynomials. In order to construct some fundamental properties of these polynomials, we first derive a generating function relation. By using definition and this generating relation, we arrive at several recurrence relations, an integral representation, some implicit summation formulae, a symmetry identity for these new two-variable polynomials. Furthermore, we obtain some results which give various classes of multilinear and multilateral generating functions. Then, some special cases are presented. Finally, we also give a general class of these new polynomials and prove explicit closed-form formulae of them. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce some new polynomials obtained from second- and third-order algebraic equations by using a simple iterative method. One-variable polynomials obtained in this study deal with special form of Pöschl–Teller potential with constant energy, and the two-variable polynomials are related to time-dependent wave equations. We present some recurrence relations, Binet formula and get various families of linear, multilinear and multilateral generating functions for these polynomials. In addition, we derive some special cases. At the end of the paper we also give an extension to the multidimensional case of our results. [ABSTRACT FROM AUTHOR]

The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver's hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions. [ABSTRACT FROM AUTHOR]

The energy eigenvalues with any l≠0 states and mass of heavy quark-antiquark system (quarkonium) are obtained by using Asymptotic Iteration Method in the view of nonrelativistic quantum chromodynamics, in which the quarks are considered as spinless for easiness and are bounded by Cornell potential. A semianalytical formula for energy eigenvalues and mass is achieved via the method in scope of the perturbation theory. The accuracy of this formula is checked by comparing the eigenvalues with the ones numerically obtained in this study and with exact ones in literature. Furthermore, semianalytical formula is applied to cc-, bb-, and cb- meson systems for comparing the masses with the experimental data. [ABSTRACT FROM AUTHOR]

This study is focused on the investigation of electrocatalytic effect of glucose oxidase (GOx) immobilized on the graphite rod (GR) electrode. The enzyme modified electrode was prepared by encapsulation of immobilized GOx within enzymatically formed poly(1,10-phenanthroline-5,6-dione) (pPD) film. The electrochemical responses of such enzymatic electrode (pPD/GOx/GR) vs . different glucose concentrations were examined chronoamperometrically in acetate-phosphate buffer solution (A-PBS), pH 6.0, under aerobic or anaerobic conditions. Amperometric signals of the pPD/GOx/GR electrode exhibited well-defined hyperbolic dependence upon glucose concentration. Amperometric signals at 100 mM of glucose were 41.17 and 32.27 μA under aerobic and anaerobic conditions, respectively. Amperometric signals of the pPD/GOx/GR electrode decreased by 6% within seven days. The pPD/GOx/GR electrode showed excellent selectivity in the presence of dopamine and uric acid. Furthermore it had a good reproducibility and repeatability with standard deviation of 9.4% and 8.0%, respectively. [ABSTRACT FROM AUTHOR]

The asymptotic iteration method (AIM) is used to obtain both special exact solutions and general approximate solutions for a Hydrogen-like atom confined in a spherical box of arbitrary radius R. Critical box radii, at which states are no longer bound, are also calculated. The results are compared with those in the literature. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

In a previous paper (J. Phys. A36, 11807 (2003)), the "asymptotic iteration method" was introduced and developed for solving second-order homogeneous linear differential equations. In this paper we use the method to study the quantum quartic anharmonic oscillator problem. We obtain accurate eigenvalues for both small and large coupling parameters. [ABSTRACT FROM AUTHOR]

Abstract: In a previous paper [J. Phys. A 36 (2003) 11807], we introduced the ‘asymptotic iteration method’ for solving second-order homogeneous linear differential equations. In this Letter, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem. [Copyright &y& Elsevier]

The properties of new heavy mesons containing new heavy quarks have been investigated. As an example, the fourth SM family quarks and weak iso-singlet quarks predicted by E[SUB6] GUT are considered. Production of these hadrons at TeV energy lepton colliders due to resonant formation of corresponding quarkonia have been analyzed. [ABSTRACT FROM AUTHOR]

Abstract: We discuss alternative perturbation expansions for partially solvable quantum-mechanical models. We consider a sextic anharmonic oscillator as a particular example. [Copyright &y& Elsevier]

A new methacrylate monomer 2-(4-nitrophenyl)-2-oxoethyl-2-methacrylate (NFM) was synthesized and its radical copolymerization with glycidyl methacrylate (GMA) was studied in 1,4-dioxane solution at 65°C using 2,2′-azobisisobutyronitrile as an initiator. The synthesized monomer and copolymers were characterized by FTIR,1H and13C-NMR spectroscopy. The analysis of reactivity ratios revealed that NFM is less reactive than GMA, and copolymers formed are statistically in nature. Thermogravimetric analysis of the polymers reveals that the thermal stability of the copolymers increases with an increasing in the mole fraction of NFM in the copolymers. Glass transition temperatures of the copolymers decreased with an increasing of NFM molar fraction in copolymers. In addition, according to the results obtained from the contact angle and zeta potential measurements the hydrophobic character of the polymer decreases (it means surface free energy increases) and its zeta potential becomes more negative with increase of NFM ratio in the copolymer. Polymers with carbonyl functional groups have been particularly interesting because of their use as photoresists. [ABSTRACT FROM AUTHOR]

The aim of this research was to investigate the effect of the several nanomaterials in electrochemical determination of Cu(II) ions. For this aim, firstly the deposition of graphene oxide (GO), graphene, magnetite (Fe 3 O 4 ), gold-chitosan (AuChts) or multilayer carbon nanotubes (MWCNTs) on the glassy carbon (GC) electrode surface was performed. Then the electrochemical modification of electrode by poly-3-nitroaniline (poly-3NA) was performed by 100 potential cycles in the range between +0.9 V and +1.4 V vs. Ag/AgNO 3 at the sweep rate of 100 mV/s. For electrochemical reduction of nitro groups present on modified GC electrode surface, potential cycling was performed in 100 mM HCl between −0.1 V and −0.8 V vs. Ag/AgCl/(KCl sat. ) at the sweep rate of 100 mV/s. Nanomaterial and poly-3NA modified electrodes were applied in the determination of Cu(II) ions by differential pulse voltammetry. It was determined that GC electrodes consecutively modified with MWCNTs, poly-3NA and then by electrochemical reduction of nitro groups were the most sensitive towards Cu(II) ions with detection limit of 0.5 × 10 −9 M. [ABSTRACT FROM AUTHOR]