design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

codes for iterative decoding from partial geometries this paper develops codes suitable for iterative decoding using the sum product algorithm by considering a large class of combinatorial structures known as partial geometries we are able to define classes of low density parity check ldpc codes which include several previously known families of codes as special cases the existing range of algebraic ldpc codes is limited so the new families of codes obtained by generalizing to partial geometries significantly increase the range of choice of available code lengths and rates we derive bounds on minimum distance rank and girth for all the codes from partial geometries and present constructions and performance results for the classes of partial geometries which have not previously been proposed for use with iterative decoding we show that these new codes can achieve improved error correction performance over randomly constructed ldpc codes and in some cases achieve this with a significant decrease in decoding complexity

the determinants of matrices with recursive entries abstract we prove a result concerning the evaluation of determinant of a matrix whose entries are given by certain linear inhomogeneous recurrence relations this result generalizes previous determinants evaluations due to krattenthaler neuwirth and the authors in c krattenthaler evaluations of some determinants of matrices related to the pascal triangle sem lothar combin 47 2002 19 article b47g e neuwirth treeway galton arrays and generalized pascal like determinants technical report university of vienna 2004 pp 1 16 a r moghaddamfar s m h pooya s navid salehy s nima salehy evaluating and generalizing certain determinants submitted for publication the main tool for proving our result is lu factorization of the recursive arrays introduced in c krattenthaler advanced determinant calculus a complement linear algebra appl 411 2005 68 166

on optimal performance of nonlinear energy sinks in multiple degree of freedom systems abstract we study the problem of optimizing the performance of a nonlinear spring mass damper attached to a class of multiple degree of freedom systems we aim to maximize the rate of one way energy transfer from primary system to the attachment and focus on impulsive excitation of a two degree of freedom primary system with an essentially nonlinear attachment the nonlinear attachment is shown to be able to perform as a nonlinear energy sink nes by taking away energy from the primary system irreversibly for some types of impulsive excitations using perturbation analysis and exploiting separation of time scales we perform dimensionality reduction of this strongly nonlinear system our analysis shows that efficient energy transfer to nonlinear attachment in this system occurs for initial conditions close to homoclinic orbit of the slow time scale undamped system a phenomenon that has been previously observed for the case of single degree of freedom primary systems analytical formulae for optimal parameters for given impulsive excitation input are derived generalization of this framework to systems with arbitrary number of degrees of freedom of the primary system is also discussed the performance of both linear and nonlinear optimally tuned attachments is compared while nes performance is sensitive to magnitude of the initial impulse our results show that nes performance is more robust than linear tuned mass damper to several parametric perturbations hence our work provides evidence that homoclinic orbits of the underlying hamiltonian system play a crucial role in efficient nonlinear energy transfers even in high dimensional systems and gives new insight into robustness of systems with essential nonlinearity

new constructions of quasi cyclic ldpc codes based on special classes of bibd s for the awgn and binary erasure channels this paper presents new methods for efficiently constructing encodable quasi cyclic low density parity check ldpc codes based on special balanced incomplete block designs bibds codes constructed perform well over both the additive white gaussian noise awgn and binary erasure channels with iterative decoding

the linear algebra of the generalized pascal matrix abstract this paper discusses three kinds of generalized pascal matrix and generalizes the results of r brawer and m pirovino

a unified approach to the construction of binary and nonbinary quasi cyclic ldpc codes based on finite fields a unified approach for constructing binary and nonbinary quasi cyclic ldpc codes under a single framework is presented six classes of binary and nonbinary quasi cyclic ldpc codes are constructed based on primitive elements additive subgroups and cyclic subgroups of finite fields numerical results show that the codes constructed perform well over the awgn channel with iterative decoding

asymptotic analysis of passive nonlinear suppression of aeroelastic instabilities of a rigid wing in subsonic flow we study theoretically passive suppression of aeroelastic instabilities of a rigid wing in subsonic flow with an essentially nonlinear attachment the analysis is performed by constructing a reduced order model applying complexification averaging and slow fast partition of the dynamics the resulting slow flow dynamics is then analyzed by singular perturbation we fully recover computational and experimental results for this system reported in previous works and prove the existence of trivial nontrivial stable attractors as well as relaxation oscillations in the slow flow dynamics these in turn correspond to complete partial instability suppression and periodic or quasi periodic strongly modulated responses in the full order dynamics moreover we demonstrate the existence of shilnikov bifurcations in the dynamics the analysis of the slow flow dynamics is confirmed by numerical simulations of the full order system the methodology developed in this work can be used in a predictive capacity when ap

analytic treatment of a system with a vibro impact nonlinear energy sink abstract this communication reports on an approximate analytic procedure for analysis of transient damped response in a system comprising a primary linear oscillator and vibro impact nonlinear energy sink nes multiple scale expansion reduces the problem in the first approximation to low dimensional vibro impact system with forcing and damping the latter problem yields to direct analytic approach the results computed by this way fairly correlate with direct numeric simulations the analysis takes advantage of small ratio of the nes and the primary masses but does not require the restitution coefficient to be close to unity the proposed approach paves the way for efficient design of systems with vibro impact ness

construction and encoding of qc ldpc codes using group rings quasi cyclic qc low density parity check ldpc codes which are known as qc ldpc codes have many applications due to their simple encoding implementation by the means of cyclic shift registers in this paper we construct qc ldpc codes from group rings a group ring is a free module at the same time a ring constructed in a natural way from any given ring and any given group we present a structure based on the elements of a group ring for constructing qc ldpc codes some of the previously addressed methods for constructing qc ldpc codes based on finite fields are special cases of the proposed construction method the constructed qc ldpc codes perform very well over the additive white gaussian noise channel with iterative decoding in terms of bit error probability and block error probability simulation results demonstrate that the proposed codes have competitive performance in comparison with the similar existing ldpc codes finally we propose a new encoding method for the proposed group ring based qc ldpc codes that can be implemented faster than the current encoding methods the encoding complexity of the proposed method is analyzed mathematically and indicates a significate reduction in the required number of operations even when compared to the available efficient encoding methods that have linear time and space complexities

on the automaticity of the hankel determinants of a family of automatic sequences abstract hankel determinants and automatic sequences are two classical subjects widely studied in mathematics and theoretical computer science however these two topics were considered totally independently until in 1998 when allouche peyriere wen and wen proved that all the hankel determinants of the thue morse sequence are nonzero this property allowed bugeaud to prove that the irrationality exponents of the thue morse mahler numbers are exactly 2 since then the hankel determinants of several other automatic sequences in particular the paperfolding sequence the stern sequence the period doubling sequence are studied by coons vrbik guo wu wen bugeaud fu han fokkink kraaikamp and shallit on the other hand it is known that the hankel determinants of a rational power series are ultimately zero and the hankel determinants of a quadratic power series over finite fields are ultimately periodic it is therefore natural to ask if we can obtain similar results about the hankel determinants of algebraic series in the present paper we provide a partial answer to this question by establishing the automaticity of the reduced hankel determinants modulo 2 of a family of automatic sequences as an application of our result we give upper bounds for the irrationality exponent of a family of automatic numbers

dynamics of forced system with vibro impact energy sink abstract the paper treats forced response of primary linear oscillator with vibro impact energy sink this system exhibits some features of dynamics which resemble forced systems with other types of nonlinear energy sinks such as steady state and strongly modulated responses however the differences are crucial in the system with vibro impact sink the strongly modulated response consists of randomly distributed periods of resonant and non resonant motion this salient feature allows us to identify this type of dynamic behavior as chaotic strongly modulated response csmr it is demonstrated that the csmr exists due to special structure of a slow invariant manifold sim the latter is derived in a course of a multiple scale analysis of the system in the considered system this manifold has only one stable and one unstable branch this feature defines new class of universality for the nonlinear energy sinks very different physical system with topologically similar sim the oscillator with rotational energy sink also exhibits csmrs in the system with the vibro impact sink such responses are observed even for very low level of the external forcing this feature makes such system viable for possible energy harvesting applications

on the rapid computation of various polylogarithmic constants we give algorithms for the computation of the d th digit of certain transcendental numbers in various bases these algorithms can be easily implemented multiple precision arithmetic is not needed require virtually no memory and feature run times that scale nearly linearly with the order of the digit desired they make it feasible to compute for example the billionth binary digit of log 2 or on a modest work station in a few hours run time

elliptic hypergeometric series on root systems abstract we derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems a n c n and d n in the special cases of classical and q series our approach leads to new elementary proofs of the corresponding identities

a generalized ordered bell polynomial abstract in this paper we consider a generalized ordered bell polynomial p n q defined by the following exponential generating function n 0 p n q n t n e t q q e t 1 using the method of exponential riordan arrays and orthogonal polynomials we give the jacobi continued fraction expansion of n 0 p n q t n then we get the q stieltjes moment property strong q log convexity 3 q log convexity and hankel determinants of p n q n 0

construction of quasi cyclic ldpc codes for awgn and binary erasure channels a finite field approach in the late 1950s and early 1960s finite fields were successfully used to construct linear block codes especially cyclic codes with large minimum distances for hard decision algebraic decoding such as bose chaudhuri hocquenghem bch and reed solomon rs codes this paper shows that finite fields can also be successfully used to construct algebraic low density parity check ldpc codes for iterative soft decision decoding methods of construction are presented ldpc codes constructed by these methods are quasi cyclic qc and they perform very well over the additive white gaussian noise awgn binary random and burst erasure channels with iterative decoding in terms of bit error probability block error probability error floor and rate of decoding convergence collectively particularly they have low error floors since the codes are qc they can be encoded using simple shift registers with linear complexity

construction of low density parity check codes based on balanced incomplete block designs this correspondence presents a method for constructing structured regular low density parity check ldpc codes based on a special type of combinatoric designs known as balance incomplete block designs codes constructed by this method have girths at least 6 and they perform well with iterative decoding furthermore several classes of these codes are quasi cyclic and hence their encoding can be implemented with simple feedback shift registers

hankel transform of a series reversion of a certain rational function abstract starting from a sequence v n n n 0 defined by the series reversion of a certain rational function b x we use the method based on orthogonal polynomials to give closed form evaluation of the hankel transform of sequence v n n n 0 and corresponding shifted sequences that gives a proof the conjecture by barry 4 concerning the ratio equalities connecting those terms moreover in a special case we compute lu decomposition of the hankel matrix of a shifted sequence v n n n 0 which reproves the expression for the hankel transform of that sequence

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

riordan arrays generalized narayana triangles and series reversion abstract using elements of the group of riordan arrays we define a family of generalized narayana triangles and their associated generalized catalan numbers and study their links to series reversion in particular we use lagrange inversion techniques to determine the generating functions for these generalized catalan numbers

iterative decoding of one step majority logic deductible codes based on belief propagation previously the belief propagation bp algorithm has received a lot of attention in the coding community mostly due to its near optimum decoding for low density parity check ldpc codes and its connection to turbo decoding in this paper we investigate the performance achieved by the bp algorithm for decoding one step majority logic decodable osmld codes the bp algorithm is expressed in terms of likelihood ratios rather than probabilities as conventionally presented the proposed algorithm fits better the decoding of osmld codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding ldpc codes although it has been believed that osmld codes are far inferior to ldpc codes we show that for medium code lengths say between 200 1000 bits the bp decoding of osmld codes can significantly outperform bp decoding of their equivalent ldpc codes the reasons for this behavior are elaborated

excursion processes associated with elliptic combinatorics researching elliptic analogues for equalities and formulas is a new trend in enumerative combinatorics which has followed the previous trend of studying q analogues recently schlosser proposed a lattice path model in the square lattice with a family of totally elliptic weight functions including several complex parameters and discussed an elliptic extension of the binomial theorem in the present paper we introduce a family of discrete time excursion processes on mathbb z starting from the origin and returning to the origin in a given time duration 2t associated with schlosser s elliptic combinatorics the processes are inhomogeneous both in space and time and hence expected to provide new models in non equilibrium statistical mechanics by numerical calculation we show that the maximum likelihood trajectories on the spatio temporal plane of the elliptic excursion processes and of their reduced trigonometric versions are not straight lines in general but are nontrivially curved depending on parameters we analyze asymptotic probability laws in the long term limit t rightarrow infty for a simplified trigonometric version of excursion process emergence of nontrivial curves of trajectories in a large scale of space and time from the elementary elliptic weight functions exhibits a new aspect of elliptic combinatorics

decomposition of some hankel matrices generated by the generalized rencontres polynomials abstract using the algebraic techniques of formal series we obtain a combinatorial decomposition of some matrices generated by the generalized rencontres polynomials specifically for the complete matrix and the hankel matrix we obtain an ldu decomposition r d s t where d is a diagonal matrix and r and s are two sheffer matrices then for the shifted matrices we obtain an ltu decomposition r t s t where t is a tridiagonal matrix and r and s are two sheffer matrices furthermore we give an algebraic characterization of the generalized rencontres numbers and polynomials in terms of hankel determinants finally we determine a relation between the complete matrices and the hankel matrices

sobolev orthogonal polynomials in computing of hankel determinants abstract in this paper we study closed form evaluation for some special hankel determinants arising in combinatorial analysis especially for the bidirectional number sequences we show that such problems are directly connected with the theory of quasi definite discrete sobolev orthogonal polynomials it opens a lot of procedural dilemmas which we will try to exceed a few examples deal with fibonacci numbers and power sequences will illustrate our considerations we believe that our usage of sobolev orthogonal polynomials in hankel determinant computation is quite new

permutations moments measures which combinatorial sequences correspond to moments of probability measures on the real line we present a generating function in the form of a continued fraction for a fourteenparameter family of such sequences and interpret these in terms of combinatorial statistics on the symmetric groups special cases include several classical and noncommutative probability laws along with a substantial subset of the orthogonalizing measures in the q askey scheme now given a new combinatorial interpretation in terms of elementary permutation statistics this framework further captures a variety of interesting combinatorial sequences including notably the moment sequences associated to distributions of the numbers of occurrences of classical and vincular permutation patterns of length three this connection between pattern avoidance and broader ideas in classical and noncommutative probability is among several intriguing new corollaries which generalize and unify results previously appearing in the literature while opening up new lines of inquiry the fourteen combinatorial statistics further generalize to signed and colored permutations and as an infinite family of statistics to the k arrangements permutations with k colored fixed points introduced here along with several related results and conjectures

constructions of type ii qc ldpc codes with girth eight from sidon sequence in this paper we consider the constructions of type ii quasi cyclic qc low density parity check ldpc codes with girth eight from a sidon sequence we first derive the necessary and sufficient conditions guaranteeing a girth eight type ii qc ldpc code by combining these conditions with the concept of the sidon sequence three classes of type ii qc ldpc codes are subsequently proposed with girth eight to the best of our knowledge the second and the third classes we proposed are the first series of systematic and algebraic constructions for the girth eight type ii qc ldpc codes that have rates being greater than a half and at the same time have distance upper bounds being not limited to 12 via simulations we show the promising performance of the proposed type ii qc ldpc codes with girth eight in addition a set of general bounds and explicit random constructions without using a sidon sequence are also presented for the type ii qc ldpc codes with girth six or eight we observe that the proposed codes perform better than or equally well as the random qc ldpc codes from peg and quadr congr methods while the novel codes possess both highly structured parity check matrices and very flexible choices in circulant size

binomial determinants paths and hook length formulae abstract we give a combinatorial interpretation for any minor or binomial determinant of the matrix of binomial coefficients this interpretation involves configurations of nonintersecting paths and is related to young tableaux and hook length formulae

high rate quasi cyclic low density parity check codes derived from finite affine planes this paper shows that several attractive classes of quasi cyclic qc low density parity check ldpc codes can be obtained from affine planes over finite fields one class of these consists of duals of one generator qc codes presented here for codes contained in this class are the exact minimum distance and a lower bound on the multiplicity of the minimum weight codewords further it is shown that the minimum hamming distance of a code in this class is equal to its minimum additive white gaussian noise awgn pseudoweight also discussed is a class consisting of codes from circulant permutation matrices and an explicit formula for the rank of the parity check matrix is presented for these codes additionally it is shown that each of these codes can be identified with a code constructed from a constacyclic maximum distance separable code of dimension 2 the construction is similar to the derivation of reed solomon rs based ldpc codes presented by chen and djurdjevic experimental results show that a number of high rate qc ldpc codes with excellent error performance are contained in these classes

hankel hyperdeterminants and selberg integrals we investigate the simplest class of hyperdeterminants defined by cayley in the case of hankel hypermatrices tensors of the form ai1i2 ik f i1 i2 ik it is found that many classical properties of hankel determinants can be generalized and a connection with selberg type integrals is established in particular selberg s original formula amounts to the evaluation of all hankel hyperdeterminants built from the moments of the jacobi polynomials many higher dimensional analogues of classical hankel determinants are evaluated in closed form the toeplitz case is also briefly discussed in physical terms both cases are related to the partition functions of one dimensional coulomb systems with logarithmic potential

power series expansion of a hankel determinant abstract in this article we find a power series expansion for the hankel determinant whose entries are the moments of a linear functional related to discrete semiclassical orthogonal polynomials we provide explicit formulas that allow the computation of coefficients to arbitrary order and give examples for the first few terms in the series we reinterpret these results in the context of the theory of young tableaux and schur functions and find closed form expressions for the cases corresponding to the charlier and meixner polynomials we also discuss further research directions

an algorithmic proof theory for hypergeometric ordinary and q multisum integral identities it is shown that every proper hypergeometric multisum integral identity orq identity with a fixed number of summations and or integration signs possesses a short computer constructible proof we give a fast algorithm for finding such proofs most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here we give many examples of the method including computer generated proofs of identities of mehta dyson selberg hille hardy q saalschutz and others the prospect of using the method for proving multivariate identities that involve an arbitrary number of summations integrations is discussed

macdonald denominators for affine root systems orthogonal theta functions and elliptic determinantal point processes rosengren and schlosser introduced notions of rn theta functions for the seven types of irreducible reduced affine root systems rn an 1 bn bn cn cn bcn dn n n and gave the macdonald denominator formulas we prove that if the variables of the rn theta functions are properly scaled with n they construct seven sets of biorthogonal functions each of which has a continuous parameter t 0 t with given 0 t following the standard method in random matrix theory we introduce seven types of one parameter t 0 t families of determinantal point processes in one dimension in which the correlation kernels are expressed by the biorthogonal theta functions we demonstrate that they are elliptic extensions of the classical determinantal point processes whose correlation kernels are expressed by trigonometric and rational functions in the scaling limits associated with n we obtain four types of elliptic determinantal point processes with an infinite number of points and parameter t 0 t we give new expressions for the macdonald denominators using the karlin mcgregor lindstrom gessel viennot determinants for noncolliding brownian paths and show the realization of the associated elliptic determinantal point processes as noncolliding brownian brides with a time duration t which are specified by the pinned configurations at time t 0 and t t rosengren and schlosser introduced notions of rn theta functions for the seven types of irreducible reduced affine root systems rn an 1 bn bn cn cn bcn dn n n and gave the macdonald denominator formulas we prove that if the variables of the rn theta functions are properly scaled with n they construct seven sets of biorthogonal functions each of which has a continuous parameter t 0 t with given 0 t following the standard method in random matrix theory we introduce seven types of one parameter t 0 t families of determinantal point processes in one dimension in which the correlation kernels are expressed by the biorthogonal theta functions we demonstrate that they are elliptic extensions of the classical determinantal point processes whose correlation kernels are expressed by trigonometric and rational functions in the scaling limits associated with n we obtain four types of elliptic determinantal point processes with an infinite number of points and parameter t

dynamics and energy exchanges between a linear oscillator and a nonlinear absorber with local and global potentials abstract the dynamical behavior of a two degree of freedom system made up of a linear oscillator and a coupled nonlinear energy sink with nonlinear global and local potentials is studied the nonlinear global potential of the energy sink performs direct interactions with the linear oscillator while its local potential depends only on its own behavior during vibratory energy exchanges between two oscillators a time multiple scale method around 1 1 1 resonance is used to detect slow invariant manifold of the system its equilibrium and singular points detected equilibrium points permit us to predict periodic regime s while singular points can lead the system to strongly modulated responses characterized by persistent bifurcations several possible scenarios occurring during these strongly modulated regimes are highlighted all analytical predictions are compared with those which are obtained by direct numerical integration of system equations

elliptic determinantal process of type a we introduce an elliptic extension of dyson s brownian motion model which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle using elliptic determinant evaluations related to the reduced affine root system of type a we give determinantal martingale representation dmr for the process when it is started at the configuration with equidistant spacing on the circle dmr proves that the process is determinantal and the spatio temporal correlation kernel is determined by taking temporally homogeneous limits of the present elliptic determinantal process trigonometric and hyperbolic versions of noncolliding diffusion processes are studied

multiply refined enumeration of alternating sign matrices four natural boundary statistics and two natural bulk statistics are considered for alternating sign matrices asms specifically these statistics are the positions of the 1 s in the first and last row and column of an asm and the numbers of generalized inversions and 1 s in an asm previously known results for the exact enumeration of asms with prescribed values of some of these statistics are reviewed in detail a quadratic relation which fully determines the generating function associated with all six statistics is then obtained the derivation of the relation involves combining the desnanot jacobi determinant identity with the izergin korepin formula for the partition function of the six vertex model with domain wall boundary conditions

on the matrices related to the m arithmetic triangle abstract in this paper we first introduce the m arithmetic triangle which is a generalization of pascal s triangle then we put forward some computational results on the evaluations of determinants of matrices related to it we also try to find the inverse matrix and some factorizations of this type of matrices

hankel determinants of sums of consecutive motzkin numbers abstract we use combinatorial methods to evaluate hankel determinants for the sequence of sums of consecutive t motzkin numbers more specifically we consider the following determinant det m i j r t m i j r 1 t 0 i j n 1 where t is a real number and m k t is the total weight of all paths from 0 0 to k 0 that stay above the x axis and use up and down steps of weight one and level steps of weight t

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

quasi cyclic ldpc codes an algebraic construction this paper presents two new large classes of qc ldpc codes one binary and one non binary codes in these two classes are constructed by array dispersions of row distance constrained matrices formed based on additive subgroups of finite fields experimental results show that codes constructed perform very well over the awgn channel with iterative decoding based on belief propagation codes of a subclass of the class of binary codes have large minimum distances comparable to finite geometry ldpc codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low complexity reliability based iterative decoding algorithms such as binary message passing decoding algorithms non binary codes decoded with a fast fourier transform based sum product algorithm achieve significantly large coding gains over reed solomon codes of the same lengths and rates decoded with either the hard decision berlekamp massey algorithm or the algebraic soft decision kotter vardy algorithm they have potential to replace reed solomon codes in some communication or storage systems where combinations of random and bursts of errors or erasures occur

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

some composition determinants abstract we compute several parametric determinants in which rows and columns are indexed by compositions where the entries are either products of binomial coefficients or products of powers these results generalize previous determinant evaluations due to the first and fourth author siam j matrix anal appl 23 2001 459 471 and a polynomial generalization of the power compositions determinant linear multilinear algebra in press and they prove two conjectures of the second author advanced determinant calculus a complement preliminary version

a lattice based systematic recursive construction of quasi cyclic ldpc codes this paper presents a low complexity recursive and systematic method to construct good well structured low density parity check ldpc codes the method is based on a recursive application of a partial kronecker product operation on a given gamma x q q ges 3 a prime integer lattice l gamma x q the n 1 fold product of l gamma x q by itself denoted ln gamma x q represents a regular quasi cyclic qc ldpc code denoted see pdf of high rate and girth 6 the minimum distance of see pdf is equal to that of the core code see pdf introduced by l gamma x q the support of the minimum weight codewords in see pdf are characterized by the support of the same type of codewords in see pdf from performance perspective the constructed codes compete with the pseudorandom ldpc codes

symmetry classes of alternating sign matrices under one roof in a previous article math co 9712207 we derived the alternating sign matrix asm theorem from the izergin korepin determinant for a partition function for square ice with domain wall boundary here we show that the same argument enumerates three other symmetry classes of alternating sign matrices vsasms vertically symmetric asms even htsasms half turn symmetric asms and even qtsasms quarter turn symmetric asms the vsasm enumeration was conjectured by mills the others by robbins math co 0008045 we introduce several new types of asms uasms asms with a u turn side uuasms two u turn sides osasms off diagonally symmetric asms oosasms off diagonally off antidiagonally symmetric and uosasms off diagonally symmetric with u turn sides uasms generalize vsasms while uuasms generalize vhsasms vertically and horizontally symmetric asms and another new class vhpasms vertically and horizontally perverse osasms oosasms and uosasms are related to the remaining symmetry classes of asms namely dsasms diagonally symmetric dasasms diagonally anti diagonally symmetric and tsasms totally symmetric asms we enumerate several of these new classes and we provide several 2 enumerations and 3 enumerations our main technical tool is a set of multi parameter determinant and pfaffian formulas generalizing the izergin korepin determinant for asms and the tsuchiya determinant for uasms solv int 9804010 we evaluate specializations of the determinants and pfaffians using the factor exhaustion method

addition theorems via continued fractions we show connections between a special type of addition formulas and a theorem of stieltjes and rogers we use different techniques to derive the desirable addition formulas we apply our approach to derive special addition theorems for bessel functions and confluent hypergeometric functions we also derive several additions theorems for basic hypergeometric functions applications to the evaluation of hankel determinants are also given

relaxation oscillations in r3 abstract the existence of periodic relaxation oscillations in singularly perturbed systems with two slow and one fast variable is analyzed geometrically it is shown that near a singular periodic orbit a return map can be defined which has a one dimensional slow manifold with a stable invariant foliation under a natural hyperbolicity assumption on the singular periodic orbit this allows to prove the existence of a periodic relaxation orbit for small values of the perturbation parameter additionally the existence of an invariant torus is proved for the periodically forced van der pol oscillator the analysis is based on methods from geometric singular perturbation theory the blow up method is used to analyze the dynamics near the fold curves

4 cycle free ldpc codes based on difference sets difference sets are used to give a novel method for constructing structured regular quasi cyclic low density parity check codes let fq be a field with q elements and assume that d d1 dk is a v k 1 difference set for zv with d1 d2 dk depending on v q 1 v 2dk or v 2dk 1 three code construction methods are given that produce regular 4 cycle free codes that is codes with girth at least 6 simulation results show that the constructed codes perform well over the awgn channel with an iterative sum product message passing decoding algorithm

nonintersecting paths pfaffians and plane partitions gessel and viennot have developed a powerful technique for enumerating various classes of plane partitions the purpose of this article is to show by similar means that one may use pfaffiants to enumerate configurations of nonintersecting paths in which the initial and or terminal vertices of the paths are allowed to vary over specified regions of the digraph this leads to the possibility of enumerating classes of plane partitions in which the shape is allowed to vary whereas the previous applications of gessel and viennot were largely confined to plane partitions of a given shape

decoding algorithms for nonbinary ldpc codes over gf q in this letter we address the problem of decoding nonbinary low density parity check ldpc codes over finite fields gf q with reasonable complexity and good performance in the first part of the letter we recall the original belief propagation bp decoding algorithm and its fourier domain implementation we show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding in the second part of the letter we introduce a simplified decoder which is inspired by the min sum decoder for binary ldpc codes we called this decoder extended min sum ems we show that it is possible to greatly reduce the computational complexity of the check node processing by computing approximate reliability measures with a limited number of values in a message by choosing appropriate correction factors or offsets we show that the ems decoder performance is quite good and in some cases better than the regular bp decoder the optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution our simulations on ultra sparse codes over very high order fields show that nonbinary ldpc codes are promising for applications which require low frame error rates for small or moderate codeword lengths the ems decoder is a good candidate for practical hardware implementations of such codes

exact solution of the lock step model of vicious walkers the lock step model of vicious walkers on a one dimensional lattice allows each walker at the tick of a clock to move either one lattice site to the left or one lattice site to the right the only restriction is that no two walkers may arrive at the same lattice site or pass one another in periodic boundary conditions the partition function and correlation function for this model are calculated exactly taking the continuum limit gives an exactly solvable model of vicious walkers undergoing brownian motion

targeted energy transfer in systems with non polynomial nonlinearity abstract targeted energy transfer tet in a 2dof system consisting of primary linear oscillator and nonlinear energy sink nes with non polynomial potential is investigated use of non polynomial and even non analytic potential functions is motivated by needs of practical design it is demonstrated that the complexification averaging technique of analysis developed before can be successfully extended for these cases with proper modifications the procedure is illustrated by examples involving softening non polynomial and piecewise linear non analytic nes

quasicyclic low density parity check codes from circulant permutation matrices in this correspondence the construction of low density parity check ldpc codes from circulant permutation matrices is investigated it is shown that such codes cannot have a tanner graph representation with girth larger than 12 and a relatively mild necessary and sufficient condition for the code to have a girth of 6 8 10 or 12 is derived these results suggest that families of ldpc codes with such girth values are relatively easy to obtain and consequently additional parameters such as the minimum distance or the number of redundant check sums should be considered to this end a necessary condition for the codes investigated to reach their maximum possible minimum hamming distance is proposed

some extensions of brioschi s double alternant abstract we evaluate some determinants related to brioschi s extension of the classical double alternant of cauchy and scott s extension of brioschi s

evaluation of minors associated to weighing matrices in the present paper we focus our research on calculating minors of weighing matrices of order n and weight n k denoted by w n n k we provide analytical determinant computations counting techniques for specifying the existence of certain submatrices inside a w n n k and an algorithm for computing the n j n j minors of a w n n k which is realized with the notion of symbolic manipulation these results are valid of general n the ideas presented in this work can be used as the fundamental basis on which the calculation of minors of other weighing matrices and in general of orthogonal matrices can be developed an application of the derived formulas to an interesting problem of numerical analysis the growth problem is also presented

confluent q extensions of some classical determinants abstract we evaluate two determinants the first is a q h extension of the classical confluent extension of the vandermonde determinant the second is a similar extension of cauchy s double alternant

advanced determinant calculus a complement abstract this is a complement to my previous article advanced determinant calculus c krattenthaler advanced determinant calculus seminaire lotharingien combin 42 1999 the andrews festschrift article b42q 67 pp in the present article i share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory g almkvist c krattenthaler j petersson some new formulas for experiment math 12 2003 441 456 moreover i add a list of determinant evaluations which i consider as interesting which have been found since the appearance of the previous article or which i failed to mention there including several conjectures and open problems

ruijsenaars commuting difference operators as commuting transfer matrices for belavin s elliptic quantum r matrix we construct an l operator as a set of difference operators acting on functions on the type a weight space according to the fundamental relation rll llr taking the trace of the l operator gives a set of commuting difference operators we show that for the above mentioned l operator this approach gives macdonald type operators with elliptic theta function coefficient actually equivalent to ruijsenaars operators the relationship between the difference l operator and krichever s lax matrix is given and an explicit formula for elliptic commuting differential operators is derived we also study the invariant subspace for the system which is spanned by symmetric theta functions on the weight space

matrix methods for determinants of pascal like matrices abstract using the ldu like factorization method the evaluations of the determinants of some pascal like matrices are derived the entries of these matrices satisfy the recurrence relation a i j a i 1 j a i j 1 a i 1 j 1 i j 1 and the values of the first row a 0 j and the column a i 0 have eight cases part of the results is due to c krattenthaler 2002 3

strongly modulated response in forced 2dof oscillatory system with essential mass and potential asymmetry abstract dynamic responses of a linear oscillator coupled to a nonlinear energy sink nes under harmonic forcing in the regime of 1 1 1 resonance are investigated primary attention is paid to the detailed investigation of the so called strongly modulated response smr which is not related to the fixed points of average modulation equations of the system essential mass asymmetry allows a global analysis of the responses despite strong nonlinearity it is demonstrated that the strongly modulated response is related to a relaxation type motion and its description in the limit of small mass ratio maybe reduced to the 1d return map of a subset at a fold line of slow invariant manifold the smr exists in the o e vicinity of the exact resonance where e 1 characterizes the mass asymmetry it is also shown that the smr appears in the system as a result of global fold bifurcation of limit cycles and exhibits some properties pertinent to generic 1d nonlinear maps such as period doubling transient responses with finite number of relaxation cycles and subsequent attraction to stable periodic attractor are revealed analytic results are compared to numeric simulations and a good agreement is observed

hankel continued fraction and its applications abstract the hankel determinants of a given power series f can be evaluated by using the jacobi continued fraction expansion of f however the existence of the jacobi continued fraction needs that all hankel determinants of f are nonzero we introduce hankel continued fraction whose existence and uniqueness are guaranteed without any condition for the power series f the hankel determinants can also be evaluated by using the hankel continued fraction it is well known that the continued fraction expansion of a quadratic irrational number is ultimately periodic we prove a similar result for power series if a power series f over a finite field satisfies a quadratic equation then the hankel continued fraction is ultimately periodic as an application we derive the hankel determinants of several automatic sequences in particular the regular paperfolding sequence thus we provide an automatic proof of a result obtained by guo wu and wen which was conjectured by coons vrbik

invariant algebras and major indices for classical weyl groups given a classical weyl group w that is a weyl group of type a b or d one can associate with it a polynomial with integral coefficients z w given by the ratio of the hilbert series of the invariant algebras of the natural action of w and w t on the ring of polynomials bf c x 1 ldots x n otimes t we introduce and study several statistics on the classical weyl groups of type b and d and show that they can be used to give an explicit formula for z d n more precisely we define two mahonian statistics that is statistics having the same distribution as the length function dmaj and ned on d n the statistic dmaj defined in a combinatorial way has an analogous algebraic meaning to the major index for the symmetric group and the flag major index of adin and roichman for b n namely it allows us to find an explicit formula for z d n our proof is based on the theory of t partite partitions introduced by gordon and further studied by garsia and gessel using similar ideas we define the mahonian statistic ned also on b n and we find a new and simpler proof of the adin roichman formula for z b n finally we define a new descent number ddes on d n so that the pair ddes dmaj gives a generalization to d n of the carlitz identity on the eulerian mahonian distribution of descent number and major index on the symmetric group

descent representations and multivariate statistics combinatorial identities on weyl groups of types a and b are derived from special bases of the corresponding coinvariant algebras using the garsia stanton descent basis of the coinvariant algebra of type a we give a new construction of the solomon descent representations an extension of the descent basis to type b using new multivariate statistics on the group yields a refinement of the descent representations these constructions are then applied to refine well known decomposition rules of the coinvariant algebra and to generalize various identities