collocation software for boundary value differential algebraic equations we describe the methods and implementation of a general purpose code coldae this code can solve boundary value problems for nonlinear systems of semi explicit differential algebraic equations daes of index at most 2 fully implicit index 1 boundary value dae problems can be handled as well the code coldae is an extension of the package colnew colsys for solving boundary value odes the implemented method is piecewise polynomial collocation at gaussian points extended as needed by the projection method of ascher petzold for general semi explicit index 2 problems as well as for fully implicit index 1 problems we define a em selective projected collocation method and demonstrate its use the mesh selection procedure of colsys is modified for the case of index 2 constraints we also discuss shooting for initial guesses the power and generality of the code are demonstrated by examples

a generalized euclidean algorithm for multisequence shift register synthesis the problem of finding a linear feedback shift register of shortest length capable of generating prescribed multiple sequences is considered a generalized euclidean algorithm which is based on a generalized polynomial division algorithm is presented a necessary and sufficient condition for the uniqueness of the solution is given when the solution is not unique the set of all possible solutions is also derived it is shown that the algorithm can be applied to the decoding of many cyclic codes for which multiple syndrome sequences are available when it is applied to the case of a single sequence the algorithm reduces to that introduced by y sugiyama et al inf control vol 27 p 87 9 feb 1975 in the decoding of bch codes

pseudospectral method for numerical solution of daes with an error estimation in e babolian m m hosseini reducing index and pseudospectral methods for differential algebraic equations appl math comput 140 2003 77 90 numerical solution of linear differential algebraic equations daes has been presented by pseudospectral method in this paper a new error estimation technique is proposed to pseudospectral method such that is well done for linear semi explicit daes when the daes has index 2 the obtained approximate solution can be improved by using the proposed error estimation technique furthermore with providing some examples the proposed error estimation method is dealt with numerically

applications of differential transform method to differential algebraic equations in this paper numerical solution of linear differential algebraic equations daes is considered by differential transform method two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions differential transform method can easily be applied to daes and series solutions are obtained after the transformation here we have formulated series coefficients very simply for the considered problems

sequential regularization methods for nonlinear higher index daes sequential regularization methods relate to a combination of stabilization methods and the usual penalty method for differential equations with algebraic equality constraints this paper extends an earlier work siam j numer anal 33 1996 pp 1921 1940 to nonlinear problems and to differential algebraic equations daes with an index higher than 2 rather than having one winning method this is a class of methods from which a number of variants are singled out as being particularly effective methods in certain circumstances we propose sequential regularization methods for index 2 and index 3 daes both with and without constraint singularities in the case of no constraint singularity we prove convergence results numerical experiments confirm our theoretical predictions and demonstrate the viability of the proposed methods the examples include constrained multibody systems

reducing index method for differential algebraic equations with constraint singularities this paper extends an earlier work appl math comput 140 2003 77 to differential algebraic equations with constraint singularities numerical solution of these problems is considered by pseudospectral method with domain decomposition and by giving a condition under which the general linear form problem can easily be transformed to the index reduced form by a simple formulation furthermore with providing some examples the aforementioned cases are dealt with numerically

a modified spectral method for numerical solution of ordinary differential equations with non analytic solution in this article there is an attempt to introduce generally spectral methods for numerical solution of ordinary differential equations also to focus on those problems in which some coefficient functions or solution function is not analytic then by expressing weak and strong aspects of spectral methods to solve this kind of problems a modified spectral method which is more efficient than other spectral methods is suggested furthermore with providing some examples the aforementioned cases are dealt with numerically

adomian decomposition method for solution of differential algebraic equations solutions of differential algebraic equations is considered by adomian decomposition method in e babolian m m hosseini reducing index and spectral methods for differential algebraic equations j appl math comput 140 2003 77 and m m hosseini an index reduction method for linear hessenberg systems j appl math comput in press an efficient technique to reduce index of semi explicit differential algebraic equations has been presented in this paper adomian decomposition method is applied to reduced index problems the scheme is tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

a generalization of the berlekamp massey algorithm for multisequence shift register synthesis with applications to decoding cyclic codes a generalization of the berlekamp massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences a more general problem is first considered that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field which includes the multisequence problem as a special case a simple iterative algorithm the fundamental iterative algorithm fia is presented for solving this problem the generalized algorithm is then derived through a refinement of the fia application of this generalized algorithm to decoding cyclic codes up to the hartmann tzeng ht bound and roos bound making use of multiple syndrome sequences is considered conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error locator polynomial are determined with respect to decoding up to the ht bound and special cases of the roos bound

projected implicit runge kutta methods for differential algebraic equations in this paper a new class of numerical methods projected implicit runge kutta methods is introduced for the solution of index 2 hessenberg systems of initial and boundary value differential algebraic equations daes these types of systems arise in a variety of applications including the modeling of singular optimal control problems and parameter estimation for differential algebraic equations such as multibody systems the new methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for linear problems we define an essential underlying boundary value ode and prove well conditioning of the differential or state space solutio

on the linear complexity of some new q ary sequences some new q ary sequences with period q 3 e k 1 q p m p an odd prime m e k integers are first constructed and then inspired by antweiler s method their linear complexity is examined the exact value of linear complexity k 6e w is determined when email protected i 1 wp e i furthermore an upper bound of the linear complexity is given for the other values of r our results show that this sequence has larger linear span than gmw sequence with the same parameters finally the results of a maple program are included to illustrate the validity of the results

reducing index and pseudospectral methods for differential algebraic equations in this paper numerical solution of linear differential algebraic equations is considered by pseudospectral method also an index reduction technique for them is suggested for hessenberg index 2 system the index reduction technique is defined and its use is demonstrated we give a condition under which the general linear form problem can be easily transformed to the index reduced form by a simple formulation furthermore with providing some examples the aforementioned cases are dealt with numerically

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

observability of permutations and stream ciphers we study the observability of a permutation on a finite set by a complex valued function the analysis is done in terms of the spectral theory of the unitary operator on functions defined by the permutation any function f can be written uniquely as a sum of eigenfunctions of this operator we call these eigenfunctions the eigencomponents of f it is shown that a function observes the permutation if and only if its eigencomponents separate points and if and only if the function has no nontrivial symmetry that preserves the dynamics some more technical conditions are discussed an application to the security of stream ciphers is discussed

stability of computational methods for constrained dynamics systems many methods have been proposed for numerically integrating the differential algebraic systems arising from the euler lagrange equations for constrained motion these are based on various problem formulations and discretizations we offer a critical evaluation of these methods from the standpoint of stability nconsidering a linear model we first give conditions under which the differential algebraic problem is well conditioned this involves the concept of an essential underlying ode we review a variety of reformulations which have been proposed in the literature and show that most of them preserve the well conditioning of the original problem then we consider stiff and nonstiff discretizations of such reformulated models in some cases the same implicit discretization may behave in a very different way when applied to different problem formulations acting as a stiff integrator on some formulations and as a nonstiff integrator on others we present the approach of projected invariants as a method for yielding problem reformulations which are desirable in this sense

wg a family of stream ciphers with designed randomness properties in this paper we present a family of stream ciphers which generate a keystream with ideal two level autocorrelation the design also guarantees other randomness properties i e balance long period ideal tuple distribution and high and exact linear complexity we discuss how these properties are achieved by the proposed design and show how to select various parameters to obtain an efficient stream cipher for the desired security level we also show that the proposed generators are secure against time memory data tradeoff attacks algebraic attacks and correlation attacks finally we present wg 128 as a concrete example of a wg stream cipher with a key size of 128bits

ode methods for the solution of differential algebraic systems in this paper we study the numerical solution of the differential algebraic systems f t y y 0 many of these systems can be solved conveniently and economically using a range of ode methods others can be solved only by a small subset of ode methods and still others present insurmountable difficulty for all current ode methods we examine the first two groups of problems and indicate which methods we believe to be best for them then we explore the properties of the third group which cause the methods to fail we describe a reduction technique which allows systems to be reduced to ones that can be solved it also provides a tool for the analytical study of the structure of systems

a modified pseudospectral method for numerical solution of ordinary differential equations systems in this paper numerical solution of first order systems of ordinary differential equations odes is considered and an error estimation method is proposed by this method the efficiency of pseudospectral method to solve the systems is determined and a modified pseudospectral method is presented furthermore with providing some examples the aforementioned cases are dealt with numerically

what is the weakest topology in which feedback stability is robust mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations the space of systems with transfer functions in for example has many advantages mathematically but includes large classes of non physical systems and one must be careful in drawing inferences from results in that setting similarly the graph topology has long been known to be the weakest or coarsest topology in which 1 feedback stability is a robust property i e preserved in small neighbourhoods and 2 the map from open to closed loop transfer functions is continuous however it is not known whether continuity is a necessary part of this statement or only required for the existing proofs it is entirely possible that the answer depends on the underlying classes of systems used the class of systems we concern ourselves with here is the set of systems that can be approximated in the graph topology by real rational transfer function matrices that is lumped parameter

differential transform method applied to high index differential algebraic equations abstract in ayaz 2004 f ayaz applications of differential transform method to differential algebraic equations appl math comput 152 2004 649 657 numerical solution of linear differential algebraic equations daes is considered by differential transform method two index 1 daes have been solved by using the method and the numerical solutions coincide with the exact solution very well in this paper high index daes are considered index 2 daes can be done in a similar way a counter example is proposed to explain that the method is not suitable for all index 3 daes

sequential regularization methods for higher index daes with constraint singularities the linear index 2 case standard stabilization techniques for higher index differential algebraic equations daes often involve elimination of the algebraic solution components this may not work well if there are singularity points where the constraint jacobian matrix becomes rank deficient this paper proposes instead a sequential regularization method srm a functional iteration procedure for solving problems with isolated singularities which have smooth differential solution components for linear index 2 daes we consider both initial value problems ivps and boundary value problems bvps the convergence of the srm is described and proved in detail we believe that this is the first convergence proof for any method for daes with this type of constraint singularities moreover the regularization parameter in our method is not necessarily very small so the srm is an important improvement over usual regularization methods various aspects of the subsequent numerical discretization of the regularized problems are discussed as well and some numerical verifications are carried out

utilization of automatic differentiation in control algorithms symbolic languages are increasingly being used in the analysis and implementation of control algorithms many of these control procedures involve some type of differentiation or jacobian formulation automatic differentiation provides an alternative means of computing this information which is rarely considered in the control literature this correspondence discusses the use of automatic differentiation numerical results comparing the use of automatic differentiation and symbolic approaches in the context of a particular nonlinear control system are given

numerical solutions of linear time varying descriptor systems via hybrid functions state analysis of linear time varying descriptor systems via hybrid functions are proposed in this paper based upon some useful properties of hybrid functions a special product matrix and a related coefficient matrix are applied to solve the descriptor systems the unknown coefficient matrix will be in generalized lyapunov equation form which is solved via the kronecker product method the advantages of hybrid functions are not only the values of n and m are adjustable but also it can yield more accurate numerical solutions than orthogonal functions and orthogonal polynomials to the problems of solving the descriptor systems we propose that the available optimal values of n and m can minimize the relative errors in the numerical solutions the high accuracy and the wide applicability of hybrid function approach will be demonstrated with numerical examples

studies on the distribution of the shortest linear recurring sequences the distribution of the shortest linear recurrence slr sequences in the z p field and over the z p e ring is studied it is found that the length of the shortest linear recurrent slrl is always equal to n 2 if n is even and n 2 1 if n is odd in the z p field respectively on the other hand over the z p e ring the number of sequences with length n can also be calculated the recurring distribution regulation of the shortest linear recurring sequences is also found to solve the problem of calculating the slrl a new simple representation of the berlekamp massey algorithm is developed as well

an index reduction method for linear hessenberg systems in e babolian m m hosseini reducing index and pseudospectral methods for differential algebraic equations appl math comput 140 2003 77 90 a reducing index method has been proposed for some cases of semi explicit daes differential algebraic equations in this paper this method is generalized to more cases also it is focused on hessenberg index 2 systems and proposed reduction index method will be illustrated for this problem the hessenberg system and its obtained reduced index system are numerically solved through pseudospectral method in addition aforementioned methods will be considered by one example

numerical solution of linear differential algebraic equations in appl math comput 140 2003 77 and appl math comput in press a reducing and modified reducing index methods have been proposed for some cases of semi explicit daes differential algebraic equations in this paper these methods are generalized to more cases also numerical implementation of generalized methods will be presented through pseudospectral method with domain decomposition in addition aforementioned methods will be considered by some examples

approximation and stabilization of distributed systems by lumped systems in this note we study two questions regarding linear time invariant distributed systems namely 1 when can the given system be approximated by a lumped system 2 when can the given system be stabilized by a lumped system in each case we obtain a complete answer to the question in terms of the behaviour of the purely atomic parts of the stable numerator and denominator of the plant

fast s box security mechanism research based on the polymorphic cipher in this study we propose a new design method for fast s box construction its security is dependent upon the length of pseudorandom numbers generated by two communication parties as the s box is being built we demonstrate that boolean functions play an important role in the design of both block and stream ciphers to satisfy a variety of cryptographic test methods such as strict avalanche criterion sac bit independence criterion bic and nonlinearity we apply polymorphic cipher pmc theory to the permutation function construction correlations among the test criteria in a real network environment are also evaluated