bifix codes and sturmian words we prove new results concerning the relation between bifix codes episturmian words and subgroups of free groups we study bifix codes in factorial sets of words we generalize most properties of ordinary maximal bifix codes to bifix codes maximal in a recurrent set f of words f maximal bifix codes in the case of bifix codes contained in sturmian sets of words we obtain several new results let f be a sturmian set of words defined as the set of factors of a strict episturmian word our results express the fact that an f maximal bifix code of degree d behaves just as the set of words of f of length d an f maximal bifix code of degree d in a sturmian set of words on an alphabet with k letters has k 1 d 1 elements this generalizes the fact that a sturmian set contains k 1 d 1 words of length d moreover given an infinite word x if there is a finite maximal bifix code x of degree d such that x has at most d factors of length d in x then x is ultimately periodic our main result states that any f maximal bifix code of degree d on the alphabet a is the basis of a subgroup of index d of the free group on a

philos type oscillation criteria for linear differential equations with impulsive effects abstract the present paper deals with the problem of oscillation for a second order linear differential equation in which an impulsive effect is considered this equation can be regarded as an equation of motion in which the moving speed of a mass point changes sharply by some influence it is proved that there is a case that the mass point may oscillate due to the influence of the impulsive effect even if the mass point does not oscillate in the model removing the impulsive effect it is also shown that the obtained results extend some previous ones through the use of an example

introducing privileged words privileged complexity of sturmian words in this paper we introduce a new class of so called privileged words which have been previously considered only a little we develop the basic properties of privileged words which turn out to share similar properties with palindromes privileged words are studied in relation to previously studied classes of words rich words sturmian words and episturmian words a new characterization of sturmian words is given in terms of privileged complexity the privileged complexity of the thue morse word is also briefly studied

on the fixed points of the iterated pseudopalindromic closure operator first introduced in the study of the sturmian words by de luca in 1997 iterated palindromic closure was generalized to pseudopalindromes by de luca and de luca in 2006 this operator allows one to construct words with infinitely many pseudopalindromic prefixes called pseudostandard words we provide here several combinatorial properties of the fixed points under iterated pseudopalindromic closure

analysis of the response of a strongly nonlinear damped system using a differential transformation technique the differential transformation technique is applied to solve a nonlinear differential equation that describes the underdamped and the overdamped motion of a system subjected to external excitations numerical results are compared to those obtained by the runge kutta method to illustrate the preciseness and effectiveness of the proposed method

principal and nonprincipal solutions of impulsive differential equations with applications we introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained the arguments are based on polya and trench factorizations as in non impulsive differential equations so we first establish these factorizations making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations examples are provided with numerical simulations to illustrate the relevance of the results

characteristic morphisms of generalized episturmian words in a recent paper with l q zamboni the authors introduced the class of q episturmian words an infinite word over a is standard q episturmian where q is an involutory antimorphism of a if its set of factors is closed under q and its left special factors are prefixes when q is the reversal operator one obtains the usual standard episturmian words in this paper we introduce and study q characteristic morphisms that is morphisms which map standard episturmian words into standard q episturmian words they are a natural extension of standard episturmian morphisms the main result of the paper is a characterization of these morphisms when they are injective in order to prove this result we also introduce and study a class of biprefix codes which are overlap free i e any two code words do not overlap properly and normal i e no proper suffix prefix of any code word is left right special in the code a further result is that any standard q episturmian word is a morphic image by an injective q characteristic morphism of a standard episturmian word

convergent series solution of nonlinear equations abstract the author s decomposition method 1 provides a new efficient computational procedure for solving large classes of nonlinear and or stochastic equations these include differential equations containing polynomial exponential and trigonometric terms negative or irrational powers and product nonlinearities 2 also included are partial differential equations 3 delay differential equations 4 algebraic equations 5 and matrix equations 6 which describe physical systems essentially the method provides a systematic computational procedure for equations containing any nonlinear terms of physical significance the procedure depends on calculation of the author s a n a finite set of polynomials 1 13 in terms of which the nonlinearities can be expressed this paper shows important properties of the a n which ensure an accurate and computable convergent solution by the author s decomposition method 1 since the nonlinearities and or stochasticity which can be handled are quite general the results are potentially extremely useful for applications and make a number of common approximations such as linearization unnecessary

fine and wilf s theorem for three periods and a generalization of sturmian words we extend the theorem of fine and wilf to words having three periods we then define the set 3 per of words of maximal length for which such result does not apply we prove that the set 3 per and the sequences of complexity 2n 1 introduced by arnoux and rauzy to generalize sturmian words have the same set of factors

episturmian words and episturmian morphisms infinite episturmian words are a generalization of sturmian words which includes the arnoux rauzy sequences we continue their study and that of episturmian morphisms begun previously in relation with the action of the shift operator palindromic and periodic factors of these words are described we consider in particular the case where these words are generated by morphisms and introduce then a notion of intercept generalizing that of sturmian words finally we prove that the frequencies of the factors in a strong sense do exist for all episturmian words

oscillation criteria for second order quasi linear neutral delay differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t x t p t x t m 1 x t p t x t q t f x t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel

second order quasilinear oscillation with impulses abstract sufficient conditions for oscillation of all solutions of a class of second order quasilinear differential equations with fixed moments of impulse effect are found

asymptotic representation of solutions for second order impulsive differential equations abstract we obtain sufficient conditions which guarantee the existence of a solution of a class of second order nonlinear impulsive differential equations with fixed moments of impulses possessing a prescribed asymptotic behavior at infinity in terms of principal and nonprincipal solutions an example is given to illustrate the relevance of the results

symbolic computation of analytic approximate solutions for nonlinear differential equations with boundary conditions the adomian decomposition method adm is one of the most effective methods for constructing analytic approximate solutions in this paper based on the new definitions of the adomian polynomials and the double decomposition method a new algorithm is proposed to construct analytic approximations for nonlinear differential equations with coupled boundary conditions furthermore a maple software package is developed to implement our new algorithm which is user friendly and efficient one only needs to input the system boundary conditions and several necessary parameters then our package will deliver the analytic approximate solution within a few seconds several different types of nonlinear examples are given to illustrate the scope and demonstrate the validity of our software package especially for nonlinear multi order and multi point boundary value problems our package provides a helpful and easy to use tool in science and engineering to deal with the most frequently encountered boundary value problems this maple package is free to download on the website http www cs ecnu edu cn lizb index htm

status of the differential transformation method abstract further to a recent controversy on whether the differential transformation method dtm for solving a differential equation is purely and solely the traditional taylor series method it is emphasized that the dtm is currently used often only as a technique for analytically calculating the power series of the solution in terms of the initial value parameters sometimes a piecewise analytic continuation process is implemented either in a numerical routine e g within a shooting method or in a semi analytical procedure e g to solve a boundary value problem emphasized also is the fact that at the time of its invention the currently used basic ingredients of the dtm that transform a differential equation into a difference equation of same order that is iteratively solvable were already known for a long time by the traditional taylor method users notably in the elaboration of software packages numerical routines for automatically solving ordinary differential equations at now the defenders of the dtm still ignore the though much better developed studies of the traditional taylor method users who in turn seem to ignore similarly the existence of the dtm the dtm has been given an apparent strong formalization set on the same footing as the fourier laplace or mellin transformations though often used trivially it is easily attainable and easily adaptable to different kinds of differentiation procedures that has made it very attractive hence applications to various problems of the taylor method and more generally of the power series method including noninteger powers has been sketched it seems that its potential has not been exploited as it could be after a discussion on the reasons of the misunderstandings which have caused the controversy the preceding topics are concretely illustrated it is concluded that for the sake of clarity when the dtm is applied to odes it should be mentioned that the dtm exactly coincides with the traditional taylor method contrary to what is currently written

a multi step differential transform method and application to non chaotic or chaotic systems the differential transform method dtm is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form in this paper we propose a reliable new algorithm of dtm namely multi step dtm which will increase the interval of convergence for the series solution the multi step dtm is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations this new algorithm is applied to lotka volterra chen and lorenz systems then a comparative study between the new algorithm multi step dtm classical dtm and the classical runge kutta method is presented the results demonstrate reliability and efficiency of the algorithm developed

factor versus palindromic complexity of uniformly recurrent infinite words we study the relation between the palindromic and factor complexity of infinite words we show that for uniformly recurrent words one has p n p n 1 email protected n 2 for all email protected n for a large class of words this is a better estimate of the palindromic complexity in terms of the factor complexity than the one presented in j p allouche m baake j cassaigne d damanik palindrome complexity theoret comput sci 292 2003 9 31 we provide several examples of infinite words for which our estimate reaches its upper bound in particular we derive an explicit prescription for the palindromic complexity of infinite words coding r interval exchange transformations if the permutation p connected with the transformation is given by p k r 1 k for all k then there is exactly one palindrome of every even length and exactly r palindromes of every odd length

sturmian words structure combinatorics and their arithmetics abstract we prove some new results concerning the structure the combinatorics and the arithmetics of the set per of all the words w having two periods p and q p q which are coprimes and such that w p q 2 a basic theorem relating per with the set of finite standard sturmian words was proved in de luca and mignosi 1994 the main result of this paper is the following simple inductive definition of per the empty word belongs to per if w is an already constructed word of per then also aw and bw belong to per where denotes the operator of palindrome left closure i e it associates to each word u the smallest palindrome word u having u as a suffix we show that by this result one can construct in a simple way all finite and infinite standard sturmian words we prove also that up to the automorphism which interchanges the letter a with the letter b any element of per can be codified by the irreducible fraction p q this allows us to construct for any n 0 a natural bijection that we call farey correspondence of the set of the farey series of order n 1 and the set of special elements of length n of the set st of all finite sturmian words finally we introduce the concepts of farey tree and farey monoid this latter is obtained by defining a suitable product operation on the developments in continued fractions of the set of all irreducible fractions p q

pseudopalindrome closure operators in free monoids we consider involutory antimorphisms of a free monoid a and their fixed points called palindromes or pseudopalindromes a palindrome reduces to a usual palindrome when is the reversal operator for any word w a the right resp left palindrome closure of w is the shortest palindrome having w as a prefix resp suffix we prove some results relating palindrome closure operators with periodicity and conjugacy and derive some interesting closure properties for the languages of finite sturmian and episturmian words in particular a finite word w is sturmian if and only if both its palindromic closures are so moreover in such a case both the palindromic closures of w share the same minimal period of w a new characterization of finite sturmian words follows in terms of periodicity and special factors of their palindromic closures some weaker results can be extended to the episturmian case by using the right palindrome closure we extend the construction of standard episturmian words via directive words in this way one obtains a family of infinite words called standard words which are morphic images of episturmian words as well as a wider family of infinite words including the thue morse word on two symbols

powers in a class of a strict standard episturmian words this paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic sturmian words in particular we explicitly determine all integer powers occurring in such infinite words extending recent results of damanik and lenz d damanik d lenz powers in sturmian sequences european j combin 24 2003 377 390 doi 10 1016 s0195 6698 03 00026 x who studied powers in sturmian words the key tools in our analysis are canonical decompositions and a generalization of singular words which were originally defined for the ubiquitous fibonacci word our main results are demonstrated via some examples including the k bonacci word a generalization of the fibonacci word to a k letter alphabet k 2

picone s formula for linear non selfadjoint impulsive differential equations in this paper we derive a picone type formula for second order linear non selfadjoint impulsive differential equations having fixed moments of impulse actions and obtain a wirtinger type inequality a leighton type comparison theorem and a sturm picone comparison theorem for such equations moreover several oscillation criteria are also derived as applications

analytic solution of nonlinear boundary value problems in several dimensions by decomposition abstract nonlinear partial differential equations are systematically solved by the decomposition method of g adomian for general boundary conditions described by boundary operator equations linear partial differential equations and linear or nonlinear ordinary differential equations become special cases all dealt with by a single procedure

balancing and clustering of words in the burrows wheeler transform compression algorithms based on burrows wheeler transform bwt take advantage of the fact that the word output of bwt shows a local similarity and then turns out to be highly compressible the aim of the present paper is to study such clustering effect by using notions and methods from combinatorics on words the notion of balance of a word plays a central role in our investigation empirical observations suggest that balance is actually the combinatorial property of input word that ensure optimal bwt compression moreover it is reasonable to assume that the more balanced the input word is the more local similarity we have after bwt and therefore the better the compression is this hypothesis is here corroborated by experiments on real text by using local entropy as a measure of the degree of balance of a word in the setting of combinatorics on words a sound confirmation of previous hypothesis is given by a result of mantaci et al 2003 27 which states that in the case of a binary alphabet there is an equivalence between circularly balanced words words having a clusterized bwt and the conjugates of standard words in the case of alphabets of size greater than two there is no more equivalence the last section of the present paper is devoted to investigate the relationships between these notions and other related ones as for instance palindromic richness in the case of a general alphabet

solution of different type of the partial differential equation by differential transform method and adomian s decomposition method abstract in this paper the definitions and operations of the differential transform method j k zhou differential transformation and its applications for electrical circuits huarjung university press wuuhahn china 1986 and adomian s decomposition method which is given by george adomian for approximate solution of linear and non linear differential equations are expressed g adomian convergent series solution of nonlinear equation comput appl math 11 1984 113 117 different partial differential equations are solved under the view of these methods and compared with the approximate solution and analytic solution at the end these solutions are illustrated by tables and figures

sturmian comparison theory for linear and half linear impulsive differential equations in this paper we investigate sturmian comparison theory for second order half linear differential equations with fixed moments of impulse actions it is shown that impulse actions may greatly change the behavior of solutions in comparison several oscillation criteria are also derived to illustrate the results

fractional powers in sturmian words abstract given an infinite sturmian word s we calculate the function l m which gives the length of the longest factor of s having period m the expression of l m makes use of the continued fraction of the irrational associated with s

complexity of trajectories in rectangular billiards to a trajectory of the billiard in a cube we assign its symbolic trajectory the sequence of numbers of coordinate planes to which the faces met by the trajectory are parallel the complexity of the trajectory is the number of different words of lengthn occurring in it we prove that for generic trajectories the complexity is well defined and calculate it confirming the conjecture of arnoux mauduit shiokawa and tamura amst

palindromic ziv lempel and crochemore factorizations of m bonacci infinite words abstract we introduce a variation of the ziv lempel and crochemore factorizations of words by requiring each factor to be a palindrome we compute these factorizations for the fibonacci word and more generally for all m bonacci words

fixed points of sturmian morphisms and their derivated words abstract any infinite uniformly recurrent word u can be written as concatenation of a finite number of return words to a chosen prefix w of u ordering of the return words to w in this concatenation is coded by derivated word d u w in 1998 durand proved that a fixed point u of a primitive morphism has only finitely many derivated words d u w and each derivated word d u w is fixed by a primitive morphism as well in our article we focus on sturmian words fixed by a primitive morphism we provide an algorithm which to a given sturmian morphism lists the morphisms fixing the derivated words of the sturmian word u u we provide a sharp upper bound on length of the list

episturmian words and some constructions of de luca and rauzy abstract in this paper we study infinite episturmian words which are a natural generalization of sturmian words to an arbitrary alphabet a characteristic property is they are closed under reversal and have at most one right special factor of each length they are first obtained by a construction due to de luca which utilizes the palindrome closure they can also be obtained by the way of extended rauzy rules

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

a characterization of fine words over a finite alphabet to any infinite word t over a finite alphabet a we can associate two infinite words min t and max t such that any prefix of min t resp max t is the lexicographically smallest resp greatest amongst the factors of t of the same length we say that an infinite word t over a is fine if there exists an infinite word s such that for any lexicographic order min t as where a min a in this paper we characterize fine words specifically we prove that an infinite word t is fine if and only if t is either a strict episturmian word or a strict skew episturmian word this characterization generalizes a recent result of g pirillo who proved that a fine word over a 2 letter alphabet is either an aperiodic sturmian word or an ultimately periodic but not periodic infinite word all of whose factors are finite sturmian

generalized differential transform method application to differential equations of fractional order abstract in this paper we propose a new generalization of the one dimensional differential transform method that will extend the application of the method to differential equations of fractional order the new generalization is based on generalized taylor s formula and caputo fractional derivative several illustrative examples are given to demonstrate the effectiveness of the obtained results the new generalization introduces a promising tool for many linear and nonlinear models containing fractional derivatives

fractional hawkes processes abstract hawkes processes have a self excitation mechanism used for modeling the clustering of events observed in natural or social phenomena in the first part of this article we find the forward differential equations ruling the probability density function and the laplace s transform of the intensity of a hawkes process with an exponential decaying kernel in the second part we study the properties of the fractional version of this process the fractional hawkes process is obtained by subordinating the point process with the inverse of a stable levy process this process is not markov but the probability density function of its intensity is solution of a fractional fokker planck equation finally we find closed form expressions for moments and autocovariance of the fractional intensity

equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations abstract we consider the solution of partial differential equations for initial boundary conditions using the decomposition method the partial solutions obtained from the seperate equations for the highest ordered linear operator terms are shown to be identical when the boundary conditions are general and asymptotically equal when the boundary conditions in one independent variable are independet of other variables

on z factorization and c factorization of standard episturmian words abstract ziv lempel and crochemore factorization are two kinds of factorizations of words related to text processing in this paper we find these factorizations for standard epiesturmian words thus the previously known c factorization of characteristic sturmian words is provided as a special case moreover the two factorizations are compared

solving partial differential equations by two dimensional differential transform method using two dimensional differential transform to solve partial differential equations pde is proposed in this study first the theory of two dimensional differential transform is introduced second taking two dimensional differential transform of a pde problem a set of difference equations is derived doing some simple mathematical operations on these equations we can get a closed form series solution or an approximate solution quickly finally three pde problems with constant and variable coefficients are solved by the present method the calculated results are compared very well with those obtained by other analytical or approximate methods

inequalities characterizing standard sturmian and episturmian words considering the smallest and the greatest factors with respect to the lexicographic order we associate to each infinite word r two other infinite words min r and max r in this paper we prove that the inequalities as min s max s bs characterize standard sturmian words proper ones and periodic ones and that the condition for any x a and lexicographic order satisfying x min a one has xs min s characterizes standard episturmian words

on different generalizations of episturmian words in this paper we study some classes of infinite words generalizing episturmian words and analyse the relations occurring among such classes in each case the reversal operator r is replaced by an arbitrary involutory antimorphism q of the free monoid a in particular we define the class of q words with seed whose standard elements q standard words with seed are constructed by an iterative q palindrome closure process starting from a finite word u 0 called the seed when the seed is empty one obtains q words episturmian words are exactly the r words one of the main theorems of the paper characterizes q words with seed as infinite words closed under q and having at most one left special factor of each length n n where n is some nonnegative integer depending on the word when n 0 we call such words q episturmian further results on the structure of q episturmian words are proved in particular some relationships between q words with or without seed and q episturmian words are shown

on a generalization of christoffel words epichristoffel words sturmian sequences are well known as the ones having minimal complexity over a 2 letter alphabet they are also the balanced sequences over a 2 letter alphabet and the sequences describing discrete lines they are famous and have been extensively studied since the 18th century one of the extensions of these sequences over a k letter alphabet with k 3 is the episturmian sequences which generalizes a construction of sturmian sequences using the palindromic closure operation there exists a finite version of the sturmian sequences called the christoffel words they have been known since the works of christoffel and have interested many mathematicians in this paper we introduce a generalization of christoffel words for an alphabet with 3 letters or more using the episturmian morphisms we call them the epichristoffel words we define this new class of finite words and show how some of the properties of the christoffel words can be generalized naturally or not for this class

solution of the fully fuzzy linear systems using the decomposition procedure abstract this paper tries to extend the adomian decomposition method for solving fully fuzzy linear systems shown as ffls for finding a positive fuzzy vector x that satisfies a x b where a and b are respectively a fuzzy matrix and a fuzzy vector we employ dubois and prade s approximate arithmetic operators on lr fuzzy numbers we also transform the ffls and use the adomian decomposition method for solving an ffls then we compare this method with the jacobi iterative technique additionally we give some numerical examples

on stabilizers of infinite words the stabilizer of an infinite word w over a finite alphabet s is the monoid of morphisms over s that fix w in this paper we study various problems related to stabilizers and their generators we show that over a binary alphabet there exist stabilizers with at least n generators for all n over a ternary alphabet the monoid of morphisms generating a given infinite word by iteration can be infinitely generated even when the word is generated by iterating an invertible primitive morphism stabilizers of strict epistandard words are cyclic when non trivial while stabilizers of ultimately strict epistandard words are always non trivial for this latter family of words we give a characterization of stabilizer elements

two dimensional differential transform for partial differential equations the differential transform is a numerical method for solving differential equations in this paper we present the definition and operation of the two dimensional differential transform a distinctive feature of the differential transform is its ability to solve linear and nonlinear differential equations partial differential equation of parabolic hyperbolic elliptic and nonlinear types can be solved by the differential transform we demonstrate that the differential transform is a feasible tool for obtaining the analytic form solutions of linear and nonlinear partial differential equation

conjugacy of morphisms and lyndon decomposition of standard sturmian words using the notions of conjugacy of morphisms and of morphisms preserving lyndon words we answer a question of g melancon we characterize cases where the sequence of lyndon words in the lyndon factorization of a standard sturmian word is morphic in each possible case the corresponding morphism is given

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

sturmian words and words with a critical exponent let s be a standard sturmian word that is a fixed point of a non trivial homomorphism associated to the infinite word s is a unique irrational number with 0 0 it contains a fractional power with exponent greater than e here is a constant that depends on the constant is given explicitly using these results we are able to give a short proof of mignosi s theorem and give an exact evaluation of the maximal power that can occur in a standard sturmian word

numerical comparison of methods for solving a special fourth order boundary value problem in this paper we implement relatively new analytical techniques the differential transform method adomian decomposition and homotopy perturbation method for solving a fourth order boundary value problem in these schemes the solution takes the form of a convergent series with easily computable components this paper will present a numerical comparison between the three methods for solving a fourth order boundary value problem the numerical results demonstrates that the new methods are quite accurate and efficient for this kind of problems

a generalized palindromization map in free monoids the palindromization map j in a free monoid a was introduced in 1997 by the first author in the case of a binary alphabet a and later extended by other authors to arbitrary alphabets acting on infinite words j generates the class of standard episturmian words including standard arnoux rauzy words in this paper we generalize the palindromization map starting with a given code x over a the new map j x maps x to the set pal of palindromes of a in this way some properties of j are lost and some are saved in a weak form when x has a finite deciphering delay one can extend j x to x w generating a class of infinite words much wider than standard episturmian words for a finite and maximal code x over a we give a suitable generalization of standard arnoux rauzy words called x ar words we prove that any x ar word is a morphic image of a standard arnoux rauzy word and we determine some suitable linear lower and upper bounds to its factor complexity for any code x we say that j x is conservative when j x x x we study conservative maps j x and conditions on x assuring that j x is conservative we also investigate the special case of morphic conservative maps j x i e maps such that email protected email protected email protected email protected email protected for an injective morphism f finally we generalize j x by replacing palindromic closure with q palindromic closure where q is any involutory antimorphism of a this yields an extension of the class of q standard words introduced by the authors in 2006

palindromes and sturmian words abstract an infinite word x over the alphabet a is sturmian if and only if g x n n 1 for any integer n where g x n is the number of distinct words of length n occurring in x a palindrome is a word that can be read indistinctly from left to right or from right to left we prove that x is sturmian if and only if h x n 1 n mod 2 for any integer n where h x n is the number of palindromes of length n occurring in x an infinite word x over the alphabet a is generated by a morphism f if there exists a letter c a such that lim n f n c x we prove the existence of a morphism that generates the palindromes of any infinite sturmian word generated by a morphism

palindrome complexity we study the palindrome complexity of infinite sequences on finite alphabets i e the number of palindromic factors blocks of given length occurring in a given sequence we survey the known results and obtain new results for some sequences in particular for rote sequences and for fixed points of primitive morphisms of constant length belonging to class p of hof knill simon we also give an upper bound for the palindrome complexity of a sequence in terms of its block complexity

quasiperiodic and lyndon episturmian words recently the second two authors characterized quasiperiodic sturmian words proving that a sturmian word is non quasiperiodic if and only if it is an infinite lyndon word here we extend this study to episturmian words a natural generalization of sturmian words by describing all the quasiperiods of an episturmian word which yields a characterization of quasiperiodic episturmian words in terms of their directive words even further we establish a complete characterization of all episturmian words that are lyndon words our main results show that unlike the sturmian case there is a much wider class of episturmian words that are non quasiperiodic besides those that are infinite lyndon words our key tools are morphisms and directive words in particular normalized directive words which we introduced in an earlier paper also of importance is the use of return words to characterize quasiperiodic episturmian words since such a method could be useful in other contexts

conjugacy and episturmian morphisms episturmian morphisms generalize sturmian morphisms here we study some intrinsic properties of these morphisms invertibility presentation cancellativity unitarity characterization by conjugacy most of them are generalizations of known properties of sturmian morphisms but we present also some results on episturmian morphisms that have not already been stated in the particular case of sturmian morphisms characterization of the episturmian morphisms that preserve palindromes new algorithms to compute conjugates we also study the conjugation of morphisms in the general case and show that the monoid of invertible morphisms on an alphabet containing at least three letters is not finitely generated

a condition of boshernitzan and uniform convergence in the multiplicative ergodic theorem this paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts if such a subshift satisfies a certain condition originally introduced by boshernitzan every locally constant sl 2 r valued cocycle is uniform as a consequence the corresponding schrodinger operators exhibit cantor spectrum of lebesgue measure zero an investigation of boshernitzan s condition then shows that these results cover all earlier results of this type and moreover provide various new ones in particular boshernitzan s condition is shown to hold for almost all circle maps and almost all arnoux rauzy subshifts

linear perturbations of a nonoscillatory second order difference equation ii abstract let x 1n and x 2n be recessive and dominant solutions of the nonoscillatory difference equation r n 1 x n 1 p n x n 0 in an earlier paper we showed that if f n x 1n x 2n converges perhaps conditionally and a related infinite series converges absolutely and sufficiently rapidly then the difference equation r n 1 y n 1 p n y n f n y n is also nonoscillatory and has recessive and dominant solutions y 1n and y 2n which behave asymptotically like x 1n and x 2n here we consider the case where f n x 2n 2 converges perhaps conditionally without any additional assumption requiring absolute convergence

a novel method for nonlinear fractional partial differential equations combination of dtm and generalized taylor s formula in this article a novel numerical method is proposed for nonlinear partial differential equations with space and time fractional derivatives this method is based on the two dimensional differential transform method dtm and generalized taylor s formula the fractional derivatives are considered in the caputo sense several illustrative examples are given to demonstrate the effectiveness of the present method results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order

solutions of non linear oscillators by the modified differential transform method a numerical method for solving nonlinear oscillators is proposed the proposed scheme is based on the differential transform method dtm laplace transform and pade approximants the modified differential transform method mdtm technique introduces an alternative framework designed to overcome the difficulty of capturing the periodic behavior of the solution which is characteristic of oscillator equations and give a good approximation to the true solution in a very large region the numerical results demonstrate the validity and applicability of the new technique and a comparison is made with existing results