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

signal space characterization of iterative decoding by tracing the flow of computations in the iterative decoders for low density parity check codes we formulate a signal space view for a finite number of iterations in a finite length code on a gaussian channel maximum a posteriori map codeword decoding or maximum likelihood decoding decodes to the codeword signal that is closest to the channel output in euclidean distance in contrast we show that iterative decoding decodes to the pseudosignal that has highest correlation with the channel output the set of pseudosignals corresponds to pseudocodewords only a vanishingly small number of which correspond to codewords we show that some pseudocodewords cause decoding errors but that there are also pseudocodewords that frequently correct the deleterious effects of other pseudocodewords

the ordinary successive approximations method and pade approximants for solving a differential equation with variant retarded argument the aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument x t a t x t t t f t x t f t l 0 0 0

design of irregular ldpc codes with optimized performance complexity tradeoff the optimal performance complexity tradeoff for error correcting codes at rates strictly below the shannon limit is a central question in coding theory this paper proposes a numerical approach for the minimization of decoding complexity for long block length irregular low density parity check ldpc codes the proposed design methodology is applicable to any binary input memoryless symmetric channel and any iterative message passing decoding algorithm with a parallel update schedule a key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence this paper shows that the proposed complexity measure can be accurately estimated from a density evolution and extrinsic information transfer chart analysis of the code a sufficient condition is presented for convexity of the complexity measure in the variable edge degree distribution when it is not satisfied numerical experiments nevertheless suggest that the local minimum is unique the results presented herein show that when the decoding complexity is constrained the complexity optimized codes significantly outperform threshold optimized codes at long block lengths within the ensemble of irregular codes

multichain markov decision processes with a sample path constraint a decomposition approach we consider finite state finite action markov decision processes which accumulate both a reward and a cost at each decision epoch we study the problem of finding a policy that maximizes the expected long run average reward subject to the constraint that the long run average cost be no greater than a given value with probability one we establish that if there exists a policy that meets the constraint then there exists an e optimal stationary policy furthermore an algorithm is outlined to locate the e optimal stationary policy the proof of the result hinges on a decomposition of the state space into maximal recurrent classes and a set of transient states

numerical solution of differential algebraic equation systems and applications in this paper the method is developed to differential algebraic equations systems more effective method is presented and illustrated by numerical example the solution for a differential algebraic equation can be expanded up to arbitrary order using maple computer algebra systems first we calculate power series of the given equations system then transform it into pade series form which give an arbitrary order for solving differential algebraic equation numerically

asymptotic enumeration methods for analyzing ldpc codes we show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low density parity check ldpc codes in particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular ldpc code ensembles we then consider the binary erasure channel bec using these estimates we derive lower bounds on the error exponent under iterative decoding of ldpc codes used over the bec both regular and irregular code structures are considered these bounds are compared to the corresponding bounds when optimal maximum likelihood ml decoding is applied

on the numerical solution of chemical differential algebraic equations by pade series in this paper the solution of chemical differential algebraic equation model of general type f y y x 0 has been done using the method the example including a model of an absorption tower is given to illustrate the utility of the method using maple computer algebra systems

numerical solutions of chemical differential algebraic equations in this paper the solution for a chemical differential algebraic equation dae can be expanded up to arbitrary order using maple computer algebra systems first we calculate power series of the given equations system then transform it into pade series form which give an arbitrary order for solving chemical dae numerically

an algorithm for solving daes with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving differential algebraic equation systems was established and a new maple procedures mainproc was established too ten examples are presented to illustrate the implementation of the program

pryce pre analysis adapted to some dae solvers abstract the ode solver hbt 12 5 of order 12 t nguyen ba h hao h yagoub r vaillancourt one step 5 stage hermite birkho taylor ode solver of order 12 appl math comput 211 2009 313 328 doi 10 1016 j amc 2009 01 043 which combines a taylor series method of order 9 with a runge kutta method of order 4 is expanded into the dae solver hbt 12 5dae of order 12 dormand prince s dp 8 7 13m is also expanded into the dae solver dp 8 7 dae pryce structural pre analysis extended odes and ode first order forms are adapted to these dae solvers with a stepsize control based on local error estimators and a modified pryce algorithm to advance integration hbt 12 5dae uses only the first nine derivatives of the unknown variables as opposed to the first 12 derivatives used by the taylor series method t12dae of order 12 numerical results show the advantage of hbt 12 5dae over t12dae dp 8 7 dae and other known dae solvers

finite length analysis of low density parity check codes on the binary erasure channel in this paper we are concerned with the finite length analysis of low density parity check ldpc codes when used over the binary erasure channel bec the main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of ldpc codes when decoded iteratively we also give expressions for upper bounds on the average bit and block erasure probability for regular ldpc ensembles and the standard random ensemble under maximum likelihood ml decoding finally we present what we consider to be the most important open problems in this area

communicating zero sum product stochastic games abstract we study two classes of zero sum stochastic games with compact action sets and a finite product state space these two classes assume a communication property on the state spaces of the players for strongly communicating on one side games we prove the existence of the uniform value for weakly communicating on both sides games we prove that the asymptotic value and therefore the uniform value may fail to exist

arbitrary order numerical method for solving differential algebraic equation by pade series in this paper the solution for a differential algebraic equation can be expanded up to arbitrary order using maple computer algebra systems maple v crc press boca raton fl 33431 1996 first we calculate power series of the given equations system then transform it into pade series form which give an arbitrary order for solving differential algebraic equation numerically

constructing ldpc codes by error minimization progressive edge growth a novel approach to constructing tanner graphs using progressive edge growth peg is introduced it yields ldpc codes providing minimized block error probability in binary erasure channels bec the constructed codes exhibit superior performance over codes generated by previously known algorithms both for bec and awgn channels furthermore an upper bound on the expected block error probability in the error floor region of the generated codes is derived this allows analytical prediction of the codes error floor performance finally the method is generalized for generating simple in implementation ldpc codes based on lifted graphs

regular and irregular progressive edge growth tanner graphs we propose a general method for constructing tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge by edge manner called progressive edge growth peg algorithm lower bounds on the girth of peg tanner graphs and on the minimum distance of the resulting low density parity check ldpc codes are derived in terms of parameters of the graphs simple variations of the peg algorithm can also be applied to generate linear time encodeable ldpc codes regular and irregular ldpc codes using peg tanner graphs and allowing symbol nodes to take values over gf q q 2 are investigated simulation results show that the peg algorithm is a powerful algorithm to generate good short block length ldpc codes

a tauberian theorem for nonexpansive operators and applications to zero sum stochastic games we prove a tauberian theorem for nonexpansive operators and apply it to the model of zero sum stochastic game under mild assumptions we prove that the value of the discounted game converges uniformly when goes to zero if and only if the value of the n stage game converges uniformly when n goes to infinity this generalizes the tauberian theorem of lehrer and sorin lehrer e sorin s 1992 a uniform tauberian theorem in dynamic programming math oper res 17 2 303 307 to the two player zero sum case we also provide the first example of a stochastic game with public signals on the state and perfect observation of actions with finite state space signal sets and action sets in which for some initial state known by both players the value of the discounted game and the value of the n stage game starting at that initial state converge to distinct limits

asymptotic spectra of trapping sets in regular and irregular ldpc code ensembles we evaluate the asymptotic normalized average distributions of a class of combinatorial configurations in random regular and irregular binary low density parity check ldpc code ensembles among the configurations considered are trapping and stopping sets these sets represent subsets of variable nodes in the tanner graph of a code that play an important role in determining the height and point of onset of the error floor in its performance curve the techniques used for deriving the spectra include large deviations theory and statistical methods for enumerating binary matrices with prescribed row and column sums these techniques can also be applied in a setting that involves more general structural entities such as subcodes and or minimal codewords that are known to characterize other important properties of soft decision decoders of linear block codes

a new approach to the electrostatic pull in instability of nanocantilever actuators using the adm pade technique in this paper the adomian decomposition method and pade approximants are integrated to study the deflection and pull in instability of nanocantilever electromechanical switches in a distributed parameter model intermolecular forces including casimir forces are taken into account considering their range of application a closed form power series solution based on adomian polynomials is obtained the obtained analytic results are compared with numerical solution the adomian method is accurate for small deflections but the results of a pull in instability study demonstrate that the accuracy of the adomian solution is not as good for small deflections thus to increase the accuracy of the adomian solution for the pull in instability the adomian power series is converted to pade approximants the results of the present method are compared with the numerical results as well as those of the adomian decomposition method and other methods reported in the literature the results obtained using the adm pade are remarkably accurate compared with the numerical results the proposed technique can be easily extended to solve a wide range of instability problems finally the minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular attractions which is an important parameter for the pull in instability of a nanocantilever actuator are calculated using adomian pade approximants

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

on the numerical solution of stiff systems abstract in this paper we use power series method to solve stiff ordinary differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one theoretical considerations has been discussed and some examples were presented to show the ability of the method for linear and nonlinear systems of differential equations we use maple computer algebra systems for numerical calculations g frank maple v crc press inc florida 1996

pseudocodewords of tanner graphs this paper presents a detailed analysis of pseudocodewords of tanner graphs pseudocodewords arising on the iterative decoder s computation tree are distinguished from pseudocodewords arising on finite degree lifts lower bounds on the minimum pseudocodeword weight are presented for the bec bsc and awgn channel some structural properties of pseudocodewords are examined and pseudocodewords and graph properties that are potentially problematic with min sum iterative decoding are identified an upper bound on the minimum degree lift needed to realize a particular irreducible lift realizable pseudocodeword is given in terms of its maximal component and it is shown that all irreducible lift realizable pseudocodewords have components upper bounded by a finite value t that is dependent on the graph structure examples and different tanner graph representations of individual codes are examined and the resulting pseudocodeword distributions and iterative decoding performances are analyzed the results obtained provide some insights in relating the structure of the tanner graph to the pseudocodeword distribution and suggest ways of designing tanner graphs with good minimum pseudocodeword weight

improved low density parity check codes using irregular graphs we construct new families of error correcting codes based on gallager s 1973 low density parity check codes we improve on gallager s results by introducing irregular parity check matrices and a new rigorous analysis of hard decision decoding of these codes we also provide efficient methods for finding good irregular structures for such decoding algorithms our rigorous analysis based on martingales our methodology for constructing good irregular codes and the demonstration that irregular structure improves performance constitute key points of our contribution we also consider irregular codes under belief propagation we report the results of experiments testing the efficacy of irregular codes on both binary symmetric and gaussian channels for example using belief propagation for rate 1 4 codes on 16000 bits over a binary symmetric channel previous low density parity check codes can correct up to approximately 16 errors while our codes correct over 17 in some cases our results come very close to reported results for turbo codes suggesting that variations of irregular low density parity check codes may be able to match or beat turbo code performance