numerical solution of fractional differential equations with a collocation method based on muntz polynomials this paper presents a computational technique based on the collocation method and muntz polynomials for the solution of fractional differential equations an appropriate representation of the solution via the muntz polynomials reduces its numerical treatment to the solution of a system of algebraic equations the main advantage of the present method is its superior accuracy and exponential convergence consequently one can obtain good results even by using a small number of collocation points the accuracy and performance of the proposed method are examined by means of some numerical experiments

on efficient numerical approximation of the bilinear form c a 1 b let a in mathbb c n times n be a nonsingular complex matrix and b and c be complex vectors of length n the goal of this paper is to investigate approaches for efficient approximations of the bilinear form c a 1 b equivalently we wish to approximate the scalar value c x where x solves the linear system ax b here the matrix a can be very large or its elements can be too costly to compute so that a is not explicitly available and it is used only in the form of the matrix vector product therefore a direct method is not an option for a hermitian positive definite b a 1 b can be efficiently approximated as a by product of the conjugate gradient iterations which is mathematically equivalent to the matching moment approximations computed via the gauss christoffel quadrature in this paper we propose a new method using the biconjugate gradient iterations which is applicable to the general complex case the proposed approach will be compared with existing ones using analytic arguments and numerical experiments

code design for the noisy slepian wolf problem we consider a noisy slepian wolf problem where two correlated sources are separately encoded using codes of fixed rate and transmitted over two independent binary memoryless symmetric channels the capacity of each channel is characterized by a single parameter that is not known at the transmitter system performance is evaluated by computing the set of channel parameters for which the system can successfully decode this set is called the achievable channel parameter region acpr the goal is to design systems whose acprs are as large as possible the main result is the design of irregular low density parity check ldpc ensembles whose acprs are significantly larger than previous designs some previous attempts to achieve large acprs with ldpc codes failed because systematic codes were used in this work we start with systematic encoders but puncture all the systematic bits before transmission we also show that additional gains are possible using a staggered structure which enables codes optimized for single user channels to perform well under symmetric channel conditions the main analysis tool is a generic density evolution framework for the analysis of joint iterative decoding for this problem

bounds on maximum likelihood decoding performance for linear codes at low rates for a given linear code ensemble upper bounds on the error probability under maximum likelihood decoding are investigated at low rates a class of symmetric memoryless channels suitable for bhattacharyya type bounds which are particularly of importance at low rates is introduced over a symmetric channel a lower bound on the error exponent is derived for a given linear code a sufficient condition for achieving the expurgated exponent which is the best among known error exponents at low rates within a fixed discrepancy is given over a general discrete memoryless channel the same analysis provides a lower bound on the average error exponent for an ensemble of coset codes generated by a given linear code the bounding technique is extended to the case of generalized maximum likelihood decoding with erasure and list decoding options

error correcting capabilities of concatenated codes with mds outer codes on memoryless channels with maximum likelihood decoding error correcting capabilities of concatenated codes with maximum distance separable mds outer codes and time varying inner codes used on memoryless discrete channels with maximum likelihood decoding are investigated it is proved that asymptotically the gallager random coding theorem can be obtained for all rates by such codes further the expurgated coding theorem as well is proved to be valid for all rates on regular channels the latter result implies that the gilbert varshamov bound for block codes over any finite field can be obtained asymptotically for all rates by linear concatenated codes

legendre wavelets operational method for the numerical solutions of nonlinear volterra integro differential equations system in this paper legendre wavelet method is developed to approximate the solutions of system of nonlinear volterra integro differential equations the properties of legendre wavelets are first presented the properties of legendre wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved numerically by newton s method also the results obtained by present method have been compared with that of by b spline wavelet method illustrative examples have been discussed to demonstrate the validity and applicability of the present method

algebraic constructions of shannon codes for regular channels the problem of the explicit construction of encoders achieving shannon s capacity and admitting a simple decoding algorithm is considered a solution based on justesen s idea of variable concatenated codes is given for the case of a symmetric memoryless channel with an input alphabet of prime power order under the assumption that the information messages are equiprobable this construction remains good for a nonsymmetric channel provided the encoding rate is smaller than a well defined pseudocapacity in case the channel is regular it is shown that the error probability after decoding is an exponentially decreasing function of the block length for any encoding rate less than the channel capacity

sphere bound achieving coset codes and multilevel coset codes a simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array l and its error probability on an additive white gaussian noise awgn channel it is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding including certain binary lattices these codes have structure of the kind that has been found to be useful in practice capacity curves and design guidance for practical codes are given exponential error bounds for coset codes are developed generalizing poltyrev s 1994 bounds for lattices these results are based on the channel coding theorems of information theory rather than the minkowski hlawka theorem of lattice theory

numerical solutions of nonlinear two dimensional partial volterra integro differential equations by haar wavelet a non linear kernel comprising a function of partial derivatives of arbitrary order is approximated by theorem 2 in ref 12 after substituting the kernel approximation in the original equation a nonlinear system is obtained using the haar wavelet solving the nonlinear system the nonlinear two dimensional integro differential volterra equation with partial derivatives is converted to a simple equation containing partial derivatives solving this simple equation we can approximate the solution of the nonlinear two dimensional integro differential volterra equation

tight exponential analysis of universally composable privacy amplification and its applications motivated by the desirability of universal composability we analyze in terms of l1 distinguishability the task of secret key generation from a joint random variable under this secrecy criterion using the renyi entropy of order 1 s for s 0 1 we derive a new upper bound of eve s distinguishability under the application of the universal2 hash functions it is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions the result is applied to the wiretap channel model and to secret key generation distillation by public discussion

constructive codes for arbitrary discrete memoryless channels in 1982 delsarte and piret constructed a concatenated code for which the error probability decreases exponentially with the block length for a subclass of symmetric channels called regular channels in the case of arbitrary discrete memoryless channels they were not able to prove an exponential bound but one for which the error probability decreases as log n n sup spl alpha where spl alpha is related to the random coding exponent and n is the block length the present author shows that indeed the codes also satisfy the much stronger exponential bound for arbitrary discrete memoryless channels and hence are good in this sense it is also indicated that the codes are valid for the bandlimited additive gaussian noise channel

an effective scheme for solving system of fractional volterra fredholm integro differential equations based on the muntz legendre wavelets abstract in this study a class of wavelet techniques is used for finding approximate solutions of systems of fractional integro differential volterra fredholm fidvf equations based on the muntz legendre wavelets mlw for the suggested method operational matrices of the riemann liouville fractional rlf integral and caputo fractional cf derivative operators are obtained and used for converting the system of the integral equations into a system of linear or nonlinear algebraic equations using the lipschitz s condition for multivariate functions and the fixed point theorem the existence and uniqueness of the solution are shown and also convergence stability and error bound of the solution in interval 0 1 are investigated in this work at the end three examples are indicated and the results of the proposed method are compared with the first and second kind wavelet chebyshev methods

numerical solution of differential equations by using chebyshev wavelet operational matrix of integration in this paper we present operational matrix of integration omi of chebyshev wavelets basis and the product operation matrix pom of it some comparative examples are included to demonstrate the superiority of operational matrix of chebyshev wavelets to those of legendre wavelets

numerical research of nonlinear system of fractional volterra fredholm integral differential equations via block pulse functions and error analysis abstract in this study a numerical scheme for approximating the solutions of nonlinear system of fractional order volterra fredholm integral differential equations vfides has been proposed this method is based on the orthogonal functions defined over 0 1 combined with their operational matrices of integration and fractional order differentiation the main characteristic behind this approach is that it reduces such problems to a linear system of algebraic equations in addition the error analysis of the system is investigated in detail lastly several numerical examples are presented to test the effectiveness and feasibility of the given method

invariance properties of binary linear codes over a memoryless channel with discrete input this work studies certain properties of the probability density function pdf of the bit log likelihood ratio llr for binary linear block codes over a memoryless channel with discrete input and discrete or continuous output we prove that under a set of mild conditions the pdf of the bit llr of a specific bit position is independent of the transmitted codeword it is also shown that the pdf of a given bit llr when the corresponding bit takes the values of zero and one are symmetric with respect to each other reflection of one another with respect to the vertical axis for the case of channels with binary input a sufficient condition for two bit positions to have the same pdf is presented

linear codes based lossless joint source channel coding for multiple access channels a general lossless joint source channel coding jscc scheme based on linear codes and random interleavers for multiple access channels macs is presented and then analyzed in this paper by the information spectrum approach and the code spectrum approach it is shown that a linear code with a good joint spectrum can be used to establish limit approaching lossless jscc schemes for correlated general sources and general macs where the joint spectrum is a generalization of the input output weight distribution some properties of linear codes with good joint spectra are investigated a formula on the ldquodistancerdquo property of linear codes with good joint spectra is derived based on which it is further proved that the rate of any systematic codes with good joint spectra cannot be larger than the reciprocal of the corresponding alphabet cardinality and any sparse generator matrices cannot yield linear codes with good joint spectra the problem of designing arbitrary rate coding schemes is also discussed a novel idea called ldquogeneralized puncturingrdquo is proposed which makes it possible that one good low rate linear code is enough for the design of coding schemes with multiple rates finally various coding problems of macs are reviewed in a unified framework established by the code spectrum approach under which criteria and candidates of good linear codes in terms of spectrum requirements for such problems are clearly presented

application of the fractional differential transform method to fractional order integro differential equations with nonlocal boundary conditions in this paper the fractional differential transform method is developed to solve fractional integro differential equations with nonlocal boundary conditions the method is described and illustrated with numerical examples the results reveal that the method is accurate and easy to apply

adomian decomposition method for solving bvps for fourth order integro differential equations the adomian decomposition method adm is applied to solve both linear and nonlinear boundary value problems bvps for fourth order integro differential equations the numerical results obtained with minimum amount of computation or mathematics compare reasonably well with exact solutions

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

chebyshev wavelets approach for nonlinear systems of volterra integral equations in this paper a new approach for solving nonlinear systems of volterra integral equations has been proposed the method is based on chebyshev wavelets approximations the method is described and after that the error is analyzed at the end some examples are presented to illustrate the ability and simplify of the method and the results reveal the effectiveness of the technique

exponential decreasing rate of leaked information in universal random privacy amplification we derive a new upper bound for eve s information in secret key generation from a common random number without communication this bound improves on bennett s bound based on the renyi entropy of order 2 because the bound obtained here uses the renyi entropy of order 1 s for s 0 1 this bound is applied to a wire tap channel then we derive an exponential upper bound for eve s information our exponent is compared with hayashi s exponent for the additive case the bound obtained here is better the result is applied to secret key agreement by public discussion

averaging bounds for lattices and linear codes general random coding theorems for lattices are derived from the minkowski hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out a new version of the minkowski hlawka theorem itself is obtained as the limit for p spl rarr spl infin of a simple lemma for linear codes over gf p used with p level amplitude modulation the relation between the combinatorial packing of solid bodies and the information theoretic soft packing with arbitrarily small but positive overlap is illuminated the soft packing results are new when specialized to the additive white gaussian noise channel they reduce to a version of the de buda poltyrev result that spherically shaped lattice codes and a decoder that is unaware of the shaping can achieve the rate 1 2 log sub 2 p n

the bem for numerical solution of partial fractional differential equations a numerical method is presented for the solution of partial fractional differential equations fdes arising in engineering applications and in general in mathematical physics the solution procedure applies to both linear and nonlinear problems described by evolution type equations involving fractional time derivatives in bounded domains of arbitrary shape the method is based on the concept of the analog equation which in conjunction with the boundary element method bem enables the spatial discretization and converts a partial fde into a system of coupled ordinary multi term fdes then this system is solved using the numerical method for the solution of such equations developed recently by katsikadelis the method is illustrated by solving second order partial fdes and its efficiency and accuracy is validated

estimation of the bilinear form y f a x for hermitian matrices abstract for a hermitian matrix a c p p given vectors x y c p and for suitable functions f the bilinear form y f a x is estimated by extending the extrapolation method proposed by c brezinski in 1999 families of one term and two term estimates e f c and e f n k n k z respectively are derived by extrapolation of the moments of the matrix a for the positive definite case bounds for the optimal value of which leads to an efficient one term estimate in only one matrix vector product are derived for f a a 1 a formula approximating this optimal value of is specified numerical results for several matrix functions and comparisons are provided to demonstrate the effectiveness of the extrapolation method

numerical solution of nonlinear volterrafredholmhammerstein integral equations in two dimensional spaces based on block pulse functions in this paper the numerical technique based on block pulse functions bpfs has been developed to approximate the solutions of nonlinear volterrafredholmhammerstein integral equations in two dimensional spaces these functions are orthogonal and have compact support on 0 1 the proposed method reduces the integral equations to a system of nonlinear algebraic equations that can be easily solved by any numerical method also the convergence of the proposed approach is discussed furthermore in order to show the accuracy and reliability of the above mentioned algorithm the new approach is verified through some numerical examples a numerical technique based on block pulse functions is proposed two dimensional nonlinear volterrafredholmhammerstein integral equations are firstly numerically solved the proposed method is to transform the volterrafredholm integral equations into a system of algebraic equations the main characteristic behind the algorithm is operator theory