connective constant of the self avoiding walk on the triangular lattice the author uses a recently developed monte carlo method to study the connective constant of the self avoiding walk saw on the triangular lattice assuming gamma 43 32 one finds mu t 4 15096 or 0 00010 or 0 00026 95 confidence limits and mu t 4 15096 or 0 00020 or 0 00037 99 confidence limits where the first error bar represents systematic error due to corrections to scaling and the second error bar represents statistical error this rules out the conjecture mu t mu h 6 at the greater than 99 confidence level

a note on convergence under dynamical thresholds with delays we complement the study of the asymptotic behaviour of the dynamical threshold neuron model with delay introduced by gopalsamy and leung 1997 by providing a description of the dynamics of the system in the remaining parameters range we characterize the regions of harmless delays and those in which delay induced oscillations appear

optimal robust filtering with time varying parameter uncertainty stochastic linear systems subject to time varying parameter uncertainties affecting both system dynamics and noise statistics are considered a linear filter is used to estimate a linear combination of the states of the system when the filter is given the stabilizing solution of a suitable riccati equation is shown to yield an upper bound for the covariance of the estimator error the main problem addressed in the paper is the design of an optimal robust filter that minimizes such a covariance bound necessary conditions are given for the existence of an optimal reduced order robust filter as well as necessary and sufficient conditions for the full order case the computation of the optimal filter calls for the solution of a riccati equation that generalizes the standard riccati equation for the kalman filtering problem a numerical example is provided in which the new filter is compared with both the kalman and h filters

universality class of trails in two dimensions a trail is a walk on a lattice that may visit a site more than once but a bond at most once we have carried out transfer matrix studies of trails on the square lattice and of hybrid walks that interpolate between self avoiding walks and trails the results are in agreement with the same universal exponents as self avoiding walks however the finite size corrections are much larger than for self avoiding walks an explanation in terms of an irrelevant variable with scaling index is given

linear quadratic differential games with cheap control abstract this paper considers a linear quadratic differential game in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the value of the game will approach zero as the weighting on the minimizing control approaches zero

correction to scaling exponents and amplitudes for the correlation length of linear polymers in two dimensions we consider the scaling behaviour of the radius of gyration for a system of dilute linear polymers we focus on pn the mean square end to end distance of an n step self avoiding walk for which an additional two terms were recently calculated for the close packed triangular lattice combining several extrapolation methods we find that a consistent description of the scaling behaviour exists if and only if the correction to scaling exponent a is roughly half as large as commonly believed we conclude that all data ale consistent with the equation pn an2 1 b na c n where y a a 1 j2 abso 21 and c lo

an lmi approach to discrete time observer design with stochastic resilience much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant or the measurement model the present work addresses the important problem of stochastic resilience or non fragility of a discrete time luenberger observer which is the maintenance of convergence and or performance when the observer is erroneously implemented possibly due to computational errors i e round off errors in digital implementation or sensor errors etc a common linear matrix inequality framework is presented to address the stochastic resilient design problem for various performance criteria in the implementation based on the knowledge of an upper bound on the variance of the random error in the observer gain present results are compared to earlier designs for stochastic robustness illustrative examples are given to complement the theoretical results

bifurcation properties for a sequence of approximation of delay equations where 1 0 and b ay f x y oforx o see 4 lo or theevenmore restricted equation dx dt a x t 1 the outstanding fact established for the first time by wright lo is the existence of a class of slowly oscillating solutions for 1 in which the trivial solution x 0 appears as an equilibrium whose stability changes with 2 this class determines a convex cone of initial data invariant under the equation and the change of equilibrium the bifurcation to new equilibria can be expressed through a family of poincare operators on the cone in contrast little has been done regarding equations of the type

monte carlo series analysis of irreversible self avoiding walks i the indefinitely growing self avoiding walk igsaw high precision monte carlo data are used to estimate the exponents which govern the asymptotic behaviour of the recently introduced indefinitely growing self avoiding walk in two dimensions for this walk the exponent gamma is by definition equal to one applying the same methods which are used to extract the exponents from exact series enumeration the authors give an estimate for the exponent nu of 0 567 or 0 003 the leading corrections to this asymptotic behaviour are also calculated

dissipativity based resilient filtering of periodic markovian jump neural networks with quantized measurements the problem of dissipativity based resilient filtering for discrete time periodic markov jump neural networks in the presence of quantized measurements is investigated in this paper due to the limited capacities of network medium a logarithmic quantizer is applied to the underlying systems considering the fact that the filter is realized through a network randomly occurring parameter uncertainties of the filter are modeled by two mode dependent bernoulli processes by establishing the mode dependent periodic lyapunov function sufficient conditions are given to ensure the stability and dissipativity of the filtering error system the filter parameters are derived via solving a set of linear matrix inequalities the merits and validity of the proposed design techniques are verified by a simulation example

end to end distance distributions and asymptotic behaviour of self avoiding walks in two and three dimensions we use monte carlo methods to study the reduced moments and full end to end distance distributions of self avoiding walks in two and three dimensions we find that the reduced moments scale with length via delta pg a b n delta pq with corrections to the scaling exponents that vary with the order of the moment we also find that the complete end to end distance distributions are well described by a redner des cloizeaux rdc model qn x cx theta n exp kx tn x being the rescaled length we develop a method that allows reliable estimation of the exponents theta n and tn from the extrapolated reduced moments and use this method to extrapolate to chain lengths beyond those investigated here we find that in three dimensions the optimal tn for n 1000 is smaller than the theoretically expected value t 2 445 this implies that care must be taken in using the rdc ansatz to interpret the behaviour of self avoiding walks even in the asymptotic limit

self avoiding path walks on lattices a new universality class the trails problem self avoiding path walks is reconsidered by the conventional series expansion approach an exact enumeration on the square triangular and simple cubic lattices is done by computer up to 18 12 and 11 steps respectively the more self consistent and refined results between the connective constant and the corresponding critical exponent indicate the possibility of there being a different universality class from that of the self avoiding walk an average approach based on stolz s theorem is proposed which often appears to be smoother and better than the traditional one

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

the geometrical properties of planar lattice trails the authors investigate the winding angle and mean square end to end distance of lattice trails on a square lattice by both exact enumeration and monte carlo methods they find similar behaviour to that of self avoiding walks to the extent that the complete distribution is found to agree with the recent exact calculation of the winding angle distribution function for self avoiding walks by duplantier and saleur 1988 who found a gaussian distribution the exponent nu was found to be indistinguishable from 3 4

position space renormalisation group for isolated polymer chains we develop a cell position space renormalisation group psrg with which we study the scaling properties of isolated polymer chains we model a chain by a self avoiding walk constrained to a lattice for rescaling factors b s 6 we calculate recursion relations analytically on the square lattice with several different choices for the psrg weight function we also calculate implicit cell to cell transformations in which a cell of size b is rescaled to a cell of size b the results of these psrgs improve both as b increases and as b b 1 in addition we construct a true infinitesimal psrg transformation which appears to become exact as the dimensionality d approaches 1 we obtain the closed form expression for the correlation length exponent u d l d in d the flory formula deviates from this already at first order in d 1 we also develop a constant fugacity monte carlo method which enables us to simu late in an unbiased way within the grand canonical ensemble chains of up to lo3 bonds with this method we extend the psrg to larger cells b s 150 on the square lattice our numerical method provides high statistical accuracy for all cell sizes however in the range of b we study the asymptotic behaviour of our results appears to depend on the choice of weight function one weight function provides smooth behaviour as a function of b and with it we extrapolate to find u 0 756 0 004 further work is required to resolve the apparent anomalies in the results based on the other weight functions

integral comparison theorems and extremal points for linear differential equations abstract comparison theorems of integral type are developed for linear differential equations of the form 1 l n y p t y 0 and 2 l n y q t y 0 under the assumption that 2 has no nontrivial solution satisfying given homogeneous two point boundary conditions it follows that the same is true for 1 provided certain sign and integral conditions hold the criteria may be thought of as rather general extensions of the hille wintner type and also include and extend recent results of elias

a generalised self avoiding walk the authors study a generalised self avoiding walk on a lattice in which each vertex may be visited less than k time turban 1983 has argued that for this model the critical exponents should change continuously with k from the standard self avoiding walk exponents k 2 to mean field exponents by generating series expansions for both two and three dimensional lattices the authors find strong support for the conventional and opposing view that the critical exponents remain unchanged for finite k only taking on their mean field values in the limit k to infinity

study of the θ point by enumeration of self avoiding walks on the triangular lattice the author reports series expansion analyses of self avoiding walks with nearest neighbour bond interactions the estimates 2 nu t 1 07 or 0 05 and phi 0 64 or 0 05 for the correlation and crossover exponents at the theta point were obtained by examining the number of walks and the end to end distance data up to 16 steps on the triangular lattice

lattice trails i exact results considers the problem of lattice trails introduced by malakis 1975 1976 the author proves the existence of a finite connective constant and establishes a result for the growth of n step trails tn analogous to the best known result for self avoiding walks tn lambda n expt o n for the honeycomb d 2 and lave s lattice d 3 the author establishes a counting theorem from which one can deduce the exact value of the connective constant lambda for the honeycomb lattice lambda 2 2 square root 2 further it follows that the trail problem is in the same universality class as the self avoiding walk problem for those lattices an exact amplitude relation between trails and self avoiding walks and between dumb bells and trails and self avoiding walks is established the non existence of a counting theorem for arbitrary lattices is established an inequality for the triangular lattice connective constant is proved a high density expansion for lambda for the d dimensional hybercubic lattice is also obtained the author argues that contrary to recent suggestions the model is in the same universality class as the self avoiding walk model

scaling of self avoiding walks and self avoiding trails in three dimensions motivated by recent claims of a proof that the length scale exponent for the end to end distance scaling of self avoiding walks is precisely 7 12 0 5833 we present results of large scale simulations of self avoiding walks and self avoiding trails with repulsive contact interactions on the simple cubic lattice we find no evidence to support this claim our estimate 0 5874 2 is in accord with the best previous results from simulations

four dimensional polymer collapse ii interacting self avoiding trails we have simulated four dimensional interacting self avoiding trails isat on the hypercubic lattice with standard interactions at a wide range of temperatures up to length 4096 and at some temperatures up to length 16384 the results con3rm the earlier prediction using data from a non standard model at a single temperature of a collapse phase transition occurring at 3nite temperature moreover they are in accordwith the phenomenological theory originally proposed by lifshitz grosberg andkhokhlov in three d andrecently given new impetus by its use in the description of simulational results for four dimensional interacting self avoiding walks isaw in fact we argue that the available data is consistent with the conclusion that the collapse transitions of isat andisaw lie in the same universality class in contrad iction with long standing predictions we deduce that there exists a pseudo 3rst order transition for isat in four dimensions at 3nite lengths while the thermodynamic limit is described by the standard polymer mean 3eld theory giving a second order transition in contradiction to the prediction that the upper critical dimension for isat is du 4 c 2001 elsevier science b v all rights reserved

brief paper non fragile h filter design for linear continuous time systems this paper studies the problem of non fragile h filter design for linear continuous time systems the filter to be designed is assumed to include additive gain variations which result from filter implementations a notion of structured vertex separator is proposed to approach the problem and exploited to develop sufficient conditions for the non fragile h filter design in terms of solutions to a set of linear matrix inequalities lmis the designs guarantee the asymptotic stability of the estimation errors and the h performance of the system from the exogenous signals to the estimation errors below a prescribed level a numerical example is given to illustrate the effect of the proposed method

extremal solutions for nth order linear difference equations abstract after the fashion of uri elias we analyze the characteristics of extremal solutions for linear difference equations of the form ly t p t y t 0 where l is an n th order disconjugate linear difference operator given its polya hartman factorization and where p t is nonzero and of constant sign on the interval i a a a 1 this work is based on and extends the work concerning the classification of solutions done by allan peterson and darrel hankerson

critical exponents of the self avoiding walks on a family of finitely ramified fractals the authors have studied the self avoiding walks saw on a family of finitely ramified fractals the first member b 2 of the family is the two dimensional sierpinski gasket while the last member b infinity appears to be a wedge of the homogeneous triangular lattice by means of the exact renormalisation group transformations they have calculated the critical exponents alpha nu and gamma and the connectivity constant mu of saw on each member of a sequence 2 or b or 8 of the studied fractal family the obtained exact results are compared with the recent phenomenological proposals and with the results believed to be exact in the case of a homogeneous two dimensional lattice

periodic solutions for ẋ t λf x t x t 1 on presente un nouveau resultat sur l existence des solutions periodiques pour l equation x t f x t x t 1 pour tous les parametres positifs suffisamment grands

metastable periodic patterns in singularly perturbed state dependent delayed equations abstract we consider the scalar delayed differential equation x t x t f x t r where 0 r r x 1 r x and f represents either a monotone positive feedback d f d x 0 or a monotone negative feedback d f d x 0 plus some other hypotheses when the delay is a constant i e r x 1 this equation can support metastable rapidly oscillating solutions that are transients whose duration is of order exp c for some c 0 in this paper combining analytic and numerical techniques we investigate whether this metastable behavior persists when the delay r x depends non trivially on the state variable x more precisely we proceed in three steps first we explore theoretically and numerically the existence of branches of rapid periodic solutions for these equations then to predict conditions for metastability we introduce transition layer equations that depict the asymptotic shape of transient oscillations when tends to zero and finally these predictions are validated by numerical simulations numerical explorations are also performed for other scalings of with our conclusions are i when 0 0 there are no metastable transients ii when 0 0 and 0 is finite for monotone negative feedback the metastable oscillations exist irrespective of choices of f and r iii for monotone positive feedback they require that the feedback f and the delay r satisfy extra conditions such as f being an odd function and the delay r x an even function one novel result is that state dependent delays may lead to metastable dynamics in equations that cannot support such regimes when the delay is constant

lattice trails ii numerical results for pt i see ibid vol 18 p 567 1985 a numerical study of the properties of lattice trails on the honeycomb square triangular and simple cubic lattices is made critical points are estimated for all lattices and upper and lower bounds established extensive series have been obtained and series analysis of both trail generating functions and mean square end to end distance series are not inconsistent with the conclusion that the problem is in the same universality class as the self avoiding walk problem a pseudo star triangle transformation is defined and the analyticity properties of that function coupled with previous exact results clearly supports that conclusion for the triangular lattice as well as providing excellent unbiased critical point estimates the author also shows that the connective constant for d or 2 dimensional hypercubic trails is strictly greater than the corresponding quantity for saws

fractal dimensionality of polymer chains the authors suggest that the concept of fractal dimensionality provides a useful characterisation of the configurational properties of a single polymer from numerical studies of long polymers traced out by self avoiding walks on a planar lattice they find that the fractal dimensionality is well defined and has a constant value for most scales of length of the chain renormalisation group theory provides a theoretical basis for the concept of fractal dimensionality in polymers

robust kalman filtering for uncertain systems abstract this paper studies the problem of kalman filter design for uncertain systems the system under consideration is subjected to time varying norm bounded parameter uncertainties in both the state and measurement matrices the problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties a riccati equation approach is proposed to solve the above problem furthermore a suboptimal covariance upper bound can be computed by a convex optimization

robust reduced order nonstrictly proper state estimation via the optimal projection equations with guaranteed cost bounds a state estimation design problem involving parametric plant uncertainties is considered an estimation error bound suggested by multiplicative white noise modeling is utilized for guaranteeing robust estimation over a specified range of parameter uncertainties necessary conditions that generalize the optimal projection equations for reduced order state estimation are used to characterize the estimator that minimizes the error bound the design equations thus effectively serve as sufficient conditions for synthesizing robust estimators additional features include the presence of a static estimation gain in conjunction with the dynamic kalman estimator to obtain a nonstrictly proper estimator

on the factorizations of ordinary linear differential operators etude des modes de factorisation de certains operateurs differentiels lineaires d ordre n a l aide des wronskiens

h and l 2 l finite horizon filtering with randomly occurring gain variations and quantization effects this paper investigates the h and l 2 l filtering problem for discrete stochastic nonlinear system with randomly occurring gain variations and quantization effects over a finite horizon the system under consideration is subject to time varying parameters and exogenous signals a bernoulli distributed white sequence with a known conditional probability is introduced to describe the binary switching phenomenon between two types of nonlinear disturbances the randomly occurring filter gain variations are utilized to express the random change of filter parameters that is governed by a binary sequences taking values on 0 or 1 moreover the quantization effects of measurements are also taken into account where a form of logarithmic quantizer is applied by using the recursive linear matrix inequalities rlmis approach sufficient conditions are established for the existence of the desired finite horizon filter to guarantee the h and l 2 l performance specifications at the same time a numerical example is proposed to show the correctness and effectiveness of the proposed design method

discrete polynomial interpolation green s functions maximum principles error bounds and boundary value problems abstract we construct discrete interpolating polynomials provide explicit representations of discrete green s functions give several identities and inequalities for these green s functions use the explicit forms of the interpolating polynomials and that of green s functions to establish several maximum principles further we obtain error bounds in discrete polynomial interpolation and use them to study existence and uniqueness of the discrete boundary value problems these bounds are also used to provide sufficient conditions for the convergence of the picard s method the approximate picard s method quasilinearization and the approximate quasilinearization the monotone convergence of the picard s iterative method is also analysed

a classification of the solutions of a differential equation according to their behaviour at infinity ii the solutions of the differential equation l n y p y 0 where l n is a disconjugate operator are classified according to their behaviour as the solution space is decomposed into disjoint sets we study the dominance properties of the solutions which belong to different sets

spiral self avoiding walks self avoiding walks with a spiral constraint on the square lattice are enumerated up to 40 steps numerical evidence suggests that they belong to a new universality class

non perturbative tricritical exponents of trails ii exact enumerations on square and simple cubic lattices for pt i see ibid vol 21 p 773 1988 the authors present exact enumerations of trails self intersecting but non overlapping lattice walks tabulated according to their length l number of intersection i and end to end distance for the square lattice up to l 21 i 7 and for the simple cubic lattice up to l 15 i 5 they introduce a fugacity for intersection to explore the transition to a collapsed phase through a novel tricritical point which is unaccessible by the renormalisation group approach the existence of tricritical points in both lattices is manifested by the divergence of the specific heat the values of the tricritical couplings and exponents are extracted by a dlogpade analysis they find for the three dimensional lattice nu t approximately 0 48 and gamma t approximately 0 43 nu t approximately 0 52 and gamma t approximately 1 25 for the square lattice

end to end distance of linear polymers in two dimensions a reassessment recent exact enumeration studies of the two dimensional self avoiding walk have produced evidence in support of non analytic scaling corrections newly extended series for the triangular and square lattices to n 19 and 25 respectively are examined in the light of recent monte carlo results suggesting the absence of corrections of this type using a modified approach to series analysis it is concluded that the end to end distance can best be understood in terms of analytic corrections alone in view of the lack of theoretical support there is little reason to introduce additional kinds of correction in attempting to explain the data

brief paper insensitive h filter design for continuous time systems with respect to filter coefficient variations this paper is concerned with the problem of designing insensitive h filters for linear continuous time systems coefficient sensitivity functions of transfer functions with respect to filter additive multiplicative coefficient variations are defined and the h norms of the sensitivity functions are used to measure the sensitivity of the transfer functions with respect to additive filter coefficient variations in addition in order to deal with the filter design problem for the multiplicative filter coefficient variation case new measures based on the average of the sensitivity functions are also defined consequently the insensitive h filter design problem is reduced to a multi objective filter design problem which minimizes the coefficient s sensitivity and meets the prescribed h norm constraint simultaneously first a novel method for designing insensitive h filters subjected to additive filter coefficient variations is given in terms of the linear matrix inequality lmi optimization techniques furthermore based on the new sensitivity measures the obtained results are extended to the multiplicative coefficient variation case in addition an indirect method for solving the multiplicative variations is also proposed finally two numerical examples are provided to demonstrate the effectiveness of the proposed method

technical communique resilient linear filtering of uncertain systems the problem of resilient linear filtering for a class of linear continuous time systems with norm bounded uncertainties is investigated we have considered additive filter gain variations to reflect the imprecision in filter implementation the design problem of resilient linear filter is formulated as a convex optimization problem over linear matrix inequalities as a limiting procedure the case of resilient kalman filter is derived all the developed results are conveniently extended to the case of multiplicative filter gain variations simulation studies are carried out to support the theoretical findings

monte carlo series analysis of irreversible self avoiding walks ii the growing self avoiding walk for pt i see ibid vol 18 p 1515 1985 the authors study the scaling behaviour of the recently introduced growing saw they apply a ratio type analysis of monte carlo generated enumeration data to extract the critical indices for the two dimensional walk they find the usual saw values for these indices for the two dimensional walk the true asymptotic behaviour can only be studied for extremely long chains however on the basis of this data they can exclude the possibility of an upper critical dimension dc 3

spiral bond animals ratio approach bond animals with a constraint of a given winding direction on the square lattice are enumerated up to 14 bonds numerical evidence further confirms the previous conjecture using the position space renormalisation group approach that they belong to a new universality class

the self avoiding walk on the honeycomb lattice the author analyses the chain generating function for the self avoiding walk problem on the honeycomb lattice she uses the exact critical point value of nienhuis and finds exponent values of gamma approximately 1 344 and delta 1 approximately 0 93 for the dominant and first confluent exponents the former value is in agreement with nienhuis exact result second and third confluent exponents delta 2 approximately 1 2 and delta 3 approximately 1 5 are also identified these exponents being consistent with monte carlo results and nienhuis exact irrelevant eigenvalue respectively

a classification of the solutions of a difference equation according to their behavior at infinity on considere l equation aux differences lineaires d ordre n ly t p t y t 0 ou p t est de signe defini sur a a a 1 a est un entier

induced l sub 2 and generalized h sub 2 filtering for systems with repeated scalar nonlinearities this paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks both induced l sub 2 and generalized h sub 2 indexes are introduced to evaluate the filtering performance for a given stable discrete time systems with repeated scalar nonlinearities our purpose is to design a stable full order or reduced order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l sub 2 or generalized h sub 2 performance sufficient conditions are obtained for the existence of admissible filters since these conditions involve matrix equalities the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities which can be readily solved by using standard numerical software if these conditions are feasible a desired filter can be easily constructed these filtering results are further extended to discrete time systems with both state delay and repeated scalar nonlinearities the techniques used in this paper are very different from those used for previous controller synthesis problems which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix a numerical example is provided to show the applicability of the proposed theories

enumeration of self avoiding trails on a square lattice using a transfer matrix technique the authors describe a new algebraic technique utilizing transfer matrices for enumerating self avoiding trails on the square lattice they have enumerated trails to 31 steps and find increased evidence that trails are in the self avoiding walk universality class assuming that trails behave like a lambda nn1132 they find lambda 2 72062 or 0 000006 and a 1 272 or 0 002

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy

a monte carlo study of lattice trails the authors use the recently developed monte carlo algorithm of berretti and sokal j stat phys vol 40 p 483 1985 to study the critical behaviour of lattice trails on the square and triangular lattices they find support for the earlier belief that this problem is in the same universality class as self avoiding walks accepting this they obtain the most precise estimates to date of the connective constants it is argued that this problem is particularly well suited to study by monte carlo methods rather than by series analysis

robust nonfragile h_ infty filtering of fuzzy systems with linear fractional parametric uncertainties this paper is concerned with the h filtering problem for continuous time takagi sugeno t s fuzzy systems different from existing results for fuzzy h filtering the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by a descriptor representation approach two sufficient conditions for the h filter design are proposed in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of the desired filter is given a simulation example will be given to show the efficiency of the proposed methods

growth properties of solutions to a linear differential equation on compare les proprietes de dominance des solutions de lny p x y 0 ou ln est un operateur non conjugue aux proprietes de dominance des solutions de son adjointe

focal boundary value problems for nonlinear difference equations ii on considere l unicite des solutions impliquant l existence des solutions de problemes aux valeurs limites de type focal pour l equation aux differences non lineaire d ordre n u t n f t u t u t n 1 ou f a r n r est continue et l equation u n 1 f t u 1 u n peut etre resolue pour u 1 comme fonction continue des variables t u 2 u u 1

convergence and extrapolation in finite size scaling renormalization abstract finite size renormalization technique is studied by examining a test model which is exactly solvable and the problem of lattice animals and self avoiding walks bulk estimates of the leading irrelevant rg eigenvalue are found and compared with independent estimates from finite size data we introduce an extrapolation technique which is applicable to non monotonic sequences of exponent approximants

the growing self avoiding walk the authors introduce a new self avoiding walk with one step probabilities which depend on the local environment as a consequence this walk is irreversible and models the growth process of a linear polymer in a good solvent to calculate its properties they have performed exact enumerations up to 22 steps on the square lattice and on the diamond lattice this gives for the critical indices the values v 0 68 gamma 1 16 in two dimensions and v 0 525 and gamma 1 in three dimensions

robust nonfragile kalman filtering for uncertain linear systems with estimator gain uncertainty the note is concerned with the problem of a robust nonfragile kalman filter design for a class of uncertain linear systems with norm bounded uncertainties the designed state estimator can tolerate multiplicative uncertainties in the state estimator gain matrix the robust nonfragile state estimator designs are given in terms of solutions to algebraic riccati equations the designs guarantee known upper bounds on the steady state error covariance a numerical example is given to illustrate the results

the growing self avoiding trail the author introduces a new random walk which can be used as a model for the theta polymer the walk belongs to a different universality class from the usual saw extensive monte carlo calculations have been performed to calculate the exponents gamma and nu the author finds in two dimensions nu 0 535 and gamma 1 025 and in three dimensions nu 0 50 and gamma 1 0 this result strongly suggests that the upper critical dimension is equal to three

tests of hyperuniversality for self avoiding walks a universal combination of amplitudes for the end to end distance of n step self avoiding walks and for the number of n step self avoiding polygons is estimated numerically for various lattices in d 2 universality of this amplitude combination is confirmed to good accuracy while in d 3 the data are consistent with universality but the error limits are rather large for finite width square lattice strips the authors calculate universal critical point correlation amplitudes by fixed fugacity monte carlo simulations in addition these amplitudes are calculated analytically either exactly or approximately by cardy s conformal mapping approach numerical values agree well with the theoretical predictions

on three dimensional self avoiding walks long self avoiding walks of up to 2400 steps have been generated on the sc and bcc lattices using an improved monte carlo technique analysis of the asymptotic length dependence of the end to end distance and radius of gyration of the walks leads to values in the range 0 591 0 593 for the critical exponent nu the simple power law dependence on length provides an excellent fit to the data over walk lengths between 120 and 2400 with fluctuations around the asymptotic results averaging to a mere 0 13 systematic deviations from asymptotic behaviour in short self avoiding walks have also been examined using monte carlo generated walks ranging in length from 12 to 60 the results do not support the existence of the non analytic correction predicted by the renormalisation group in the light of this unexpected result available series expansions for walks on the fcc lattice have been re examined and previous claims to have observed non analytic behaviour questioned equal if not better convergence of the extrapolated series can be obtained without resorting to non analytic correction terms finally an analysis has been made of the radius of gyration series to which several new terms have been added

on the correction to scaling exponent of linear polymers in two dimensions the authors present new results which indicate that the leading correction to scaling exponent in the mean squared end to end distance in two dimensions is the analytic term a potential source of the various correction to scaling terms reported in the literature is pointed out

robust minimum variance filtering this paper deals with the robust minimum variance filtering problem for linear systems subject to norm bounded parameter uncertainty in both the state and the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty two methods for designing robust filters are investigated the first one deals with constant parameter uncertainty and focuses on the design of steady state filters that yield an upper bound to the worst case asymptotic error variance this bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system and it can be made tighter if a tight bound on the latter power spectrum can be obtained the second method allows for time varying parameter uncertainty and for general time varying systems and is more systematic we develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems

a new algorithm to enumerate the self avoiding random walk presents a new algorithm for enumerating the self avoiding walk and extend the existing series of 19 terms by one more term on a triangular lattice the leading correction to scaling exponent delta 1 for the mean square end to end distance of the self avoiding walk is found to be less than one

two dimensional polymers universality and correction to scaling improved monte carlo methods have been used to study the asymptotic behaviour of self avoiding walks on two dimensional lattices the mean square end to end distance rn2 and radius of gyration sn2 are both found to scale as n2v with exponent values very close to the expected v 3 4 and an amplitude ratio that is universal small n deviations of rn2 from the asymptotic results indicate a correction to scaling exponent delta 1 a value that differs from previous estimates

the trail problem on finitely ramified fractals using an exact real space renormalisation group technique the authors show that self avoiding trails sat and self avoiding walks saw on the sierpinski gasket obey the same critical exponent nu for the correlation length and therefore belong to the same universality class on the other hand it is shown that sat on branching koch curves with maximum ramification number rmax 3 is in a different universality class from that of saw

self avoiding walks on percolation clusters the author studies self avoiding walks saws on percolation clusters a scaling function representation for r the mean end to end distance is proposed which describes a crossover from ordinary saws to saws on fractals he distinguishes between saws on a single cluster for which r approximately nx where x nu 1 and saws on all clusters for which r approximately nz where z nu 2 and n is the number of monomers in the walk he estimates nu 1 d 2 approximately 1 285 and the correction to scaling exponent omega d 2 approximately 1 3 and nu 1 d 3 approximately 1 38 two plausible generalisations of the flory 1953 approximation for nu 1 are investigated and it is argued that none of them provides a satisfactory approximation for nu 1 at all dimensions

bounds on connective constants for self avoiding walks new lower bounds on the connective constant of the square and simple cubic lattice self avoiding walks are obtained by enumerating a particular subset of self avoiding walks and using a result of kesten the author finds mu sq 2 5680 and mu sc 4 352

on two dimensional self avoiding random walks following nienhuis 1982 exact evaluation of the connective constant of the honeycomb lattice self avoiding walk model and the exact exponent values he has conjectured the author has re examined the available data on all three regular two dimensional lattices in the case of the triangular lattice the author has additionally corrected and extended the extant series the author finds support for nienhuis value gamma 111 32 for all three lattices and further finds that alpha 1 2 for all three lattices as given by nienhuis result nu 3 4 and the hyperscaling relation d nu 2 alpha the author is unable to find any consistent evidence of a correction to scaling exponent delta 1 1 cannot be ruled out

the pivot algorithm a highly efficient monte carlo method for the self avoiding walk the pivot algorithm is a dynamic monte carlo algorithm first invented by lal which generates self avoiding walks saws in a canonical fixed n ensemble with free endpoints heren is the number of steps in the walk we find that the pivot algorithm is extraordinarily efficient one effectively independent sample can be produced in a computer time of ordern this paper is a comprehensive study of the pivot algorithm including a heuristic and numerical analysis of the acceptance fraction and autocorrelation time an exact analysis of the pivot algorithm for ordinary random walk a discussion of data structures and computational complexity a rigorous proof of ergodicity and numerical results on self avoiding walks in two and three dimensions our estimates for critical exponents are 0 7496 0 0007 ind 2 and 0 592 0 003 ind 3 95 confidence limits based on saws of lengths 200 n 10000 and 200 n 3000 respectively

nonfragile filtering for discrete time linear systems in finite frequency domain this article investigates the problem of nonfragile filter design for discrete time linear systems subject to noises with known frequency ranges additive interval uncertainty reflecting imprecision in filter implementation is considered by the aid of generalised kyp lemma both deterministic and randomised filtering algorithms are proposed to deal with noises in low middle and high frequency domain respectively the proposed nonfragile finite frequency filters can get a better noise attenuation performance when frequency ranges of noises are known beforehand an example about f 18 aircraft model is given to illustrate the effectiveness of the proposed algorithms