l 1 stability estimates for n x n conservation laws let u t f u x 0 be a strictly hyperbolic n times n system of conservation laws each characteristic field being linearly degenerate or genuinely nonlinear in this paper we explicitly define a functional phi phi u v equivalent to the l 1 distance which is almost decreasing i e phi big u t v t big phi big u s v s big leq o ve cdot t s quad hbox for all t s geq 0 for every pair of e approximate solutions u v with small total variation generated by a wave front tracking algorithm the small parameter e here controls the errors in the wave speeds the maximum size of rarefaction fronts and the total strength of all non physical waves in u and in v from the above estimate it follows that front tracking approximations converge to a unique limit solution depending lipschitz continuously on the initial data in the vec l 1 norm this provides a new proof of the existence of the standard riemann semigroup generated by a n n system of conservation laws

systems of numeration and fractal functions relating to substitutions french abstract let a be a finite alphabet a substitution over a un n n a fixed point for and for each a a a a real number we establish under some assumptions an asymptotic formula concerning the sum s n i n u i n n this result generalizes some previous results from coquet or brillhart erdos and morton moreover relations with self affine functions in a sense which generalizes a definition from kamae are proved the calculi leave over systems of representation of integers and real numbers

matrices of 3 iet preserving morphisms we study matrices of morphisms preserving the family of words coding 3 interval exchange transformations it is well known that matrices of morphisms preserving sturmian words i e words coding 2 interval exchange transformations with the maximal possible factor complexity form the monoid m n 2 x 2 detm 1 m n 2 x 2 mem t e where e 01 10 we prove that in the case of exchange of three intervals the matrices preserving words coding these transformations and having the maximal possible subword complexity belong to the monoid m n 3 x 3 mem t e detm 1 where e 011 101 1 10

symmetrized β integers this article deals with b numeration systems which are numeration systems with a non integral base b 1 in this framework there exist elements which naturally play the role of integers which are called b integers the set of non negative b integers denoted by z b has various equivalent definitions which arise from different points of view nevertheless these definitions may be generalized on negative real numbers in a non unique way depending on the chosen framework we focus in this article on confluent parry units they are the positive roots of the polynomials x d i 1 d 1kx i 1 where the integers d and k satisfy d 2 and k 1 for any of these numbers we prove that there exists a discrete subset of r that we denote by z b s which is locally isomorphic to z b and such that z b s z b s moreover z b s is a model set and satisfies the inflation property there exists l 1 such that lz b s z b s l is then called the inflation factor for z b s finally we compute inflation factors for z b s of the form b i i being a positive integer

vanishing viscosity solutions of nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n system in one space dimension ut a u ux 0 assuming that the initial data have small total variation we show that the solutions of the viscous approximations ut a u ux euxx are defined globally in time and satisfy uniform bv estimates independent of e moreover they depend continuously on the initial data in the l 1 distance with a lipschitz constant independent of t e letting e 0 these viscous solutions converge to a unique limit depending lipschitz continuously on the initial data in the conservative case where a df is the jacobian

growth rate of binary words avoiding xxxr consider the set of those binary words with no non empty factors of the form x x x r du mousavi schaeffer and shallit asked whether this set of words grows polynomially or exponentially with length in this paper we demonstrate the existence of upper and lower bounds of the form n lg n o lg n on the number of such words of length n where lg n denotes the base 2 logarithm of n

decision algorithms for fibonacci automatic words ii we use a decision procedure for the fibonacci automatic words to solve problems about a number of different sequences in particular we prove that there exists an aperiodic infinite binary word avoiding the pattern x x x r this is the first avoidability result concerning a nonuniform morphism proven purely mechanically

sharp convergence rate of the glimm scheme for general nonlinear hyperbolic systems consider a general strictly hyperbolic quasilinear system in one space dimesion u t a u u x 0 quad quad quad quad quad quad 1 where u mapsto a u u in omega subset mathbb r n is a smooth matrix valued map given an initial datum u 0 with small total variation let u t be the corresponding unique vanishing viscosity solution of 1 obtained as a limit of solutions to the viscous parabolic approximation u t a u u x u xx as 0 for every t 0 we prove the a priori bound left u varepsilon t cdot u t cdot right mathbb l 1 o 1 cdot sqrt varepsilon log varepsilon quad quad quad quad quad quad 1 for an approximate solution u varepsilon of 1 constructed by the glimm scheme with mesh size delta x delta t varepsilon and with a suitable choice of the sampling sequence this result provides for general hyperbolic systems the same type of error estimates valid for glimm approximate solutions of hyperbolic systems of conservation laws u t f u x 0 satisfying the classical lax or liu assumptions on the eigenvalues k u and on the eigenvectors r k u of the jacobian matrix a u df u

boundary layers on sobolev besov spaces and poisson s equation for the laplacian in lipschitz domains we study inhomogeneous boundary value problems for the laplacian in arbitrary lipschitz domains with data in sobolev besov spaces as such this is a natural continuation of work in jerison and kenig j funct anal 1995 16 219 where the inhomogeneous dirichlet problem is treated via harmonic measure techniques the novelty of our approach resides in the systematic use of boundary integral methods in this regard the key results are establishing the invertibility of the classical layer potential operators on scales of sobolev besov spaces on lipschitz boundaries for optimal ranges of indices applications tolp based helmholtz type decompositions of vector fields in lipschitz domains are also presented

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

square function non tangential maximal function estimates and the dirichlet problem for non symmetric elliptic operators a we consider divergence form elliptic operators l div a x defined in the half space rn 1 n 2 where the coefficient matrix a x is bounded measurable uniformly elliptic t independent and not necessarily symmetric we establish square function non tangential maximal function estimates for solutions of the homogeneous equation lu 0 and we then combine these estimates with the method of approximability to show that l harmonic measure is absolutely continuous with respect to surface measure i e n dimensional lebesgue measure on the boundary in a scale invariant sense more precisely that it belongs to the class a with respect to surface measure equivalently that the dirichlet problem is solvable with data in lp for some p previously these results had been known only in the case n 1

decay estimate for a new measure of rarefaction waves in general systems of conservation laws abstract the sharp decay estimate of rarefaction waves in terms of a partial ordering among positive measures is not only interesting in itself but also crucial in the study of convergence rate of vanishing viscosity approximations cf bressan and yang 2004 10 such an estimate is well established for genuinely nonlinear system of conservation laws cf bressan and yang 2004 9 but similar result is not available for non genuinely nonlinear system in this paper we give a new measure about the rarefaction waves in addition a sharp decay estimate of the new measure is given for the cubic nonlinear system of conservation laws

error bounds for a deterministic version of the glimm scheme consider the hyperbolic system of conservation laws u t f u x 0 let u be the unique viscosity solution with initial condition u 0 x bar u x and let ue be an approximate solution constructed by the glimm scheme corresponding to the mesh sizes delta x delta t o delta x with a suitable choice of the sampling sequence we prove the estimate big u ve t cdot u t cdot big bf l 1 strut l 1 o 1 cdot sqrt delta x big ln delta x big

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

the neumann problem for higher order elliptic equations with symmetric coefficients in this paper we establish well posedness of the neumann problem with boundary data in l 2 or the sobolev space dot w 2 1 in the half space for linear elliptic differential operators with coefficients that are constant in the vertical direction and in addition are self adjoint this generalizes the well known well posedness result of the second order case and is based on a higher order and one sided version of the classic rellich identity and is the first known well posedness result for an elliptic divergence form higher order operator with rough variable coefficients and boundary data in a lebesgue or sobolev space

equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form we study the heat kernel of higher order elliptic operators or systems under divergence form on rn ellipticity is in the sense of garding inequality we show that for homogeneous operators gaussian upper bounds and holder regularity of the heat kernel is equivalent to local regularity of weak solutions we also show stability of such bounds under l perturbations of the coefficients or under perturbations with bounded coefficients lower order terms such a criterion allows us to obtain heat kernel bounds for operators or systems with uniformly continuous or vmo coefficients

analyticity of layer potentials and l 2 solvability of boundary value problems for divergence form elliptic equations with complex l infty coefficients we consider divergence form elliptic operators of the form l dv a x nabla defined in r n 1 x t in r n times r n geq 2 where the l infty coefficient matrix a is n 1

combinatorial properties of sequences defined by the billiard in paved triangles resume nous etudions certaines proprietes combinatoires de la dynamique symbolique du billard dans le triangle rectangle isocele et le demi triangle equilateral dans le cas du triangle rectangle isocele nous developpons un algorithme de construction des suites obtenues comme codage et nous calculons la complexite de ces suites lorsqu elles ne sont pas periodiques nous donnons des regles de construction des mots infinis qui codent les trajectoires de billard dans le demi triangle equilateral ceci nous a conduit a etablir un algorithme de construction du codage d un point sous une rotation munie d une partition en intervalles

abelian properties of parry words abelian complexity of a word u is a function that counts the number of pairwise non abelian equivalent factors of u of length n we prove that for any c balanced parry word u the values of the abelian complexity function can be computed by a finite state automaton the proof is based on the notion of relative parikh vectors the approach works for any function f n that can be expressed in terms of the set of relative parikh vectors corresponding to the length n for example we show that the balance function of a c balanced parry word is computable by a finite state automaton as well

a new glimm functional and convergence rate of glimm scheme for general systems of hyperbolic conservation laws in this paper we introduce a new glimm functional for general systems of hyperbolic conservation laws this new functional is consistent with the classical glimm functional for the case when each characteristic field is either genuinely nonlinear or linearly degenerate so that it can be viewed as optimal in some sense with this new functional the consistency of the glimm scheme is proved clearly for general systems moreover the convergence rate of the glimm scheme is shown to be the same as the one obtained in bressan marson arch ration mech anal 142 2 155 176 1998 for systems with each characteristic field being genuinely nonlinear or linearly degenerate

sharp decay estimates for hyperbolic balance laws abstract we consider strictly hyperbolic and genuinely nonlinear systems of hyperbolic balance laws in one space dimension sharp decay estimates are derived for the positive waves in an entropy weak solution the result is obtained by introducing a partial ordering within the family of positive radon measures using symmetric rearrangements and a comparison with a solution of burgers s equation with impulsive sources as well as lower semicontinuity properties of continuous glimm type functionals

abelian complexity of infinite words associated with quadratic parry numbers we derive an explicit formula for the abelian complexity of infinite words associated with quadratic parry numbers

on the least number of palindromes contained in an infinite word we investigate the least number of palindromic factors in an infinite word we first consider general alphabets and give answers to this problem for periodic and non periodic words closed or not under reversal of factors we then investigate the same problem when the alphabet has size two

relaxation limit of interacting shock waves for non isentropic gas dynamics abstract in this paper we study the relaxation limit of interacting shock waves for non isentropic gas dynamics such a model is introduced by jin and xin for numerical analysis and named as jin xin relaxation system given any entropy solution of non isentropic gas dynamics which consists of two different families of shocks interacting at some positive time we show that such solution is the relaxation limit for a family of smooth global solutions of the jin xin relaxation system we remark that after the interacting time not only shocks but also contact discontinuity is generated

on a combinatorial property of sturmian words recall that a semigroup has the property pn if for any sequence of n of its elements two differently permuted products of these n elements are equal let s be an infinite sturmian word on a 2 letter alphabet a we prove that the rees quotient of a by the set of the non factors of s has p4 and that this result is the best possible we prove also that if st is the set of all finite sturmian words then the rees quotient a a st has p8

the sharpness of kuznetsov s o d x l 1 error estimate for monotone difference schemes we derive a lower error bound for monotone difference schemes to the solution of the linear advection equation with bv initial data a rigorous analysis shows that for any monotone difference scheme the lower l 1 error bound is o x where x is the spatial stepsize

the dirichlet problem for higher order equations in composition form the present paper commences the study of higher order differential equations in composition form specifically we consider the equation lu divb adiva u 0 where a and b are elliptic matrices with complex valued bounded measurable coefficients and a is an accretive function elliptic operators of this type naturally arise for instance via a pull back of the bilaplacian 2 from a lipschitz domain to the upper half space more generally this form is preserved under a lipschitz change of variables contrary to the case of divergence form fourth order differential equations we establish well posedness of the dirichlet problem for the equation lu 0 with boundary data in l2 and with optimal estimates in terms of nontangential maximal functions and square functions

quasiperiodic sturmian words and morphisms we characterize all quasiperiodic sturmian words a sturmian word is not quasiperiodic if and only if it is a lyndon word moreover we study links between sturmian morphisms and quasiperiodicity

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

viscous limits for piecewise smooth solutions to systems of conservation laws in this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity it is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order e as the viscosity coefficient e goes to zero the proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles

the solution of the kato square root problem for second order elliptic operators on rn we prove the kato conjecture for elliptic operators on jfin more precisely we establish that the domain of the square root of a uniformly complex elliptic operator l div av with bounded measurable coefficients in ietn is the

the semigroup generated by 2 2 conservation laws consider the cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension ie1 01 assuming that each characteristic field is either linearly degenerate or genuinely nonlinear this paper develops a new algorithm based on wave front tracking which yields a cauchy sequence of approximate solutions converging to a unique limit depending continuously on the initial data the solutions that we obtain constitute a semigroup s defined on a set ie1 02 of integrable functions with small total variation for some lipschitz constant l we have the estimate ie1 03

fibonacci morphisms and sturmian words abstract marton kosa 1987 has stated five conjectures devoted to the study of some binary morphisms and the factors of infinite words these morphisms generate positive answers to the first four of these conjectures are given in this paper the main result being the characterization of a class of morphisms whose stationary words are sturmian

the lp boundary value problems on lipschitz domains abstract let be a bounded lipschitz domain in r n we develop a new approach to the invertibility on l p of the layer potentials associated with elliptic equations and systems in as a consequence for n 4 and 2 n 1 n 1 e p 2 where e 0 depends on we obtain the solvability of the l p neumann type boundary value problems for second order elliptic systems the analogous results for the biharmonic equation are also established

a note on symmetries in the rauzy graph and factor frequencies we focus on infinite words with languages closed under reversal if frequencies of all factors are well defined we show that the number of different frequencies of factors of length n 1 does not exceed email protected n 1 where dc n is the first difference of factor complexity c n of the infinite word

global existence of dissipative solutions to the hunter saxton equation via vanishing viscosity abstract using the vanishing viscosity method we prove the global existence of dissipative weak solutions to the hunter saxton equation that describes the propagation of waves in a massive director field of a nematic liquid crystal our main tool is the l p young measure theory we also derive the upper bound on the convergence rate for the vanishing viscosity approximations

additive and multiplicative properties of point sets based on beta integers to each number 1 correspond abelian groups in rd of the form i 1d z ei which obey the set z of beta integers is a countable set of numbers it is precisely the set of real numbers which are polynomial in when they are written in basis and z z when n we prove here a list of arithmetic properties of z addition multiplication relation with integers when is a quadratic pisot vijayaraghavan unit quasicrystallographic inflation factors are particular examples we also consider the case of a cubic pisot vijayaraghavan unit associated with the seven fold cyclotomic ring at the end we show how the point sets are vertices of d dimensional tilings

on some generalizations of abelian power avoidability we prove that 2 abelian cubes are avoidable over a binary alphabet and that 3 abelian squares are avoidable over a ternary alphabet answering positively to two questions of karhumaki et al we also show the existence of infinite additive cube free words on several ternary alphabets to achieve this we give sufficient conditions for a morphism to be k abelian n power free resp additive n power free and then we give several morphisms which respect these conditions additionally all our constructions show that the number of such words grows exponen tially as a corollary we get a new lower bound of 3 1 19 1 059526 for the growth rate of abelian cube free words

the neumann problem for elliptic equations with non smooth coefficients in this paper we study the neumann and regularity problems for divergence form symmetric elliptic operators l div av where a aifix is a matrix of bounded measurable functions and ellipticity is the existence of a 0 such that 2 114 2 ais ir 21412 for all i r we assume that l is defined in the unit ball b but the methods of proof are sufficiently general to allow b to be a bounded starlike lipschitz domain the neumann problem lu 0 in b avun q f

a locally quadratic glimm functional and sharp convergence rate of the glimm scheme for nonlinear hyperbolic systems consider the cauchy problem for a strictly hyperbolic n n quasilinear system in one space dimension u t a u u x 0 qquad u 0 x bar u x quad quad quad quad 1 where u mapsto a u is a smooth matrix valued map and the initial data overline u is assumed to have small total variation we investigate the rate of convergence of approximate solutions of 1 constructed by the glimm scheme under the assumption that letting k u rk u denote the k th eigenvalue and a corresponding eigenvector of a u respectively for each k th characteristic family the linearly degenerate manifold mathcal m k doteq left u in omega nabla lambda k u cdot r k u 0 right is either the whole space or it is empty or it consists of a finite number of smooth n 1 dimensional connected manifolds that are transversal to the characteristic vector field rk we introduce a glimm type functional which is the sum of the cubic interaction potential defined in bianchini discrete contin dyn syst 9 133 166 2003 and of a quadratic term that takes into account interactions of waves of the same family with strength smaller than some fixed threshold parameter relying on an adapted wave tracing method and on the decrease amount of such a functional we obtain the same type of error estimates valid for glimm approximate solutions of hyperbolic systems satisfying the classical lax assumptions of genuine nonlinearity or linear degeneracy of the characteristic families

existence theory by front tracking for general nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n quasilinear system in one space dimension u t a u u x 0 qquad u 0 x bar u x 1 where u u t x u 1 t x dots u n t x u mapsto a u is a smooth matrix valued map and the initial data overline u is assumed to have small total variation we present a front tracking algorithm that generates piecewise constant approximate solutions converging in mathbb l loc 1 to the vanishing viscosity solution of 1 which by the results in 6 is the unique limit of solutions to the artificial viscous parabolic approximation u t a u u x mu u xx qquad u 0 x bar u x as mu to 0 in the conservative case where a u is the jacobian matrix of some flux function f u with values in mathbb r n the limit of front tracking approximations provides a weak solution of the system of conservation laws ut f u x 0 satisfying the liu admissibility conditions

some combinatorial properties of the thue morse sequence and a problem in semigroups abstract some combinatorial properties of the special factors of the thue morse sequence in a two letter alphabet are considered an application of this analysis to a problem in semigroups is given

layer potentials and boundary value problems for elliptic equations with complex l coefficients satisfying the small carleson measure norm condition abstract we consider divergence form elliptic equations l u a u 0 in the half space r n 1 x t r n 0 whose coefficient matrix a is complex elliptic bounded and measurable in addition we suppose that a satisfies some additional regularity in the direction transverse to the boundary namely that the discrepancy a x t a x 0 satisfies a carleson measure condition of fefferman kenig pipher type with small carleson norm under these conditions we establish a full range of boundedness results for double and single layer potentials in l p hardy sobolev bmo and holder spaces furthermore we prove solvability of the dirichlet problem for l with data in l p r n bmo r n and c r n and solvability of the neumann and regularity problems with data in the spaces l p r n h p r n and l 1 p r n h 1 p r n respectively with the appropriate restrictions on indices assuming invertibility of layer potentials for the t independent operator l 0 a 0

substitutions and b systems of numbers resume dans son fameux article cobham a montre que la suite des etats d un k automate etait le point fixe d une substitution de longueur constante cobham 1972 apres avoir introduit de nouvelles notions substitution de longueur suite automatique nous donnons un theoreme analogue pour les systemes de numeration associes a des nombres

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

symmetry groups for beta lattices we present a construction of symmetry plane groups for quasiperiodic point sets named beta lattices the framework is issued from beta integers counting systems beta lattices are vector superpositions of beta integers when 1 is a quadratic pisot vijayaraghavan algebraic unit the set of beta integers can be equipped with an abelian group structure and an internal multiplicative law when 1 5 2 1 2 and 2 3 we show that these arithmetic and algebraic structures lead to freely generated symmetry plane groups for beta lattices these plane groups are based on repetitions of discrete adapted rotations and translations we shall refer to as beta rotations and beta translations hence beta lattices endowed with beta rotations and beta translations can be viewed like lattices the quasiperiodic function s n defined on the set of beta integers as counting the number of small tiles between the origin and the nth beta integer plays a central part in these new group structures in particular this function behaves asymptotically like a linear function as an interesting consequence beta lattices and their symmetries behave asymptotically like lattices and lattice symmetries respectively

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

on the convergence rate of vanishing viscosity approximations given a strictly hyperbolic genuinely nonlinear system of conservation laws we prove the a priori boundu t u e t l1 o 1 1 t e ln e on the distance between an exact bv solution u and a viscous approximation u e letting the viscosity coefficient e 0 in the proof starting from u we construct an approximation of the viscous solution u e by taking a mollification u e and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed e error estimates are then obtained by introducing new lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families c 2004 wiley periodicals inc

on the l2 and l1 convergence rates of viscous solutions of the keyfitz kranzer system with piecewise smooth and large bv data abstract we study the zero dissipation problem of the keyfitz kranzer system in l 2 and l 1 spaces when the solution of the inviscid problem is piecewise smooth and has finitely many noninteracting shocks with finite strength there exists for each e the viscosity unique solution to the viscous problem with modified initial data and it converges to the given inviscid solution away from shock discontinuities as e tends to zero convergence rates are given in terms of e the proof is given by a matched asymptotic analysis and a weighted elementary energy method

functional calculus of dirac operators and complex perturbations of neumann and dirichlet problems we prove that the neumann dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in l 2 for small complex l infty perturbations of a coefficient matrix which is either real symmetric of block form or constant all matrices are assumed to be independent of the transversal coordinate we solve the neumann dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order dirac type operator we establish quadratic estimates for this dirac operator which implies that the associated hardy projection operators are bounded and depend continuously on the coefficient matrix we also prove that certain transmission problems for k forms are well posed for small perturbations of block matrices

on the factors of the sturmian sequences resume cet article a pour objet l etude d une construction associant a toute droite de pente p q p et q premiers entre eux et q n un mot de longueur n sur l alphabet 0 1 nous montrons que nous obtenons par cette construction le langage constitue de tous les facteurs des suites de sturm nous formulons apres avoir obtenu une equation fonctionelle dont la solution est la serie generatrice de ce langage une conjecture reliant cette serie generatrice a la fonction d euler

on the equivalence problem for binary dol systems it is shown that to test whether two dol sequences in the binary case coincide it is enough to test whether four first words of these sequences are the same the result is optimal

some properties of the factors of sturmian sequences in this paper we introduce the singular words of sturmian sequences which play an important role in studying the properties of the factors of sturmian sequence we also completely determine the powers of the factors the overlaps of the factors and the structure of the palindromes of the factors

weighted maximal regularity estimates and solvability of non smooth elliptic systems i we develop new solvability methods for divergence form second order real and complex elliptic systems above lipschitz graphs with l 2 boundary data the coefficients a may depend on all

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

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

the regularity problem for second order elliptic operators with complex valued bounded measurable coefficients the present paper establishes a certain duality between the dirichlet and regularity problems for elliptic operators with t independent complex bounded measurable coefficients t being the transversal direction to the boundary to be precise we show that the dirichlet boundary value problem is solvable in l p subject to the square function and non tangential maximal function estimates if and only if the corresponding regularity problem is solvable in l p moreover the solutions admit layer potential representations in particular we prove that for any elliptic operator with t independent real possibly non symmetric coefficients there exists a p 1 such that the regularity problem is well posed in l p

computing abelian complexity of binary uniform morphic words although a lot of research has been done on the factor complexity also called subword complexity of morphic words obtained as fixed points of iterated morphisms there has been little development in exploring algorithms that can efficiently compute their abelian complexity the factor complexity counts the number of factors of a given length n while the abelian complexity counts that number up to letter permutation we propose and analyze a simple o n algorithm for quickly computing the exact abelian complexities for all indices from 1 up to n when considering binary uniform morphisms using our algorithm we also analyze the structure in the abelian complexity for that class of morphisms our main result implies in particular that the infinite word over the alphabet 1 0 1 constructed from the consecutive forward differences of the abelian complexity of a fixed point of a binary uniform morphism is in fact an automatic sequence with the same morphic length since the proof produces morphisms that typically contain many redundant letters we present an efficient algorithm to eliminate them in order to simplify the morphisms and to see the patterns produced more clearly

sturmian morphisms and a words abstract in this paper we prove that the set w of words over 0 1 coincides with the set of images of 0 under sturmian morphisms this gives an alternative approach of generating words for each w w a sturmian solution h of the equation w h 0 which is a composition of sturmian morphisms of special forms can be constructed explicitly in order to demonstrate how results on sturmian morphic images are reformulated as results on words and vice versa we give a sturmian proof for the conjugation and reversion theorem of words obtained by the present author in an earlier paper

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

bv solutions of the semidiscrete upwind scheme consider the strictly hyperbolic system of conservation laws u t f u x 0 1 where u n f n n smooth the system is said to be strictly hyperbolic provided that the jacobian matrix a u df u has n distinct eigenvalues 1 u n u

hardy spaces and the neumann problem in l p for laplace s equation in lipschitz domains on donne des resultats optimaux pour la resolubilite du probleme de neumann dans des domaines de lipschitz a donnees dans l p on obtient des resultats du point extreme correspondant pour des espaces de hardy

abelian complexity and abelian co decomposition we propose a technique for exploring the abelian complexity of recurrent infinite words focusing particularly on infinite words associated with parry numbers using that technique we give an affirmative answer to the open question posed by richomme saari and zamboni whether the abelian complexity of the tribonacci word attains each value in 4 5 6 infinitely many times

two infinite families of polyominoes that tile the plane by translation in two distinct ways it has been proved that among the polyominoes that tile the plane by translation the so called squares tile the plane in at most two distinct ways in this paper we focus on double squares that is the polyominoes that tile the plane in exactly two distinct ways our approach is based on solving equations on words which allows us to exhibit properties about their shape moreover we describe two infinite families of double squares the first one is directly linked to christoffel words and may be interpreted as segments of thick straight lines the second one stems from the fibonacci sequence and reveals some fractal features