bertrand numeration systems and recognizability abstract there exist various well known characterizations of sets of numbers recognizable by a finite automaton when they are represented in some integer base p 2 we show how to modify these characterizations when integer bases p are replaced by linear numeration systems whose characteristic polynomial is the minimal polynomial of a pisot number we also prove some related interesting properties

on number systems with finite degree of ambiguity abstract we show that it is decidable whether or not a given n recognizable set is representable by a number system having finite degree of ambiguity as a corollary we obtain an algorithm for computing the degree of ambiguity of a given set defined by a number system

a generic model for long self avoiding chain molecules a generic model which applies rigorously to finite chains in the absence of inter segmental interactions and to subchains of infinite chains with practically arbitrary interactions furnishes a simple recurrence relation self avoiding walks on the diamond lattice saw d form the paradigmatic example for polymer science the generic model as a whole is solved in terms of parameters for configurational statistics asymptotically large number n of segments and on stated plausible conjectures by classical methods i e without postulating a singularity of power law form the appropriate generalisation of the power law form of scaling theory emerges very simply e g in terms of kummer s hypergeometric function extensive computations on the saw d model lead to two correction terms to the crude scaling form in this way some arguments in the literature on asymptotic theories can be settled several examples illustrate the danger of mistaking non asymptotic experimental results for those desired in the asymptotic range thus contrary to his own conclusions and those of fleming 1979 brun s data 1977 data for freely hinged hard sphere chains are here reconciled with the universal exponent gamma of le guillou and zinn justin 1977 for the saw d model subject always to further refinements which will never produce a final answer the present experimental estimate for gamma is also shown to be about 1 2 in line with conjectural estimates from many forms of modern theory

critical exponents of self avoiding walks on a family of truncated n simplex lattices the authors have studied self avoiding walks saws on a family of truncated n simplex lattices which provide a family of fractals in which the fractal dimension d can be varied to a wide range while the spectral dimension d is held almost fixed by means of exact renormalisation group transformations they have calculated the critical exponents nu alpha and gamma and the connectivity constant mu of the saws for n 5 and 6 they propose an approximate theory for calculating the critical exponents of the saws on fractals which is expected to be accurate at large values of n they show that the theory gives results which are in good agreement with exact values even for small values of n and leads to simple closed relations for the exponents

monte carlo generation of self avoiding walks with fixed endpoints and fixed length we propose a new class of dynamic monte carlo algorithms for generating self avoiding walks uniformly from the ensemble with fixed endpoints and fixed length in any dimension and prove that these algorithms are ergodic in all cases we also prove the ergodicity of a variant of the pivot algorithm

numeration systems linear recurrences and regular sets a numeration system based on a strictly increasing sequence of positive integers u0 1 u1u2 expresses a non negative integer n as a sum n j 0 i ajuj in this case we say the string a i a i 1 a1 a0 is a representation for n

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

the equivalence problem of multitape finite automata abstract using a result of b h neumann we extend eilenberg s equality theorem to a general result which implies that the multiplicity equivalence problem of two nondeterministic multitape finite automata is decidable as a corollary we solve a long standing open problem in automata theory namely the equivalence problem for multitape deterministic finite automata the main theorem states that there is a finite test set for the multiplicity equivalence of finite automata over conservative monoids embeddable in a fully ordered group

on dol power series abstract we study d0l power series we show how elementary morphisms introduced by ehrenfeucht and rozenberg can be used in connection with power series characterize the sequences of rational numbers and integers which can appear as coefficients in d0l power series and establish various decidability results

linear numeration systems of order two abstract a numeration system is a sequence of integers such that any integer can be represented by means of the sequence using integers of bounded size we study numeration systems defined by linear recurrences of order two we give a necessary and sufficient condition on the system such that every integer has a canonical representation we show that this canonical representation can be computed from any representation by a rational function this rational function is the composition of two subsequential functions that are simply obtained from the system the addition of two integers represented in the system can be performed by a subsequential machine

generalization of automatic sequences for numeration systems on a regular language let l be an infinite regular language on a totally ordered alphabet feeding a finite deterministic automaton with output with the words of l enumerated lexicographically with respect to leads to an infinite sequence over the output alphabet of the automaton this process generalizes the concept of k automatic sequence for abstract numeration systems on a regular language instead of systems in base k here we study the first properties of these sequences and their relations with numeration systems

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

two variable quasi scaling for three dimensional lattice polymers in a poor solvent regime the context of the renormalization group applied to the lattice polymer statistical mechanics with the nearest neighbour triplet interaction in addition to the usual nearest neighbour pair interaction yields a two variable quasi scaling relation it asserts that a reduced moment is described by two arbitrary reduced moments the validity of the two variable quasi scaling has been examined for lattice polymers with polymerization degree up to 1000 in the poor solvent regime and was confirmed it is well known that single variable scaling fails in this solvent regime linear relations connecting three reduced moments which are valid near the respective gaussian points and considered to be universal are presented the results however are not consistent with the premise employed in the continuous polymer model the working rg is nonlinear the consistency may be attained by polymers with polymerization degree much larger than 1000 for which the linearized rg will work the authors basic equation involves no particular reference point such as the theta point this is in contrast to previous scaling simulations and experiments

the stochastic wave equation in two spatial dimensions keywords stochastic wave equation gaussian noise process solution reference prob article 1998 001view record in web of science record created on 2008 12 01 modified on 2017 05 12

bounded delay l codes abstract three natural notions of bounded delay for l codes are investigated all interrelations many of them rather surprising between ordinary codes of bounded delay and l codes of bounded delay of various types are established

nonlocal monte carlo algorithm for self avoiding walks with fixed endpoints we study a new monte carlo algorithm for generating self avoiding walks with variable length controlled by a fugacity and fixed endpoints the algorithm is a hybrid of local bfacf and nonlocal cut and paste moves we find that the critical slowing down measured in units of computer time is reduced compared to the pure bfacf algorithm cpu n 2 3 versus n 3 0 we also prove some rigorous bounds on the autocorrelation time for these and related monte carlo algorithms

critical exponents hyperscaling and universal amplitude ratios for two and three dimensional self avoiding walks we make a high precision monte carlo study of two and three dimensional self avoiding walks saws of length up to 80 000 steps using the pivot algorithm and the karp luby algorithm we study the critical exponents v and 2 triangle sub 4 gamma as well as several universal amplitude ratios in particular we make an extremely sensitive test of the hyperscaling relation dv 2 triangle sub 4 gamma in two dimensions we confirm the predicted exponent v 3 4 and the hyperscaling relation we estimate the universal ratios 0 14026 0 00007 0 43961 0 00034 and psi 0 66296 0 00043 68 confidence limits in three dimensions we estimate v 0 5877 0 0006 with a correction to scaling exponent triangle sub 1 0 56 0 03 subjective 68 confidence limits this value for v agrees excellently with the field theoretic renormalization group prediction but there is some discrepancy for triangle 1 earlier monte carlo estimates of v which were approximately 0 592 are now seen to be biased by corrections to scaling we estimate the universal ratios 0 1599 0 0002 and psi 0 2471 0 0003 since psi 0 hyperscaling holds the approach to psi is from above contrary to the prediction of the two parameter renormalization group theory we critically reexamine this theory and explain where the error lies in an appendix we prove rigorously modulo some standard scalingmore assumptions the hyperscaling relation dv 2 triangle sub 4 gamma for two dimensional saws less

polymer conformations through wiggling a new monte carlo method is proposed which allows for the efficient generation of equilibrium conformations of polymer chains in two and three dimensions the method treats each site monomer as a potential pivot around which a new conformation may be generated by rotating a portion of the chain the method does not suffer from the severe attrition associated with the simple sampling of self avoiding walks and may be extended to treat the interacting polymer chain the authors find in two dimensions that nu 0 748 or 0 005 exact 0 750 and in three dimensions nu 0 595 or 0 005 series expansion and renormalisation group predict nu approximately 0 588 the end end distances calculated for shorter chains are in good agreement with the exact values from enumeration techniques

on lengths of words in context free languages we consider slender languages that is languages for which the number of words of the same length is bounded from above by a constant we prove that the slenderness problem is decidable for context free languages and that the maximal number of words of the same length in a given context free language is computable some effective representations of slender context free languages as well as other related decidability problems are investigated

self avoiding random loops a random loop or polygon is a simple random walk whose trajectory is a simple jordan curve the study of random loops is extended in two ways first the probability p sub n x y that a random n step loop contains a point x y in the interior of the loop is studied and 1 2 1 2 is shown to be 1 2 1 n it is plausible that p sub n x y tends toward 1 2 for all x y but this is not proved even for x y 3 2 1 2 a way is offered to simulate random n step self avoiding loops numerical evidence obtained with this simulation procedure suggests that the probability p sub n 3 2 1 2 approximately 1 2 c n for some fixed c

properties of set valued integrals and set valued stochastic equations driven by two parameter martingales abstract in the paper we study properties of aumann s stochastic integral driven by a two parameter increasing process and set valued ito s integral with respect to the two parameter martingale both types of integrals are understood as set valued processes next the existence uniqueness and convergence properties of solutions to set valued stochastic integral equations with respect to such integrators are investigated we present new types of such equations that generalize those studied earlier the results obtained in the paper present a set valued counterpart dealing with this topic known both in single valued deterministic and stochastic cases

bases and ambiguity of number systems abstract the degree of ambiguity of a given number system can be effectively computed we show also that all degrees of ambiguity do exist both as regards number systems and the sets represented by them in contrast to language theory there are inherently unambiguous sets the paper contains also results concerning the possibility of changing the base of a number system

on generalized dtol systems and their fixed points abstract we study a generalization of dt0l systems obtained by considering noncommutative polynomials together with mappings attaching a morphism to each variable we call the least fixed points of such pairs generalized dt0l languages and study their basic properties

random walks with short range interaction and mean field behavior we introduce a model of self repelling random walks where the short range interaction between two elements of the chain decreases as a power of the difference in proper time the model interpolates between the lattice edwards model and the ordinary random walk we show by means of monte carlo simulations in two dimensions that the exponentvmf obtained through a mean field approximation correctly describes the numerical data and is probably exact as long as it is smaller than the corresponding exponent for self avoiding walks we also compute the exponent and present a numerical study of the scaling functions

on the existence and position of the farthest peaks of a family of stochastic heat and wave equations we study the stochastic heat equation partial t u mathcal l u sigma u dot w in 1 1 dimensions where dot w is space time white noise r r is lipschitz continuous and mathcal l is the generator of a symmetric levy process that has finite exponential moments and u0 has exponential decay at we prove that under natural conditions on i the th absolute moment of the solution to our stochastic heat equation grows exponentially with time and ii the distances to the origin of the farthest high peaks of those moments grow exactly linearly with time very little else seems to be known about the location of the high peaks of the solution to the stochastic heat equation under the present setting see however gartner et al in probab theory relat fields 111 17 55 1998 gartner et al in ann probab 35 439 499 2007 for the analysis of the location of the peaks in a different model finally we show that these results extend to the stochastic wave equation driven by laplacian

uniqueness for stochastic non linear wave equations abstract we prove uniqueness of solutions of the equation u t t u f u g u w u 0 u 0 u t 0 v 0 on r d in the class of processes with paths in h 1 here u 0 v 0 is a random variable in h 1 l 2 w is a spatially homogeneous wiener process with finite spectral measure and f g are locally lipschitz functions of subcritical growth

parisi s mean field solution for spin glasses as an analytic continuation in the replica number parisi s replica symmetry breaking solution for spin glasses is extended to finite replica number n the free energy fp n obtained this way as well as its first two derivatives with respect to n are shown to join the corresponding values in the sherrington kirkpatrick sk solution at a characteristic value ns t where stability breaks down in the latter the continuation composed of the sk branch fsk n for n or ns t and the parisi branch fp n for 0 or n or ns t fulfils the requirements of convexity monotonicity and stability for all n

nonergodicity of local length conserving monte carlo algorithms for the self avoiding walk it is proved that every dynamic monte carlo algorithm for the self avoiding walk based on a finite repertoire of local n conserving elementary moves is nonergodic heren is the number of bonds in the walk indeed for largen each ergodic class forms an exponentially small fraction of the whole space this invalidates at least in principle the use of the verdier stockmayer algorithm and its generalizations for high precision monte carlo studies of the self avoiding walk

critical properties of the three dimensional self avoiding walk accurate monte carlo data are used to determine the critical exponent nu 0 590 or 0 001 or inverse fractal dimension of the three dimensional self avoiding walk the leading correction to scaling term is non analytic and is near 0 5

determination of the exponent for saws on the two dimensional manhattan lattice we present a high statistics monte carlo determination of the exponent for self avoiding walks on a manhattan lattice in two dimensions a conservative estimate is in agreement with the universal value on regular lattices but in conflict with predictions from conformal field theory and with a recent estimate from exact enumerations we find strong corrections to scaling that seem to indicate the presence of a non analytic exponent if we assume we find where the error is purely statistical

join and cut algorithm for self avoiding walks with variable length and free endpoints we introduce a new monte carlo algorithm for generating self avoiding walks of variable length and free endpoints the algorithm works in the unorthodox ensemble consisting of all pairs of saws such that the total number of stepsntot in the two walks is fixed the elementary moves of the algorithm are fixed n e g pivot moves on the individual walks and a novel join and cut move that concatenates the two walks and then cuts them at a random location we analyze the dynamic critical behavior of the new algorithm using a combination of rigorous heuristic and numerical methods in two dimensions the autocorrelation time in cpu units grows as n 1 5 and the behavior improves in higher dimensions this algorithm allows high precision estimation of the critical exponent

the pivot algorithm and polygons results on the fcc lattice the authors consider the pivot algorithm for polygons on the face centred cubic lattice and prove ergodicity a numerical study of the algorithm is carried out in particular the authors look at the acceptance fraction of the elementary moves and find that it goes only slowly to zero as the length of the polygons is increased the numerical properties of polygons on the fcc lattice are also considered they calculate the exponent nu by considering the mean square radius of gyration of the polygons and compare the result to the expected value from field theory they also consider the mean span of the polygons and discuss corrections to scaling and their influence on the numerical calculation of critical exponents

the use and usefulness of numeration systems the proper choice of a counting system may solve mathematical problems or lead to improved algorithms this is illustrated by a problem in combinatorial group theory compression of sparse binary strings encoding of contiguous binary strings of unknown lengths ranking of permutations and combinations strategies of games and other examples two abstract counting systems are given from which the concrete ones used for the applications can be derived

l codes and number systems abstract the notion of an l code is introduced as a generalization of the customary notion of a code attention is focused on unary l codes where the target alphabet consists of one letter only unary l codes can be identified with such number systems where the representation is unique surprisingly many unary morphisms are l codes furthermore even for non l codes there is only one exceptional length we also give a complete classification for the binary case

on the sequentiality of the successor function abstract letube a strictly increasing sequence of integers by a greedy algorithm every nonnegative integer has a greedyu representation the successor function maps the greedyu representation ofnonto the greedyu representation ofn 1 we characterize the sequencesusuch that the successor function associated withuis a left resp a right sequential function we also show that the odometer associated touis continuous if and only if the successor function is right sequential

conformational space renormalisation group theory of tricritical theta point exponents for a polymer chain the marked difference between the n to 0 limit of o n phi 4 phi 6 field theory tricritical exponents and accepted values for a polymer in d 2 are shown to persist when renormalisation is performed away from the tricritical point the difference is removed by introducing a physically dictated renormalisation prescription for the field theoretic formulation of the polymer problem or the equivalent chain conformational space method

strong solutions to stochastic wave equations with values in riemannian manifolds let m be a d dimensional compact riemannian manifold we prove existence of a unique global strong solution of the stochastic wave equation dt tu dx xu yu tu xu w where y is a c1 smooth transformation and w is a spatially homogeneous wiener process on r whose spectral measure has finite moments up to order 2

the sharp markov property of levy sheets keywords brownian sheet two parameter levy processes sharp field poisson sheet splitting field reference prob article 1992 002doi 10 1214 aop 1176989793 record created on 2008 12 01 modified on 2017 05 12

on lindenmayerian algebraic sequences abstract we define and study lindenmayerian algebraic sequences these sequences are a generalization of algebraic sequences k regular sequences and automatic sequences

the ring of k regular sequences ii in this paper we continue our study of k regular sequences begun in 1992 we prove some new results give many new examples from the literature and state some open problems

collapse transition and crossover scaling for self avoiding walks on the diamond lattice a monte carlo study of self avoiding walks on the diamond lattice is presented this model incorporates some of the steric effects and short range stiffness of real alkanes and for a nearest neighbour attractive interaction epsilon is found to have a collapse transition at kb theta epsilon 2 25 or 0 05 the behaviour of the chains in the vicinity of this theta temperature is analysed with the help of recent crossover scaling theories it is shown that for finite chain length n there is a rather broad theta region where the chains behaviour is quasi ideal the width of this region wtheta behaves as omega 0 varies as n 12 consistent with the blob picture the peak of the specific heat occurs at the boundary between the theta region and the region of collapsed chains the authors also give rough estimates for the scaling functions describing the crossovers of the end to end distance and structure factor of the chains

real numbers having ultimately periodic representations in abstract numeration systems using a genealogically ordered infinite regular language we know how to represent an interval of r numbers having an ultimately periodic representation play a special role in classical numeration systems the aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language the syntactical properties of these words are also investigated finally we show the equivalence of the classical expansions with our generalized representations in some special case related to a pisot number

ambiguity and decision problems concerning number systems the representation of integers in arbitrary number systems is considered the main emphasis is on problems concerning ambiguity completeness and equivalence a rather general automata theoretic method for solving such in essence purely number theoretic problems is developed the method seems to be applicable in a variety of different situations

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

bilocal dynamics for self avoiding walks we introduce several bilocal algorithms for lattice self avoiding walks we discuss their ergodicity in different confined geometries for instance in strips and in slabs a short discussion of the dynamical properties in the absence of interactions is given

a generalization of automatic sequences abstract we generalize the uniform tag sequences of cobham which arise as images of fixed points of k uniform homomorphisms to the case where the homomorphism is not necessarily uniform but rather satisfies the analogue of an algebraic equation we show that these sequences coincide with 1 a the class of sequences accepted by a finite automaton with generalized digits as input and 2 b generalizations of the locally catenative formula of rozenberg and lindenmayer examples include the infinite fibonacci word which is generated as the fixed point of the homomorphism a ab b a and sequences of rauzy and de bruijn

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

numeration systems on a regular language arithmetic operations recognizability and formal power series abstract generalizations of numeration systems in which n is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language l for these systems we obtain a characterization of recognizable sets of integers in terms of n rational formal series after a study of the polynomial regular languages we show that if the complexity of l is n l resp if l is the complement of a polynomial language then multiplication by n preserves recognizability only if l 1 resp if for some n finally we obtain sufficient conditions for the notions of recognizability for abstract systems and some positional number systems to be equivalent

random nonlinear wave equations propagation of singularities on etudie les proprietes de lissite des solutions d equations d ondes unidimensionnelles avec forcing aleatoire non lineaire on definit les singularites comme anomalies dans le modulo local de continuite des solutions

a new method for simulation of real chains scanning future steps a new method for simulating real polymer chains is developed and applied to self avoiding walks saws of length 49 599 on a three choice square lattice very good results for the entropy are obtained which deviate from the series expansion estimates by 0 1 2 the author also discusses how to extend the method to models of polymer chains with both excluded volume and finite interactions attractive or repulsive the author s method is expected to be more efficient than other simulation methods for treating self interacting saws and chains which are subject to various lattice constraints

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

renormalized four point coupling constant in the three dimensional o n model with n 0 we simulate self avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths this allows us to determine the critical value of the renormalized four point coupling constant in the three dimensional n vector universality class for n 0 we obtain g 1 4005 5 where g is normalized so that the three dimensional field theoretical beta function behaves as beta g g g 2 for small g as a byproduct we also obtain precise estimates of the interpenetration ratio psi psi 0 24685 11 and of the exponent nu nu 0 5876 2

stochastic wave equation with critical nonlinearities temporal regularity and uniqueness we consider a nonlinear wave equation utt u f u g u w on r d driven by a spatially homogeneous wiener process w with a finite spectral measure and with nonlinear terms f g of critical growth we study pathwise uniqueness and norm continuity of paths of u ut in h 1 rd l2 rd under the hypothesis that there exists a local solution u such that u ut has weakly continuous paths in h 1

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

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

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

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

on lindenmayerian algebraic power series abstract we define lindenmayerian algebraic power series and study their properties these series generalize both algebraic series and etol languages

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

automata and languages generalized to ω continuous semirings abstract we generalize the following two language and automata theoretic results to continuous semirings i the family of languages accepted by finite automata is the smallest class containing all finite languages and closed under union product and star kleene s theorem ii the family of languages accepted by pushdown automata is the family ofcontext free languages

decimations of languages and state complexity let the words of a language l be arranged in increasing radix order l w 0 w 1 w 2 we consider transformations that extract terms from l in an arithmetic progression for example two such transformations are even l w 0 w 2 w 4 and odd l w 1 w 3 w 5 lecomte and rigo observed that if l is regular then so are even l odd l and analogous transformations of l we find good upper and lower bounds on the state complexity of this transformation we also give an example of a context free language l such that even l is not context free

on d0l systems with immigration abstract we study dol systems with immigration we show that sequence and growth equivalence are decidable we establish regularity and decidability results concerning degrees of ambiguity as a consequence of results about subword complexity we show that regularity and regularity are decidable for languages generated by growing systems

random non linear wave equations smoothness of the solutions we show existence and uniqueness for the solution of a onedimensional wave equation with non linear random forcing then we give sufficient conditions for the solution at a given time and a given point to have a density and for this density to be smooth the proof uses the extension of the malliavin calculus to the two parameters wiener functionals