The Noether map II

Let be a faithful representation of a finite group . In this paper we proceed with the study of the image of the associated Noether map

In our 2005 paper it has been shown that the Noether map is surjective if is a projective -module. This paper deals with the converse. The converse is in general not true: we illustrate this with an example. However, for -groups (where is the characteristic of the ground field ) as well as for permutation representations of any group the surjectivity of the Noether map implies the projectivity of .

     

Oxidative polymerization of N-substituted carbazoles

Poly(N-vinylcarbazole), poly(N-carbazole) and poly(N-ethylcarbazole) powders were chemically synthesized by the reaction of ceric ammonium nitrate (CAN) with N-vinylcarbazole carbazole and N-ethylcarbazole in acetonitrile. Products were characterized by elemental analysis, Fourier transform infrared spectroscopy, scanning electron microscopy and viscosity, X-ray fluorescence and four-probe conductivity measurement. It is found that when a suitable concentration of CAN is used in the polymerization process, the conductivity of chemically synthesized polymers can be improved further by controlling the CAN addition. © 1997 John Wiley & Sons, Ltd.     

A taylor collocation method for solving high‐order linear pantograph equations with linear functional argument

A numerical method based on the Taylor polynomials is introduced in this article for the approximate solution of the pantograph equations with constant and variable coefficients. Some numerical examples, which consist of the initial conditions, are given to show the properties of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:1628–1638, 2011     

A collocation approach for solving linear complex differential equations in rectangular domains

In this paper, a collocation method is presented to find the approximate solution of high‐order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a). Copyright © 2012 John Wiley & Sons, Ltd.     

Spectroscopic Observation of Calcium‐Induced Reorientation of Cellobiose Dehydrogenase Immobilized on Electrodes and its Effect on Electrocatalytic Activity

Cellobiose dehydrogenase catalyzes the oxidation of various carbohydrates and is considered as a possible anode catalyst in biofuel cells. It has been shown that the catalytic performance of this enzyme immobilized on electrodes can be increased by presence of calcium ions. To get insight into the Ca²⁺‐induced changes in the immobilized enzyme we employ surface‐enhanced vibrational (SERR and SEIRA) spectroscopy together with electrochemistry. Upon addition of Ca²⁺ ions electrochemical measurements show a shift of the catalytic turnover signal to more negative potentials while SERR measurements reveal an offset between the potential of heme reduction and catalytic current. Comparing SERR and SEIRA data we propose that binding of Ca²⁺ to the heme induces protein reorientation in a way that the electron transfer pathway of the catalytic FAD center to the electrode can bypass the heme cofactor, resulting in catalytic activity at more negative potentials.     

Analytical approach to Boussinesq equation with space‐ and time‐fractional derivatives

In this paper, the homotopy perturbation method (HPM) is developed to obtain approximate analytical solutions of a fractional Boussinesq equation with initial condition. The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made, the comparisons show that the HPM is very effective and convenient and overcomes the difficulty of traditional methods. The numerical results show that the approaches are easy to implement and accurate when applied to space‐ and time‐fractional equations. Copyright © 2010 John Wiley & Sons, Ltd.     

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     

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.