Linear and nonlinear optical absorption coefficients and binding energy of a spherical quantum dot

The binding energy and wavefunctions of the 1s, 1p, 1d and 1f energy states of a spherical quantum dot (QD) with parabolic potential were calculated by using a method which is a combination of the quantum genetic algorithm (QGA) and the Hartree–Fock–Roothaan (HFR) approach. In addition, the linear and the third-order nonlinear optical absorption coefficients based on optical transitions in QDs with and without impurity were calculated. The results show that the parabolic potential has a great effect not only on the binding energies and but also on the optical absorption coefficients. Moreover, the calculated results also reveal that the linear and nonlinear optical absorption coefficients are strongly affected by the existence of impurity and the incident optical intensity.     

Solving high‐order linear differential equations by a Legendre matrix method based on hybrid Legendre and Taylor polynomials

A numerical method for solving the high‐order linear differential equations with variable coefficients under the mixed conditions is presented. The method is based on the hybrid Legendre and Taylor polynomials. The solution is obtained in terms of Legendre polynomials. Comparison of the present solution is made with the existing solution and excellent agreement is noted. Illustrative examples are included to demonstrate the validity and applicability of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Carbonyl ylide reactions of α-benzylidene-β-dicarbonyl compounds: competitive formation of dihydrofurans and dihydrobenzoxepines

α-Benzylidene-β,β′-biscarbonyl compounds were reacted with dimethyl diazomalonate using Cu(II) acetylacetonate as a catalyst. Dihydrofurans or mixtures of dihydrofurans and dihydrobenzoxepines were obtained depending on the nature of the carbonyl group present in the starting material.     

Reactions of α,β‐Enones with Diazo Compounds,Part 3

Carbonyl ylides arising from ethyl acetodiazoacetate/dimethyl diazomalonate and α,β‐enones with mainly s‐cis conformations underwent disrotatory cyclization to produce dihydrofuran derivatives. This process proved to be sensitive to steric effects. The corresponding ylides arising from rather s‐trans α,β‐enals yielded dioxole derivatives. The mechanisms of the reactions are discussed.     

Electro‐induced oxidative polymerization of N‐vinylcarbazole

In this study, a novel procedure to increase the yield of the non‐crosslinked, photoconductive, white form of linear poly(N‐vinylcarbazole) (LPVCz) is reported. The yield of LPVCz is increased (up to 53%) by the addition of catalytic amounts of ceric ammonium nitrate as an oxidant during the electrochemical polymerization of N‐vinylcarbazole in a divided electrochemical cell. The concentration of Ce(IV) remained constant during the polymerization since Ce(III) is readily oxidized to Ce(IV) electrochemically. Since the electrochemical oxidation of Ce(III) to Ce(IV) took place simultaneously at the anode, the deposition of dark green crosslinked polyvinylcarbazole on the electrode surface, which hinders the formation of white LPVCz, can be prevented. The Fourier transform infrared, ultraviolet–visible and fluorescence spectra of white LPVCz showed that the structures of polymers are the same as those produced by conventional polymerization. Copyright © 1999 John Wiley & Sons, Ltd.     

Sequential testing of simple hypotheses about compound Poisson processes

One of two simple hypotheses for the unknown arrival rate and jump distribution of a compound Poisson process is correct. We start observing the process, and the problem is to decide on the correct hypothesis as soon as possible and with the smallest probability of wrong decision. We find a Bayes-optimal sequential decision rule and describe completely how to calculate its parameters without any restrictions on the arrival rate and the jump distribution.     

Approximate solution of multi-pantograph equation with variable coefficients

This paper deals with the approximate solution of multi-pantograph equation with nonhomogenous term in terms of Taylor polynomials. The technique we have used is based on a Taylor matrix method. In addition, some numerical examples are presented to show the properties of the given method and the results are discussed.     

The effect of support locations on the steady-state response of viscoelastically point-supported rectangular orthotropic plates

The vibration of orthotropic rectangular plates having viscoelastic point supports symmetrically located on its diagonals is analyzed. The plate is under the effect of a sinusoidally varying force at its center. The Lagrange equations are used in the solution process. To apply the Lagrange equations, the trial function denoting the deflection of the plate is expressed in polynomial form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The influence of the mechanical properties, the damping of the supports and the locations of point supports on the steady-state response of the viscoelastically point-supported rectangular plates is investigated numerically for the concentrated load at center for various values of the mechanical properties characterizing the anisotropy of the plate material and for various values of damping and location of the supports for a certain stiffness value of the supports. The results are given for the considered frequency range of the external force. Convergence studies are made. The validity of the obtained results is demonstrated by comparing them with other solutions based on the Kirchhoff–Love plate theory.     

Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

In this study, a practical matrix method based on Laguerre polynomials is presented to solve the higher‐order linear delay differential equations with constant coefficients and functional delays under the mixed conditions. Also, an error analysis technique based on residual function is developed and applied to some problems to demonstrate the validity and applicability of the method. In addition, an algorithm written in Matlab is given for the method. Copyright © 2013 John Wiley & Sons, Ltd.