an algebraic proof of the cyclic sum formula for multiple zeta values abstract we introduce an algebraic formulation of the cyclic sum formulas for multiple zeta values and for multiple zeta star values we also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta star values by reducing them to kawashima s relation

modules of the 0 hecke algebra and quasisymmetric schur functions abstract we begin by deriving an action of the 0 hecke algebra on standard reverse composition tableaux and use it to discover 0 hecke modules whose quasisymmetric characteristics are the natural refinements of schur functions known as quasisymmetric schur functions furthermore we classify combinatorially which of these 0 hecke modules are indecomposable from here we establish that the natural equivalence relation arising from our 0 hecke action has equivalence classes that are isomorphic to subintervals of the weak bruhat order on the symmetric group focussing on the equivalence classes containing a canonical tableau we discover a new basis for the hopf algebra of quasisymmetric functions and use the cardinality of these equivalence classes to establish new enumerative results on truncated shifted reverse tableau studied by panova and adin king roichman generalizing our 0 hecke action to one on skew standard reverse composition tableaux we derive 0 hecke modules whose quasisymmetric characteristics are the skew quasisymmetric schur functions of bessenrodt et al this enables us to prove a restriction rule that reflects the coproduct formula for quasisymmetric schur functions which in turn yields a quasisymmetric branching rule analogous to the classical branching rule for schur functions

wavelet based fractal analysis of dna sequences abstract the fractal scaling properties of dna sequences are analyzed using the wavelet transform mapping nucleotide sequences onto a dna walk produces fractal landscapes that can be studied quantitatively by applying the so called wavelet transform modulus maxima method this method provides a natural generalization of the classical box counting techniques to fractal signals the wavelets playing the role of generalized oscillating boxes from the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima this method allows us to determine the singularity spectrum of the considered signal and thereby to achieve a complete multifractal analysis moreover by considering analyzing wavelets that make the wavelet transform microscope blind to patches of different nucleotide composition that are observed in genomic sequences we demonstrate and quantify the existence of long range correlations in the noncoding regions although the fluctuations in the patchy landscape of the dna walks reconstructed from both noncoding and protein coding regions are found homogeneous with gaussian statistics our wavelet based analysis allows us to discriminate unambiguously between the fluctuations of the former which behave like fractional brownian motions from those of the latter which cannot be distinguished from uncorrelated random brownian walks we discuss the robustness of these results with respect to various legitimate codings of the dna sequences finally we comment about the possible understanding of the origin of the observed long range correlations in noncoding dna sequences in terms of the nonequilibrium dynamical processes that produce the isochore structre of the genome

on posets and hopf algebras abstract we generalize the notion of the rank generating function of a graded poset namely by enumerating different chains in a poset we can assign a quasi symmetric function to the poset this map is a hopf algebra homomorphism between the reduced incidence hopf algebra of posets and the hopf algebra of quasi symmetric functions this work implies that the zeta polynomial of a poset may be viewed in terms hopf algebras in the last sections of the paper we generalize the reduced incidence hopf algebra of posets to the hopf algebra of hierarchical simplicial complexes

weak quasi symmetric functions rota baxter algebras and hopf algebras abstract we introduce the hopf algebra of quasi symmetric functions with semigroup exponents generalizing the hopf algebra qsym of quasi symmetric functions as a special case we obtain the hopf algebra qsym n of weak quasi symmetric functions which provides a framework for the study of a question proposed by g c rota relating symmetric type functions and rota baxter algebras we provide the transformation formulas between the weak monomial and fundamental quasi symmetric functions which extends the corresponding results for quasi symmetric functions moreover we show that qsym is a hopf subalgebra and a hopf quotient algebra of qsym n rota s question is addressed by identifying qsym n with the free commutative unitary rota baxter algebra x of weight 1 on one generator x which also allows us to equip x with a hopf algebra structure

eulerian quasisymmetric functions we introduce a family of quasisymmetric functions called eulerian quasisymmetric functions which specialize to enu merators for the joint distribution of the permutation statistics major index and excedance number on permutations of fixed cycle type this family is analogous to a family of quasisymmetric func tions that gessel and reutenauer used to study the joint distribu tion of major index and descent number on permutations of fixed cycle type our central result is a formula for the generating func tion for the eulerian quasisymmetric functions which specializes to a new and surprising q analog of a classical formula of euler for the exponential generating function of the eulerian polynomials this q analog computes the joint distribution of excedance number and major index the only of the four important euler mahonian distributions that had not yet been computed our study of the eulerian quasisymmetric functions also yields results that include the descent statistic and refine results of gessel and reutenauer we also obtain q analogs q p analogs and quasisymmetric func tion analogs of classical results on the symmetry and unimodality of the eulerian polynomials our eulerian quasisymmetric functions refine symmetric functions that have occurred in various represen tation theoretic and enumerative contexts including macmahon s study of multiset derangements work of procesi and stanley on toric varieties of coxeter complexes stanley s work on chromatic symmetric functions and the work of the authors on the homology of a certain poset introduced by bjorner and welker

the algebra of multiple harmonic series abstract recently there has been much interest in multiple harmonic series i 1 i 2 i k n 1 n 2 n k 1 1 n 1 i 1 n 2 i 2 n k i k which converge when the exponentsijare positive integers andi1 1 also known as multiple zeta values or euler zagier sums starting with the noncommutative polynomial algebraq x y we define a second multiplication which is commutative and associative and call the resulting structure the harmonic algebra h as a graded commutative algebra h turns out to be a free polynomial algebra with the number of generators in degreengiven by the witt formula for the numbern n of basis elements of degreenin the free lie algebra on two generators multiple harmonic series can be thought of as images under a map h 0 rwhich is a homomorphism with respect to the commutative multiplication where h 0is an appropriate subalgebra of h if we calli1 ikthe weight of the series i1 ik then forn 1 there are at mostn n series of weightnthat are irreducible in the sense that they are not sums of rational multiples of products of multiple harmonic series of lower weight in fact our approach gives an explicit set of algebraically irreducible multiple harmonic series we also show that there is a subalgebra h 0 h 1 h related to the shuffle algebra which contains the algebra s of symmetric functions in fact maps the elements of s h 0to algebraic combinations of zeta values i for integeri 2 the map is not injective we show how several results about multiple harmonic series can be recast as statements about the kernel of and propose some conjectures on the structure of the algebra h 0 ker

combinatorial models for coalgebraic structures abstract we introduce a convenient category of combinatorial objects known as cell sets on which we study the properties of the appropriate free abelian group functor we obtain a versatile generalization of the notion of incidence coalgebra giving rise to an abundance of coalgebras hopf algebras and comodules all of whose structure constants are positive integers with respect to certain preferred bases our category unifies and extends existing constructions in algebraic combinatorics providing proper functorial descriptions it is inspired in part by the notion of cw complex and is also geared to future applications in algebraic topology and the theory of formal group laws

kawashima s relations for interpolated multiple zeta values abstract recently yamamoto introduced polynomials in one variable t which interpolates multiple zeta and zeta star values t mzvs for short provided new prospects on two one conjecture of ohno and zudilin and proved the cyclic sum formula for t mzvs in this paper we establish a generalization of kawashima s relations t kawashima relations for t mzvs we prove the cyclic sum formula for t mzvs using a type of derivation operator together with the t kawashima relations

mean field diffusion limited aggregation a density model for viscous fingering phenomena we explore a universal density formalism to describe nonequilibrium growth processes specifically the immiscible viscous fingering in hele shaw cells usually referred to as the saffman taylor problem for that we develop an alternative approach to the viscous fingering phenomena whose basic concepts have been recently published in a rapid communication phys rev e 63 045305 r 2001 this approach uses the diffusion limited aggregation dla paradigm as a core we introduce a mean field dla generalization in stochastic and deterministic formulations the stochastic model a quasicontinuum dla simulates monte carlo patterns which demonstrate a striking resemblance to natural hele shaw fingers and for steady state growth regimes follow precisely the saffman taylor analytical solutions in channel and sector configurations the relevant deterministic theory a complete set of differential equations for a time development of density fields is derived from that stochastic model as a principal conclusion we prove an asymptotic equivalency of both the stochastic and deterministic mean field dla formulations to the classic saffman taylor hydrodynamics in terms of an interface evolution

golden mean arithmetic in the fractal branching of diffusion limited aggregates we use the wavelet transform microscope to explore the intricate fractal geometry of witten and sander s diffusion limited aggregates we report on the discovery of fibonacci sequences in the internal hierarchical structure of these clusters we discuss the relevance of the golden mean arithmetic to the numerically well established statistical self similarity of these aggregates

multivariable hoffman ihara operators and the operad of formal power series abstract we introduce a family of multilinear operators on a quasi shuffle algebra h which we call hoffman ihara operators it generalizes the linear operators constructed by hoffman and further studied by hoffman and ihara we prove the formula on the composition of these operators and show that this formula provides a unified and transparent understanding of some results on shuffle and quasi shuffle products an interpretation as an action of the operad of formal power series is also given

peak quasisymmetric functions and eulerian enumeration abstract via duality of hopf algebras there is a direct association between peak quasisymmetric functions and enumeration of chains in eulerian posets we study this association explicitly showing that the notion of cd index long studied in the context of convex polytopes and eulerian posets arises as the dual basis to a natural basis of peak quasisymmetric functions introduced by stembridge thus eulerian posets having a nonnegative cd index for example face lattices of convex polytopes correspond to peak quasisymmetric functions having a nonnegative representation in terms of this basis we diagonalize the operator that associates the basis of descent sets for all quasisymmetric functions to that of peak sets for the algebra of peak functions and study the g polynomial for eulerian posets as an algebra homomorphism

galois connections for incidence hopf algebras of partially ordered sets abstract an important well known result of rota describes the relationship between the mobius functions of two posets related by a galois connection we present an analogous result relating the antipodes of the corresponding incidence hopf algebras from which the classical formula can be deduced to motivate the derivation of this more general result we first observe that a simple conceptual proof of rota s classical formula can be obtained by interpreting it in terms of bimodules over the incidence algebras bimodules correct the apparent lack of functoriality of incidence algebras with respect to monotone maps the theory of incidence hopf algebras is reviewed from scratch and centered around the notion of cartesian posets also the universal multiplicative function on a poset is constructed and an analog for antipodes of the classical mobius inversion formula is presented

cyclic sum formula for multiple l values abstract the cyclic sum formula for multiple l values which can be viewed as a generalization of the cyclic sum formula for multiple zeta values proved by hoffman and ohno or ohno and wakabayashi is shown an algebraic formulation of the cyclic sum formula is also presented

multiple q zeta values we introduce a q analog of the multiple harmonic series commonly referred to as multiple zeta values the multiple q zeta values satisfy a q stuffle multiplica tion rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values additionally multiple q zeta values can be viewed as special values of the multiple q polylogarithm which admits a multiple jackson q integral representation whose limiting case is the drinfel d simplex integral for the ordinary multiple polylogarithm when q 1 the multiple jackson q integral representation for multiple q zeta values leads to a second multiplication rule satisfied by them referred to as a q shuffle despite this it appears that many numerical relations satisfied by ordinary multiple zeta values have no interesting q extension for example a suitable q analog of broadhurst s formula for 3 1 n if one exists is likely to be rather complicated nevertheless we show that a number of infinite classes of relations inc luding hoffman s partition identities ohno s cyclic sum identities granville s sum formula euler s convolution formula ohno s generalized duality relation and the derivation relations of ihara and kaneko extend to multiple q zeta values

the thermodynamics of fractals revisited with wavelets abstract the multifractal formalism originally introduced to describe statistically the scaling properties of singular measures is revisited using the wavelet transform this new approach is based on the definition of partition functions from the wavelet transform modulus maxima we demonstrate that very much like thermodynamic functions the generalized fractal dimensions d q and the f singularity spectrum can be readily determined from the scaling behavior of these partition functions we show that this method provides a natural generalization of the classical box counting techniques to fractal signals the wavelets playing the role of generalized boxes we illustrate our theoretical considerations on pedagogical examples e g devil s staircases and fractional brownian motions we also report the results of some recent application of the wavelet transform modulus maxima method to fully developed turbulence data that we emphasize the wavelet transform as a mathematical microscope that can be further used to extract microscopic informations about the scaling properties of fractal objects in particular we show that a dynamical system which leaves invariant such an object can be uncovered form the space scale arrangement of its wavelet transform modulus maxima we elaborate on a wavelet based tree matching algorithm that provides a very promising tool for solving the inverse fractal problem this step towards a statistical mechanics of fractals is illustrated on discrete period doubling dynamical systems where the wavelet transform is shown to reveal the renormalization operation which is essential to the understanding of the universal properties of this transition to chaos finally we apply our technique to analyze the fractal hierarchy of dla azimuthal cantor sets defined by intersecting the inner frozen region of large mass off lattice diffusion limited aggregates dla wit a circle this study clearly lets out the existence of an underlying multiplicative process that is likely to account for the fibonacci structural ordering recently discovered in the apparently disordered arborescent dla morphology

on harmonic numbers and nonlinear euler sums abstract in this paper we are interested in euler type sums with products of harmonic numbers stirling numbers and bell numbers we discuss the analytic representations of euler sums through values of polylogarithm function and riemann zeta function moreover we provide explicit evaluations for almost all euler sums with weight 5 which can be expressed in terms of zeta values and polylogarithms furthermore we give explicit formula for several classes of euler related sums in terms of zeta values and harmonic numbers and several examples are given the given representations are new

skew quasisymmetric schur functions and noncommutative schur functions abstract recently a new basis for the hopf algebra of quasisymmetric functions qsym called quasisymmetric schur functions has been introduced by haglund luoto mason van willigenburg in this paper we extend the definition of quasisymmetric schur functions to introduce skew quasisymmetric schur functions these functions include both classical skew schur functions and quasisymmetric schur functions as examples and give rise to a new poset l c that is analogous to young s lattice we also introduce a new basis for the hopf algebra of noncommutative symmetric functions nsym this basis of nsym is dual to the basis of quasisymmetric schur functions and its elements are the pre image of the schur functions under the forgetful map nsym sym we prove that the multiplicative structure constants of the noncommutative schur functions equivalently the coefficients of the skew quasisymmetric schur functions when expanded in the quasisymmetric schur basis are nonnegative integers satisfying a littlewood richardson rule analogue that reduces to the classical littlewood richardson rule under as an application we show that the morphism of algebras from the algebra of poirier reutenauer to sym factors through nsym we also extend the definition of schur functions in noncommuting variables of rosas sagan in the algebra ncsym to define quasisymmetric schur functions in the algebra ncqsym we prove these latter functions refine the former and their properties and project onto quasisymmetric schur functions under the forgetful map lastly we show that by suitably labeling l c skew quasisymmetric schur functions arise in the theory of pieri operators on posets

corrigendum to inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators linear algebra appl 586 2020 43 63 abstract in this corrigendum note we provide a correct statement and a proof of 3 th 2 1 parts a4 a4 b4 b4 as well as a correct statement and a proof for the inequality 34 in 3 cor 2 3

the depth structure of motivic multiple zeta values in this paper we construct some maps related to the motivic galois action on depth graded motivic multiple zeta values from these maps we give some short exact sequences about depth graded motivic multiple zeta values in depth two and three in higher depth we conjecture that there are exact sequences of the same type we will show from three conjectures about depth graded motivic lie algebra we can nearly deduce the exact sequences conjectures in higher depth at last we give a new proof of the result that the modulo zeta mathfrak m 2 version motivic double zeta values are generated by the totally odd part we reduce the well known conjecture that the modulo zeta mathfrak m 2 version motivic triple zeta values are generated by the totally odd part to an isomorphism conjecture in linear algebra

fractal dimension and unscreened angles measured for radial viscous fingering we have examined fractal patterns formed by the injection of air into oil in a thin 0 127 phantom rule 0 3em 0ex mathrm mm layer contained between two cylindrical glass plates of 288 phantom rule 0 3em 0ex mathrm mm diameter a hele shaw cell for pressure differences in the range 0 25 ensuremath leqslant ensuremath delta p ensuremath leqslant 1 75 phantom rule 0 3em 0ex mathrm atm we find that an asymptotic structure is reached at large values of the ratio r b where r is the pattern radius and b the gap between the plates both the driving force and the size of the pattern which reaches r b 900 are far larger than in past experiments the fractal dimension d 0 of the pattern for large r b is 1 70 ifmmode pm else textpm fi 0 02 further the generalized dimensions d q of the pattern are independent of q d q ensuremath simeq 1 70 for the range examined ensuremath 11lql17 thus the pattern is self similar within the experimental uncertainty the results for d q agree well with recent calculations for diffusion limited aggregation dla clusters we have also measured the probability distribution of unscreened angles at late times the distribution approaches a universal i e forcing and size independent asymptotic form that has mean 145 ifmmode circ else textdegree fi and standard deviation 36 ifmmode circ else textdegree fi these results indicate that the distribution function for the unscreened angle is an invariant property of the growth process

evaluation of the multiple zeta values zeta 2 dots 2 3 2 dots 2 a formula is given for the special multiple zeta values occurring in the title as rational linear combinations of products m p 2n with m odd the existence of such a formula had been proved using motivic arguments by francis brown but the explicit formula more precisely certain 2 adic properties of its coefficients were needed for his proof in cite1 of the conjecture that all periods of mixed tate motives over z are q 2pi 1 linear combinations of multiple zeta values the formula is proved indirectly by computing the generating functions of both sides in closed form one as the product of a sine function and a 3 f 2 hypergeometric function and one as a sum of 14 products of sine functions and digamma functions and then showing that both are entire functions of exponential growth and that they agree at sufficiently many points to force their equality we also show that the space spanned by the multiple zeta values in question coincides with the space of double zeta values of odd weight and find a relation between this space and the space of cusp forms on the full modular group

random walks on quasisymmetric functions abstract conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations spectral results are also obtained several important random walks are now realized this way stanley s qs distribution results from endomorphisms given by evaluation maps a shuffles result from the a th convolution power of the universal character and the tchebyshev operator of the second kind introduced recently by ehrenborg and readdy yields traditional riffle shuffles a conjecture of ehrenborg regarding the spectra for a family of random walks on ab words is proven a theorem of stembridge from the theory of enriched p partitions is also recovered as a special case

dynamical integral transform on fractal sets and the computation of entropy we introduce an integral transform of wavelet type which we call dynamical integral transform and we show that it can be used to compute the second renyi entropy for a large class of invariant measures the method is then generalized to the whole spectrum of the renyi entropies and establishes a correspondence between thermodynamic formalism and the dynamical integral transform of expanding strange sets numerical examples are presented

kondo effect in single atom contacts the importance of the atomic geometry co single atom junctions on copper surfaces are studied by scanning tunneling microscopy and ab initio calculations the kondo temperature of single cobalt atoms on the cu 111 surface has been measured at various tip sample distances ranging from tunneling to the point contact regime the experiments show a constant kondo temperature for a whole range of tip substrate distances consistently with the predicted energy position of the spin polarized d levels of co this is in striking difference to experiments on co cu 100 junctions where a substantial increase of the kondo temperature has been found our calculations reveal that the different behavior of the co adatoms on the two cu surfaces originates from the interplay between the structural relaxations and the electronic properties in the near contact regime

multiple zeta values vs multiple zeta star values abstract we discuss an algebraic connection between two kinds of multiple zeta values or their q analogues the q multiple zeta values and the q multiple zeta star values these two classes of values generate the same algebra but in this paper we show that the translation map between these two classes has a quite interesting algebraic property in a general setting for example the compatibility with the harmonic product we also study several applications of the result

the hopf algebra approach to feynman diagram calculations the hopf algebra structure underlying feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed recent progress is briefly summarized with an emphasis on further directions of research

structure of the malvenuto reutenauer hopf algebra of permutations we analyze the structure of the malvenuto reutenauer hopf algebra ssym of permutations in detail we give explicit formulas for its antipode prove that it is a cofree coalgebra determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the hopf algebra of quasi symmetric functions in addition we describe the structure constants of the multiplication as a certain number of facets of the permutahedron as a consequence we obtain a new interpretation of the product of monomial quasi symmetric functions in terms of the facial structure of the cube the hopf algebra of malvenuto and reutenauer has a linear basis indexed by permutations our results are obtained from a combinatorial description of the hopf algebraic structure with respect to a new basis for this algebra related to the original one via mobius inversion on the weak order on the symmetric groups this is in analogy with the relationship between the monomial and funda mental bases of the algebra of quasi symmetric functions our results reveal a close relationship between the structure of the malvenuto reutenauer hopf algebra and the weak order on the symmetric groups

shuffle relations for regularised integrals of symbols we prove shuffle relations which relate a product of regularised integrals of classical symbols int reg sigma i d xi i i 1 ldots k to regularised nested iterated integrals prod i 1 k int reg sigma i d xi i sum tau in sigma k int reg d xi 1 int vert xi 2 vert leq vert xi 1 vert d xi 2 cdots int vert xi l vert leq vert xi k 1 vert d xi k otimes i 1 k sigma tau i where k is the group of permutations over k elements we show that these shuffle relations hold if all the symbols i have vanishing residue this is true of non integer order symbols on which the regularised integrals have all the expected properties such as stokes property mmp in general the shuffle relations hold up to finite parts of corrective terms arising from a renormalisation on tensor products of classical symbols a procedure adapted from renormalisation methods to compute feynman diagrams familiar to physicists we relate the shuffle relations for regularised integrals of symbols with shuffle relations for multiple zeta functions adapting the above constructions to the case of a symbol on the unit circle

new properties of multiple harmonic sums modulo p and p analogues of leshchiner s series in this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences 1 a c 1 b 2 a c 2 b and prove a number of congruences for these sums modulo a prime p the congruences obtained allow us to find nice p analogues of leshchiner s series for zeta values and to refine a result due to m hoffman and j zhao about the set of generators of the multiple harmonic sums of weight 7 and 9 modulo p moreover we are also able to provide a new proof of zagier s formula for zeta 2 a 3 2 b based on a finite identity for partial sums of the zeta star series

quantum quasi shuffle algebras ii we establish some properties of quantum quasi shuffle algebras they include the necessary and sufficient condition for the construction of the quantum quasi shuffle product the universal property and the commutativity condition as an application we use the quantum quasi shuffle product to construct a linear basis of t v for a special kind of yang baxter algebras v m

the genus and a regularization of an s1 equivariant euler class we show that a new multiplicative genus in the sense of hirzebruch can be obtained by generalizing a calculation due to atiyah and witten we introduce this as the genus compute its value for some examples and highlight some of its interesting properties we also indicate a connection with the study of multiple zeta values which gives an algebraic interpretation for our proposed regularization procedure

relations of multiple zeta values and their algebraic expression abstract we establish a new class of relations which we call the cyclic sum identities among the multiple zeta values k1 kl n1 nl 11 n1k1 nkkl these identities have an elementary proof and imply the sum theorem for multiple zeta values they also have a succinct statement in terms of cyclic derivations as introduced by rota sagan and stein in addition we discuss the expression of other relations of multiple zeta values via the shuffle and harmonic products on the underlying vector space h of the noncommutative polynomial ring q x y and also using an action of the hopf algebra of quasi symmetric functions on q x y

wavelet based estimators of scaling behavior various wavelet based estimators of self similarity or long range dependence scaling exponent are studied extensively these estimators mainly include the bi orthogonal wavelet estimators and the wavelet transform modulus maxima wtmm estimator this study focuses both on short and long time series in the framework of fractional autoregressive integrated moving average farima processes we advocate the use of approximately adapted wavelet estimators for these ideal processes the scaling behavior actually extends down to the smallest scale i e the sampling period of the time series if an adapted decomposition is used but in practical situations there generally exists a cutoff scale below which the scaling behavior no longer holds we test the robustness of the set of wavelet based estimators with respect to that cutoff scale as well as to the specific density of the underlying law of the process in all situations the wtmm estimator is shown to be the best or among the best estimators in terms of the mean squared error mse we also compare the wavelet estimators with the detrended fluctuation analysis dfa estimator which was previously proved to be among the best estimators which are not wavelet based estimators the wtmm estimator turns out to be a very competitive estimator which can be further generalized to characterize multiscaling behavior

irreducible representations of semisimple algebraic groups and supersolvable lattices abstract let be the cross section lattice of an irreducible representation of a semisimple algebraic group certain combinatorial properties of are studied supersolvable s are determined in terms of dynkin diagrams the characteristic polynomial of a supersolvable is computed

multiple series connected to hoffman s conjecture on multiple zeta values abstract recent results of zlobin and cresson fischler rivoal allow one to decompose any suitable p uple series of hypergeometric type into a linear combination over the rationals of multiple zeta values of depth at most p in some cases only the multiple zeta values with 2 s and 3 s are involved as in hoffman s conjecture in this text we study the depth p part of this linear combination namely the contribution of the multiple zeta values of depth exactly p we prove that it satisfies some symmetry property as soon as the p uple series does and make some conjectures on the depth p 1 part of the linear combination when p 3 our result generalizes the property that very well poised univariate hypergeometric series involve only zeta values of a given parity which is crucial in the proof by rivoal and ball rivoal that 2 n 1 is irrational for infinitely many n 1 the main feature of the proof is an algebraic approach based on representations of z 2 z p s p

shuffle products for multiple zeta values and partial fraction decompositions of zeta functions of root systems the shuffle product plays an important role in the study of multiple zeta values mzvs this is expressed in terms of multiple integrals and also as a product in a certain non commutative polynomial algebra over the rationals in two indeterminates in this paper we give a new interpretation of the shuffle product in fact we prove that the procedure of shuffle products essentially coincides with that of partial fraction decompositions of mzvs of root systems as an application we give a proof of extended double shuffle relations without using drinfel d integral expressions for mzvs furthermore our argument enables us to give some functional relations which include double shuffle relations

duality between quasi symmetrical functions and the solomon descent algebra abstract the ring qsym of quasi symmetric functions is naturally the dual of the solomon descent algebra the product and the two coproducts of the first extending those of the symmetric functions correspond to a coproduct and two products of the second which are defined by restriction from the symmetric group algebra a consequence is that qsym is a free commutative algebra

interpolation of multiple zeta and zeta star values we define polynomials of one variable t whose values at t 0and1 are the multiple zeta values and the multiple zeta star values respectively we give an application to the two one conjecture of ohno zudilin and also prove the sum formula and the cyclic sum formula for these polynomials

norm inequalities for a class of elementary operators generated by analytic functions with non negative taylor coefficients in ideals of compact operators related to p modified unitarily invariant norms

hopf algebras and the logarithm of the s transform in free probability let k be a positive integer and let g k denote the set of all joint distributions of k tuples a 1 a k in a noncommutative probability space a such that a 1 a k 1 g k is a group under the operation of the free multiplicative convolution we identify g k as the group of characters of a certain hopf algebra y k then by using the log map from characters to infinitesimal characters of y k we introduce a transform ls for distributions g k ls is a power series in k noncommuting indeterminates z 1 z k its coefficients can be computed from the coefficients of the r transform of by using summations over chains in the lattices nc n of noncrossing partitions the ls transform has the linearizing property that ls ls ls g k such that in the particular case k 1 one has that y 1 is naturally isomorphic to the hopf algebra sym of symmetric functions and that the ls transform is very closely related to the logarithm of the s transform of voiculescu by the formula ls z z log s z g 1 in this case the group g 1 can be identified as the group of characters of sym in such a way that the s transform its reciprocal 1 s and its logarithm log s relate in a natural sense to the sequences of complete elementary and respectively power sum symmetric functions

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

duality and q multiple zeta values abstract following bachmann s recent work on bi brackets and multiple eisenstein series zudilin introduced the notion of multiple q zeta brackets which provides a q analog of multiple zeta values possessing both shuffle as well as quasi shuffle relations the corresponding products are related in terms of duality in this work we study zudilin s duality construction in the context of classical multiple zeta values as well as various q analogs of multiple zeta values regarding the former we identify the derivation relation of order two with a hoffman ohno type relation then we describe relations between the ohno okuda zudilin q multiple zeta values and the schlesinger zudilin q multiple zeta values

numerical investigations of discrete scale invariance in fractals and multifractal measures fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems here we focus on lattice multifractals which exhibit complex exponents associated with observable log periodicity we perform detailed numerical analyses of lattice multifractals and explain the origin of three different scaling regions found in the moments a novel numerical approach is proposed to extract the log frequencies in the non lattice case there is no visible log periodicity i e no preferred scaling ratio since the set of complex exponents spreads irregularly within the complex plane a non lattice multifractal can be approximated by a sequence of lattice multifractals so that the sets of complex exponents of the lattice sequence converge to the set of complex exponents of the non lattice one an algorithm for the construction of the lattice sequence is proposed explicitly

renormalization of multiple zeta values abstract multiple zeta values mzvs in the usual sense are the special values of multiple variable zeta functions at positive integers their extensive studies are important in both mathematics and physics with broad connections and applications in contrast very little is known about the special values of multiple zeta functions at non positive integers since the values are usually undefined we define and study multiple zeta functions at integer values by adapting methods of renormalization from quantum field theory and following the hopf algebra approach of connes and kreimer this definition of renormalized mzvs agrees with the convergent mzvs and extends the work of ihara kaneko zagier on renormalization of mzvs with positive arguments we further show that the important quasi shuffle stuffle relation for usual mzvs remains true for the renormalized mzvs

hopf algebras and edge labeled posets abstract given a finite graded poset with labeled hasse diagram we construct a quasi symmetric generating function for chains whose labels have fixed descents this is a common generalization of a generating function for the flag f vector defined by ehrenborg and of a symmetric function associated with certain edge labeled posets that arose in the theory of schubert polynomials we show that this construction gives a hopf morphism from an incidence hopf algebra of edge labeled posets to the hopf algebra of quasi symmetric functions

structural five fold symmetry in the fractal morphology of diffusion limited aggregates abstract the statistical self similarity of the geometry of diffusion limited aggregates and the multifractal nature of the growth probability distribution on the surface of the growing clusters are investigated using the wavelet transform this study reveals the existence of a predominant structural five fold symmetry in the internal frozen region as well as in the active outer region of the interface this observation is corroborated by a statistical analysis of the screening effects that govern diffusion limited aggregation dla growth in linear and sector shaped cells the existence of this symmetry is likely to be a clue to a hierarchichal fractal ordering we report on the discovery of fibonacci sequences in the inner extinct region of large mass off lattice dla clusters with a branching ratio which converges asymptotically to the golden mean we suggest an interpretation of the dla morphology as a quasifractal counterpart of the well ordered snowflake fractal architecture

wavelet packet computation of the hurst exponent wavelet packet analysis was used to measure the global scaling behaviour of homogeneous fractal signals from the slope of decay for discrete wavelet coefficients belonging to the adapted wavelet best basis a new scaling function for the size distribution correlation between wavelet coefficient energy magnitude and position in a sorted vector listing is described in terms of a power law to estimate the hurst exponent profile irregularity and long range correlations in self affine systems can be identified and indexed with the hurst exponent and synthetic one dimensional fractional brownian motion fbm type profiles are used to illustrate and test the proposed wavelet packet expansion we also demonstrate an initial application to a biological problem concerning the spatial distribution of local enzyme concentration in fungal colonies which can be modelled as a self affine trace or an enzyme walk the robustness of the wavelet approach applied to this stochastic system is presented and comparison is made between the wavelet packet method and the root mean square roughness and second moment approaches for both examples the wavelet packet method to estimate the global hurst exponent appears to have similar accuracy compared with other methods but its main advantage is the extensive choice of available analysing wavelet filter functions for characterizing periodic and oscillatory signals

square lattice ising model susceptibility series expansion method and differential equation for χ 3 in a previous paper 2004 j phys a math gen 37 9651 68 we have given the fuchsian linear differential equation satisfied by 3 the three particle contribution to the susceptibility of the isotropic square lattice ising model this paper gives the details of the calculations with some useful tricks and tools allowing one to obtain long series in polynomial time the method is based on series expansion in the variables that appear in the n 1 dimensional integrals representing the n particle contribution to the isotropic square lattice ising model susceptibility the integration rules are straightforward due to remarkable formulae we derived for these variables we obtain without any numerical approximation 3 as a fully integrated series in the variable w s 2 1 s2 where s sh 2k with k j kt the conventional ising model coupling constant we also give some perspectives and comments on these results

explicit double shuffle relations and a generalization of eulerʼs decomposition formula abstract we give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms as an application we generalize the well known decomposition formula of euler that expresses the product of two riemann zeta values as a sum of double zeta values to a formula that expresses the product of two multiple polylogarithm values as a sum of other multiple polylogarithm values