lattice models of branched polymers effects of geometrical constraints the authors consider uniform brushes on subsets of the square and simple cubic lattices they show that in a slab geometry in three dimensions the connective constant of a brush is identical to that of a walk in that slab in two dimensions in a slit geometry the connective constant of a brush is strictly less than that of a walk they also consider the intermediate case of a rectangular prism and show that the connective constant of a brush is strictly less than that of a walk similar results are presented for combs stars and polygons

power monoids a bridge between factorization theory and arithmetic combinatorics abstract we extend a few fundamental aspects of the classical theory of non unique factorization as presented in geroldinger and halter koch s 2006 monograph on the subject to a non commutative and non cancellative setting in the same spirit of baeth and smertnig s work on the factorization theory of non commutative but cancellative monoids baeth and smertnig 2015 5 then we bring in power monoids and applying the abstract machinery developed in the first part we undertake the study of their arithmetic more in particular let h be a multiplicatively written monoid the set p fin h of all non empty finite subsets of h is naturally made into a monoid which we call the power monoid of h and is non cancellative unless h is trivial by endowing it with the operation x y x y x y x y power monoids are in disguise one of the primary objects of interest in arithmetic combinatorics and here for the first time we tackle them from the perspective of factorization theory proofs lead to consider various properties of finite subsets of n that can or cannot be split into a sumset in a non trivial way giving rise to a rich interplay with additive number theory

the liapunov dimension of strange attractors abstract many papers have been published recently on studies of dynamical processes in which the attracting sets appear quite strange in this paper the question of estimating the dimension of the attractor is addressed while more general conjectures are made here particular attention is paid to the idea that if the jacobian determinant of a map is greater than one and a ball is mapped into itself then generically the attractor will have positive two dimensional measure and most of this paper is devoted to presenting cases with such jacobians for which the attractors are proved to have non empty interior

the radius of gyration of a branch of a uniform star polymer the authors use monte carlo methods and perturbation calculations to study the mean square radius of gyration of a branch of a uniform star with excluded volume as a function of the number f of branches and of the number n of monomers per branch they show that the mean square radius of gyration s n f 2 scales like a f n2v f fixed n to infinity where the exponent is independent of f they estimate the amplitude ratios a f a 1 for various values of f and show that these ratios are lattice independent the amplitude ratio increases as f increases but the effect is small the numerical agreement between the two methods is good especially for small values of f

branched polymers attached in a wedge geometry the authors use exact enumeration and monte carlo techniques to test some recent predictions by duplantier and saleur 1986 of the values of the critical exponent gamma for uniform star branched polymers in a wedge geometry in two dimensions results support their predictions the authors have also estimated the exponent v and amplitude governing the n dependence of the mean square radius of gyration and the mean square end to end branch length in some cases the branches are distinguished and have different mean lengths but the exponent v is equal to the bulk self avoiding walk value in every case

huneke wiegand conjecture for complete intersection numerical semigroup rings abstract we give a positive answer to the huneke wiegand conjecture for monomial ideals over free numerical semigroup rings and for two generated monomial ideals over complete intersection numerical semigroup rings

factorizations of matrices over semirings in this paper as a generalization of prime boolean matrices and prime fuzzy matrices we study semiprime matrices over chain semirings using the relationship between semiprime matrices and their row spaces we show that a nonmonomial matrix with full semiring rank can be expressed as a product of elementary matrices and semiprime matrices furthermore we show that a nonmonomial regular matrix with full semiring rank can be expressed as a product of elementary matrices

dynamics of a higher dimensional fractional order chaotic map abstract fractional calculus has been a hot topic in nonlinear science because it can describe physical phenomena more accurately in recent years the theory of fractional difference has become one of the foundations for fractional order chaotic maps based on this concept a higher dimensional fractional order chaotic map is investigated different from other proposed fractional order chaotic maps it has multiple dimensions and can be set as incommensurate fractional order the bifurcation diagrams and attractors of this system with changing fractional orders are plotted by numerical simulations and the maximum lyapunov exponent mle the permutation entropy complexity and the probability density distribution are also calculated results show it has rich dynamical behaviors many of the periodic windows in the integer order map become chaos when they are in the fractional order form and the complexity of the fractional order form is higher than that of its integer order counterpart and other nine typical chaotic maps in addition the distribution of fractional order system is also better than that of the integer order one these results lay the theoretical foundation for its practical applications and relevant to the study of other fractional order chaotic maps

lattice models of branched polymers statistics of uniform stars the authors investigate the statistical properties of uniform star polymers with f branches modelled on lattices in two and three dimensions it is shown that the growth constant exists and is equal to mu f where mu is the self avoiding walk limit the f dependence of the corresponding critical exponent gamma f is studied using exact enumeration and monte carlo techniques and the results are compared with the predictions of miyake and freed 1983 obtained using chain conformation space renormalisation group method

synchronization of chaotic systems involving fractional operators of liouville caputo type with variable order abstract in this paper we propose a state observer based approach to synchronize variable order fractional vof chaotic systems in particular this work is focused on complete synchronization with a so called unidirectional master slave topology the master is described by a dynamical system in state space representation whereas the slave is described by a state observer the slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization the differential equations of the vof chaotic system are described by the liouville caputo and atangana baleanu caputo derivatives numerical simulations involving the synchronization of rossler oscillators chua s systems and multi scrolls are studied the simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval 0 1 are used as the variable order of the fractional derivatives furthermore simulations show that the vof chaotic systems can be synchronized

factorization theory from commutative to noncommutative settings abstract we study the non uniqueness of factorizations of non zero divisors into atoms irreducibles in noncommutative rings to do so we extend concepts from the commutative theory of non unique factorizations to a noncommutative setting several notions of factorizations as well as distances between them are introduced in addition arithmetical invariants characterizing the non uniqueness of factorizations such as the catenary degree the invariant and the tame degree are extended from commutative to noncommutative settings we introduce the concept of a cancellative semigroup being permutably factorial and characterize this property by means of corresponding catenary and tame degrees also we give necessary and sufficient conditions for there to be a weak transfer homomorphism from a cancellative semigroup to its reduced abelianization applying the abstract machinery we develop we determine various catenary degrees for classical maximal orders in central simple algebras over global fields by using a natural transfer homomorphism to a monoid of zero sum sequences over a ray class group we also determine catenary degrees and the permutable tame degree for the semigroup of non zero divisors of the ring of n n upper triangular matrices over a commutative domain using a weak transfer homomorphism to a commutative semigroup

the growth constant of uniform star polymers in a slab geometry the authors consider uniform star branched polymer molecules modelled by the corresponding graph weakly embedded in a simple cubic lattice confined to a parallel sided slab in three and higher dimensions they show that the limiting entropy per bond is independent of the number of branches in the star and is equal to the connective constant of a self avoiding walk on that subset of the lattice in two dimensions however the limiting entropy per bond of a three branch star is shown to be strictly less than that for a self avoiding walk and present numerical evidence that this is a general result in two dimensions

new exact exponents for two dimensional self avoiding walks the author establishes using standard coulomb gas methods the values of a new set of geometrical exponents that have been previously conjectured these exponents give for any p the number of configurations of p two dimensional self avoiding walks of the same length l which are attached by their ends

on the atomicity of monoid algebras abstract let m be a commutative cancellative monoid and let r be an integral domain the question of whether the monoid ring r x m is atomic provided that both m and r are atomic dates back to the 1980s in 1993 roitman gave a negative answer to the question for m n 0 he constructed an atomic integral domain r such that the polynomial ring r x is not atomic however the question of whether a monoid algebra f x m over a field f is atomic provided that m is atomic has been open since then here we offer a negative answer to this question first we exhibit for any infinite cardinal a torsion free atomic monoid m of rank satisfying that the monoid domain r x m is not atomic for any integral domain r then for every n 2 and for each field f of finite characteristic we find a torsion free atomic monoid m of rank n such that f x m is not atomic finally we construct a torsion free atomic monoid m of rank 1 such that z 2 x m is not atomic

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

image encryption using 2d logistic adjusted sine map with complex properties of ergodicity unpredictability and sensitivity to initial states chaotic systems are widely used in cryptography this paper proposes a two dimensional logistic adjusted sine map 2d lasm performance evaluations show that it has better ergodicity and unpredictability and a wider chaotic range than many existing chaotic maps using the proposed map this paper further designs a 2d lasm based image encryption scheme las ies the principle of diffusion and confusion are strictly fulfilled and a mechanism of adding random values to plain image is designed to enhance the security level of cipher image simulation results and security analysis show that las ies can efficiently encrypt different kinds of images into random like ones that have strong ability of resisting various security attacks

factorizations in upper triangular matrices over information semialgebras abstract an integral domain or a commutative cancellative monoid is atomic if every nonzero nonunit element factors into atoms and it satisfies the accp if every ascending chain of principal ideals eventually stabilizes the interplay between these two properties has been investigated since the 1970s an atomic domain or monoid satisfies the finite factorization property ffp if every element has only finitely many factorizations and it satisfies the bounded factorization property bfp if for each element there is a bound for the number of atoms in each of its factorizations these two properties have been systematically studied since they were introduced by anderson anderson and zafrullah in 1990 noetherian domains satisfy the bfp while dedekind domains satisfy the ffp it is well known that for commutative cancellative monoids and in particular for multiplicative monoids of integral domains ffp bfp accp atomic for n 2 we show that each of these four properties transfers back and forth between an information semialgebra s certain commutative cancellative semiring and the multiplicative monoid t n s consisting of n n upper triangular matrices over s we also show that a similar transfer behavior takes place if one replaces t n s by its submonoid u n s consisting of upper triangular matrices with units along their main diagonals as a consequence we find that the atomic chain ffp bfp accp atomic also holds for the two classes comprising the noncommutative monoids t n s and u n s finally we construct various rational information semialgebras to verify that in general none of the established implications is reversible

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

dimensions of the branches of a uniform brush polymer excluded volume effects increase the dimensions of the various branches of a uniform brush polymer to different extents the authors use monte carlo methods and perturbation calculations to study the mean square end to end branch lengths of a uniform brush with two branch points as a function of the number n of monomers in a branch and the functionalities f1 and f2 of the branch points the mean square end to end length rn2 of a branch scales like bn2v and they investigate how the amplitude b varies for the different types of branch as f1 and f2 vary the amplitude ratios are expected to be lattice independent and they find good agreement between their numerical estimates of these ratios from perturbation and monte carlo calculations they have extended the perturbation calculations to make predictions for the corresponding amplitude ratios for the mean square radii of gyration of the various branches

monte carlo simulation of many arm star polymers in two dimensional good solvents in the bulk and at a surface a monte carlo technique is proposed for the simulation of statistical properties of many arm star polymers on lattices in this vectorizing algorithm the length of each arml is increased by one step by step from a starting configuration withl 1 orl 2 which is generated directly this procedure is carried out for a large sample e g 100 000 configurations as an application we have studied self avoiding stars on the square lattice with arm lengths up tolmax 125 and up tof 20 arms both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface the total number of configurations which behaves asn l g 1 fl where 2 6386 is the usual effective coordination number for self avoiding walks on the square lattice is analyzed and the resulting exponents g f and s f for the bulk and surface geometries are found to be compatible with predictions of duplantier and saleur based on conformai invariance methods we also obtain distribution functions for the monomer density and the distance of the end of an arm from its center the results are consistent with a scaling theory developed by us

polygons and stars in a slit geometry the authors consider self avoiding polygons uniform 3 stars and uniform 4 stars weakly embeddable in the square lattice and confined between two parallel lines y 0 and y l they show rigorously that the connective constants of these three structures provided that the corresponding limits exist are all strictly less than the connective constant kappa l of self avoiding walks with the same geometrical constraint they also derive lower bounds on the connective constants of uniform 3 stars and 4 stars these bounds appear to be strong at least for small l

critical behaviour at an edge for the saw and ising model the authors have studied the behaviour of two and three dimensional self avoiding walks confined to a wedge of wedge angle alpha series have been obtained and analysed for the angular dependent critical exponents characterising various edge susceptibilities in terms of a general scaling form for the edge free energy fe approximately t d 2 nu psi e ht y0 nu h1t y1 nu h2t y2 nu they find for the two dimensional case the following scaling indices y0 91 48 y1 3 8 y2 alpha 5 pi 8 alpha they argue that these results are exact from which follow all exponents for the bulk surface and edge problem in three dimensions the authors obtain y0 approximately 2 488 y1 0 65 or 0 02 y2 alpha alpha b pi alpha where a 0 51 or 0 04 b 0 847 or 0 017 which for y2 is precisely of the functional form given by mean field theory y2 alpha 1 2 pi 2 they argue that a 1 2 for all three dimensional o n models this simple angular dependence of y2 is different from that suggested by cardy s one loop epsilon expansion 1983 for the square lattice they have also studied the case in which the wedge is rotated through an angle of pi 4 and find that the various exponents are unchanged for the three dimensional ising model in a wedge analogy with the saw results plus mean field results in conjunction with rg and series work yield y0 approximately 2 485 y1 0 71 or 0 02 and y2 a b pi alpha with a 1 2 and b 0 79 or 0 02

branched polymers in a wedge geometry in three dimensions we investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and we show that the growth constant is equal to f where is the self avoiding walk limit thef and dependences of the corresponding critical exponent f are studied using monte carlo techniques in the casef 1 our results are compared with existing predictions obtained from series expansion and renormalization group methods we have also estimated the amplitudes for the mean square radius of gyration and the mean square end to end branch length our results for the ratio of the mean square radius of gyration of anf star to that of a linear polymer of the same degree of polymerization attached in a similar wedge and the analogous ratio for the mean square end to end branch length are consistent with these ratios being lattice independent quantities

lattice trees with a restricted number of branch points the authors investigate the asymptotic behaviour of the number of trees having n vertices weakly embeddable in the d dimensional hypercubic lattice with restrictions on the number n of vertices with degree greater than two they show rigorously that if n o n log n the growth constant is equal to the corresponding quantity for self avoiding walks for n increasing linearly with n they show that the growth constant still exists and present arguments indicating that it is strictly greater than that for self avoiding walks

exact critical exponents for two dimensional dense polymers using conformal invariance and coulomb gas results the author gives the exact value in two dimensions of the eta exponent of l dense polymers attached by their extremities eta l l2 4 8 the value in two dimensions of the gamma exponent of a dense branched polymer of fixed topology with nl l leg vertices l or 1 is then deduced to be gamma sigma l or 1 nl 2 l l 18 32 these values correspond to a conformally invariant theory with central charge c 2

factorizations of upper triangular matrices if d is an integral domain in which every element can be factored as a product of irreducible elements then every element a tn d the semigroup of upper triangular matrices with nonzero determinant can be factored as a product of irreducible elements we classify both the irreducible elements and units of this cancellative semigroup having achieved this we provide a means of measuring the uniqueness or non uniqueness of these factorizations in terms of the uniqueness or non uniqueness of factorizations in d in addition to using well studied invariants from factorization theory of commutative semigroups we introduce a new tool weak transfer homomorphisms which are more appropriate for noncommutative settings

tensor products of modules and the rigidity of tor let r be a hypersurface domain that is a ring of the form s f where s is a regular local ring and f is a prime element suppose m and n are finitely generated r modules we prove two rigidity theorems on the vanishing of tor in the first theorem we assume that the regular local ring s is unramified that m r n has finite length and that dim m dim n dim r with these assumptions if tor r m n 0 for some j 0 then tor r m n 0 for all i j the second rigidity theorem states that if m r n is reflexive then tor r m n 0 for all i 1 we use these theorems to prove the following theorem valid even if s is ramified if m r n is a maximal cohen macaulay r module then both m and n are maximal cohen macaulay modules and at least one of them is free

multivariate permutation entropy and its application for complexity analysis of chaotic systems abstract to measure the complexity of multivariate systems the multivariate permutation entropy mvpe algorithm is proposed it is employed to measure complexity of multivariate system in the phase space as an application mvpe is applied to analyze the complexity of chaotic systems including hyperchaotic henon map fractional order simplified lorenz system and financial chaotic system results show that mvpe algorithm is effective for analyzing the complexity of the multivariate systems it also shows that fractional order system does not become more complex with derivative order varying compared with pe mvpe has better robustness for noise and sampling interval and the results are not affected by different normalization methods

upper triangular matrices over information algebras abstract factorization in matrix rings has been investigated in a wide variety of contexts recently this study has provided a wealth of information about how factorization works in noncommutative settings it is often the case that when s is a ring of matrices over a base ring r multiplicative factorization in r drives the multiplicative factorization in s that is the additive structure of r is largely irrelevant to how elements of s factor multiplicatively recently chen et al studied factorization of the semiring of upper triangular matrices with entries in n 0 the semiring of nonnegative integers in this work we show that their results fit within the larger context of factorization in upper triangular matrices over reduced information algebras we illustrate that factorization in t n h 0 depends on both the multiplicative and additive structure of h 0 if h 0 is such an information algebra we classify the irreducible elements of t n h 0 and describe the degree to which factorization in t n h 0 is nonunique by considering elasticities delta sets and unions of sets in addition we show that unlike many important classes of semigroups whose arithmetic has been studied t n h 0 is not transfer krull for h 0 n 0 we extend previously known results and give explicit descriptions of nonunique factorization in t n n 0

on unique factorization domains abstract in this paper we attempt to generalize the notion of unique factorization domain in the spirit of half factorial domain it is shown that this new generalization of ufd implies the now well known notion of half factorial domain as a consequence we discover that one of the standard axioms for unique factorization domains is slightly redundant

puiseux monoids and transfer homomorphisms abstract there are several families of atomic monoids whose arithmetical invariants have received a great deal of attention during the last two decades the factorization theory of finitely generated monoids strongly primary monoids krull monoids and c monoids are among the most systematically studied puiseux monoids which are additive submonoids of q 0 consisting of nonnegative rational numbers have only been studied recently in this paper we provide evidence that this family comprises plenty of monoids with a basically unexplored atomic structure we do this by showing that the arithmetical invariants of the well studied atomic monoids mentioned earlier cannot be transferred to most puiseux monoids via homomorphisms that preserve atomic configurations i e transfer homomorphisms specifically we show that transfer homomorphisms from a non finitely generated atomic puiseux monoid to a finitely generated monoid do not exist we also find a large family of puiseux monoids that fail to be strongly primary in addition we prove that the only nontrivial puiseux monoid that accepts a transfer homomorphism to a krull monoid is n 0 finally we classify the puiseux monoids that happen to be c monoids

two dimensional polymers and conformal invariance abstract the critical properties of self avoiding walks percolation clusters and critical exponents associated with the planar brownian motion are reviewed in two dimensions 2d the conformal spectrum of these geometrical critical systems is made of an infinite descrete series of scaling dimensions the latter are calculated in the framework of coulomb gas methods and conformal invariance the statistical mechanics of the same critical models on a random 2d lattice i e on a random surface namely in presence of a critically fluctuating metric in the so called 2d quantum gravity is also addressed and the above critical geometrical systems are exactly solvable in this case the new gravitational conformal spectrum is related to the standard conformal spectrum in the plane as predicted recently

increasing positive monoids of ordered fields are ff monoids abstract given an ambient ordered field k a positive monoid is a countably generated additive submonoid of the nonnegative cone of k in this paper we first generalize several atomic features exhibited by puiseux monoids of the field of rational numbers to the more general setting of positive monoids of archimedean fields accordingly arguing that such generalizations might fail if the ambient field is not archimedean in particular we show that a positive monoid p of an archimedean field is a bf monoid provided that p 0 does not have 0 as a limit point then we prove our main result every increasing positive monoid of an ordered field is an ff monoid finally we deduce that every increasing positive monoid is hereditarily atomic

adaptive umbrella sampling self consistent determination of the non boltzmann bias a self consistent procedure is described for the determination of the non boltzmann bias for the umbrella sampling technique of valleau patey and torrie the new procedure offers more reliable results with less human interference the problem of matching several differently normalized probability distributions on overlapping domains has been treated in detail the algorithm has been tested on the calculation of the solvent contribution to the free energy difference between the c7 and r conformation of the alanine dipeptide treated earlier with the conventional umbrella sampling technique

factorizations of block triangular matrices abstract transfer homomorphisms have long been used as tools in factorization theory the idea is to transfer information about factorizations in a semigroup of interest from simpler easier to understand semigroups unfortunately there exist noncommutative semigroups which admit no transfer homomorphism to any commutative semigroup the weak transfer homomorphism was introduced to study such semigroups in particular these weak transfer homomorphisms were used to study factorizations of semigroups of upper triangular matrices with entries coming from a commutative integral domain in this work we extend this study finding weak transfer homomorphisms to both commutative and noncommutative semigroups from upper triangular matrices with entries coming from noncommutative rings in particular we study factorizations of block triangular matrices

a lattice model of uniform star polymers the authors present monte carlo and exact enumeration results for three and four arm stars on a variety of lattices they estimate the exponents for the number of stars and the mean square end to end length of a branch and compare these results with scaling and renormalisation group predictions

adsorption of ideal polymers on an infinitely ramified fractal we study ideal polymer chains interacting attractively with the borders of the lacunas of an infinitely ramified fractal the sierpinski carpet ideal chains are simulated on finite stages of construction of this fractal at various temperatures the mean square displacement and the mean number of adsorbed monomers of n step chains are estimated in these lattices and extrapolations to the fractal limit infinite lattice consider the exact forms of finite size corrections as previously predicted by the series expansion method in the noninteracting case a finite fraction of the monomers is adsorbed and this fraction increases as the temperature decreases however there is evidence that the critical exponent v which governs the growth of the chains varies with the temperature in a nonmonotonic way at high temperatures v increases with decreasing temperature and thus the chains are more stretched than in the noninteracting case at an intermediate temperature v starts to decrease and is still positive at very low temperatures when the chains grow along the borders of several lacunas occasionally crossing the bulk between them

chaotic vibration bifurcation stabilization and synchronization control for fractional discrete time systems abstract the main intention of this paper is to investigate the dynamics of fractional cubic map and fractional holmes map from four perspectives chaos bifurcation stabilization and synchronization via jacobian matrix algorithm we estimate the largest lyapunov exponents of fractional maps to examine the existence of chaos in accordance with the observation of chaotic vibration affected by fractional difference order in addition with the help of the novel asymptotic stability criterion for linear incommensurate fractional difference systems the effective control laws of stabilization and synchronization for fractional chaotic maps are achieved respectively besides experimental investigations and numerical simulations are implemented to further verify the effectiveness of the proposed results

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

self avoiding walks in wedges the authors consider the number of self avoiding walks confined to a subset zd f of the d dimensional hypercubic lattice zd such that the coordinates x1 x2 xd of each vertex in the walk satisfy x1 or 0 and 0 or xk or fk x1 for k 2 3 d they show that if fk x to infinity as x to infinity the connective constant of walks in zd f is identical to the convective constant of walks in zd they also explore conditions on fk which lead to a smaller connective constant for walks in zd f and in particular consider walks between two parallel d 1 dimensional hyperplanes finally they contrast some of these results with recent work by grimmett on percolation on subsets of the square lattice

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

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

a monte carlo study of non trapped self avoiding walks in this paper we study non trapped self avoiding walks saws which are saws that can be extended to an arbitrary length we apply the flatperm monte carlo method for this purpose generating non trapped saws of length up to 1024 on the square triangular and hexagonal lattices and calculating their number and mean squared end to end distance we find strong numerical evidence that the growth constant and entropic and metric exponents and are identical for non trapped and all saws and in particular that the exponents are also universal for non trapped saws we also calculate the limiting ratio of non trapped to all saws we see some evidence of an n 1 2 correction to scaling term which is not present for all saws

a study of uniform stars using 1 d expansions and numerical methods we study a lattice model of an interacting uniform self avoiding star polymer with f branches a 1 d expansion for the limiting reduced free energy is derived through order 1 d for general f and for f 3 to order 1 d 2 the terms in the expansion are independent of f and agree term by term with the corresponding expansion for interacting self avoiding walks we also present a miscellany of numerical results obtained by more conventional series and monte carlo techniques all our results both past and present support the conjecture that the limiting reduced free energies of f stars walks and polygons are identical for all values of the interaction parameter

sets of lengths in maximal orders in central simple algebras abstract let o be a holomorphy ring in a global field k and r a classical maximal o order in a central simple algebra over k we study sets of lengths of factorizations of cancellative elements of r into atoms irreducibles in a large majority of cases there exists a transfer homomorphism to a monoid of zero sum sequences over a ray class group of o which implies that all the structural finiteness results for sets of lengths valid for commutative krull monoids with finite class group hold also true for r if o is the ring of algebraic integers of a number field k we prove that in the remaining cases no such transfer homomorphism can exist and that several invariants dealing with sets of lengths are infinite

lattice models of branched polymers uniform combs in two dimensions the authors establish rigorously the relationship between the growth constant of uniform trees with two branch points and that of self avoiding walks for combs they estimate the corresponding exponent and study the mean square lengths of the internal and external branches

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

geometric and combinatorial aspects of submonoids of a finite rank free commutative monoid abstract if f is an ordered field and m is a finite rank torsion free monoid then one can embed m into a finite dimensional vector space over f via the inclusion m gp m f z gp m where gp m is the grothendieck group of m let c be the class consisting of all monoids up to isomorphism that can be embedded into a finite rank free commutative monoid here we investigate how the atomic structure and arithmetic properties of a monoid m in c are connected to the combinatorics and geometry of its conic hull cone m f z gp m first we show that the submonoids of m determined by the faces of cone m account for all divisor closed submonoids of m then we appeal to the geometry of cone m to characterize whether m is a factorial half factorial and other half factorial monoid finally we investigate the cones of finitary primary finitely primary and strongly primary monoids in c along the way we determine the cones that can be realized by monoids in c and by finitary monoids in c

nonuniform star polymers in two dimensions we present simulation results for nonuniform 2d star polymers using a recursive implementation of the enrichment method we show that the choice of parameters in this method is not trivial and that a good choice can lead to extremely efficient code we find that the exponents gamma f governing the increase of the f star partition function with n are compatible with the prediction gamma funiform f 1 by duplantier 1986

lattice trees with specified topologies the authors study the total numbers of lattice trees with specified topologies for strongly embeddable or site clusters with ni branching points of degree i they show how to prove rigorously that the growth constants exist and are all equal to the neighbour avoiding walk limit nu they derive some exact upper bounds for the critical exponents associated with the star comb and brush topologies exact enumeration data are derived and analysed for both weak and strong embeddings of some stars combs and brushes on the square triangular simple cubic and d 4 simple hypercubic lattices using the exact enumeration data for the general d dimensional simple hypercubic lattice and the exact results for the interior of a bethe lattice they derive expansions for the growth constants in inverse powers of the dimensionality these results are consistent with the growth constants being equal to the appropriate walk limits mu or nu

observation of a strange attractor abstract phase space portraits have been constructed and analyzed for noisy nonperiodic data obtained in an experiment on a nonequilibrium homogeneous chemical reaction the phase space trajectories define a limit set that is an attractor following a perturbation the trajectory quickly returns to the attracting set this attracting set is shown to be strange nearby trajectories separate exponentially on the average moreover the poincare sections exhibit the stretching and folding that is characteristic of strange attractors

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

statistical properties of biased sampling methods for long polymer chains the authors present a detailed statistical analysis of the rosenbluth method 1955 of generating self avoiding walks this method became one of the standard methods for simulating long polymers they show that this method although very successful in yielding large samples becomes exponentially poor with increasing chain length this has to be taken into account for simulations and was not done yet they describe a way to quantify the number of chains needed however when compared to direct simple sampling the method still carefully used yields better results especially in the vicinity of the theta point of polymers special care has to be taken for d 2 some extensions to improve the situation are also discussed

statistics of confined self avoiding walks part i chain dimensions and concentration profiles self avoiding saws and random flight rfws walks of varying number n of steps have been generated inside spheres of varying diameter r using a random number generator and an ad hoc computer program the monte carlo samples usually of 100 000 walks thus obtained allowed the determination of the following ratios as a function of n and r first the ratio a r n r r n infinity where r n r stands for the mean in modulus end to end distance of an n step confined walk and r n infinity the same quantity for an n step non confined walk also the corresponding ratios b c and d for the root mean square end to end distance r2 12 the mean radius of gyration rg and finally the root mean square radius of gyration rg2 12 if reduced lengths are used where the reduction length is of the form nv v being a scaling exponent it is found that scaling i e independence of the above ratios with respect to the step number in the walk is well obeyed the scaling exponent is equal to 0 592 for saws and to 0 500 for rfws in order to determine the concentration profiles of end mid and overall steps inside the sphere the last has been divided in a prescribed number of spherical shells up to 22 of the same thickness and the number of steps falling inside each shell registered again using reduced lengths it was thus found that all concentration profiles obey scaling that is the concentration profile as a function of the reduced distance from the centre of the sphere is defined through a single curve whatever the value of n our results allow a comparison of the parameters for confined saws and rfws