on lie gradings ii abstract to obtain fine gradings of gl n c it is necessary to study maximal abelian subgroups mad subgroups of diagonizable automorphisms in a ut gl n c we described two finite sets h n and k n such that each mad subgroup consisting only from inner automorphisms is conjugated to some element of h n and each mad subgroup containing at least one outer automorphism is conjugated to some element of k n using these results concerning k n we then easily find all mad subgroups in a ut o n c for n 8 and in a ut sp 2n c

group gradings on associative algebras abstract let r g g rg be a g graded ring we describe all types of gradings on r if g is torsion free and r is artinian semisimple if r is a matrix algebra over an algebraically closed field f then we give a description of all g gradings on r provided that g is an abelian group in the case of an abelian group g we also classify all finite dimensional graded simple algebras and finite dimensional graded division algebras over an algebraically closed field of characteristic zero

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

z graded identities of the lie algebra w1 abstract let k be a field of characteristic 0 and let w 1 be the lie algebra of the derivations of the polynomial ring k t the algebra w 1 admits a natural z grading we describe the graded identities of w 1 for this grading it turns out that all these z graded identities are consequences of a collection of polynomials of degree 1 2 and 3 and that they do not admit a finite basis recall that the ordinary non graded identities of w 1 coincide with the identities of the lie algebra of the vector fields on the line and it is a long standing open problem to find a basis for these identities we hope that our paper might be a step to solving this problem

classification of involutions on graded division simple real algebras abstract we classify up to isomorphism and up to equivalence involutions on graded division finite dimensional simple real associative algebras when the grading group is abelian

exponential difference operator approximation for the sixth order onsager equation an accurate easy to program method of solving the one dimensional form of the sixth order onsager equation is presented boundary conditions are included naturally aip

application of generalized differential quadrature rule in blasius and onsager equations the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to third order non linear differential equations of the blasius type and to sixth order linear onsager differential equations high 3rd order differential equations in fluid mechanics are dealt with without using point techniques the half space domain is simplified in a practical way accurate results are obtained for both kinds of problems the wide applicability of the gdqr in high order differential equations is manifested further through this work copyright 2001 john wiley sons ltd

classification of group gradings on simple lie algebras of types a b c and d abstract for a given abelian group g we classify the isomorphism classes of g gradings on the simple lie algebras of types a n n 1 b n n 2 c n n 3 and d n n 4 in terms of numerical and group theoretical invariants the ground field is assumed to be algebraically closed of characteristic different from 2

differential quadrature solutions of eighth order boundary value differential equations special cases of linear eighth order boundary value problems have been solved using polynomial splines however divergent results were obtained at points adjacent to boundary points this paper presents an accurate and general approach to solve this class of problems utilizing the generalized differential quadrature rule gdqr proposed recently by the authors explicit weighting coefficients are formulated to implement the gdqr for eighth order differential equations a mathematically important by product of this paper is that a new kind of hermite interpolation functions is derived explicitly for the first time linear and non linear illustrations are given to show the practical usefulness of the approach developed using frechet derivatives non linear eighth order problems are also solved for the first time numerical results obtained using even only seven sampling points are of excellent accuracy and convergence in an entire domain the present gdqr has shown clear advantages over the existing methods and demonstrated itself as a general stable and accurate numerical method to solve high order differential equations

gradings on simple algebras of finitary matrices abstract we describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries over an algebraically closed field of characteristic zero

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

a corner free truncation strategy for fdtd method in target scattering in this paper the corner free truncation cft strategy is proposed to terminate the circular boundary out of finite difference time domain fdtd region using the principle of reflection free optimal thin film the permittivity e and the permeability have been extended to the complex field the electric conductivity e and the equivalent magnetic loss m relate to the complex value and are suitable for the impedance matched condition imc the propagation wave can be absorbed well at the circular boundary moreover computational efficiency has been much enhanced when those useless square corners have been eliminated by using the proposed method in tm z wave the sinusoidal wave is set near the circular boundary applying the cft strategy the e z amplitudes and phases show the concentric circles in the different timesteps compared with the square pml numerical experiments in near and far field have come to the fulfillment at the same numerical example the cft strategy has higher accuracy than the conformal pml these results have fully verified the effectiveness of the proposed algorithm

conformal pml fdtd schemes for electromagnetic field simulations a dynamic stability study we present a study on the dynamic stability of the perfectly matched layer pml absorbing boundary condition for finite difference time domain fdtd simulations of electromagnetic radiation and scattering problems in body conformal orthogonal grids this work extends a previous dynamic stability analysis of cartesian cylindrical and spherical pmls to the case of a conformal pml it is shown that the conformal pml defined over surface terminations with positive local radii of curvature concave surfaces as viewed from inside the computational domain is dynamically stable while the conformal pml defined over surface terminations with a negative local radius convex surfaces as viewed from inside the computational domain is dynamically unstable numerical results illustrate the analysis

on herstein s lie map conjectures iii abstract in the two papers on herstein s lie map conjectures i and ii solutions of all of herstein s problems concerning lie isomorphisms and derivations were given under the assumption that the algebras involved were of sufficiently high dimension in the present paper we remove this restriction thereby solving herstein s problems in full generality

fdtd implementation and application of high order impedance boundary condition using rational functions an algorithm is proposed for the implementation of the high order surface impedance boundary condition using the finite difference time domain method the surface impedance function of a lossy medium is approximated by a series of rational functions in the laplace domain whereas the dyadic differential operator is approximated by a second order power series by assuming that the fields are piecewise linear the time domain convolution integrals are computed using a recursive formula the impedance function of a coating layer is approximated by a third order power series the algorithm can be applied to scattering problems of a three dimensional coating for both vertically and horizontally polarized waves the advantage of the proposed method is that the result can be applied to media of arbitrary conductivities with a wide range of incident angles from zero to graze some numerical examples are given to substantiate the theory

stability and accuracy of the iterative differential quadrature method in this paper the stability and accuracy of an iterative method based on differential quadrature rules will be discussed the method has already been proposed by the author in a previous work where its good performance has been shown nevertheless discussion about stability and accuracy remained open an answer to this question will be provided in this paper where the conditional stability of the method will be pointed out in addition to an examination of the possible errors which arise under certain conditions the discussion will be preceded by an overview of the method and its foundations i e the differential quadrature rules and followed by a numerical case which shows how the method behaves when applied to reduce continuous systems to two degree of freedom systems in the non linear range in particular here the case of oscillators coupled in non linear terms will be treated the numerical results used to draw poincare maps will be compared with those obtained by using the runge kutta method with a high precision goal copyright 2003 john wiley sons ltd

superabsorption a method to improve absorbing boundary conditions electromagnetic waves the authors propose a technique which they call superabsorption for improving absorbing boundary conditions in finite difference time domain methods this method can be applied to every known absorbing boundary condition and greatly reduces the numerical error caused by the boundary reflection the principle and analysis of the superabsorption method are presented numerical tests indicating the improvements obtained on many absorbing boundary conditions are reported

gradings on simple jordan and lie algebras abstract in this paper we describe all group gradings by a finite abelian group g of several types of simple jordan and lie algebras over an algebraically closed field f of characteristic zero

the generalized differential quadrature rule for initial value differential equations abstract the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to solve initial value differential equations of the 2nd to 4th order differential quadrature expressions are derived based on the gdqr for these equations the hermite interpolation functions are used as trial functions to obtain the explicit weighting coefficients for an easy and efficient implementation of the gdqr the numerical solutions for example problems demonstrate that the gdqr has high efficiency and accuracy a detailed discussion on the present method is presented by comparing with other existing methods the present method can be extended to other types of differential equation systems

gradings on the lie algebra d4 revisited abstract we classify group gradings on the simple lie algebra l of type d 4 over an algebraically closed field of characteristic different from 2 fine gradings up to equivalence and g gradings with a fixed group g up to isomorphism for each g grading on l we also study graded l modules assuming characteristic 0

gradings on octonions abstract all the different ways of grading any cayley dickson or octonion algebra as well as the associated central simple malcev algebras will be obtained

involutions on graded matrix algebras abstract in this paper we describe graded antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of characteristic different from 2

simulating non linear coupled oscillators by an iterative differential quadrature method abstract an iterative method based on differential quadrature rules is proposed as a new unified frame of resolution for non linear two degree of freedom systems dynamical systems with duffing type non linearity have been considered differential quadrature rules have been applied with a careful distribution of sampling points to reduce the governing equation of motion to two second order non linear non autonomous ordinary differential equations and to solve the time domain problem the time domain of the problem is discretized by means of time intervals with the same distribution of sampling points used to discretize the space domain which can be seen as a single interval it will be shown that accurate solutions depend not only on the choice of the distribution of sampling points but also on the length of the time interval one refers to in the computations the numerical results utilized to draw poincare maps are successfully compared with those obtained using the runge kutta method

graded polynomial identities and specht property of the lie algebra sl2 abstract let g be a group the lie algebra sl 2 of 2 2 traceless matrices over a field k can be endowed up to isomorphism with three distinct non trivial g gradings induced by the groups z 2 z 2 z 2 and z it has been recently shown koshlukov 2008 8 that for each grading the ideal of g graded identities has a finite basis in this paper we prove that when char k 0 the algebra sl 2 endowed with each of the above three gradings has an ideal of graded identities id g sl 2 satisfying the specht property i e every ideal of graded identities containing id g sl 2 is finitely based

free vibration analysis of circular plates using generalized differential quadrature rule the free vibration of solid circular plates has been studied using the generalized differential quadrature rule gdqr the effects such as stepped thickness intermediate concentric ring supports and elastic restraints have been considered discrete system equations for natural frequency analysis were derived based on the gdqr issues related to the implementation of the boundary and compatibility conditions were addressed two regularity conditions at the solid circular plate center were formularized since they were not quite clear in the present literature some wrong applications in the implementation of both differential quadrature methods and regularity conditions at the solid circular plate center have been pointed out excellent results have been obtained with the presented examples

the symmetries of the fine gradings of sl nk c associated with direct product of pauli groups a grading of a lie algebra is called fine if it could not be further refined for a fine grading of a simple lie algebra we define its weyl group to describe the symmetry of this grading it is already known that the weyl group of the fine grading of sl n c induced by the action of the group n of the generalized pauli matrices of rank n is sl 2 zn where zn is the cyclic group of order n in this paper we consider the fine grading of sl nk c induced by the action of the group of k fold tensor product of the generalized pauli matrices of rank n we prove that its weyl group is sp 2k zn and is generated by transvections therefore this generalizes the previous result

simple graded division algebras over the field of real numbers abstract we classify up to equivalence all finite dimensional simple graded division algebras over the field of real numbers the grading group is any finite abelian group

the generalized differential quadrature rule for fourth order differential equations the generalized differential quadrature rule gdqr proposed here is aimed at solving high order differential equations the improved approach is completely exempted from the use of the existing point technique by applying multiple conditions in a rigorous manner the gdqr is used here to static and dynamic analyses of bernoulli euler beams and classical rectangular plates numerical error analysis caused by the method itself is carried out in the beam analysis independent variables for the plate are first defined the explicit weighting coefficients are derived for a fourth order differential equation with two conditions at two different points it is quite evident that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems the gdqr are implemented through a number of examples good results are obtained in this work copyright 2001 john wiley sons ltd

application of the generalized differential quadrature rule to initial boundary value problems partial differential equations pdes for the forced vibration of structural beams are solved in this paper using the recently proposed generalized differential quadrature rule gdqr the gdqr techniques are first applied to both spatial and time dimensions simultaneously as a whole no other classical methods are needed in the time dimension the objective of this paper is to formularize the gdqr expressions and corresponding explicit weighting coefficients while the derivation of explicit weighting coefficients is one of the most important aspects in the differential quadrature methods it should be emphasized that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems and they are distinctly different for pdes of different orders an euler beam and a timoshenko beam are employed as examples accurate results are obtained the proposed procedures can be applied to problems in other disciplines of sciences and technology where the problems may be governed by other pdes with different orders in the time or spatial dimension

specht property for some varieties of jordan algebras of almost polynomial growth abstract let f be a field of characteristic zero in 25 it was proved that u j 2 the jordan algebra of 2 2 upper triangular matrices can be endowed up to isomorphism with either the trivial grading or three distinct non trivial z 2 gradings or by a z 2 z 2 grading in this paper we prove that the variety of jordan algebras generated by u j 2 endowed with any g grading has the specht property i e every t g ideal containing the graded identities of u j 2 is finitely based moreover we prove an analogue result about the ordinary identities of a 1 a suitable infinitely generated metabelian jordan algebra defined in 27

a generalized differential quadrature rule for bending analysis of cylindrical barrel shells the generalized differential quadrature rule gdqr proposed recently by the present authors is applied here to solve an eighth order boundary value differential equation with four boundary conditions at each boundary which governs the bending analysis of circular cylindrical barrel shells thus multiple boundary conditions are implemented exactly at boundaries without applying the approximate point non boundary point technique both hermite interpolation functions and gdqr s explicit weighting coefficients are obtained while the latter are the most important for an accurate implementation of the gdqr the analytical results for various cylindrical barrel shells are derived and calculated here in order to verify the accuracy of the calculated gdqr results in implementation of multiple conditions at one point the gdqr gains a clear advantage over the existing point technique in the differential quadrature applications and manifests a great potential for applications in many fields of applied mathematics

a theoretical analysis of piezoelectric composite laminate with larger amplitude deflection effect part ii hermite differential quadrature method and application incorporating the effects of larger amplitude deflection and electro elastical properties of piezoelectric lamina the hamilton s variation principle was used to deduce the fundamental formulations of smart anisotropic composite plate in part i in terms of reddy s simple higher order theory in order to solve the five highly coupled nonlinear partial differential equations with complicated overlapping boundary conditions a novel numerical method hermite differential quadrature hdq method was developed to implement the differential equations with complicated overlapping boundary conditions based on the presently developed hdq method any orders derivatives of the unknown functions or any boundary conditions can be point collocation based discretized by a set of point values along x and y direction then a system of complete algebraic nonlinear equations can be constructed to calculate out the final point values of the mid plane displacements by using the governing equations and relative boundary conditions with hdq method finally some detailed numerical examples for the anisotropic piezoelectric composite laminate with the distributed poling directions of piezoelectric layer and fiber orientations of composite layers were studied to validate the developed theoretical analysis model and hdq numerical method