α words and the radix order let a a 1 a 2 be a sequence finite or infinite of integers with a 1 0 and a n 1 for all n 2 let a b be an alphabet for n 1 and r r 1r 2 r n n n with 0 r i a i for 1 i n there corresponds an nth order a word u n r with label r derived from the pair a b these a words are defined recursively as follows u 1 b u 0 a u 1 r 1 a a 1 r 1ba r 1 u i r 1r 2 r i u i 1 r 1r 2 r i 1 a i r iu i 2 r 1r 2 r i 2 u i 1 r 1r 2 r i 1 r i i 2 many interesting combinatorial properties of a words have been studied by chuan in this paper we obtain some new methods of generating the distinct a words of the same order in lexicographic order among other results we consider another function r w r from the set of labels of a words to the set of a words the string r is called a new label of the a word w r using any new label of an nth order a word w we can compute the number of the nth order a words that are less than w in the lexicographic order with the radix orders r on n n regarding n as an alphabet and a b with a rb we prove that there exists a subset d of the set of all labels such that w r rw s whenever r s d and r rs

locating factors of the infinite fibonacci word let 5 1 2 let a b be two distinct letters the infinite fibonacci word is the infinite word g babbababbabbababbababbabba whose nth letter is a resp b if n 1 n 0 resp 1 for a factor w of g the location of w is the set of all positions in g at which w occurs only the locations of the following factors of g are already known squares singular words and those factors of g whose lengths are fibonacci numbers the purpose of this paper is to determine the locations of all factors of g our results contain all the known ones as consequences moreover using our results we are able to identify any factor of g whenever its starting position and length are given also we are able to tell whether two suffixes of g have a common prefix of a certain length

locating factors of a characteristic word via the generalized zeckendorf representation of numbers let a be an irrational number with 0 1 for a factor w of f a the location of w is the set of all positions in f a at which w occurs the locations of all factors of f a have been determined by chuan and ho recently in this paper we obtain other formulas for the locations of factors of f a using the generalized zeckendorf representation of nonnegative integers these results are equivalent to the known results obtained by chuan and ho in the case a 3 52 we compute the longest common prefix of any two suffixes of f a and compute the order number and location index of each factor of f a given its length and a position in f a at which it begins

every completely polynomially bounded operator is similar to a contraction it is proved that a bounded operator on a hilbert space is similar to a contraction if and only if it is completely polynomially bounded this gives a partial answer to problem 6 of halmos bull amer math soc 76 1970 877 933 the set of completely bounded maps between c algebras is studied to obtain some structure representation and extension theorems for this class of maps these allow a characterization of the completely bounded representations on a hilbert space of any subalgebra of a c algebra to be obtained the result in the title follows by applying this characterization to the disk algebra

factors of characteristic words location and decompositions let a be an irrational number with 0 a 1 and let f a be the characteristic word of a the location of a factor w of f a is defined to be the set of all positions in f a at which w occurs in this paper an explicit formula of the location of each factor w of f a is obtained the decompositions red a w and sod a w of f a associated with w are established the former one involves all return words of w while the latter one involves all occurrences of w and the corresponding separate factors and overlap factors these results generalize the work by the present authors 2005 z x wen and z y wen 1994 g melancon 1999 w t cao and z y wen 2003 i m araujo and v bruyere 2005 and a glen 2006

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

comments on an improved formula for the resonant frequency of the triangular microstrip path antenna with reply the commenters claim to have found several errors in the paper by garg and long see ibid vol 36 no 4 p 570 apr 1988 an author s reply is presented

some combinatorial properties of sturmian words abstract in this paper we give a characterization of finite sturmian words by palindrome words which generalizes a property of the fibonacci words we prove that the set st of finite sturmian words coincides with the set of the factors of all the words w such that w ab cxy with a b c palindromes x y a b and x y moreover using this result we prove that st is equal to the set of the factors of all words w having two periods p and q which are coprimes and such that w p q 2 several other combinatorial properties concerning special and bispecial elements of st are shown as a consequence we give a new and purely combinatorial proof of the enumeration formula of st

almost everywhere convergence of powers of some positive lp contractions abstract we extend the solution of burkholder s conjecture for products of conditional expectations obtained by delyon and delyon for l 2 and by cohen for l p 1 p to the context of badea and lyubich let t be a finite convex combination of operators t j which are products of finitely many conditional expectations then t n f converges a e for every f l p 1 p with sup n t n f l p the proof uses the work of le merdy and xu on positive l p contractions satisfying ritt s resolvent condition as another application of the work of le merdy and xu we extend a result of bellow jones and rosenblatt proving that if a probability a k k z has bounded angular ratio then for every positive invertible isometry s of an l p space 1 p the operator t k z a k s k is a positive l p contraction such that for every f l p t n f converges a e and sup n t n f l p if a k is supported on n the same result is true when s is only a positive contraction of l p similar results are obtained for averages of bounded continuous representations of a compact lca group by positive operators in one l p space 1 p for a positive contraction t on l p which satisfies ritt s condition and f i t l p 0 1 we prove that n t n f 0 a e and sup n n t n f l p

moments of conjugacy classes of binary words for each nonempty binary word w c1c2 cq where ci 0 1 the nonnegative integer i 1q q 1 i ci is called the moment of w and is denoted by m w let w denote the conjugacy class of w define m w m u u w n w m u m w u w and w max m u m v u v w using these objects we obtain equivalent conditions for a binary word to be an word respectively a power of an word for instance we prove that the following statements are equivalent for any binary word w with w 2 a w is an word b w w 1 c w is a cyclic balanced primitive word d m w is a set of w consecutive positive integers c n w is a set of w consecutive integers and 0 n w f w is primitive and w st

factors of characteristic words of irrational numbers let be an irrational number between 0 and 1 the characteristic word f of is defined to be the infinite word over 0 1 whose nth letter is n 1 n n 1 it is well known that for each m 1 f has exactly m 1 distinct factors of length m in this paper we shall develop a method to construct these factors under our construction the 1 sets of these m 1 factors x0 m x1 m xm m are determined these factors are increasing in the lexicographic order and their moments m x0 m m x1 m m xm m form an increasing sequence of m 1 consecutive integers some known results about generating factors of f using the unbordered words and their conjugates turn out to be consequences of our main theorem

computer analysis method for arbitrarily shaped microstrip antenna with multiterminals an analysis method is presented for an arbitrarily shaped microstrip antenna with multiterminals the method is based on the variational method and the modal expansion technique eigenvalues and eigenfunctions are determined using the rayleigh ritz method input impedance and other antenna parameters are derived at nonresonance furthermore the network model useful for the network analysis of a microstrip antenna with multiterminals is presented by introducing an ideal transformer finally numerical examples are compared with experimental results the agreement is quite good and the validity of the present method is confirmed

the sequence of return words of the fibonacci sequence let be a factor of the fibonacci sequence f x 1 x 2 then it occurs in the sequence infinitely many times let p be the p th occurrence of and r p be the p th return word over in this paper we study the structure of the sequence of return words r p p 1 we first introduce the singular kernel word s k for any factor of f and give a decomposition of with respect to s k using the singular kernel and the decomposition we prove that the sequence of return words over the alphabet r 1 r 2 is still a fibonacci sequence we also determine the expressions of return words completely for each factor finally we introduce the spectrum for studying some combinatorial properties such as power overlap and separate of factors

integral equation formulation of microstrip antennas the problem of a microstrip antenna covered by a dielectric is formulated in terms of coupled integro differential equations with the current distribution on the microstrip patch as an unknown variable galerkin s method is used to solve for the unknown patch current using the present formulation the resonant frequency and bandwidth of a rectangular microstrip antenna are determined and compared with experimental results

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

a characterization of the squares in a fibonacci string a finite fibonacci stringfn is defined as follows f0 b f1 a for every integer n 2 fn fn 1fn 2 for n 1 the length of fn is denoted by the infinite fibonacci stringf is the string which contains every fn n 1 as a prefix apart from their general theoretical importance fibonacci strings are often cited as worst case examples for algorithms which compute all the repetitions or all the abelian squares in a given string in this paper we provide a characterization of all the squares in f hence in every prefix fn this characterization naturally gives rise to a algorithm which specifies all the squares of fn in an appropriate encoding this encoding is made possible by the fact that the squares of fn occur consecutively in runs the number of which is by contrast the known general algorithms for the computation of the repetitions in an arbitrary string require time and produce outputs when applied to a fibonacci string fn

lyndon words and singular factors of sturmian words abstract two different factorizations of the fibonacci infinite word were given independently in wen and wen 1994 and melancon 1996 in a certain sense these factorizations reveal a selfsimilarity property of the fibonacci word we first describe the intimate links between these two factorizations we then propose a generalization to characteristic sturmian words

occurrences of palindromes in characteristic sturmian words this paper is concerned with palindromes occurring in characteristic sturmian words c of slope where 0 1 is an irrational as c is a uniformly recurrent infinite word any palindromic factor of c occurs infinitely many times in c with bounded gaps our aim is to completely describe where palindromes occur in c in particular given any palindromic factor u of c we shall establish a decomposition of c with respect to the occurrences of u such a decomposition shows precisely where u occurs in c and this is directly related to the continued fraction expansion of

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

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

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

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

fibonacci word patterns in two way infinite fibonacci words the studies of 1 fibonacci word patterns and 0 fibonacci word patterns were initiated by turner 1988 18 and chuan 1993 2 respectively it is known that each proper suffix of the infinite fibonacci word is an r fibonacci word pattern email protected 0 1 in this paper we consider the suffixes of the two two way infinite extensions g and g of the infinite fibonacci word we obtain necessary and sufficient conditions for suffixes of g and g to be r fibonacci word patterns this gives us all the mechanical words with slope a 5 12 which are r fibonacci word patterns all possible r seed words of each of them are determined finally images of suffixes of g and g under the action of certain sturmian morphisms are computed

unbordered factors of the characteristic sequences of irrational numbers abstract a finite word w over an alphabet is said to be bordered if there is a word which is both a proper prefix and a proper suffix of w in this paper the unbordered factors of the characteristic sequences f of irrational numbers between 0 and 1 are determined by definition f is the infinite word over the alphabet lcub 0 1 rcub whose nth letter is n l n n 1 it is proved that the unbordered factors of f are precisely the lyndon words over lcub 0 1 rcub and their mirror images as a biproduct a characterization of words is obtained