a new class of sequences with zero or low correlation zone based on interleaving technique by interleaving one length n perfect sequence or ideal sequence according to elaborate phases a new method of construction of zero correlation zone zcz and low correlation zone lcz sequence sets is presented the resultant sequence sets are optimal or almost optimal with respect to tang fan and matsufuji bound furthermore the new method provides flexible choice for the zcz and lcz lengths

on the characterizations of cofinite complexes over affine curves and hypersurfaces abstract let a be a homomorphic image of a gorenstein ring of finite krull dimension j an ideal of a of dimension one and n a bounded below complex of a modules suppose that a is complete with respect to a j adic topology in this paper we prove that n is a j cofinite complex if and only if h i n is a j cofinite module for all i the same result is also proved for principal ideals j consequently for the fourth question given by r hartshorne cf 6 fourth question p 149 we obtain an answer over the ring on affine curves and hypersurfaces

cofiniteness with respect to ideals of dimension one we prove that the category of modules cofinite with respect to an ideal of dimension one in a noetherian ring is a full abelian subcategory of the category of modules the proof is based on a criterion for cofiniteness with respect to an ideal of dimension one namely for such ideals it suffices that the two first ext modules in the definition for cofiniteness are finitely generated this criterion is also used to prove very simply that all local cohomology modules of a finitely generated module with respect to an ideal of dimension one in an arbitrary noetherian ring are cofinite with respect to the ideal

new families of binary sequences with low correlation for a positive integer n new families s and u of binary sequences of period 2 sup n 1 with low correlations are proposed where for some positive integer e s is defined for odd n e and u for even n e the family s has four valued correlations and is a generalization of the family of gold like sequences introduced by s boztas and p v kumar see ibid vol 40 p 532 7 1994 the family u which is also a generalization of the sequence family defined by p udaya polyphase and frequency hopping sequences obtained from finite rings ph d dissertation dept elec eng indian inst technol kanpur 1992 has six valued correlations the relationship between gold like sequences and gold sequences is the same as the relationship between the family s and the family constructed from the binary sequences partially contributed by r gold see ibid vol it 14 p 154 6 1968 t kasami see coordinated sci lab univ of illinois urbana champaign tech rep r 285 ad 632574 1966 and welch using a lifting idea no j s and kumar p v ibid vol 35 p 371 9 1989 for the families s and u families of binary sequences with the same correlation distributions and large linear span are also constructed

on the noncyclic property of sylvester hadamard matrices in this paper we are concerned with hadamard matrices with a certain noncyclic property first we show that when the first column of a sylvester hadamard matrix of order 2m m 2 a positive integer is removed the number of shift distinct row vectors in the matrix is given by 2m m then for m 4 we construct an infinite family of hadamard matrices with a property that when the first column of the hadamard matrix is removed all the row vectors of the matrix are shift distinct these hadamard matrices are useful in constructing low correlation zone sequences

global stability for two species lotka volterra systems with delay abstract in this paper a two species delayed lotka volterra system without delayed intraspecific competitions is considered it is proved that the system is globally stable for all off diagonal delays 12 21 0 if and only if the interaction matrix of the system satisfies condition wdd

cofiniteness of local cohomology modules for ideals of small dimension abstract let r be a commutative noetherian ring and let m be a non zero finitely generated r module let i be an ideal of r and t a non negative integer such that dim supp h i i m 1 for all i t it is shown that the r modules h i 0 m h i 1 m h i t 1 m are i cofinite and the r module hom r r i h i t m is finitely generated this immediately implies that if i has dimension one i e dim r i 1 then h i i m is i cofinite for all i 0 this is a generalization of the main results of delfino and marley d delfino t marley cofinite modules and local cohomology j pure appl algebra 121 1997 45 52 and yoshida k i yoshida cofiniteness of local cohomology modules for ideals of dimension one nagoya math j 147 1997 179 191 for an arbitrary noetherian ring r also we prove that if r is local and dim supp h i i m 2 for all i t then the r modules ext r j r i h i i m and hom r r i h i t m are weakly laskerian for all i t and all j 0 as a consequence it follows that the set of associated primes of h i i m is finite for all i 0 whenever dim r i 2

a class of pseudonoise sequences over gf p with low correlation zone a new class of pseudonoise sequences over gf p based on gordon mills welch 1962 sequences is constructed the sequences have the property that in a specified zone the out of phase autocorrelation and cross correlation values are all equal to 1 such sequences with low correlation zone lcz are suitable for approximately synchronized code division multiple access cdma system

global dynamics for lotka volterra systems with infinite delay and patch structure we study some aspects of the global dynamics of an n dimensional lotka volterra system with infinite delay and patch structure such as extinction persistence existence and global asymptotic stability of a positive equilibrium both the cases of an irreducible and reducible linear community matrix are considered and no restriction on the signs of the intra and inter specific delayed terms is imposed although the system is not cooperative our approach often uses comparative results with an auxiliary cooperative system some models in recent literature are generalized and results improved

threshold dynamics and ergodicity of an sirs epidemic model with markovian switching abstract this work studies the threshold dynamics and ergodicity of a stochastic sirs epidemic model with the disease transmission rate driven by a semi markov process the semi markov process used in this paper for describing a randomly changing environment is a very large extension of the most common markov regime switching process we define a basic reproduction number for the semi markov regime switching environment and show that its position with respect to 1 determines the extinction or persistence of the disease in the case of disease persistence we give mild sufficient conditions for ensuring the existence and absolute continuity of the invariant probability measure under the same conditions we also prove the global attractivity of the limit set of the system and the convergence in total variation norm of the transition probability to the invariant measure compared with the existing results in the markov regime switching environment the results generalized require almost no additional conditions

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

a stochastic model of aids and condom use in this paper we introduce stochasticity into a model of aids and condom use via the technique of parameter perturbation which is standard in stochastic population modelling we show that the model established in this paper possesses non negative solutions as desired in any population dynamics we also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system

p ary unified sequences p ary extended d form sequences with the ideal autocorrelation property in this paper for a prime number p a construction method to generate p ary d form sequences with the ideal autocorrelation property is proposed and using the ternary sequences found by helleseth kumar and martinsen 2000 ternary d form sequences with the ideal autocorrelation property are constructed by combining the methods for generating p ary extended sequences a special case of geometric sequences and p ary d form sequences a construction method of p ary unified extended d form sequences which also have the ideal autocorrelation property is proposed this is a very general class of p ary sequences including the binary and nonbinary extended sequences and the d form sequences from the ternary sequences by helleseth kumar and martinsen ternary unified sequences with the ideal autocorrelation property are also generated

new design of quaternary low correlation zone sequence sets and quaternary hadamard matrices in this correspondence we present new construction methods for quaternary low correlation zone lcz sequence sets from a binary sequence with good autocorrelation we show that the sets obtained by our methods are optimal or nearly optimal with respect to the tang fan matsufuji bound and that our construction methods are more flexible than any other previous constructions in the sense of period family size and zone size we also give a construction method for a quaternary lcz sequence set from a binary lcz sequence set finally we give a new construction method for quaternary hadamard matrices by the inverse of the gray map

unique stationary distribution and ergodicity of a stochastic logistic model with distributed delay abstract dynamics of a stochastic logistic model with distributed delay are considered we first transfer a scalar stochastic logistic model with strong kernel or weak kernel into an equivalent stochastic system through the linear chain technique then we obtain the sufficient and necessary conditions for extinction and persistence of the species with probability one moreover in the case of persistence we prove that there exists a unique stationary distribution by the markov semigroups theory the results show that the stronger white noise results in the extinction of the species and the weaker white noise guarantees the existence of a unique stationary distribution though for the deterministic model with strong kernel or weak kernel the average delay may induce the existence of a group of small amplitude periodic solutions

on a characterization of cofinite complexes theorem 1 let a be a ring which is a homomorphic image of a gorenstein ring of finite krull dimension j an ideal of a suppose that a is complete with respect to a jadic topology let n be a complex of a modules in d a where d a is the derived category consisting of complexes bounded below if the ideal j is of dimension one then the complex n is j cofinite if and only if h i n is in m a j cof for all i where m a j cof is the category of j cofinite modules see definition 3 below theorem 2 let a and n be as in theorem 1 let j be an ideal of a if j is principal up to radical then the complex n is j cofinite if and only if h i n is in m a j cof for all i

on a category of cofinite modules which is abelian let a be a noetherian local ring and i an ideal of a of dimension one our purpose of this paper is to prove that the category mathcal m a i cof of cofinite modules is abelian consequently this assertion answers affirmatively the questions given by hartshorne invent math 9 147 1970 cf sect 2 four questions and one theorem for an ideal of dimension one over a local ring

new design of low correlation zone sequence sets in this paper we present several construction methods for low correlation zone lcz sequence sets first we propose a design scheme for binary lcz sequence sets with parameters 2n 1 2 m l 2 in this scheme we can freely set the lcz length l and the resulting lcz sequence sets have the size m which is almost optimal with respect to tang fan and matsufuji bound second given a q ary lcz sequence set with parameters n m l epsi and even q we construct another q ary lcz sequence set with parameters 2n 2m l 2epsi or 2n 2m l 1 2epsi especially the new set with parameters 2n 2m l 2 can be optimal in terms of the set size if a q ary optimal lcz sequence set with parameters n m l 1 is used

binary sequences with gold like correlation but larger linear span a new construction of optimal binary sequences identical to the well known family of gold sequences in terms of maximum nontrivial correlation magnitude and family size but having larger linear span is presented the distribution of correlation values is determined for every odd integer spl tau spl ges 3 the construction provides a family that contains 2 sup spl tau 1 cyclically distinct sequences each of period 2 sup spl tau 1 the maximum nontrivial correlation magnitude equals 2 spl tau 1 sup 2 1 with one exception each of the sequences in the family has linear span at least spl tau sup 2 spl tau 2 compared to 2 spl tau for gold sequences the sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity

binary almost perfect sequence sets sequence set with lower correlation values is highly desired for engineering applications however theoretical results e g welch bound show that max n in general that is the maximum out of phase autocorrelation and cross correlation magnitudes of a sequence set is not less than the square root of the sequence period in this paper we propose a new concept namely almost perfect sequence set apss which has the property max c except for at most m shifts where c and m are predefined small integers a uniform method is presented to construct apss and then the properties of such apss are discussed moreover a distance inequality on the apss with m 1 is obtained and several apss families such as 2p 8p 2 6 4 apss and 3p 64p2 8 3 9 9 apss for any prime p 5 are constructed based on paley and paley partial sequences finally it shows that the apss can be used to construct lcz sequences and the properties of such lcz sequences are presented

stability and bifurcation analysis of a reaction diffusion equation with spatio temporal delay abstract the spatio temporal patterns of a general reaction diffusion equation with non local delay are considered by analyzing the characteristic equations and applying the complex plane theory the stability of the constant steady state and the possible hopf bifurcations are obtained with the mean delay as a bifurcation parameter the absolute stable conditional stable and unstable region can be explicitly divided by the coefficients of the term without delay and the term with non local delay by investigating the effect of any weight function on the dynamics of the system we establish the existence of spatially homogeneous and inhomogeneous bifurcating periodic solutions and the algorithm for determining the direction and stability of hopf bifurcation is derived by computing the normal form on the center manifold the result shows that for the case of strong kernel the average delay may induce the stability switches finally the theoretical results are applied to a diffusive food limited population model numerical simulations show the existence of the orbit connecting the unstable spatially inhomogeneous periodic solutions to stable spatially homogeneous periodic solutions

cofiniteness of extension functors of cofinite modules abstract let r be a commutative noetherian ring i an ideal of r and let m and n be non zero r modules it is shown that the r modules ext r i n m are i cofinite for all i 0 whenever m is i cofinite and n is finitely generated of dimension d 2 also we prove that the r modules ext r i n m are i cofinite for all i 0 whenever n is finitely generated and m is i cofinite of dimension d 1 this immediately implies that if i has dimension one i e dim r i 1 then ext r i n h i i m is i cofinite for all i 0 and all finitely generated r modules m and n also we prove that if r is local then the r modules ext r i n m are i weakly cofinite for all i 0 whenever m is i cofinite and n is finitely generated of dimension d 3 finally it is shown that the r modules ext r i n m are i weakly cofinite for all i 0 whenever r is local n is finitely generated and m is i cofinite of dimension d 2

gmw sequences corresp the difference set design of gordon mills and welch gmw is adapted for use as a pseudorandom number generator statistical properties of the generated binary sequences including periodic correlation linear span and k tuple statistics are derived one mechanization of a gmw sequence generator is suggested and the number of sequences that can be generated with a fixed number of shift register stages and read only memory rom size is evaluated

asymptotic behavior and stability of a stochastic model for aids transmission a stochastic model for aids transmission is presented in this paper the existence and uniqueness of its solution is proved and the solution belongs to an interval satisfying the actual condition furthermore the disease equilibrium can be demonstrated to be existent and both its almost surely exponential stability and its pth moment exponential stability can be concluded based on parameter analysis the first quadrant can be integrated into several parts according to the comparison between almost surely exponential stability and pth moment exponential stability and the potential meaning of the stability is further demonstrated finally based on the above theoretical analysis some conditions for aids to decrease and then to die out are obtained by computer simulation

new sets of zero or low correlation zone sequences via interleaving techniques sequence families with zero or low correlation zone can be used in the quasi synchronous code division multiple access qs cdma communication systems interleaving techniques are very useful for sequence design in this paper we present a general construction of sequence families with zero or low correlation zone using interleaving techniques and complex hadamard matrices the component sequences are perfect or ideal two level in two cases we construct the shift sequences 1 p l 2 p is even and l p 2 mod p which results in sequence families with zero or low correlation zone of parameters np mp l p where n is the period of component sequences m is the number of inequivalent shift sequences and 0 or 1 the conditions are derived under which the new construction is optimal some examples are also given to specify the new construction

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

d form sequences families of sequences with low correlation values and large linear spans large families of binary sequences with low correlation values and large linear span are critical for spread spectrum communication systems the author describes a method for constructing such families from families of homogeneous functions over finite fields satisfying certain properties he then uses this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than no sequences no 1988

new constructions of quaternary low correlation zone sequences in this paper given a composite integer n we propose a method of constructing quaternary low correlation zone lcz sequences of period 2 sup n 1 from binary sequences of the same length with ideal autocorrelation these new sequences are optimal with respect to the bound by tang fan and matsufuji the correlation distributions of these new quaternary lcz sequences constructed from m sequences and gordon mills welch gmw sequences are derived

the criteria for globally stable equilibrium in n dimensional lotka volterra systems abstract in this paper a set of sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium point in various submodels of the classic n dimensional lotka volterra system the submodels are the following systems competition cooperative or predator prey chain system and competition cooperative or predator prey model between one and multispecies the criteria in this paper are in explicit forms of the parameters and thus are easily verifiable

stability and hopf bifurcation in a model of gene expression with distributed time delays in this paper we consider the effect of distributed time delays on dynamics of a mathematical model of gene expression both the weak and strong delay kernels are discussed sufficient conditions for the local stability of the unique equilibrium are obtained taking the average delay as a bifurcation parameter we investigate the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions by using the method of multiple time scales finally numerical simulation is carried out to illustrate our theoretical results it shows both subcritical and supercritical hopf bifurcations can happen

long time behaviors of a stochastic cooperative lotka volterra system with distributed delay abstract this article focuses on a stochastic cooperative lotka volterra system with distributed delay we first transfer the stochastic system with weak kernel into a degenerate stochastic system made up of four equations for the deterministic system global stability of the positive equilibrium is investigated for the stochastic system with distributed delay sharp sufficient conditions for the persistence of two species are established what is more we obtain the existence and uniqueness of the stationary distribution by constructing suitable lyapunov function and proving the global attraction of the positive solution the results show that the weaker white noises can ensure the existence of a unique stationary distribution and the stronger white noises can result in the extinction of one or two species though the positive equilibrium is globally stable without white noises

the necessary and sufficient condition for global stability of a lotka volterra cooperative or competition system with delays abstract this paper presents the necessary and sufficient condition for the global stability of the following lotka volterra cooperative or competition system with time delays x t x t r 1 ax t x t 11 y t 12 y t y t r 2 ay t x t 21 y t 22 it is showed that the positive equilibrium of the system is globally asymptotically stable for all delays ij 0 i j 1 2 if and only if

new sets of optimal p ary low correlation zone sequences in this correspondence three methods of constructing low correlation zone lcz sequences are proposed in the first method we constructed binary lcz sequence sets of period 2n 1 using the legendre sequences of period 2m 1 as a column sequence when m n in the second method we devise a column sequence set of length 2m 1 1 from a binary sequence of period 2m 1 having ideal autocorrelation property and this column sequence set is used to construct binary lcz sequence sets of period 2 n 1 when m 1 n in the third method p ary lcz sequence sets are constructed by adopting p ary sequence of period pm 1 with ideal autocorrelation for integers n and m such that m n as a column sequence the second and third methods give us the optimal sets with respect to the bound by tang fan and matsufuji finally a construction method of pntimespn p ary hadamard matrices from optimal lcz sequence sets is proposed

new cyclic relative difference sets constructed from d homogeneous functions with difference balanced property for a prime power q we show that a cyclic relative difference set with parameters q sup n 1 q 1 q 1 q sup n 1 q sup n 2 can be constructed from a d homogeneous function from f sub q sup n spl bsol 0 onto f sub q with difference balanced property where f sub q sup n is the finite field with q sup n elements this construction method enables us to construct several new cyclic relative difference sets with parameters p sup n 1 p sup l 1 p sup l 1 p sup n l p sup n 2l from p ary sequences of period p sup n 1 with ideal autocorrelation property introduced by helleseth and gong using a lifting idea other new cyclic relative difference sets can be constructed from the helleseth gong hg sequences also the 3 ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary hg sequences and ternary lin sequences are derived

a note on low correlation zone signal sets in this correspondence we present a connection between designing low correlation zone lcz sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors this results in lcz signal sets with huge sizes over three different alphabetic sets finite field of size integer residue ring modulo and the subset in the complex field which consists of powers of a primitive th root of unity we show a connection between these sequence designs and ldquocompletely noncyclicrdquo hadamard matrices and a construction for those sequences we also provide some open problems along this direction