effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

tree shifts of finite type a one sided resp two sided shift of finite type of dimension one can be described as the set of infinite resp bi infinite sequences of consecutive edges in a finite state automaton while the conjugacy of shifts of finite type is decidable for one sided shifts of finite type of dimension one the result is unknown in the two sided case in this paper we study the shifts of finite type defined by infinite ranked trees indeed infinite ranked trees have a natural structure of symbolic dynamical systems we prove a decomposition theorem for these tree shifts i e we show that a conjugacy between two tree shifts can be broken down into a finite sequence of elementary transformations called in splittings and in amalgamations we prove that the conjugacy problem is decidable for tree shifts of finite type this result makes the class of tree shifts closer to the class of one sided shifts of sequences than to the class of two sided ones our proof uses the notion of bottom up tree automata

dynamic programming approach to multiple objective control problem having deterministic or fuzzy goals abstract multiple objective control problems mocp are dynamic optimization problems of control systems that can be framed as multistage decision processes generalized dynamic programming or multiple objective dynamic programming is a useful technique to solve mocp levary has first given the dynamic programming approach to solve a multiple objective optimization problem involving goal objectives his formulation is valid if there is only a single decision variable in each stage generally in control problems such as multiple goal control problem mgcp a decision vector is involved in each stage therefore in this paper levary s formulation is extended to mgcp and is illustrated with an example when the mocp has fuzzy goals it is formulated as fuzzy goal control problem fgcp a new formulation of dynamic programming approach to fgcp is proposed here as dynamic fuzzy goal control problem dfgcp and the method of finding its solution is illustrated with an example

diffusion for chaotic plane sections of 3 periodic surfaces we study chaotic plane sections of some particular family of triply periodic surfaces the question about possible behavior of such sections was posed by s p novikov we prove some estimations on the diffusion rate of these sections using the connection between novikov s problem and systems of isometries some natural generalization of interval exchange transformations using thermodynamical formalism we construct an invariant measure for systems of isometries of a special class called the rauzy gasket and investigate the main properties of the lyapunov spectrum of the corresponding suspension flow

limit theorems for self similar tilings we study deviation of ergodic averages for dynamical systems given by self similar tilings on the plane and in higher dimensions the main object of our paper is a special family of finitely additive measures for our systems an asymptotic formula is given for ergodic integrals in terms of these finitely additive measures and as a corollary limit theorems are obtained for dynamical systems given by self similar tilings

balanced sequences and optimal routing the objective pursued in this paper is two fold the first part addresses the following combinatorial problem is it possible to construct an infinite sequence over n letters where each letter is distributed as evenly as possible and appears with a given rate the second objective of the paper is to use this construction in the framework of optimal routing in queuing networks we show under rather general assumptions that the optimal deterministic routing in stochastic event graphs is such a sequence

on the number of factors of sturmian words abstract we prove that for m 1 card a m 1 m i 1 m i 1 i where a m is the set of factors of length m of all the sturmian words and is the euler function this result was conjectured by dulucq and gouyou beauchamps 1987 who proved that this result implies that the language m 0 a m c is inherently ambiguous we also give a combinatorial version of the riemann hypothesis

balance properties of multi dimensional words a word u is called 1 balanced if for any two factors v and w of u of equal length we have 1 v i w i1 for each letter i where v i denotes the number of occurrences of i in the factor v the aim of this paper is to extend the notion of balance to multi dimensional words we first characterize all 1 balanced words on zn in particular we prove they are fully periodic for n 1 we then give a quantitative measure of non balancedness for some words on z2 with irrational density including two dimensional sturmian words

solution of optimal control problems with lumped parameters having single or multiple goal objectives in fuzzy environment abstract in this paper optimal control problems ocp of both linear and nonlinear type with lumped parameters are considered continuous ocp with single or multiple objectives are transformed to finite dimensional optimization problems through discretization the formulation of goal optimal control problem gocp using goal programming methodology first given by levary 1986 for equal time subintervals is extended for unequal subintervals by a generalized formulation the concept of local and global goals proposed here is very useful for multicriteria dynamic optimization problems in several physical situations ocp involve fuzziness in their goals priorities parameters or relative weights and associated linguistic variables etc a new formulation of ocp in fuzzy environment is given as a fuzzy goal optimal control problem fgocp and the solution procedure is illustrated by linear and nonlinear examples

a heuristic self tuning fuzzy controller abstract in this paper a self tuning fuzzy controller based on the tuning of scaling factors is presented the tuning schemes are tuning the scaling factors is individual tuning rules the tuning rules are transformed into numeric tuning tables by applying suitable membership functions so that the adjustings of the scaling factors are merely matrix mappings since the tuning rules are constructed with the control signal and the output error and change in output error of the plant as their antecedent parts the tuning processes have the advantage of real time property simulation results with a perturbed servo and the inverted pendulum system as the controlled plants show the performance and adaptivity of the proposed controller

multiphase conductors realizing aleksandrov s mean it is shown that aleksandrov s mean for the effective linear conductivity of multiphase conductors is exact for a class of material systems with two dimensional isotropic microstructures the systems are constructed by sucessive use of iterated dilute homogenization the result provides a more rigorous basis for the use of aleksandrov s mean to estimate effective properties

a fuzzy control model fcm for dynamic portfolio management abstract in the present study we continue previous work by recasting the portfolio management problem into a control theoretic form still retaining a recursive programming structure through time the uncertainty of future prices and risk levels is recognized by fuzzy numbers our system has interesting directions for future research improving performance through expert systems support for forecasting using the experience from the model in efforts to theory design solving the fuzzy control model fcm when the state objectives return predictions and the level of economic friction are fuzzy

entropy dimension of shift spaces on monoids we consider the entropy dimension of g shifts of finite type for the case where g is a non abelian monoid entropy dimension tells us whether a shift space has zero topological entropy suppose the cayley graph cg of g has a finite representation that is cgg g g is a finite set up to graph isomorphism and relations among generators of g are determined by a matrix a we reveal an association between the characteristic polynomial of a and the finite representation of the cayley graph after introducing an algorithm for the computation of the entropy dimension the set of entropy dimensions is related to a collection of matrices in which the sum of each row of every matrix is bounded by the number of leaves of the graph furthermore the algorithm extends to g having finitely many free followers

variational estimates for the creep behaviour of polycrystals a variational procedure is developed for estimating the effective constitutive behaviour of polycrystalline materials undergoing high temperature creep the procedure is based on a new variational principle allowing the determination of the effective potential function of a given nonlinear polycrystal in terms of the corre sponding potential for a linear comparison polycrystal with an identical geometric arrangements of its constituent single crystal grains as such it constitutes an extension to locally anisotropic behaviour of the variational procedure devel oped by ponte castaneda 1991 for nonlinear heterogeneous media with locally isotropic behaviour by way of an example the procedure is applied to the de termination of bounds of the hashin shtrikman type for the effective potentials of statistically isotropic nonlinear polycrystals the bounds are computed for the special class of untextured fcc polycrystals with isotropic pure power law viscous behaviour first considered by hutchinson 1976 in the context of a calculation of the self consistent type the new bounds are found to be more restrictive than the corresponding classical taylor bishop hill bounds and also more re strictive if only slightly so than related bounds of the hashin shtrikman type by dendievel et al 1991 the new procedure has the advantage over the self consistent procedure of hutchinson 1976 that it may be applied without any essential complications to aggregates of crystals with slip systems exhibiting dif ferent creep rules with for example different power exponents and to general loading conditions however the distinctive feature of the new variational proce dure is that it may be used in conjunction with other types of known bounds and estimates for linear polycrystals to generate corresponding bounds and estimates for nonlinear polycrystals

tree shift topological entropy abstract we give a definition of topological entropy for tree shifts prove that the limit in the definition exists and show that it dominates the topological entropy of the associated one dimensional shift of finite type when the labeling of the tree shares the same restrictions

spline membership function and its application in multiple objective fuzzy control problem abstract in fuzzy decision theory first introduced by bellman and zadeh in 1970 the use of linear membership functions is well established the rate of change in the degree of membership need not in general be constant particularly in time dependent problems or situations where it is considered as a criterion the idea of normalized spline membership function and normalized basis spline membership function is introduced here it is observed that the fuzzy decision operator corresponding to the fuzzy alternatives can be expressed in terms of these proposed membership functions a new method of solution in a multistage form is discussed for the general non linear multiple objective fuzzy control problem the application of normalized spline membership function in the multiple objective fuzzy control problem is illustrated with a numerical example

priority structure in fuzzy goal programming abstract this paper introduces priority structure in fuzzy goal programming fgp this approach utilizes the lexicographic order of goal programming gp and yields an efficient computational algorithm for solving fgp fuzzy priorities are also discussed a numerical example is given to highlight the procedure concluding remarks are also made

deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1 deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of mod ulus 1 the functions we consider are the corresponding eigen functions in theorem 1 1 we prove that the limit inferior of the ergodic sums n x 0 x n 1 n n is bounded for every point x in the phase space in theorem 1 2 we prove existence of limit distributions along certain exponential subsequences of times for substitutions of constant length under additional assumptions we prove that ergodic integrals satisfy the central limit theorem theorem 1 3 theorem 1 9

rigid perfectly plastic two dimensional polycrystals we consider rigid perfectly plastic polycrystals in the two dimensional anti plane shear context the yield sets of the grains are identified with rectangles in the plane centred at the origin whose sides have length 2 and 2 m the limit m corresponds to the grains being rigid in one direction and ductile in the orthogonal direction we show that for large values of m there exist polycrystals whose effective yield sets are large in all directions more precisely for each value of m we construct a polycrystal whose yield set contains the set f f f f where f m o 1 we also show that the yield set of any isotropic polycrystal is contained in the ball of radius 4 m centred at the origin this bound results as an application of the div curl lemma the new component of our analysis which allowed us to obtain sharper results is that we consider simultaneously not only two but an infinite number of admissible stress fields whose averages have different directions

macroscopic properties and field fluctuations in model power law polycrystals full field solutions versus self consistent estimates this paper presents comparisons between full field numerical results and homogenization estimates for the effective behaviour and statistical fluctuations of the stress and strain rate fields in vi

balancedness and coboundaries in symbolic systems abstract this paper studies balancedness for infinite words and subshifts both for letters and factors balancedness is a measure of disorder that amounts to strong convergence properties for frequencies it measures the difference between the numbers of occurrences of a given word in factors of the same length we focus on two families of words namely dendric words and words generated by substitutions the family of dendric words includes sturmian and arnoux rauzy words as well as codings of regular interval exchanges we prove that dendric words are balanced on letters if and only if they are balanced on words in the substitutive case we stress the role played by the existence of coboundaries taking rational values and show simple criteria when frequencies take rational values for exhibiting imbalancedness

properties of words and recognizability of fixed points of a substitution resume soit u un mot infini non periodique point fixe d une substitution primitive nous montrons que pour n assez grand u ne contient aucune puissance n eme de mot nous donnons ensuite une condition necessaire et suffisante pour que soit reconnaissable au sens de host et queffelec et nous montrons qu ill suffit de bilateraliser cette definition pour obtenir une propriete verifiee cette fois par toutes les substitutions primitives a point fixe non periodique

a tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function abstract this paper investigates the application of tolerance concepts to goal programming in a fuzzy environment firstly the paper presents how the fuzzy goal programming fgp problems with unequal weights can be formulated as a single linear programming problem with the concept of tolerances next it illustrates a numerical example to demonstrate how convenient the present model is to solve a fgp problem with unequal weights and unbalanced linear membership functions

homogenization models for predicting local field statistics in ellipsoidal particles reinforced composites comparisons and validations abstract this paper validates the performance of analytical homogenization models at predicting the local field statistics in randomly distributed and oriented ellipsoidal particles reinforced composites the numerical validation was based on a newly introduced load independent metric which allowed to formulate general conclusions a large validation campaign was conducted and the representative volume element rve was rigorously determined for each combination of phases mechanical properties particles volume fraction and aspect ratio the load independent properties computed numerically were compared to those predicted by a range of analytical models the study revealed that the original benveniste s interpretation of the mori tanaka scheme led to the most accurate first order moments and intra matrix second order moments provided that the mechanical properties contrast between the particles and the matrix are low for higher contrasts lielens model delivers the most accurate estimates the self consistent scheme is the most suited model to predict the intra particle second order moments when the particles aspect ratio is low for particles with high aspect ratio lielens model could be an alternative to the self consistent scheme furthermore an interpolation model has been developed and it has been shown to predict accurately the mean and covariance tensors of the intraphase stress fields

variational estimates of the self consistent type for the effective behaviour of some model nonlinear polycrystals a new class of self consistent estimates for nonlinear polycrystals is obtained by making use of the classical self consistent estimates for the linear comparison polycrystal in the nonlinear variational procedure of debotton and ponte castaneda 1995 a distinctive feature of the new self consistent estimates is that they satisfy the recent bound of kohn and little 1997 for two dimensional ideally plastic polycrystals which is known to be significantly more restrictive than the taylor bound at large grain anisotropy in addition the new self consistent estimates are found to satisfy the taylor and hashin shtrikman bounds which are sharper than the kohn little bound at low grain anisotropy this result suggests that the new self consistent estimates may also be more accurate than other self consistent estimates like those arising from the incremental model of hill 1965 for three dimensional nonlinear polycrystals

linear comparison estimates for the effective resistivity of three dimensional nonlinear polycrystals estimates for the effective resistivity of nonlinear polycrystals are obtained using the linear comparison homogenization scheme of debotton and ponte castaneda debotton ponte castaneda 1995 proc r soc a 448 121 142 computing the effective properties of linear composites with the same microstructure as the nonlinear composite is an essential part of this scheme the classical self consistent method is employed for this purpose an important characteristic of these estimates for polycrystals with field thresholds is that they satisfy the recent bound of garroni and kohn garroni kohn 2003 proc r soc a 459 2613 2625 which dramatically improves upon the classical taylor upper bound at large crystal anisotropy in addition the estimates also satisfy the hashin shtrikman bounds which are more restrictive than the garroni kohn bound at small crystal anisotropy inte restingly the scaling exponents for the linear comparison estimates are found to be inde pendent of the constitutive nonlinearity this last observation provides an explanation for the relative weakness of an earlier linear comparison bound obtained by garroni and kohn

balances for fixed points of primitive substitutions an infinite word defined over a finite alphabet a is balanced if for any pair of factors of the same length and for any letter a in the alphabet a a 1 where a denotes the number of occurrences of the letter a in the word in this paper we generalize this notion and introduce a measure of balance for an infinite sequence in the case of fixed points of primitive substitutions we show that the asymptotic behaviour of this measure is in part ruled by the spectrum of the incidence matrix associated with the substitution connections with frequencies of letters and other balance properties are also discussed

sturmian ground states in classical lattice gas models we construct for the first time examples of non frustrated two body infinite range one dimensional classical lattice gas models without periodic ground state configurations ground state configurations of our models are sturmian sequences defined by irrational rotations on the circle we present minimal sets of forbidden patterns which define sturmian sequences in a unique way our interactions assign positive energies to forbidden patterns and are equal to zero otherwise we illustrate our construction by the well known example of the fibonacci sequences

decidability of irreducible tree shifts of finite type we reveal an algorithm for determining the complete prefix code irreducibility cpc irreducibility of dyadic trees labeled by a finite alphabet by introducing an extended directed graph representation of tree shift of finite type tsft we show that the cpc irreducibility of tsfts is related to the connectivity of its graph representation which is a similar result to one dimensional shifts of finite type

fuzzy goal programming an additive model abstract an additive model to solve fuzzy goal programming fgp is formulated the method uses arithmetic addition to aggregate the fuzzy goals to construct the relevant decision function cardinal and ordinal weights for nonequivalent fuzzy goals are also incorporated in the method the solution procedure is illustrated with a numerical example

mixing properties of tree shifts the uncertainty of multidimensional shift spaces draws attracted attention of researchers for example the emptiness problem is undecidable there exist aperiodic shifts of finite type there is a nonempty shift of finite type exhibiting nonextensible local patterns this paper investigates symbolic dynamics on cayley trees and gives affirmative answers to the above questions in tree shifts beyond that with introducing block gluing tree shift a sufficient condition of exhibiting positive topological entropy is revealed