on monotonicity preserving stabilized finite element approximations of transport problems the aim of this work is to design monotonicity preserving stabilized finite element techniques for transport problems as a blend of linear and nonlinear shock capturing stabilization as linear stabilization we consider and analyze a novel symmetric projection stabilization technique based on a local scott zhang projector next we design a weighting of the aforementioned linear stabilization such that when combined with a finite element discretization enjoying a discrete maximum principle usually attained via nonlinear stabilization it does not spoil these monotonicity properties then we propose novel nonlinear stabilization schemes in the form of an artificial viscosity method where the amount of viscosity is proportional to gradient jumps at either finite element boundaries or nodes for the nodal scheme we prove a discrete maximum principle for time dependent multidimensional transport problems numerical experiments support the numerical analysis and we show that the resulting methods prov

on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

new mds self dual codes from generalized reed solomon codes both maximum distance separable and euclidean self dual codes have theoretical and practical importance and the study of mds self dual codes has attracted lots of attention in recent years in particular determining the existence of q ary mds self dual codes for various lengths has been investigated extensively the problem is completely solved for the case where q is even this paper focuses on the case where q is odd we construct a few classes of new mds self dual codes through generalized reed solomon codes more precisely we show that for any given even length n we have a q ary mds code as long as q equiv 1 bmod 4 and q is sufficiently large say q ge 4 n times n 2 furthermore we prove that there exists a q ary mds self dual code of length n if q r 2 and n satisfies one of the three conditions 1 n le r and n is even 2 q is odd and n 1 is an odd divisor of q 1 and 3 r equiv 3 mod 4 and n 2tr for any t le r 1 2

on the finite element method for singularly perturbed reaction diffusion problems in two and one dimensions second order elliptic boundary value problems which are allowed to degenerate into zero order equations are considered the behavior of the ordinary galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed

new constructions of mds codes with complementary duals linear complementary dual lcd for short codes are linear codes that intersect with their duals trivially lcd codes have been used in certain communication systems it is recently found that lcd codes can be applied in cryptography this application of lcd codes renewed the interest in the construction of lcd codes having a large minimum distance maximum distance separable mds codes are optimal in the sense that the minimum distance cannot be improved for given length and code size constructing lcd mds codes is thus of significance in theory and practice recently jin constructed several classes of lcd mds codes through generalized reed solomon codes in this paper a different approach is proposed to obtain new lcd mds codes from generalized reed solomon codes consequently new code constructions are provided and certain previously known results by jin are extended

an approximation method for the solution of nonlinear integral equations a chebyshev collocation method has been presented to solve nonlinear integral equations in terms of chebyshev polynomials this method transforms the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown chebyshev coefficients finally some examples are presented to illustrate the method and results discussed

numerical solution of delay differential equations by uniform corrections to an implicit runge kutta method in this paper we develop a class of numerical methods to approximate the solutions of delay differential equations they are essentially based on a modified version in a predictor corrector mode of the one step collocation method atn gaussian points these methods applied to ode s provide a continuous approximate solution which is accurate of order 2n at the nodes and of ordern 1 uniformly in the whole interval in order to extend the methods to delay differential equations the uniform accuracy is raised to the order 2n by some a posteriori corrections numerical tests and comparisons with other methods are made on real life problems

nonbinary quantum codes we present several results on quantum codes over general alphabets that is in which the fundamental units may have more than two states in particular we consider codes derived from finite symplectic geometry assumed to have additional global symmetries from this standpoint the analogs of calderbank shor steane codes and of gf 4 linear codes turn out to be special cases of the same construction this allows us to construct families of quantum codes from certain codes over number fields in particular we get analogs of quadratic residue codes including a single error correcting code encoding one letter in five for any alphabet size we also consider the problem of fault tolerant computation through such codes generalizing ideas of gottesman see phys rev a vol 57 no 1 p127 37 1998

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

new constructions of mds euclidean self dual codes from grs codes and extended grs codes in this paper we consider the problem for which lengths a maximum distance separable mds euclidean self dual code over mathbb f q exists this problem is completely solved for the case where q is even for q is odd some q ary mds euclidean self dual codes were obtained in the literature in this paper we construct six new classes of q ary mds euclidean self dual codes by using generalized reed solomon grs for short codes and extended grs codes

classification of quaternary hermitian self dual codes of length 20 a classification of quaternary hermitian self dual codes of length 20 is given using this classification a classification of extremal quaternary hermitian self dual codes of length 22 is also given

on the stable solution of transient convection diffusion equations a transient convection diffusion equation is considered which particularly arises in optimization problems for the asymmetric flow field flow fractionation af4 process a time dependent generalization of the monotone edge averaged finite element eafe scheme is used to obtain a stable discretization in the convection dominated regime new error estimates are proved for this scheme and a comparison with the popular supg method is presented numerical experiments demonstrate that the eafe method is more suitable for problems where boundary layers are formed we consider transient convection diffusion equation with dominating convection the model has an application in optimal control of the asymmetric flow field flow fractionation process for a stable discretization we propose a monotone edge averaged finite element eafe scheme eafe is generalized to a time dependent case and a new error estimate is proved we present numerical results for comparison with a popular supg method

classification of pseudo cyclic mds codes linear codes are considered a code is characterized by the length n the dimension k and the minimum distance d an n k d code over the finite field gf q is said to be maximum distance separable mds if d n k 1 a krishna and d v sarwate 1990 investigated the existence of pseudo cyclic mds codes over gf q of length n where n divides q 1 or q 1 it is shown that the pseudo cyclic mds codes constructed by krishna and sarwate are generalised reed solomon codes pseudo cyclic codes are studied over gf q where n and q p sup h are not relatively prime it is proven that pseudo cyclic n k mds codes modulo x sup n a over gf q exist if and only if n p furthermore any pseudo cyclic p k code modulo x sup p a over gf q turns out to be mds and generalized reed solomon it is explicitly proven that some classes of pseudo cyclic n k mds codes over gf q are generalized reed solomon codes furthermore pseudo cyclic q 1 4 mds codes over gf q q even are completely classified

on sigma lcd codes linear complementary pairs lcps of codes play an important role in armoring implementations against side channel attacks and fault injection attacks one of the most common ways to construct lcp of codes is to use euclidean linear complementary dual lcd codes in this paper we first introduce the concept of linear codes with sigma complementary dual sigma lcd which includes known euclidean lcd codes hermitian lcd codes and galois lcd codes like euclidean lcd codes sigma lcd codes can also be used to construct lcp of codes we show that for q 2 all q ary linear codes are sigma lcd and for every binary linear code mathcal c the code 0 times mathcal c is sigma lcd furthermore we study deeply sigma lcd generalized quasi cyclic gqc codes in particular we provide the characterizations of sigma lcd gqc codes self orthogonal gqc codes and self dual gqc codes respectively moreover we provide the constructions of asymptotically good sigma lcd gqc codes finally we focus on sigma lcd abelian codes and prove that all abelian codes in a semi simple group algebra are sigma lcd the results derived in this paper extend those on the classical lcd codes and show that sigma lcd codes allow the construction of lcp of codes more easily and with more flexibility

nonbinary stabilizer codes over finite fields one formidable difficulty in quantum communication and computation is to protect information carrying quantum states against undesired interactions with the environment to address this difficulty many good quantum error correcting codes have been derived as binary stabilizer codes fault tolerant quantum computation prompted the study of nonbinary quantum codes but the theory of such codes is not as advanced as that of binary quantum codes this paper describes the basic theory of stabilizer codes over finite fields the relation between stabilizer codes and general quantum codes is clarified by introducing a galois theory for these objects a characterization of nonbinary stabilizer codes over fq in terms of classical codes over fq 2 is provided that generalizes the well known notion of additive codes over f4 of the binary case this paper also derives lower and upper bounds on the minimum distance of stabilizer codes gives several code constructions and derives numerous families of stabilizer codes including quantum hamming codes quadratic residue codes quantum melas codes quantum bose chaudhuri hocquenghem bch codes and quantum character codes the puncturing theory by rains is generalized to additive codes that are not necessarily pure bounds on the maximal length of maximum distance separable stabilizer codes are given a discussion of open problems concludes this paper

constructions of self orthogonal codes from hulls of bch codes and their parameters self orthogonal codes are an interesting type of linear codes due to their wide applications in communication and cryptography it is known that self orthogonal codes are often used to construct quantum error correcting codes which can protect quantum information in quantum computations and quantum communications let mathcal c be an n k cyclic code over mathbb f q where mathbb f q is the finite field of order q the hull of mathcal c is defined to be the intersection of the code and its dual in this paper we will employ the defining sets of cyclic codes to present two general characterizations of the hulls that have dimension k 1 or k perp 1 where k perp is the dimension of the dual code mathcal c perp several sufficient and necessary conditions for primitive and projective bch codes to have k 1 dimensional or k perp 1 dimensional hulls are also developed by presenting lower and upper bounds on their designed distances furthermore several classes of self orthogonal codes are proposed via the hulls of bch codes and their parameters are also investigated the dimensions and minimum distances of some self orthogonal codes are determined explicitly in addition several optimal codes are obtained

explicit constructions of mds self dual codes in this paper we study self dual codes over finite fields using tools from algebraic function fields in one variable an algebraic geometry code of length n is defined using two divisors g and d p 1 cdots p n we characterize self orthogonality of the genus zero code in terms of the divisors g d and the value of a well chosen derivative polynomial at points p i 1 le i le n we explore the existence problem of mds self dual codes in the odd characteristic case and we explicitly construct families of new mds self dual codes

crosswind smear and pointwise errors in streamline diffusion finite element methods for a model convection dominated singularly perturbed convection diffusion prob lem it is shown that crosswind smear in the numerical streamline diffusion finite element method is minimized by introducing a judicious amount of artificial crosswind diffusion the ensuing method with piecewise linear elements converges with a pointwise accuracy of almost h 5 4 under local smoothness assumptions 1 introduction the streamline diffusion method is a finite element method for convection dominated convection diffusion problems which combines formal high accuracy with decent stability properties the method was introduced in the case of stationary problems by hughes and brooks 7 cf raithby and torrance 14 and wahlbin 15 for earlier thoughts in this direction the mathematical analysis of the method was started in johnson and navert 8 and continued with extensions to e g time dependent problems in navert 12 johnson navert and pitkaranta 9 and johnson and saranen 10 in these papers local error estimates in l2 of order o h k 1 2 in regions of smoothness with piecewise polynomial finite elements of degree k were derived together with estimates stating as a typical example that in the zero diffusion limit a sharp discontinuity in the exact solution across a streamline will be captured in a numerical crosswind layer of width 0 h1 2 essentially the purpose of the present paper is first to improve the result just mentioned on numerical crosswind smear to 0 h3 4 the improvement from 0 h1 2 to 0 h3 4 is obtained by adding a small amount 0 h3 2 of artificial crosswind diffusion to the method in the piecewise linear case k 1 this does not destroy the known o h3 2 accuracy in l2 in smooth regions using our first result we then obtain our second main result localized pointwise error estimates of order 0 h5 4 in regions of smoothness the previously known best pointwise error estimate in the piecewise linear situation is 0 h1 2 another consequence is a global l estimate of order 0 h 2 in the presence of typical crosswind and downwind singularities we shall consider the model problem of finding u u x y such that

the approximate solution of high order linear difference equations with variable coefficients in terms of taylor polynomials this paper presents a numerical method for the approximate solution of mth order linear difference equations with variable coefficients under the mixed conditions in terms of taylor polynomials about any point in addition examples that illustrate the pertinent features of the method are presented and the results of study are discussed

a construction of non reed solomon type mds codes a construction is presented of long maximum distance separable mds codes that are not generalized reed solomon grs type the construction uses subsets s mod s mod m of a finite field f gf q with the property that no t distinct elements of s add up to some fixed element of f large subsets of this kind are used to construct n m 2 k t 1 non grs mds codes over f

asymmetric quantum codes characterization and constructions the stabilizer method for constructing a class of asymmetric quantum codes aqc called additive aqc has been established by aly et al in this paper we present a new characterization of aqc which generalizes a result of the symmetric case known previously as an application of the characterization we establish a relationship of aqc with classical error correcting codes and show a few examples of good aqc with specific parameters by using this relationship we obtain an asymptotic bound on aqcs from algebraic geometry codes

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

asymmetric quantum codes constructions bounds and performance recently quantum error correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit and phase flip errors an example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel where the probabilities of bit and phase flips can be related to relaxation and dephasing time respectively we study asymmetric quantum codes that are obtained from the calderbank shor steane css construction for such codes we derive upper bounds on the code parameters using linear programming a central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes for instance we derive asymmetric codes using a combination of bose chaudhuri hocquenghem bch and finite geometry low density parity check ldpc codes we show that the asymmetric quantum codes offer two advantages namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allow a higher performance when compared with symmetric codes of comparable rates our approach is based on a css construction that combines bch and finite geometry ldpc codes

a unified approach to construct mds self dual codes via reed solomon codes mds codes and self dual codes are important families of classical codes in coding theory therefore it is of interest to investigate mds self dual codes the existence of mds self dual codes over finite field mathbb f q is competely solved for q is even in the literature there are many known constructions of mds self dual codes for q is odd in this paper we present a unified approach on the existence of mds self dual codes with concise statements and simplified proof it is illustrated that some of known results can also be stated in this framework furthermore we can obtain some new mds self dual codes especially for the case when q is not a square

adaptive streamline diffusion finite element methods for stationary convection diffusion problems adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed the underlying discretization scheme is the shock capturing streamline diffusion method the adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed a priori error estimates are used to show that the algorithms are efficient in a certain sense

constructions of linear codes with one dimensional hull the hull of a linear code is defined to be the intersection of the code and its dual and was originally introduced to classify finite projective planes the hull plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism group of a linear code it has been shown that these algorithms are very effective in general if the size of the hull is small the objective of this paper is to present some sufficient and necessary conditions that linear codes and cyclic codes have one dimensional hull it is shown that there are no such binary or ternary cyclic codes based on these characterizations some constructions of linear codes with one dimensional hull were given by employing quadratic number fields partial difference sets and difference sets we also construct cyclic codes with one dimensional hull some optimal codes with one dimensional hull are obtained

numerical treatment of delay differential equations by hermite interpolation a class of numerical methods for the treatment of delay differential equations is developed these methods are based on the wellknown runge kutta fehlberg methods the retarded argument is approximated by an appropriate multipoint hermite interpolation the inherent jump discontinuities in the various derivatives of the solution are considered automatically problems with piecewise continuous right hand side and initial function are treated too real life problems are used for the numerical test and a comparison with other methods published in literature

stability properties of numerical methods for solving delay differential equations abstract stability properties of numerical methods for delay differential equations are considered some suitable definitions for the stability of the numerical methods are included and runge kutta type methods satisfying these properties are tested on a numerical example

taylor polynomial solutions of general linear differential difference equations with variable coefficients abstract in this paper a taylor method is developed to find an approximate solution of high order linear differential difference equations with variable coefficients under the mixed conditions the solution is obtained in terms of taylor polynomials examples are presented which illustrate the pertinent features of the method

variational iteration method for solving a generalized pantograph equation the variational iteration method is applied to solve the generalized pantograph equation this technique provides a sequence of functions which converges to the exact solution of the problem and is based on the use of lagrange multipliers for identification of optimal value of a parameter in a functional employing this technique it is possible to find the exact solution or an approximate solution of the problem some examples are given to demonstrate the validity and applicability of the method and a comparison is made with existing results

asymptotic bounds on quantum codes from algebraic geometry codes we generalize a characterization of p ary p is a prime quantum codes given by feng and xing to q ary q is a prime power quantum codes this characterization makes it possible to convert an asymptotic bound of stichtenoth and xing for nonlinear algebraic geometry codes to a quantum asymptotic bound besides we also investigate the asymptotic behavior of quantum codes

on the classification of mds codes a q ary code of length n size m and minimum distance d is called an n m d q code an n q k n k 1 q code is called a maximum distance separable mds code in this paper some mds codes over small alphabets are classified it is shown that every k d 1 q k d q code with k geq 3 d geq 3 q in 5 7 is equivalent to a linear code with the same parameters this implies that the 6 5 4 3 5 code and the n 7 n 2 3 7 mds codes for n in 6 7 8 are unique the classification of one error correcting 8 ary mds codes is also finished there are 14 8 4 and 4 equivalence classes of n 8 n 2 3 8 codes for n 6 7 8 and 9 respectively one of the equivalence classes of perfect 9 8 7 3 8 codes corresponds to the hamming code and the other three are nonlinear codes for which there exists no previously known construction

on codes matroids and secure multiparty computation from linear secret sharing schemes error correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes in this paper the connections between codes matroids and a special class of secret sharing schemes namely multiplicative linear secret sharing schemes lssss are studied such schemes are known to enable multiparty computation protocols secure against general nonthreshold adversaries two open problems related to the complexity of multiplicative lssss are considered in this paper the first one deals with strongly multiplicative lssss as opposed to the case of multiplicative lssss it is not known whether there is an efficient method to transform an lsss into a strongly multiplicative lsss for the same access structure with a polynomial increase of the complexity a property of strongly multiplicative lssss that could be useful in solving this problem is proved namely using a suitable generalization of the well known berlekamp welch decoder it is shown that all strongly multiplicative lssss enable efficient reconstruction of a shared secret in the presence of malicious faults the second one is to characterize the access structures of ideal multiplicative lssss specifically the considered open problem is to determine whether all self dual vector space access structures are in this situation by the aforementioned connection this in fact constitutes an open problem about matroid theory since it can be restated in terms of representability of identically self dual matroids by self dual codes a new concept is introduced the flat partition that provides a useful classification of identically self dual matroids uniform identically self dual matroids which are known to be representable by self dual codes form one of the classes it is proved that this property also holds for the family of matroids that in a natural way is the next class in the above classification the identically self dual bipartite matroids

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

solving delay differential equations using componentwise partitioning by runge kutta method embedded singly diagonally implicit runge kutta sdirk method is used to solve stiff systems of delay differential equations ddes the delay argument is approximated using hermite interpolation initially the whole system is considered as nonstiff and solved using simple iteration when stiffness is indicated the appropriate equation is placed into the stiff subsystem and solved using newton iteration this type of partitioning is called componentwise partitioning the process is continued until all the equations have been placed in the right subsystem numerical results based on componentwise partitioning and intervalwise partitioning are tabulated and compared

on lowest density mds codes let f sub q denote the finite field gf q and let h be a positive integer mds maximum distance separable codes over the symbol alphabet f sub q sup b are considered that are linear over f sub q and have sparse low density parity check and generator matrices over f sub q that are systematic over f sub q sup b lower bounds are presented on the number of nonzero elements in any systematic parity check or generator matrix of an f sub q linear mds code over f sub q sup b along with upper bounds on the length of any mds code that attains those lower bounds a construction is presented that achieves those bounds for certain redundancy values the building block of the construction is a set of sparse nonsingular matrices over f sub q whose pairwise differences are also nonsingular bounds and constructions are presented also for the case where the systematic condition on the parity check and generator matrices is relaxed to be over f sub q rather than over f sub q sup b

on a cell entropy inequality for discontinuous galerkin methods we prove a cell entropy inequality for a class of high order dis continuous galerkin finite element methods approximating conservation laws which implies convergence for the one dimensional scalar convex case

some oscillation problems for a second order linear delay differential equation abstract for the delay differential equation formula a connection between the following properties is established non oscillation of the differential equation and the corresponding differential inequality positiveness of the fundamental function and the existence of a nonnegative solution of a generalized riccati inequality explicit conditions for non oscillation and oscillation and comparison theorems are presented

css like constructions of asymmetric quantum codes asymmetric quantum error correcting codes aqcs may offer some advantage over their symmetric counterparts by providing better error correction for the more frequent error types the well known css construction of q ary aqcs is extended by removing the fq linearity requirement as well as the limitation on the type of inner product used the proposed constructions are called css like constructions and utilize pairs of nested subfield linear codes under one of the euclidean trace euclidean hermitian and trace hermitian inner products after establishing some theoretical foundations best performing css like aqcs are constructed combining some constructions of nested pairs of classical codes and linear programming many optimal and good pure q ary css like codes for q 2 3 4 5 7 8 9 up to reasonable lengths are found in many instances removing the fq linearity and using alternative inner products give us pure aqcs with improved parameters than relying solely on the standard css construction

elementary 2 group character codes we describe a class of codes over gf q where q is a power of an odd prime these codes are analogs of the binary reed muller codes and share several features in common with them we determine the minimum weight and properties of these codes for a subclass of codes we find the weight distribution and prove that the minimum nonzero weight codewords give 1 designs

on the solutions of a system of linear retarded and advanced differential equations by the bessel collocation approximation in this study we present a numerical approximation for the solutions of the system of high order linear retarded and advanced differential equations with variable coefficients under the mixed conditions this method is based on taking the truncated bessel expansion of the functions in the retarded and advanced differential equation system by the aid of the matrix operations and the collocation points the problem is transformed into a matrix equation with the unknown bessel coefficients by solving this matrix equation the unknown coefficients of the approximate solutions are computed in addition examples that illustrate the pertinent features of the method are presented and the results of this investigation are discussed

convergence of a residual based artificial viscosity finite element method we present a residual based artificial viscosity finite element method to solve conservation laws the galerkin approximation is stabilized by only residual based artificial viscosity without any least squares supg or streamline diffusion terms we prove convergence of the method applied to a scalar conservation law in two space dimensions toward an unique entropy solution for implicit time stepping schemes

how accurate is the streamline diffusion finite element method we investigate the optimal accuracy of the streamline diffusion finite element method applied to convection dominated problems for linear bilinear elements the theoretical order of convergence given in the literature is either o h 3 2 for quasi uniform meshes or o h 2 for some uniform meshes the determination of the optimal order in general was an open problem by studying a special type of meshes it is shown that the streamline diffusion method may actually converge with any order within this range depending on the characterization of the meshes

skew selfadjoint form for systems of conservation laws abstract hyperbolic systems of conservation laws augumented with an entropy inequality are studied it is shown that such systems can be written in a quasilinear skew selfadjoint form centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered employing the above formulation in bounded regions under the nonsmooth regime as well a local entropy decay estimate is also concluded examples of the shallow water and the full gasdynamics equations are explicitly treated

measure valued solutions of scalar conservation laws with boundary conditions we define a solution concept for measure valued solutions to scalar conservation laws with initial conditions and boundary conditions and prove a uniqueness theorem for such solutions this result may be used to prove convergence towards the unique solution for approximate solutions which are uniformly bounded in l weakly consistent with certain entropy inequalities and strongly consistent with the initial condition i e without using derivative estimates as an example convergence of a finite element method is demonstrated

the simulation of texture evolution with finite elements over orientation space i development abstract a new class of finite element schemes is presented for the modeling of arbitrary polycrystalline microstructure a framework is constructed by viewing texture as arising out of maps that associate crystals with orientations drawn from a fundamental region of orientation space the state of the microstructure is characterized by an orientation distribution function and a hardness field over a fundamental region differential equations are derived to describe the evolution of the two fields finite element schemes cast over discretized fundamental regions are considered for the solution of the differential set properties of the schemes considered are illustrated by application to the texturing of a planar polycrystalline microstructure

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

stability in linear multistep methods for pure delay equations abstract the stability regions of linear multistep methods for pure delay equations are compared with the stability region of the delay equation itself a criterion is derived stating when the numerical stability region contains the analytical stability region this criterion yields an upper bound for the integration step conditional q stability these bounds are computed for the adams bashforth adams moulton and backward differentiation methods of orders 8 furthermore symmetric adams methods are considered which are shown to be unconditionally q stable finally the extended backward differentiation methods of cash are analysed

numerical crosswind smear in the streamline diffusion method abstract the streamline diffusion method is a popular element method for approximating convection dominated transport equations the solution to such equations may develop boundary or internal layers in the crosswind direction orthogonal to the flow direction and this results in numerical crosswind layers it is known that the size of these layers is o h 1 2 or perhaps o h 3 4 h being the size of the mesh used in the numerical computation but in practice o h is observed if the gridlines of the method are aligned with the streamlines of the problem this connection is studied and an explanation is given

algebraic geometry codes with complementary duals exceed the asymptotic gilbert varshamov bound it was shown by massey that linear complementary dual lcd codes are asymptotically good in 2004 sendrier proved that lcd codes meet the asymptotic gilbert varshamov gv bound until now the gv bound still remains to be the best asymptotical lower bound for lcd codes in this paper we show that an algebraic geometry code over a finite field of even characteristic is equivalent to an lcd code and consequently there exists a family of lcd codes that are equivalent to algebraic geometry codes and exceed the asymptotical gv bound

spline approximations for linear nonautonomous delay systems we develop a semi discrete approximation framework for linear nonautonomous nonhomogeneous functional differential equations of retarded type the approximation schemes are constructed and convergence results are obtained through the approximation of an associated abstract evolution operator computer implementation of the schemes is outlined and a spline based method included in the framework is constructed extensions of the semi discrete methods to schemes incorporating full discretization and difference equation approximation are also discussed numerical results for several examples demonstrating the feasibility of the schemes are presented

linear enhancements of the streamline diffusion method for convection diffusion problems abstract several computationally simple modifications of the streamline diffusion finite element method are developed for linear convection dominated convection diffusion problems in two dimensions numerical experiments show that these modifications yield significantly more accurate results than are attainable from the basic streamline diffusion method

exact and approximate solutions of second order including function delay differential equations with variable coefficients by means of the method of steps and the method of power series the exact solution of the initial value problem for coupled second order delay differential equations with variable coefficients is constructed then in a bounded domain a finite analytic solution with error bounds is provided

mds codes with hulls of arbitrary dimensions and their quantum error correction the hull of linear codes has promising utilization in coding theory and quantum coding theory in this paper we study the hull of generalized reed solomon codes and extended generalized reed solomon codes over finite fields with respect to the euclidean inner product several infinite families of mds codes with hulls of arbitrary dimensions are presented as an application using these mds codes with hulls of arbitrary dimensions we construct several new infinite families of entanglement assisted quantum error correcting codes with flexible parameters

adaptive anisotropic meshing for steady convection dominated problems obtaining accurate solutions for convection diffusion equations is challenging due to the presence of layers when convection dominates the diffusion to solve this problem we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution three main ingredients are used first the streamline upwind petrov galerkin method is used to produce a stabilized solution second an adapted metric tensor is computed from the approximate solution third optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal voronoi tessellation algorithm our algorithm is tested on a variety of two dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non physical oscillations in the numerical approximation

new mds or near mds self dual codes we construct new mds or near mds self dual codes over large finite fields in particular we show that there exists a euclidean self dual mds code of length n q over gf q whenever q 2m m ges 2 using a reed solomon rs code and its extension it turns out that this multiple description source mds self dual code is an extended duadic code we construct euclidean self dual near mds codes of length n q 1 over gf q from rs codes when q 1 mod 4 and q les 113 we also construct many new mds self dual codes over gf p of length 16 for primes 29 les p les 113 finally we construct euclidean hermitian self dual mds codes of lengths up to 14 over gf q2 where q 19 23 25 27 29

some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes abstract quantum maximal distance separable mds codes are an important class of quantum codes recently many scholars utilize constacyclic codes to construct some quantum mds codes in this paper several new families of optimal asymmetric quantum codes and optimal quantum convolutional codes are constructed by using constacyclic codes moreover these quantum codes constructed in this paper are different from the ones in the literature

additive asymmetric quantum codes we present a general construction of asymmetric quantum codes based on additive codes under the trace hermitian inner product various families of additive codes over f4 are used in the construction of many asymmetric quantum codes over f4

on the classification of hermitian self dual additive codes over rm gf 9 additive codes over gf 9 that are self dual with respect to the hermitian trace inner product have a natural application in quantum information theory where they correspond to ternary quantum error correcting codes however these codes have so far received far less interest from coding theorists than self dual additive codes over gf 4 which correspond to binary quantum codes self dual additive codes over gf 9 have been classified up to length 8 and in this paper we extend the complete classification to codes of lengths 9 and 10 the classification is obtained by using a new algorithm that combines two graph representations of self dual additive codes the search space is first reduced by the fact that every code can be mapped to a weighted graph and a different graph is then introduced that transforms the problem of code equivalence into a problem of graph isomorphism by an extension technique we are able to classify all optimal codes of lengths 11 and 12 there are 56 005 876 11 311 5 codes and 6493 12 312 6 codes we also find the smallest codes with trivial automorphism group

taylor polynomial solution of high order nonlinear volterra fredholm integro differential equations in this paper a taylor method is developed to find an approximate solution for high order nonlinear volterra fredholm integro differential equation numerical examples presented to illustrate the accuracy of the method

self dual near mds codes from elliptic curves in recent years self dual mds codes have attracted a lot of attention due to theoretical interest and practical importance similar to self dual mds codes self dual near mds nmds for short codes have nice structures as well from both theoretical and practical points of view it is natural to study self dual nmds codes although there has been lots of work on nmds codes in literature little is known for self dual nmds codes it seems more challenging to construct self dual nmds codes than self dual mds codes the only work on construction of self dual nmds codes shows existence of q ary self dual nmds codes of length q 1 for odd prime power q or length up to 16 for some small primes q with q le 197 in this paper we make use of properties of elliptic curves to construct self dual nmds codes it turns out that as long as 2 q and n is even with 4 le n le q lfloor 2 sqrt q rfloor 2 one can construct a self dual nmds code of length n over mathbb f q furthermore for odd prime power q there exists a self dual nmds code of length n over mathbb f q if q ge 4 n 3 times n 3 2

a characterisation of oscillations in the discrete two dimensional convection diffusion equation it is well known that discrete solutions to the convection diffusion equation contain nonphysical oscillations when boundary layers are present but not resolved by the discretisation however except for one dimensional problems there is little analysis of this phenomenon in this paper we present an analysis of the two dimensional problem with constant flow aligned with the grid based on a fourier decomposition of the discrete solution for galerkin bilinear finite element discretisations we derive closed form expressions for the fourier coefficients showing them to be weighted sums of certain functions which are oscillatory when the mesh peclet number is large the oscillatory functions are determined as solutions to a set of three term recurrences and the weights are determined by the boundary conditions these expressions are then used to characterise the oscillations of the discrete solution in terms of the mesh peclet number and boundary conditions of the problem

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

an adaptive finite element method for linear elliptic problems on propose une methode adaptative d elements finis basee sur une estimation d erreur optimale de norme maxima pour les problemes elliptiques lineaires

construction of mds codes with complementary duals a linear complementary dual lcd code is a linear code with complimentary dual lcd codes have been extensively studied in literature on the other hand maximum distance separable mds codes are an important class of linear codes that have found wide applications in both theory and practice however little is known about mds codes with complimentary duals the main purpose of this paper is to construct several classes of mds codes with complimentary duals i e lcd mds codes through generalized reed solomon codes

euclidean and hermitian hulls of mds codes and their applications to eaqeccs in this paper we construct several classes of maximum distance separable mds codes via generalized reed solomon grs codes and extended grs codes where we can determine the dimensions of their euclidean hulls or hermitian hulls it turns out that the dimensions of euclidean hulls or hermitian hulls of the codes in our constructions can take all or almost all possible values as a consequence we can apply our results to entanglement assisted quantum error correcting codes eaqeccs and obtain several new families of mds eaqeccs with flexible parameters the required number of maximally entangled states of these mds eaqeccs can take all or almost all possible values moreover several new classes of q ary mds eaqeccs of length n q 1 are also obtained

an algorithm to detect small solutions in linear delay differential equations this paper presents an algorithm that provides a simple reliable mechanism for the detection of small solutions in linear delay differential equations we provide background that emphasises the importance of detecting small solutions we review existing experimental results and provide a mathematical justification for our choice of algorithm the paper concludes with some examples

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100