on the avoidance of cancellations in the matrix moment problem completes a line of argument begun in an earlier paper see ibid vol 4 p 835 1978 which shows that avoidance of the cancellations that destroy the stability of the standard solutions of the matrix moment problem is possible and that it leads naturally to the lanczos method

asymptotically autonomous semiflows chain recurrence and lyapunov functions from the work of c conley it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set here we improve a result of l markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow in the special case that there is a lyapunov function for the limiting semiflow sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the lyapunov function

solving the general truncated moment problem by the r generalized fibonacci sequences method we give in this paper a new method for solving the generalized truncated power moment problem to this aim we use r generalized fibonacci sequences and their associated minimal polynomials we provide an algorithm of construction of solutions in a short method this method allows us to avoid any appeal to hankel matrices or any positive difiniteness conditions as in flessas burton whitehead fbw approach examples and general cases are discussed

attractors in coherent systems of differential equations abstract attractors of cooperative dynamical systems are particularly simple for example a nontrivial periodic orbit cannot be an attractor and orbits are nowhere dense this paper provides characterizations of attractors for the wider class of coherent systems defined by the property that all directed feedback loops are positive several new results for cooperative systems are obtained in the process connections with biological models are discussed

convergence on cooperative cascade systems with length one abstract motivated by the open problems on the generic convergence of cooperative systems without the assumption of irreducibility independently proposed by smith and sontag this paper investigates the generic convergence for the solutions of cooperative cascade systems with length one first by fixing a solution of a base system converging to an equilibrium we establish both the nonordering of limit sets and the limit set dichotomy for the solutions of the cascade system combining these tools with the idea of limiting equation we then prove the sequential limit set trichotomy and hence the quasiconvergence in generic meaning the generic convergent result is finally obtained by improving the limit set dichotomy

ordering kinetics in quasi one dimensional ising like systems we present results of a monte carlo simulation of the kinetics of ordering in the two dimensional nearest neighbor ising model in anl xm geometry with two free boundaries of length m l this model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthl we follow the ordering kinetics after quenches to temperatures 0 25 t tc 1 starting from a random initial configuration at a coverage of 0 5 in the corresponding lattice gas picture the systems evolve in time according to a glauber kinetics with nonconserved order parameter the equilibrium structure is given by a one dimensional sequence of ordered domains the ordering process evolves from a short initial two dimensional ordering process through a crossover region to a quasi one dimensional behavior the whole process is diffusive inverse half width of the structure factor peak 1 q t in contrast to a model proposed by kawasakiet al where an intermediate logarithmic growth law is expected all results are completely describable in the picture of an annihilating random walk arw of domain walls

statistical description of contact interacting brownian walkers on the line the distribution of interval lengths between brownian walkers on the line is investigated the walkers are independent until collision at collision the left walker disappears and the right walker survives with probability p this problem arises in the context of diffusion limited reactions and also in the scaling limit of the voter model a systematic expansion in correlation between neighbor intervals gives a series of approximations of increasing accuracy for the probability density functions of interval lengths the first approximation beyond mere statistical independence between successive intervals already gives excellent results as established by comparison with direct numerical simulations

finite size scaling of the time dependent structure factor in the one dimensional glauber model abstract we study the time dependent structure factor of the one dimensional glauber model upon instantaneous cooling results obtained earlier by reiss mazenko and widom and bray are linked together next finite size scaling in the limit of zero temperature long times small wave vectors and large systems is established the scaling function is compared with numerical simulation results obtained by vinals and jasnow in the case of a two dimensional glauber model quenched into the region of phase separation

maximum entropy in the generalized moment problem the generalized moment problem in the framework of the maximum entropy approach is considered a proof for the existence conditions of the solution is provided

exact exponent for the number of persistent spins in the zero temperature dynamics of the one dimensional potts model for the zero temperature glauber dynamics of theq state potts model the fractionr q t of spins which never flip up to timet decays like a power lawr q t t q when the initial condition is random by mapping the problem onto an exactly soluble one species coagulation model a a a or alternatively by transforming the problem into a free fermion model we obtain the exact expression of q for all values ofq the exponent q is in general irrational 3 0 53795082 4 0 63151575 with the exception ofq 2 andq for which 2 3 8 and 1

model of cluster growth and phase separation exact results in one dimension we present exact results for a lattice model of cluster growth in one dimension the growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable phase 1 regions by overturning the unstable phase 1 spins with probabilityp for cluster coarsening at phase coexistence p 0 the conventional structure factor scaling applies in this limit our model falls in the class of diffusion limited reactions a a inert the 1 cluster size grows diffusively t and the two point correlation function obeys scaling however forp 0 i e for the dynamics of formation of stable phase from unstable phase we find that structure factor scaling breaks down the length scale associated with the size of the growing 1 clusters reflects only the short distance properties of the two point correlations

finite size scaling studies of one dimensional reaction diffusion systems part i analytical results we consider two single species reaction diffusion models on one dimensional lattices of lengthl the coagulation decoagulation model and the annihilation model for the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions this system of differential equations grows quadratically withl in the latter case the equations are solved analytically and exact expressions for the concentration are derived we investigate the finite size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions we show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions a similarity transformation between the two models is derived and used to connect the corresponding scaling functions

the dynamics of defect ensembles in one dimensional cellular automata we investigate the dynamics of ensembles of diffusive defects in one dimensional deterministic cellular automata the work builds on earlier results on individual random walks in cellular automata here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied their equilibrium behavior is also characterized the design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis

recursive procedures for measuring disorder in non periodic sequences abstract recursive procedures are found for calculating the kth order entropy of non periodic sequences these entropies are used as measures of disorder of the sequences and we treat the fibonacci sequence and generalizations the thue morse sequence together with generalizations and the period doubling sequence a discussion of the relative ordering of the thue morse and the fibonacci sequences is given and it is found too simplistic to use any one measure for comparison

diffusive clustering in the two dimensional voter model on donne des resultats de simulation et une enquete concernant les resultats connus sur le modele du votant dans trois cas distincts trois ou plusieurs dimensions une dimension et deux dimensions

three species diffusion limited reaction with continuous density decay exponents we introduce a model of three species two particle diffusion limited reactions or b or c and or a with three persistence parameters survival probabilities in reaction of the hopping particle we consider isotropic and anisotropic diffusion hopping with a drift in one dimension we find that the particle density decays as a power law for certain choices of the persistence parameter values in the anisotropic case on one symmetric line in the parameter space the decay exponent is monotonically varying between the values close to 1 3 and 1 2 on another less symmetric line the exponent is constant for most parameter values the density does not follow a power law we also calculated various characteristic exponents for the distance of nearest particles and domain structure our results support the recently proposed possibility that one dimensional diffusion limited reactions with a drift do not fall within a limited number of distinct universality classes

exponents appearing in the zero temperature dynamics of the 1d potts model for the glauber dynamics of the one dimensional q state potts model at zero temperature the fraction of spins which have never flipped up to time t decreases as t theta q where the exponent theta q varies continuously with q the calculation of the q dependence of this exponent can be reduced to the study of a simple reaction diffusion model using finite size scaling this allows one to obtain accurate estimates of b q for all values of q one can also show that for 1 1 epsilon the expansion of theta y is given by theta 1 2 pi epsilon o epsilon 2

k moment problem for recursive sequences of order application to the zeros of analytic functions in this paper we solve the k moment problem for a family of sequences defined by linear recursive relations of order indexed by z extension of some known properties are studied and others results are established moreover we paraphrase a fundamental application on the existence of zeros of an analytic function in terms of the support of the representing measure of the former sequences

a cooperative system which does not satisfy the limit set dichotomy the fundamental property of strongly monotone systems and strongly cooperative systems in particular is the limit set dichotomy due to hirsch if x y then either x y o r x y and both sets consist of equilibria we provide here a counterexample showing that this property need not hold for non strongly cooperative systems

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

non trivial exponents in coarsening phenomena abstract one of the simplest examples of stochastic automata is the glauber dynamics of ferromagnetic spin models such as ising or potts models at zero temperature if the initial condition is random one observes a pattern of growing domains with a characteristic size which increases with time like t 1 2 in this self similar regime the fraction of spins which never flip up to time t decreases like t where the exponent is non trivial and depends both on the number q of states of the potts model and on the dimension of space this exponent can be calculated exactly in one dimension similar non trivial exponents are also present in even simpler models of coarsening where the dynamical rule is deterministic

two spin majority cellular automaton as a model of 2d cluster and interface growth a new probabilistic cellular automaton model is introduced to simulate cluster and interface growth in two dimensions the dynamics of this model is an extension to higher dimensions of the compact directed percolation studied by essam numerical results indicate that the two dimensional cluster coarsening and growth can be described only approximately by the conventional cluster size scaling due to a crossover in the growth mode the spreading of the initially flat interface follows a purely diffusional t1 2 law

universal scaling function for domain growth in the glauber ising chain the equal time correlation function is calculated at t 0 for the one dimensional ising model with glauber dynamics random initial conditions appropriate to a sudden quench from non zero temperature are imposed averaging over initial conditions yields the scaling form c r t f r2 t the scaling function is given by f x integral 01 dy pi y 1 y 1 2 exp x 4y and is universal i e independent of the probability distribution for the initial conditions

systems of differential equations that are competitive or cooperative v convergence in 3 dimensional systems abstract for 3 dimensional systems that are competitive or cooperative we present new criteria for existence of equilibria and cycles convergence of all trajectories global stability and structural stability a certain type of positive feedback loop is shown to be structurally stable

error bounds in maximum entropy approximations a useful technique in underdetermined inverse problems is that of maximum entropy a simple error bound for averages over a distribution approximated by the maximum entropy method in the case of the undetermined hausdorff moment problem was devised under the conditions specified the error bound for averages over such an approximate distribution can be very tight numerical examples to illustrate are presented

on the moment problem for non positive distributions motivated by considerations arising from many body quantum physics the authors consider the moment problem in the general case where the moments are finite real numbers they present a well defined analytic procedure for the construction of an infinite set of exact solutions to the above problem and discuss several special cases

convergence in smooth strongly monotone flows defined by semilinear parabolic equations on considere des equations paraboliques semi lineaires dy dt ay f y ou a est un operateur sectoriel sur un banach x ayant une resolvante compacte et f est une c 2 application de l espace des puissances fractionnaires x 0 1 dans x soit y t une solution qui est quasi convergente mais non convergente alors il existe un voisinage u de y 0 y 0 avec la propriete suivante si z u y 0 a une trajectoire bornee et soit z y 0 soit z y 0 alors la solution partant de z converge vers un equilibre

a soluble kinetic model for spinodal decomposition we compare the two dimensional voter model with approximate theories for spinodal decomposition the cluster size distribution and the short time dynamics of the voter model are studied by means of a monte carlo simulation the time dependent structure factor and the long time scaling of the voter dynamics are known analytically