an upper bound on the aperiodic autocorrelation function for a maximal length sequence corresp the magnitude of the out of phase aperiodic autocorrelation function for a maximal length linear feedback shift register sequence of period n is at most 1 2 pi n 1 1 2 ln 4n pi previously the best upper bound was n 1 1 2 ln en

a parallel relaxation method for quadratic programming problems with interval constraints abstract optimization problems with interval constraints are encountered in various fields such as network flows and computer tomography as these problems are usually very large they are not easy to solve without taking their sparsity into account recently row action methods which originate from the classical hildreth s method for quadratic programming problems have drawn much attention since they are particularly useful for large and sparse problems various row action methods have already been proposed for optimization problems with interval constraints but they mostly belong to the class of sequential methods based on the gauss seidel and sor methods in this paper we propose a highly parallelizable method for solving those problems which may be regarded as an application of the jacobi method to the dual of the original problems we prove convergence of the algorithm and report some computational results to demonstrate its effectiveness

on the construction of binary sequence families with low correlation and large sizes in this paper we revisit a method to produce binary sequences using the most significant bit map from z4 to the binary field this method is useful for the construction of binary sequences with low correlation and large family size there may be more cases where starting with z4 could help researchers design new low correlation sequences for code division multiple access application

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

on the odd and the aperiodic correlation properties of the kasami sequences derives a new upper bound for the odd and the aperiodic correlations of binary sequences in the small kasami family the approach is based on a technique described in s litsyn and a tietavainen 1994 that is originally due to i m vinogradov 1954 an essential ingredient in this method is a good upper bound on the discrete fourier coefficients of a shifted product of a pair of sequences the author obtains an upper bound of the order o spl radic llnl for the maximal aperiodic and odd correlation magnitudes for sequences of length l

traveling waves in a delayed sir epidemic model with nonlinear incidence we study the traveling waves of a diffusive sir epidemic model with a general nonlinear incidence we obtain the threshold dynamics for spatial spread of the disease we show that c is the minimum wave speed for the existence of traveling wave solutions we establish the existence and non existence of traveling wave solutions for a diffusive sir model with a general nonlinear incidence the existence proof is shown by introducing an auxiliary system applying schauder s fixed point theorem and then a limiting argument the nonexistence proof is obtained by two sided laplace transform when the speed is less than the critical velocity numerical simulations support the theoretical results we also point out the effects of the delay and the diffusion rate of the infective individuals on the spreading speed

on the convergence of iterative methods for symmetric linear complementarity problems we prove convergence of the whole sequence generated by any of a large class of iterative algorithms for the symmetric linear complementarity problem lcp under the only hypothesis that a quadratic form associated with the lcp is bounded below on the nonnegative orthant this hypothesis holds when the matrix is strictly copositive and also when the matrix is copositive plus and the lcp is feasible the proof is based upon the linear convergence rate of the sequence of functional values of the quadratic form as a by product we obtain a decomposition result for copositive plus matrices finally we prove that the distance from the generated sequence to the solution set and the sequence itself if its limit is a locally unique solution have a linear rate of r convergence

incomplete exponential sums over galois rings with applications to some binary sequences derived from z sub 2 sup l an upper bound for the incomplete exponential sums over galois rings is derived explicitly based on the incomplete exponential sums we analyze the partial period properties of some binary sequences derived from z sub 2 sup l in detail such as the kerdock code binary sequences and the highest level sequences of primitive sequences over z sub 2 sup l the results show that the partial period distributions and the partial period independent r pattern distributions of these binary sequences are asymptotically uniform nontrivial upper bounds for the aperiodic autocorrelation of these sequences are also given

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

convergence of splitting and newton methods for complementarity problems an application of some sensitivity results this paper is concerned with two well known families of iterative methods for solving the linear and nonlinear complementarity problems for the linear complementarity problem we consider the class of matrix splitting methods and establish under a finiteness assumption on the number of solutions a necessary and sufficient condition for the convergence of the sequence of iterates produced a rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution for the nonlinear complementarity problem we establish the convergence of the newton method under the assumption of a pseudo regular solution which generalizes robinson s concept of a strongly regular solution in both instances the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

a hybrid incomplete exponential sum with application to aperiodic hamming correlation of some frequency hopping sequences in this paper an upper bound for a hybrid incomplete exponential sum over finite fields is derived this bound is then used to obtain lower and upper bounds for aperiodic hamming correlation of frequency hopping sequences based on power functions

improved convergence theorems of multisplitting methods for the linear complementarity problem in 1999 bai 1999 1 studied the convergence of the multisplitting methods for solving the large sparse linear complementarity problems lcp presented by machida et al 1995 22 when the system matrix is an h matrix in this paper based on the multisplitting methods by bai we get a weaker convergent result for solving the linear complementarity problem when the system matrix is an h matrices moreover we drew a map show that our convergence theories extend the scope of multisplitting methods by bai in applications

convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem convergence of iterates is established for a symmetric regular matrix splitting algorithm for the solution of the symmetric monotone linear complementarity problem where the subproblems are solved inexactly the notable iterate convergence recently established by luo and tseng for exact subproblem solution is extended here to inexact subproblem solution for a symmetric matrix splitting a principal application of the present result is to iterate convergence for the inexact block jacobi method for which pang and yang established convergence of a subsequence of the iterates

spreading speed and traveling waves for a multi type sis epidemic model abstract the theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi type sis epidemic model to obtain the spreading speed c and the nonexistence of traveling waves with wave speed c c then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease free and endemic equilibria for c c this shows that the spreading speed coincides with the minimum wave speed for monotone traveling waves we also give an affirmative answer to an open problem presented by rass and radcliffe l rass j radcliffe spatial deterministic epidemics math surveys monogr 102 amer math soc providence ri 2003

a generalization of the family of p ary decimated sequences with low correlation let p be a prime and n a positive integer let e pn 1 and n pn 1 e in this paper we construct a family s of e2n p ary sequences each member of s has period n and the magnitudes of correlations of members of s are upper bounded by 2 pn 2 en 1

traveling waves in a kermack mckendrick epidemic model with diffusion and latent period abstract this paper is devoted to the study of a kermack mckendrick epidemic model with diffusion and latent period we first consider the well posedness of solutions of the model furthermore using the schauder fixed point theorem and laplace transform we show that if the threshold value r 0 1 then there exists c 0 such that for every c c the model admits a traveling wave solution and if r 0 1 and c 0 or r 0 1 and c 0 c then the model admits no traveling wave solutions hence the existence and non existence of traveling wave solutions is determined completely by r 0 and the constant c is the minimum speed for the existence of traveling wave solutions of the model

generic construction of quaternary sequences of period 2n with low correlation from quaternary sequences of odd period n in this paper a simple but generic method is proposed for transforming any family of quaternary sequences with low correlation of any odd period n to another family of quaternary sequences of period 2n with low correlation as an application of the generic method to sequence family a a new optimal quaternary sequence family with length 2 2n 1 family size 2n 1 and maximal nontrivial correlation value 2 n 1 2 2 where n is an odd integer is obtained most notably unlike all the known optimal quaternary sequence families the new family has a unique property that the odd integers 1 3 and the even integers 0 2 are allocated alternatively in all the sequences

random properties of the highest level sequences of primitive sequences over z 2 sup e using the estimates of the exponential sums over galois rings we discuss the random properties of the highest level sequences spl alpha sub e 1 of primitive sequences generated by a primitive polynomial of degree n over z 2 sup e first we obtain an estimate of 0 1 distribution in one period of spl alpha sub e 1 on the other hand we give an estimate of the absolute value of the autocorrelation function c sub n h of spl alpha sub e 1 which is less than 2 sup e 1 2 sup e 1 1 spl radic 3 2 sup 2e 1 2 sup n 2 2 sup e 1 for h spl ne 0 both results show that the larger n is the more random spl alpha sub e 1 will be

upper bound for a hybrid sum over galois rings with applications to aperiodic correlation of some q ary sequences an upper bound for a hybrid exponential sum over galois rings is derived this bound is then used to obtain an upper bound for the maximum aperiodic correlation of some sequence families over galois rings the bound is of the order of spl radic qlnq where q 1 is the period of the sequences

on a class of pseudorandom sequences from elliptic curves over finite fields following the idea of xing et al we investigate a general method for constructing families of pseudorandom sequences with low correlation and large linear complexity from elliptic curves over finite fields in this correspondence with the help of the tool of exponential sums on elliptic curves we study their periods linear complexities linear complexity profiles distributions of r patterns periodic correlation partial period distributions and aperiodic correlation in detail the results show that they have nice randomness

critical traveling waves in a diffusive disease model abstract in this paper the existence of a non trivial positive and bounded critical traveling wave solution of a diffusive disease model whose reaction system has infinitely many equilibria is obtained for the first time this gives an affirmative answer to an open problem left in wang et al 2012 19 our result shows that the critical traveling wave in this model is a mix of front s component and pulse i component type

a multisplitting method for symmetric linear complementarity problems abstract over the years many methods for solving the linear complementarity problem lcp have been developed most of these methods have their origin in solving a system of linear equations in particular much attention has recently been paid on the class of iterative methods called the splitting method which is an extension of the matrix splitting method for solving a system of linear equations such as jacobi gauss seidel and sor methods furthermore as a method for solving a system of linear equations o leary and white have proposed a parallel iterative method called the multisplitting method this method makes use of a set of different splittings of the coefficient matrix which may be dealt with independently of each other the results obtained from those splitting iterations are combined to define the multisplitting iterates thus the method may be effectively implemented on multiprocessors in this paper we extend the idea of the multisplitting to the symmetric lcp in particular we establish some convergence results for the multisplitting method which generalize the corresponding convergence results for the splitting method for lcp we also report some computational results with the proposed method

existence of traveling wave solutions for influenza model with treatment abstract to investigate the spreading speed of influenza and the influence of treatment on the spreading speed a reaction diffusion influenza model with treatment is established the existence of traveling wave solutions is shown by introducing an auxiliary system and applying the schauder fixed point theorem the non existence of traveling wave solutions is proved by a two sided laplace transform which needs a new approach for the prior estimate of exponential decay of traveling wave solutions