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

stallings foldings and subgroups of free groups we re cast in a more combinatorial and computational form the topological approach of j stallings to the study of subgroups of free groups

the variational iteration method for a reliable treatment of the linear and the nonlinear goursat problem abstract the linear and the nonlinear goursat problems are investigated the he s variational iteration method vim is used to construct exact solutions to these problems the linear and the nonlinear structures are handled in a like manner without any need to restrictive assumptions the accuracy level of the obtained results reveal the power of this method over existing numerical methods

a construction method for orthogonal latin hypercube designs summary the latin hypercube design is a popular choice of experimental design when computer simulation is used to study a physical process these designs guarantee uniform samples for the marginal distribution of each single input a number of methods have been pro posed for extending the uniform sampling to higher dimensions we show how to construct latin hypercube designs in which all main effects are orthogonal our method can also be used to construct latin hypercube designs with low correlation of first order and second order terms our method generates orthogonal latin hypercube designs that can include many more factors than those proposed by ye 1998

a new approach to the wave equation an application of the decomposition method abstract in the present paper the inhomogeneous wave equation is solved quickly easily and elegantly by adomian s decomposition method

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

on the numerical solution of the goursat problem abstract in this paper we present a nonlinear trapezoidal formula for the solution of the goursat problem the new scheme implements the harmonic mean hm averaging of the functional values rather than the arithmetic mean am or the geometric mean gm averaging a comparison is made with the existing techniques and the results obtained show better approximations related to the accuracy level in favor of the hm strategy

rules for creating certain sophic systems abstract let a be a finite set a code is a subset of the a of all finite sequences on a with the property of unique deciphering codes are related with sofic systems in two ways considering the right resolving cover with state space of a sofic system s for the set of labels of minimal paths from to itself is a rational code called the first return code conversely a rational code generates a sofic system by concatenation we show that a necessary and sufficient condition for a sofic system to be of finite type resp almost finite type is that all first return codes are local resp with unique splitting to the right and left local codes and codes with unique splitting are related to classical families local codes are circular and finite local codes are identical to finite circular codes finite codes with unique splitting are identical to finite codes with finite deciphering delay to the same side restivo proved that finite circular codes generate subshifts of finite type we show finally that finite codes with unique splitting to the right and left generate almost finite type subshifts but those two results do not hold when the finiteness hypothesis is dropped

on the maximality of languages with combined types of code properties we consider the decision problem of whether or not a given regular language is maximal with respect to certain combined types of code properties in the recent past there have been a few formal methods for defining code properties such as the trajectory based type of codes and the transducer based type of codes that allow one to decide the maximality problem including the case where maximality is tested with respect to combined properties within these formal methods the property of deciphering delay 1 also known as decoding delay 1 is not known to be definable with these methods but it is known that the maximality of this property alone is decidable for regular languages here we consider the problem of deciding maximality of a regular language with respect to deciphering delay 1 and a transducer based property such as suffix code overlap free language and error detection properties

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

regression based inverse distance weighting with applications to computer experiments inverse distance weighting idw is a simple method for multivariate interpolation but has poor prediction accuracy in this article we show that the prediction accuracy of idw can be substantially improved by integrating it with a linear regression model this new predictor is quite flexible computationally efficient and works well in problems having high dimensions and or large datasets we also develop a heuristic method for constructing confidence intervals for prediction this article has supplementary material online

words derivated from sturmian words a return word of a factor of a sturmian word starts at an occurrence of that factor and ends exactly before its next occurrence derivated words encode the unique decomposition of a word in terms of return words vuillon has proved that each factor of a sturmian word has exactly two return words we determine these two return words as well as their first occurrence for the prefixes of characteristic sturmian words we then characterize words derivated from a characteristic sturmian word and give their precise form finally we apply our results to obtain a new proof of the characterization of characteristic sturmian words which are fixed points of morphisms

studies on finite sturmian words several properties of finite sturmian words are proved the inverse of the richomme seebold bijection between factor sets of given length of sturmian sequences and left special sturmian words is constructed using circular factors of christoffel words and studied the labbe bijection between christoffel words and left special sturmian words is introduced and studied factor sets are classified by two types the two classes are characterized by conjugation and periodicity properties the two classes are related to the rauzy graph a normal form for finite sturmian words is given following a result of de luca and de luca several classes of sturmian words are characterized through this normal form left or right special words bispecial words palindromes central words the normal form is used to derive a proof of the lipatov mignosi formula for the number of sturmian words of given length to produce a linear algorithm which checks if a word is sturmian and which computes its normal form to construct algorithmically the contraction and completion in various classes of sturmian words to compute the de luca palindromic closure of any sturmian word and prove that it is sturmian the completion is related to the de luca palindromization function and it is shown that the sets of directive words of central words of even and odd length are rational group languages christoffel words are characterized in several ways an extension of a result of chuan an extension of a result of droubay pirillo by counting circular factors by counting lyndon factors a special christoffel word is constructed having length a given markoff number a bivariate count of special sturmian words is given using ideas of bedaride domenjoud jamet and remy open problems are given

a new and flexible method for constructing designs for computer experiments we develop a new method for constructing good designs for computer experiments the method derives its power from its basic structure that builds large designs using small designs we specialize the method for the construc tion of orthogonal latin hypercubes and obtain many results along the way in terms of run sizes the existence problem of orthogonal latin hypercubes is completely solved we also present an explicit result showing how large or thogonal latin hypercubes can be constructed using small orthogonal latin hypercubes another appealing feature of our method is that it can easily be adapted to construct other designs we examine how to make use of the method to construct nearly orthogonal and cascading latin hypercubes

sofic systems and encoding data techniques of symbolic dynamics are applied to prove the existence of codes suitable for certain input restricted channels this generalizes the earlier work of adler coppersmith and hassner on the same problem

multi layer designs for computer experiments space filling designs such as latin hypercube designs lhds are widely used in computer experiments however finding an optimal lhd with good space filling properties is computationally cumbersome on the other hand the well established factorial designs in physical experiments are unsuitable for computer experiments owing to the redundancy of design points when projected onto a subset of factor space in this work we present a new class of space filling designs developed by splitting two level factorial designs into multiple layers the method takes advantage of many available results in factorial design theory and therefore the proposed multi layer designs mlds are easy to generate moreover our numerical study shows that mlds can have better space filling properties than optimal lhds

state splitting for variable length graphs corresp the state splitting algorithm of adler coppersmith and hassner for graphs with edges of fixed length is extended to graphs with edges of variable lengths this has the potential to improve modulation code construction techniques although the ideas of state splitting come from dynamical systems completely graph theoretic terms are used

optimal foldover plans for two level fractional factorial designs a commonly used follow up experiment strategy involves the use of a foldover design by reversing the signs of one or more columns of the initial design defining a foldover plan as the collection of columns whose signs are to be reversed in the foldover design this article answers the following question given a 2k p design with k factors and p generators what is its optimal foldover plan we obtain optimal foldover plans for 16 and 32 runs and tabulate the results for practical use most of these plans differ from traditional foldover plans that involve reversing the signs of one or all columns there are several equivalent ways to generate a particular foldover design we demonstrate that any foldover plan of a 2k p fractional factorial design is equivalent to a core foldover plan consisting only of the p out of k factors furthermore we prove that there are exactly 2k p foldover plans that are equivalent to any core foldover plan of a 2k p design and demonstrate how these foldover plans can be const

two way string matching a new string matching algorithm is presented which can be viewed as an intermediate between the classical algorithms of knuth morris and pratt on the one hand and boyer and moore on the other hand the algorithm is linear in time and uses constant space as the algorithm of galil and seiferas it presents the advantage of being remarkably simple which consequently makes its analysis possible the algorithm relies on a previously known result in combinatorics on words called the critical factorization theorem which relates the global period of a word to its local repetitions of blocks

testing dna code words properties of regular languages one aspect of dna computing is the possibility of using dna molecules for solving some complicated computational problems in this context the dna code word design problem assumes a fundamental role given a problem encoded in dna strands and biochemical processes the final computation is a concatenation of the input dna strands that must allow us to recover the solution of the given problem in terms of the input unique decipherability thus the initial set of dna strands must be a code in addition it should satisfy some restrictions called here dna properties in order to prevent them from interacting in undesirable ways so a new interest towards the design of efficient algorithms for testing whether a language x is a code has arisen from wet dna computing but as far as we know only when x is a finite set in this paper we provide an algorithm for testing whether an infinite but regular set of words is a code that avoids some dna properties among unwanted intermolecular and intramolecular hybridizations

the use of chebyshev cardinal functions for the solution of a partial differential equation with an unknown time dependent coefficient subject to an extra measurement a numerical technique is presented for the solution of a parabolic partial differential equation with a time dependent coefficient subject to an extra measurement the method is derived by expanding the required approximate solution as the elements of chebyshev cardinal functions using the operational matrix of derivative the problem can be reduced to a set of algebraic equations from the computational point of view the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use

precircular codes and periodic biinfinite words the aim of decoding or factorizing in a single way biinfinite words with a finitary language leads us to consider two distinct notions of factorization for biinfinite words for one of these notions requiring singleness of decoding periodic biinfinite words leads us to study circular codes the other notion leads us to define the new notion of precircular codes precircular codes are defined and analyzed the family of precircular codes is compared to the family of circular codes and to the family of almost circular codes the structure of two element precircular codes is determined codes and precircular codes are characterized by their way of acting upon periodic biinfinite words

space filling fractional factorial designs fractional factorial designs are widely used in various scientific investigations and industrial applications level permutation of factors could alter their geometrical structures and statistical properties this article studies space filling properties of fractional factorial designs under two commonly used space filling measures discrepancy and maximin distance when all possible level permutations are considered the average discrepancy is expressed as a linear combination of generalized word length pattern for fractional factorial designs with any number of levels and any discrepancy defined by a reproducing kernel generalized minimum aberration designs are shown to have good space filling properties on average in terms of both discrepancy and distance several novel relationships between distance distribution and generalized word length pattern are derived it is also shown that level permutations can improve space filling properties for many existing saturated designs a two step construction pro

completing codes in a sofic shift we define a code in a sofic shift as a set of blocks of symbols of the shift such that any block of the shift has at most one decomposition into code words it is maximal if it is not strictly included in another one such a code is complete in the sofic shift if any block of the shift occurs within some concatenation of code words we prove that a maximal code in an irreducible sofic shift is complete in this shift we give an explicit construction of a regular completion of a regular code in a sofic shift this extends the well known result of ehrenfeucht and rozenberg to the case of codes in sofic systems we also give a combinatorial proof of a result concerning the polynomial of a code in a sofic shift

a connection between uniformity and aberration in regular fractions of two level factorials summary we show a link between the two apparently unrelated areas of uniformity and minimum aberration with reference to regular fractions of two level factorials we derive an expression for the centred l2 discrepancy measure for uniformity in terms of the word length pattern this result indicates in particular excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration

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

on factorially balanced sets of words a set of words is factorially balanced if the set of all the factors of its words is balanced we prove that if all words of a factorially balanced set have a finite index then this set is a subset of the set of factors of a sturmian word moreover characterizing the set of factors of a given length n of a sturmian word by the left special factor of length n 1 of this sturmian word we provide an enumeration formula for the number of sets of words that correspond to some set of factors of length n of a sturmian word

neutral and tree sets of arbitrary characteristic we study classes of minimal sets defined by restrictions on the possible extensions of the words these sets generalize the previously studied classes of neutral and tree sets by relaxing the condition imposed on the empty word and measured by an integer called the characteristic of the set we present several enumeration results holding in these sets of words these formulae concern return words and bifix codes they generalize formulae previously known for sturmian sets or more generally for tree sets we also give two geometric examples of this class of sets namely the natural coding of some interval exchange transformations and the natural coding of some linear involutions

numerical solution of the goursat problem on a triangular domain with mixed boundary conditions abstract for the goursat problem we consider a triangular domain with mixed dirichlet and impedance boundary conditions imposed on it we develop an algorithm for its numerical solution mainly based on runge kutta method and trapezoidal formula iterative techniques are constructed to compute some data for the nonlinear part of the differential equation and the impedance boundary condition error estimates are derived examples are presented to illustrate the effectiveness of the method

codes unambiguous automata and sofic systems we study the relationship between codes and unambiguous automata inside a sofic system we show that a recognizable set is a code in a sofic system if and only if a particular automaton associated to the set and the shift is unambiguous we discuss an example of a finite complete code in a sofic system in connection with the factorization conjecture

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

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

codes of central sturmian words a central sturmian word or simply central word is a word having two coprime periods p and q and length equal to p q 2 we consider sets of central words which are codes some general properties of central codes are shown in particular we prove that a non trivial maximal central code is infinite moreover it is not maximal as a code a central code is called prefix central code if it is a prefix code we prove that a central code is a prefix resp maximal prefix central code if and only if the set of its generating words is a prefix resp maximal prefix code a suitable arithmetization of the theory is obtained by considering the bijection called ratio of periods from the set of all central words to the set of all positive irreducible fractions defined as e 1 1 and w p q resp w q p if w begins with the letter a resp letter b p is the minimal period of w and q w p 2 we prove that a central code x is prefix resp maximal prefix if and only if x is an independent resp independent and full set of fractions finally two interesting classes of prefix central codes are considered one is the class of farey codes which are naturally associated with the farey series we prove that farey codes are maximal prefix central codes the other is given by uniform central codes a noteworthy property related to the number of occurrences of the letter a in the words of a maximal uniform central code is proved

on the sentence valuation in a semiring this paper proposes an algebraic way of sentence valuations in a semiring actually throughout the paper only valuations in the ring of integers with usual addition and multiplication are considered these valuations take into consideration both words and their positions within the sentences two synonymy relations with respect to a given valuation are introduced all sentences that are synonymous form a synonymy class which is actually a formal language some basic problems regarding the synonymy classes are formulated in the general setting but the results presented concern only very special valuations

finite biprefix sets of paths in a graph abstract the main results of the combinatorial theory of maximal biprefix codes of words cesari perrin schutzenberger are extended to the codes of paths in a graph in this paper degree and decoding of double infinite paths finiteness of codes of a given degree the cesari schutzenberger algorithm derivation and integration of codes will be discussed

bridge designs for modeling systems with low noise for deterministic computer simulations gaussian process models are a standard procedure for fitting data these models can be used only when the study design avoids having replicated points this characteristic is also desirable for one dimensional projections of the design since it may happen that one of the design factors has a strongly nonlinear effect on the response latin hypercube designs have uniform one dimensional projections but are not efficient for fitting low order polynomials when there is a small error variance d optimal designs are very efficient for polynomial fitting but have substantial replication in projections we propose a new class of designs that bridge the gap between d optimal designs and d optimal latin hypercube designs these designs guarantee a minimum distance between points in any one dimensional projection allowing for the fit of either polynomial or gaussian process models subject to this constraint they are d optimal for a prespecified model

rational probability measures abstract the theory of finite automata and coding has been linked to probability theory since its foundation by the work of shannon and its further enrichment especially by schutzenberger in a parallel development symbolic dynamical systems whose behaviour is governed by a finite automaton have been studied under several aspects especially by hell robertson binkowska and kaminski 4 13 17 weiss has given to them the name of sofic systems and he has shown that they constitute a generalization of topological markov chains 20 since then adler and his associates have shown how theoretical development in this field could lead to a remarkable treatment of engineering problems in coding 1 in this paper we continue the exploration of this borderline area and present some new results probability measures on words are studied in their relation with coding and finite automata we particularly insist on the notion of a rational probability measure which although perhaps not quite new has not yet received all the attention it deserves in a first section we fix the notation and prove some preliminary results in particular the basic properties of rational probability measures are established the second section deals with probability measures for which the sequences obtained after some coding are mutually independent it contains two main results the first one gives conditions under which the restriction of a probability measure to a given free submonoid is a bernoulli measure it extends a result due to schutzenberger the second result is due to langlois and is published here for the first time in the two remaining sections we consider the problem of transferring a probability measure from one free monoid into another one several new results are proved which complement the ones previously obtained in collaboration with blanchard 5 6

valuations of languages with applications to fractal geometry abstract valuations morphisms from to 0 1 are a simple generalization of bernoulli morphisms distributions measures as introduced by berstel and perrin 1988 berstel and reutenauer 1988 blanchard and hansel 1984 eilenberg 1974 and hansel and perrin 1983 1989 this paper shows that valuations are useful not only within the theory of codes but also when dealing with ambiguity especially in context free grammars or for defining outer measures on the space of words which are of some importance to the theory of fractals these connections yield new formulae to determine the hausdorff dimension of fractal sets especially in euclidean spaces defined via formal languages the class of fractals describable with context free languages strictly includes that of mrfs fractals introduced by culik and dube 1990 and mauldin and williams 1988 some of the results of this paper also appear as part of the author s ph d thesis and other works fernau 1992a b 1993

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

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

completing circular codes in regular submonoids let m be an arbitrary submonoid of the free monoid a and let x m be a variable length code for short a code x is weakly m complete iff any word in m is a factor of some word in x j neraud c selmi free monoid theory maximality and completeness in arbitrary submonoids internat j algebra comput 13 5 2003 507 516 given a regular submonoid m and given an arbitrary code x m we are interested in the existence of a weakly m complete code x that contains x actually in j neraud completing a code in a regular submonoid in acts of mcu 2004 lect notes comput sci 3354 2005 281 291 j neraud completing a code in a submonoid of finite rank fund inform 74 2006 549 562 by presenting a general formula we have established that in any case such a code x exists in the present paper we prove that any regular circular code x m may be embedded into a weakly m complete one iff the minimal automaton with behavior m has a synchronizing word as a consequence of our result an extension of the famous theorem of schutzenberger is stated for regular circular codes in the framework of regular submonoids we study also the behaviour of the subclass of uniformly synchronous codes in connection with these questions

orthogonal and nearly orthogonal designs for computer experiments we introduce a method for constructing a rich class of designs that are suitable for use in computer experiments the designs include latin hypercube designs and two level fractional factorial designs as special cases and fill the vast vacuum between these two familiar classes of designs the basic construction method is simple building a series of larger designs based on a given small design if the base design is orthogonal the resulting designs are orthogonal likewise if the base design is nearly orthogonal the resulting designs are nearly orthogonal we present two generalizations of our basic construction method the first generalization improves the projection properties of the basic method the second generalization gives rise to designs that have smaller correlations sample constructions are presented and properties of these designs are discussed

a numerical method for solving a goursat cauchy boundary value problem in this paper we propose a method to construct numerically the solution pair of a second order hyperbolic partial differential equation when two types of boundary conditions on a triangular domain are imposed specifically the pde is w x x x t w t t x t q x w x t email protected x l x t where the unknown functions are w x t and dq x one set of boundary conditions refer to one set of the triangle s boundaries we call them goursat type and the other set of boundary conditions both refer to the third boundary of the triangle we call them cauchy type to solve numerically this boundary value problem we make a change of dependent variables and place a mesh on the triangular domain with lines that are the characteristic curves of the hyperbolic pde then we shall integrate along the characteristic curves of the hyperbolic pde in such a way that numerical values of w x t and dq x will be produced at mesh nodes located on vertical lines the calculations will proceed from the vertical boundary of the domain going backwards to the origin o of the oxt coordinate system from one vertical line to another the trapezoidal formula will be used for numerical integration numerical examples will be provided

the method of poles a coding method for constrained channels a method for solving coding problems involving channels restricted by finite state constraints is presented the method was introduced by p a franaszek 1969 and is based on the computation of a set of principal states it is proved that state independent decoding is guaranteed the main result is that the transducer constructed using the method is a local automaton in its output the method is also related to recent work in symbolic dynamics by r l adler 1987 b marcus 1985 and others typical applications are coding methods for magnetic storage

projection of markov measures may be gibbsian we study the induced measure obtained from a 1 step markov measure supported by a topological markov chain after the mapping of the original alphabet onto another one we give sufficient conditions for the induced measure to be a gibbs measure in the sense of bowen when the factor system is again a topological markov chain this amounts to constructing when it does exist the induced potential and proving its holder continuity this is achieved through a matrix method we provide examples and counterexamples to illustrate our results

codes circulaires automates locaux et entropie abstract the theory of codes and finite automata is applied to prove the existence of codes suitable for coding arbitrary sequences into a constrained system of sequences called system of finite type the techniques are different from those used by adler coppersmith hassner and marcus in earlier work on the same problem

codes and sofic constraints we study the notion of a code in a sofic subshift we first give a generalization of the kraft mcmillan inequality to this case we then prove that the polynomial of the alphabet in an irreducible sofic shift divides the polynomial of any finite code which is complete for this sofic shift this settles a conjecture from reutenauer

cyclic renewal systems we present three equivalent conditions for a generating set w of a renewal system to generate a maximal monoid in the language of the system we show that if a code w generates a shift of finite type and satisfies those conditions then it is cyclic sufficient conditions are given when the converse holds

the decomposition method for approximate solution of the goursat problem abstract in this paper the adomian s decomposition method is effectively implemented to establish an analytic solution and a reliable numerical approximation to the goursat partial differential equation linear and nonlinear goursat examples are examined and the method supplied quantitatively reliable results for these types of problems the accuracy level of the results obtained indicates the superiority of the decomposition method over existing numerical methods that were applied to the goursat problem

completing prefix codes in submonoids let m be a submonoid of the free monoid a and let x m be a variable length code for short a code x is weakly m complete if any word in m is a factor of some word in x j neraud c selmi free monoid theory maximality and completeness in arbitrary submonoids internat j algorithms comput 13 5 2003 507 516 given a code x m we are interested in the construction of a weakly m complete code that contains x if it exists in the case where m and x are regular sets the existence of such a code has been established j neraud completing a code in a regular submonoid of the free monoid in acts of mcu 2004 lecture notes in computer sciences vol 3354 springer berlin 2005 pp 281 291 j neraud on the completion of codes in submonoids with finite rank fund inform to appear actually this result lays upon a method of construction that preserves the regularity of sets as well known any regular or finite code may be embedded into a regular finite prefix code that is complete in a instance a regular submonoid m of a and a regular or finite prefix code x m question does a weakly m complete regular finite prefix code containing x exist

a technique for approximate solutions to schrodinger like equations in the present paper the schro dinger like equations are solved easily quickly and elegantly using adomian s decomposition method the technique has been illustrated by some examples which are of physical interest

orthogonal array based latin hypercubes abstract in this article we use orthogonal arrays oa s to construct latin hypercubes besides preserving the univariate stratification properties of latin hypercubes these strength r oa based latin hypercubes also stratify each r dimensional margin therefore such oa based latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general latin hypercubes we prove that when used for integration the sampling scheme with oa based latin hypercubes offers a substantial improvement over latin hypercube sampling

pseudo cyclic renewal systems abstract a finite set w of words over an alphabet a is cyclic if whenever u v a and u v v u w we have u v w if it is only assumed that the property holds for all u v a with a large length then w is called pseudo cyclic that is there is n n such that whenever u v a with u v n and u v v u w we have u v w we analyze the class of pseudo cyclic sets and describe how it is related to the open question which asks whether every irreducible shift of finite type is conjugate to a renewal system

orthogonal column latin hypercubes and their application in computer experiments abstract latin hypercubes have been frequently used in conducting computer experiments in this paper a class of orthogonal latin hypercubes that preserves orthogonality among columns is proposed applying an orthogonal latin hypercube design to a computer experiment benefits the data analysis in two ways first it retains the orthogonality of traditional experimental designs the estimates of linear effects of all factors are uncorrelated not only with each other but also with the estimates of all quadratic effects and bilinear interactions second it can facilitate nonparametric fitting procedures because one can select good space filling designs within the class of orthogonal latin hypercubes according to selection criteria

codes and local constraints etude du probleme de l existance et de la construction de codes dont les elements des mots satisfont certaines contraintes concernant les sequences de lettres qu ils peuvent contenir l equivalence entre les notions de maximalite et de completude pour ces codes est etudiee

on existence and nonexistence of global solutions of cauchy goursat problem for nonlinear wave equations abstract we consider the cauchy goursat initial characteristic problem for nonlinear wave equations with power nonlinearity depending on the power of nonlinearity and the parameter in an equation we investigate the problem on existence and nonexistence of global solutions of the cauchy goursat problem the question on local solvability of the problem is also considered

optimal foldover plans for two level nonregular orthogonal designs this article considers optimal foldover plans for nonregular designs by using the indicator function we define words with fractional lengths the extended word length pattern is then used to select among nonregular foldover designs some general properties of foldover designs are obtained using the indicator function we prove that the full foldover plan that reverses the signs of all factors is optimal for all 12 run and 20 run orthogonal designs the optimal foldover plans for all 16 run regular and nonregular orthogonal designs are constructed and tabulated for practical use optimal foldover plans for higher order orthogonal designs can be constructed in a similar manner