the decomposition method applied to systems of fredholm integral equations of the second kind in this paper the adomian decomposition method is applied to solve systems of linear and nonlinear fredholm integral equations of the second kind convergence of the method is proved and some examples are presented to illustrate the method

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

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

stepped surfaces and rauzy fractals induced from automorphisms on the free group of rank 2 from irreducible unimodular pisot substitutions of rank 2 we can construct the discrete approximations of the lines the so called stepped surfaces and moreover we obtain rauzy fractals as geometric realizations of the symbolic dynamical systems in this paper we study a particular infinite family of automorphisms on the free group of rank 2 we see that for every hyperbolic quadratic unit integer l there is a corresponding automorphism in the infinite family whose incidence matrix has eigenvalue l and the automorphism is conjugate to a substitution or an alternating substitution and we construct stepped surfaces and rauzy fractals induced from automorphisms in the family by using tiling substitutions we also discuss the domain exchange transformations on rauzy fractals

a markov partition that reflects the geometry of a hyperbolic toral automorphism we show how to construct a markov partition that reflects the geometrical action of a hyperbolic automorphism of the n torus the transition matrix is the transpose of the matrix induced by the automorphism in u dimensional homology provided this is non negative here u denotes the expanding dimension that condition is satisfied at least for some power of the original automorphism under a certain non degeneracy condition on the galois group of the characteristic polynomial the nu rectangles are constructed by an iterated function system and they resemble the product of the projection of a u dimensional face of the unit cube onto the unstable subspace and the projection of minus the orthogonal n u dimensional face onto the stable subspace

palindromic length of words and morphisms in class p abstract we study the palindromic length of factors of infinite words fixed by morphisms of the so called class p introduced by hof knill and simon we show that it grows at most logarithmically with the length of the factor for the fibonacci word and the thue morse word we provide explicit bounds on their rate of growth we also construct an infinite word rich in palindromes for which the palindromic length grows as n

disklikeness of planar self affine tiles we consider the disklikeness of the planar self affine tile t generated by an integral expanding matrix a and a consecutive collinear digit set v 0 v 2v q 1 v z 2 let f x x 2 px q be the characteristic polynomial of a we show that the tile t is disklike if and only if 2 p g 2 moreover t is a hexagonal tile for all the cases except when p 0 in which case t is a square tile the proof depends on certain special devices to count the numbers of nodal points and neighbors of t and a criterion of bandt and wang 2001 on disklikeness

a mixed finite element formulation for compressible finite hyperelasticity with two fibre family reinforcement abstract a mixed finite element formulation for compressible finite hyperelasticity possibly with strongly deformation dependent stiffening fibre reinforcement is developed and verified reinforcement by two mechanically equivalent in general oblique fibre families is considered in the provided numerical experiments residual based error estimation is essential for a simple h adaptive mesh refinement strategy it is shown to be effective to resolve stress concentrations also in combination with stress oscillations checker boarding in the presence of strong anisotropy especially when mixed element constructs with enriched polynomial order are used the novel mixed generalised lagrangian metric based formulation is illustrated using a simple but fully coupled material model the ground substance is the common so called compressible neo hooke model and the standard reinforcement part is augmented by second order anisotropic invariants the theoretical formulation admits approaching the inextensible limit seamlessly by passing the use of a separate decoupled material model the hu washizu implementation used here relies on a certain extensibility for elimination of the auxiliary variables approximated in l 2 at the element level the condensation yields a purely h 1 based displacement formulation at the global level

substitution dynamical systems characterization of linear repetitivity and applications we consider dynamical systems arising from substitutions over a finite alphabet we prove that such a system is linearly repetitive if and only if it is minimal based on this characterization we extend various results from primitive substitutions to minimal substitutions this includes applications to random schrodinger operators and to number theory

a five field finite element formulation for nearly inextensible and nearly incompressible finite hyperelasticity a novel hu washizu type 5 field virtual work principle for nearly inextensible and almost incompressible finite hyperelasticity is developed and implemented the formulation is implemented in an hp adaptive code providing the proper flexible environment for finite elements with variable order and mixed interpolation the novel implementation includes residual based error estimation and mesh adaptivity in the fully constrained limit the formulation provides the constraint manifold setting of hyperelasticity with the simple internal kinematic constraints of inextensibility and incompressibility a study using a semi inverse analytical solution and h refinements and p enrichments corroborates the convergence characteristics of the 5 field implementation a new closed form solution for pure torsion of a circular cylindrical tube with inextensible fibres is derived and used for verification as typical applications are found in e g soft tissue biomechanics passive pressurisation of an ellipsoidal geometry resembling the left ventricle of a rabbit heart is analysed to demonstrate the capability of modelling transversely isotropic materials

on one dimensional self similar tilings and pq tiles let b 2 be an integer base d 0 d 1 d b 1 z a digit set and t t b d the set of radix expansions it is well known that if t has nonvoid interior then t can tile r with some translation set j t is called a tile and d a tile digit set there are two fundamental questions studied in the literature i describe the structure of j ii for a given b characterize d so that t is a tile we show that for a given pair b d there is a unique self replicating translation set j c z and it has period b m for some m n this completes some earlier work of kenyon our main result for ii is to characterize the tile digit sets for b pq when p q are distinct primes the only other known characterization is for b p l due to lagarias and wang the proof for the pq case depends on the techniques of kenyon and de bruijn on the cyclotomic polynomials and also on an extension of the product form digit set of odlyzko

second kind integral equations for the classical potential theory on open surfaces ii a second kind integral equation formulation is presented for the dirichlet problem for the laplace equation in two dimensions with the boundary conditions specified on a collection of open curves the performance of the obtained apparatus is illustrated with several numerical examples the formulation is a simplification of the equation previously constructed by the authors

on the solution of linear and nonlinear integral equation the purpose of this paper is to establish the solution of fredholm volterra integral equation of the second kind in the space l 2 w xc 0 t considering the following when fredholm integral term in li 2 w and volterra integral term in 0 t are linear also each of fredholm or volterra integral term is linear while the other term is nonlinear here w is defined as the domain of integration with respect to position while t is consider as the time email protected 0 t t also the fredholm volterra integral equation of the first kind is established as special case of these work many special in one two and three dimensional problems of integral equation are considered representing the kernel of fredholm integral term in the form of logarithmic function carleman function potential and generalized potential function and macdonald function are considered

inflations of self affine tilings are integral algebraic perron we prove that any expanding linear map phi mathbb r mathtt d rightarrow mathbb r mathtt d that is the inflation map in an inflation substitution process generating a self affine tiling of mathbb r mathtt d is integral algebraic and perron this means that phi is linearly conjugate to a restriction of an integer matrix to a subspace mathcal e satisfying a maximal growth condition that generalizes the characterization of perron numbers as numbers that are larger than the moduli of their algebraic conjugates the case of diagonalizable phi has been previously resolved by richard kenyon and boris solomyak and it is rooted in thurston s idea of lifting the tiling from the physical space mathbb r mathtt d to a higher dimensional mathematical space where the tiles their control points sit on a lattice the main novelty of our approach is in lifting the inflation substitution process to the mathematical space and constructing a certain vector valued cocycle defined over the translation induced mathbb r mathtt d action on the tiling space the subspace mathcal e is obtained then by ergodic averaging of the cocycle more broadly we assemble a powerful framework for studying self affine tiling spaces

a new algorithm for symbolic integral with application in this paper by using the theories and methods of mathematical analysis and computer algebra a new algorithm of symbolic integral was established a new maple procedure myint for it was established too and it was applied to the automatic proving the mean value theorems for derivatives the results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea excellent property for operation and powerful competence this would be useful for the problem of solving differential equations automatic proving some mathematical theorems and so on

numerical analysis of graded mesh methods for a class of second kind integral equations on the real line abstract in this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form s s r s t z t t dt s r where l 1 r z l r and bc r the space of bounded continuous complex valued functions on r are assumed known and the function bc r is to be determined we introduce some new graded meshes for the collocation method of the integral equation which are different from those used previously for the wiener hopf integral equation in the case when the solution decays exponentially at infinity and establish optimal local and global l norm error estimates under the condition that the solution decays only polynomially at infinity

tilings induced by a class of cubic rauzy fractals we study aperiodic and periodic tilings induced by the rauzy fractal and its subtiles associated with beta substitutions related to the polynomial x 3 ax 2 bx 1 for a b 1 in particular we compute the corresponding boundary graphs describing the adjacencies in the tilings these graphs are a valuable tool for more advanced studies of the topological properties of the rauzy fractals as an example we show that the rauzy fractals are not homeomorphic to a closed disc as soon as a 2b 4 the methods presented in this paper may be used to obtain similar results for other classes of substitutions

a mixed higher order fem for fully coupled compressible transversely isotropic finite hyperelasticity a higher order mixed finite element method is presented for compressible transversely isotropic finite hyperelasticity the independent variables of the three field formulation are displacement fibre tension and fibre stretch the formulation admits the description of a fully coupled stress response which evolves from an almost isotropic one into a hyper anisotropic simply nearly inextensible response with increasing fibre tension as for example observed in soft tissue biomechanics standard displacement approximation of order p in h1 is used while the auxiliary variables are approximated element wise by square integrable functions of order p 1 in l2 for finite extensibility the auxiliary variables are statically condensed out yielding a pure displacement based method it is implemented in an hp adaptive finite element code a matching residual based error estimation capability is added and exercised numerical evidence indicating stability of approximation is supplied resolving a boundary layer caused by almost inextensible fibres coupled and uncoupled stress responses are compared a generalised compressible transversely isotropic holzapfel gasser ogden model is developed for the formulation that intentionally avoids the volumetric isochoric split solutions obtained with the mixed method compare favourably to the corresponding ones obtained with pure displacement formulation the latter fails in certain strongly anisotropic cases

a class of cubic rauzy fractals in this paper we study arithmetical and topological properties for a class of rauzy fractals r a given by the polynomial x 3 a x 2 x 1 where a 2 is an integer in particular we prove the number of neighbors of r a in the periodic tiling is equal to 8 we also give explicitly an automaton that generates the boundary of r a as a consequence we prove that r 2 is homeomorphic to a topological disk

rational self affine tiles an integral self affine tile is the solution of a set equation mathbf a mathcal t bigcup d in mathcal d mathcal t d where mathbf a is an n times n integer matrix and mathcal d is a finite subset of mathbb z n in the recent decades these objects and the induced tilings have been studied systematically we extend this theory to matrices mathbf a in mathbb q n times n we define rational self affine tiles as compact subsets of the open subring mathbb r n times prod mathfrak p k mathfrak p of the adele ring mathbb a k where the factors of the finite product are certain mathfrak p adic completions of a number field k that is defined in terms of the characteristic polynomial of mathbf a employing methods from classical algebraic number theory fourier analysis in number fields and results on zero sets of transfer operators we establish a general tiling theorem for these tiles we also associate a second kind of tiles with a rational matrix these tiles are defined as the intersection of a translation of a rational self affine tile with mathbb r n times prod mathfrak p 0 simeq mathbb r n although these intersection tiles have a complicated structure and are no longer self affine we are able to prove a tiling theorem for these tiles as well for particular choices of digit sets intersection tiles are instances of tiles defined in terms of shift radix systems and canonical number systems therefore we gain new results for tilings associated with numeration systems

a modified approach to numerical solution of fredholm integral equations of the second kind a modified approach to obtain approximate numerical solutions of fredholm integral equations of the second kind is presented the error bound is explained by the aid of several illustrative examples in each example the approximate solution is compared with the exact solution wherever possible and an excellent agreement is observed in addition the error bound in each example is compared with the one obtained by the nystrom method it is found that the error bound of the present method is smaller than the ones obtained by the nystrom method further the present method is successfully applied to derive the solution of an integral equation arising in a special dirichlet problem

algebraic numbers free group automorphisms and substitutions on the plane there has been much recent work on the geometric representation of pisot substitutions and the explicit construction of markov partitions for pisot toral automorphims we give a construction that extends this to the general hyperbolic case for the sake of simplicity we consider a simple example of an automorphism of the free group on 4 generators whose associated matrix has 4 distinct complex eigenvalues two of them of modulus larger than 1 and the other 2 of modulus smaller than 1 non pisot case using this generator we build substitution polygonal tilings of the contracting plane and the expanding plane of the matrix we prove that these substitution tilings can be lifted in a unique way to stepped surfaces approximating each of these planes the vertices of each of these stepped surfaces can be projected to an atomic surface a compact set with fractal boundary contained in the other plane we prove that both tilings can be refined to exact self similar tilings whose tiles have fractal boundaries and can be obtained by iteration or by a cut and project method by using the atomic surface as the window using the self similar tiling one can build a numeration system associated to a complex lambda expansion the natural extension of the lambda expansion associated with this number system is the linear map obtained by abelianization of the free group automorphism this gives an explicit markov partition of this hyperbolic toral automorphism the fractal domains can be used to define a pseudo group of translations which gives transversal dynamics in the sense of vershik 1994 or numeration systems in the sense of kamae 2005 the construction can be extended to a larger class of free group automorphisms each of which can be used to build substitution rules and dynamical systems

self affine tiles in ℝn abstract a self affine tile in r n is a set t of positive measure with a t d d t d where a is an expanding n n real matrix with det a m an integer and d d d 2 d m r n is a set of m digits it is known that self affine tiles always give tilings of r n by translation this paper extends known characterizations of digit sets d yielding self affine tiles it proves several results about the structure of tilings of r n possible using such tiles and gives examples showing the possible relations between self replicating tilings and general tilings which clarify results of kenyon on self replicating tilings

on the joint subword complexity of automatic sequences let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m denotes the number of distinct blocks u n u n m 1 of size m in u in this paper we study the complexity of u n u 1 n u r n n 0 when each u i u i n n 0 i 1 r is a q i automatic sequence over a finite set s i and q 1 q r 2 are pairwise coprime integers as an application we answer a question of allouche and shallit regarding morphic real numbers

a simplification to fredholm s solution to the fredholm integral equation of the second kind abstract fredholm s classic solution to his linear integral equation of the second kind has been generally considered to be too complex to provide a practical solution method it gives the resolvent kernel as a ratio of two infinite series with terms in each series containing multiple integrals of determinants such that the evaluation of the nth term would seem to require n different n fold multi integrations a formidable task even for modest values of n this paper shows however that by using the methods of the combinatorics of permutations and by solving a well known recursion relation fredholm s solution can be simplified considerably in this simplified form the nth term of each series requires the evaluation of just one new multi integral thus presented is a new expression for the fredholm s solution and the practical use of this expression is demonstrated on some example problems

asymptotic orbits of primitive substitutions a primitive aperiodic substitution on d letters has at most d2 asymptotic orbits this bound is sharp since asymptotic arc components in tiling spaces associated with substitutions are in 1 1 correspondence with asymptotic words this provides a bound for those as well

fractal tiles associated with shift radix systems shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d dimensional real vector space they generalize well known numeration systems such as beta expansions expansions with respect to rational bases and canonical number systems beta numeration and canonical number systems are known to be intimately related to fractal shapes such as the classical rauzy fractal and the twin dragon these fractals turned out to be important for studying properties of expansions in several settings in the present paper we associate a collection of fractal tiles with shift radix systems we show that for certain classes of parameters r these tiles coincide with affine copies of the well known tiles associated with beta expansions and canonical number systems on the other hand these tiles provide natural families of tiles for beta expansions with non unit pisot numbers as well as canonical number systems with non monic expanding polynomials we also prove basic properties for tiles associated with shift radix systems indeed we prove that under some algebraic conditions on the parameter r of the shift radix system these tiles provide multiple tilings and even tilings of the d dimensional real vector space these tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above such a tiling may consist of tiles having infinitely many different shapes moreover the tiles need not be self affine or graph directed self affine

geometric theory of unimodular pisot substitutions we are concerned with the tiling flow t associated to a substitution over a finite alphabet our focus is on substitutions that are unimodular pisot i e their matrix is unimodular and has all eigenvalues strictly inside the unit circle with the exception of the perron eigenvalue 1 the motivation is provided by the still open conjecture asserting that t has pure discrete spectrum for any such we develop a number of necessary and sufficient conditions for pure discrete spectrum including injectivity of the canonical torus map the geometric realization geometric coincidence condition partial commutation of t and the dual r d 1 action measure and tiling properties of rauzy fractals and concrete algorithms some of these are original and some have already appeared in the literature as sufficient conditions only but they all emerge from a unified approach based on the new device the strand space f of the proof of the necessity hinges on determination of the discrete spectrum of t as that of the associated kronecker toral flow

p fems for hyperelastic anisotropic nearly incompressible materials under finite deformations with applications to arteries simulation the displacement formulation of p fems is extended to nearly incompressible hyper elastic anisotropic materials under finite deformations in a three dimensional setting to demonstrate the efficiency and accuracy of the formulation we derive analytical solutions that serve for the verification of the p fe results the locking free properties at the limit of incompressibility the high convergence rates and the robustness with respect to large aspect ratios of the p fes are demonstrated by numerical experiments and compared in terms of degrees of freedom and cpu times to equivalent classical formulations using h fems p fems are then exploited to investigate artery like structures having complex constitutive models and particularly the influence of slight allowable compressibility of orders of several percents on the stress levels copyright 2011 john wiley sons ltd

a novel computational formulation for nearly incompressible and nearly inextensible finite hyperelasticity abstract a novel approach to computational almost inextensible transversely isotropic and nearly incompressible finite hyperelastic fibre mechanics is introduced it relies on using an equivalent generalised right cauchy green stretch tensor which is volume preserving and simply stretch free in the limit of incompressibility and inextensibility in other words its third and fourth principal invariants become trivial otherwise it represents volume change and fibre stretch with the aid of point wise equivalent auxiliary measures in the continuous case the generalised kinematics implies the usual orthogonal spherical deviatoric decomposition of the stresses the deviatoric stresses are further orthogonally decomposed into axial fibre and ground substance stresses the novel approach implies that the deviatoric ground substance stresses are trivial in the fibre direction as opposed to the current standard formulation the approach is also able to represent exact inextensible fibres which is a problem recently addressed in the literature using an additive volumetric isochoric decoupled strain energy density function relying on volume preserving stretch the formulation is corroborated by a couple of numerical examples using a preliminary finite element setting the basis for the implementation is provided

an algorithm for solving daes with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving differential algebraic equation systems was established and a new maple procedures mainproc was established too ten examples are presented to illustrate the implementation of the program

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

dual systems of algebraic iterated function systems abstract we study a class of graph directed iterated function systems on r with algebraic parameters which we call algebraic gifs we construct a dual ifs of an algebraic gifs and study the relations between the two systems we determine when a dual system satisfies the open set condition which is fundamental for feasible pisot systems we construct the left and right rauzy thurston tilings and study their multiplicities and decompositions we also investigate their relation with codings space domain exchange transformation and the pisot spectrum conjecture the dual ifs provides a unified and simple framework for rauzy fractals tilings and related studies and allows us gain better understanding

an algorithm for solving nonlinear singular perturbation problems with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving nonlinear singular perturbation problems was established a new maple procedure spp was established too the procedure spp give not only the approximate analytic solutions but also the numerical solutions of spp six examples are presented to illustrate the implementation of the program the method is very simple and effective for most of singular perturbation problems this would be useful for solving differential equations

morphic words and equidistributed sequences abstract the problem we consider is the following given an infinite word w on an ordered alphabet construct the sequence w n n equidistributed on 0 1 and such that m n if and only if m w n w where is the shift operation erasing the first symbol of w the sequence w exists and is unique for every word with well defined positive uniform frequencies of every factor or in dynamical terms for every element of a uniquely ergodic subshift in this paper we describe the construction of w for the case when the subshift of w is generated by a morphism of a special kind then we overcome some technical difficulties to extend the result to all binary morphisms the sequence w in this case is also constructed with a morphism at last we introduce a software tool which given a binary morphism computes the morphism on extended intervals and first elements of the equidistributed sequences associated with fixed points of

tiling the line with translates of one tile a region t is a closed subset of the real line of positive finite lebesgue measure which has a boundary of measure zero call a region t a tile if bbb r can be tiled by measure disjoint translates of t for a bounded tile all tilings of bbb r with its translates are periodic and there are finitely many translation equivalence classes of such tilings the main result of the paper is that for any tiling of bbb r by a bounded tile any two tiles in the tiling differ by a rational multiple of the minimal period of the tiling from it we deduce a structure theorem characterizing such tiles in terms of complementing sets for finite cyclic groups

beta expansions natural extensions and multiple tilings associated with pisot units from the works of rauzy and thurston we know how to construct multiple tilings of some euclidean space using the conjugates of a pisot unit beta and the greedy beta transformation in this paper we consider different transformations generating expansions in base beta including cases where the associated subshift is not sofic under certain mild conditions we show that they give multiple tilings we also give a necessary and sufficient condition for the tiling property generalizing the weak finiteness property w for greedy beta expansions remarkably the symmetric beta transformation does not satisfy this condition when beta is the smallest pisot number or the tribonacci number this means that the pisot conjecture on tilings cannot be extended to the symmetric beta transformation closely related to these multiple tilings are natural extensions of the transformations which have many nice properties they are invariant under the lebesgue measure under certain conditions they provide markov partitions of the torus they characterize the numbers with purely periodic expansion and they allow determining any digit in an expansion without knowing the other digits

separators in infinite words generated by morphisms resume nous appelons separateur d un mot x a l indice n e n le plus petit facteur de x dont l indice du debut de la premiere occurrence est n notons sx n la longueur de ce separateur lorsqu il existe et posons sx n 0 sinon nous montrons que l application sx ainsi definie est q reguli e re au sens d allouche et shallit lorsque x est un mot infini engendre par iteration d un morphisme q uniforme et que x est circulaire de maniere equivalente cela revient a dire que la serie formelle dont les coefficients sont les valeurs sx n en base q est n rationnelle salomaa soittola

using the wpg method for solving integral equations of the second kind abstract in this paper we use the wavelet petrov galerkin wpg method based on discontinuous orthogonal multiwavelets for solving fredholm integral equations of the second kind that yields linear system that the condition number of its coefficient matrix is bounded and for showing efficiency of method we use numerical examples

anisotropic hierarchic solid finite elements for the simulation of passive active arterial wall models abstract a 3d anisotropic hierarchic solid finite element formulation is provided for the passive and active mechanical response of arteries the artery is modeled as an anisotropic nearly incompressible hyperelastic tube consisting of two layers that correspond to the media and the adventitia these layers are considered as a fiber reinforced material consisting of two collagen fiber families that are symmetrically disposed and helically oriented around the tube s axis the numerical analysis is based on a 3d anisotropic hierarchic solid finite element formulation including the possibility of varying the polynomial degree in all local directions as well as for all displacement components for the purpose of verification analytical solutions are provided for different benchmarks focusing on the aspects of compressible and incompressible 3d stretch plane strain and plane stress pure shear as well as a mono layer anisotropic incompressible circular cylindrical artery of holzapfel gasser ogden material under inflation and extension the resulting solutions including stress and strain distribution through the arterial wall are plotted to point out the passive response and different activation levels in addition the effect of various compressibility levels including nearly incompressibility is studied by numerical examples the robustness and accuracy of the proposed method is demonstrated by comparing the results of different ansatz spaces

balancedness and coboundaries in symbolic systems abstract this paper studies balancedness for infinite words and subshifts both for letters and factors balancedness is a measure of disorder that amounts to strong convergence properties for frequencies it measures the difference between the numbers of occurrences of a given word in factors of the same length we focus on two families of words namely dendric words and words generated by substitutions the family of dendric words includes sturmian and arnoux rauzy words as well as codings of regular interval exchanges we prove that dendric words are balanced on letters if and only if they are balanced on words in the substitutive case we stress the role played by the existence of coboundaries taking rational values and show simple criteria when frequencies take rational values for exhibiting imbalancedness

properties of words and recognizability of fixed points of a substitution resume soit u un mot infini non periodique point fixe d une substitution primitive nous montrons que pour n assez grand u ne contient aucune puissance n eme de mot nous donnons ensuite une condition necessaire et suffisante pour que soit reconnaissable au sens de host et queffelec et nous montrons qu ill suffit de bilateraliser cette definition pour obtenir une propriete verifiee cette fois par toutes les substitutions primitives a point fixe non periodique

a new mechanical algorithm for solving the second kind of fredholm integral equation integral equation has been one of principal tool of various areas of applied mathematics physics and engineering in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of fredholm integral equation is established and a mechanical maple algorithm fredholmproc is established too the algorithm can provide the continuous solution of the second kind of fredholm integral equation ten examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for solving the integral equation

central sets and substitutive dynamical systems abstract in this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of pisot type central sets first introduced by furstenberg using notions from topological dynamics constitute a special class of subsets of n possessing strong combinatorial properties each central set contains arbitrarily long arithmetic progressions and solutions to all partition regular systems of homogeneous linear equations we give an equivalent reformulation of the strong coincidence condition in terms of central sets and minimal idempotent ultrafilters in the stone cech compactification n this provides a new arithmetical approach to an outstanding conjecture in tiling theory the pisot substitution conjecture the results in this paper rely on interactions between different areas of mathematics some of which had not previously been directly linked they include the general theory of combinatorics on words abstract numeration systems tilings topological dynamics and the algebraic topological properties of stone cech compactification of n

algorithm for determining pure pointedness of self affine tilings overlap coincidence in a self affine tiling in rd is equivalent to pure point dynamical spectrum of the tiling dynamical system we interpret the overlap coincidence in the setting of substitution delone set in rd and find an efficient algorithm to check the pure point dynamical spectrum this algorithm is easy to implement into a computer program we give the program and apply it to several examples in the course of the proof of the algorithm we show a variant of the conjecture of urbanski solomyak 2006 40 on the hausdorff dimension of the boundaries of fractal tiles

an algorithm for adomian decomposition method in this paper a reliable technique for calculating adomian polynomials for nonlinear operators is developed the algorithm is fulfilled with symbolic computation so that the adomian decomposition methods for solving differential equations can be mechanized in maple ten examples are presented to illustrate the implementation of the program

on single matrix graph directed iterated function systems abstract we study graph directed function systems where each contraction in the system has the form f e x a 1 x d e where a is an expanding matrix we show that a certain discreteness implies the open set condition and the latter implies the strong open set condition hausdorff measures and dimensions w r t a weak norm of the invariant sets are investigated the stationary markov measures of the system are proved to be translation invariant

discontinuous galerkin approximations for near incompressible and near inextensible transversely isotropic bodies abstract this work studies discontinuous galerkin dg approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies low order approximations on triangles are adopted with the use of three interior penalty dg methods viz nonsymmetric symmetric and incomplete it is known that these methods are uniformly convergent in the incompressible limit for the isotropic case this work focuses on behaviour in the inextensible limit for transverse isotropy an error estimate suggests the possibility of extensional locking a feature that is confirmed by numerical experiments under integration of the extensional edge terms is proposed as a remedy this modification is shown to lead to an error estimate that is consistent with locking free behaviour numerical tests confirm the uniformly convergent behaviour at an optimal rate of the under integrated scheme

one dimensional gibbs states and axiom a diffeomorphisms on etudie la mecanique statistique en equilibre de systemes reticules classiques a une dimension a interactions a decroissance exponentielle pour de tels systemes les transformees de fourier des fonctions de correlation de paires sont meromorphes dans une bande et les residus des poles peuvent s exprimer en termes de distributions de gibbs on applique ces resultats aux diffeomorphismes de l axiome a de smale

an investigation into integral equation methods involving nearly singular kernels for acoustic scattering this work presents a numerical means of investigating the acoustic scattering by disk shaped bodies on the basis of burton and miller s method the singularity free formulations of helmholtz integral equation and its normal derivative are used to form a composite equation a triangle polar co ordinate transformation method is further applied to treat the nearly singular kernels arising from a situation in which the field points and source points are very close together numerical simulations consist of the acoustic scattering by a short circular cylinder and a thin circular disk respectively for the latter case with zero thickness the corresponding analytical solutions involving angular and radial oblate spheroidal wave functions are evaluated as well comparing the numerical results with the experimental data and analytical solutions demonstrates the effectiveness of the proposed method

a mixed finite element formulation for slightly compressible finite elasticity with stiff fibre reinforcement two fibre families uniaxial tension formulation abstract we propose a novel finite element based formulation for the solution of the static mechanical mixed boundary value problem of a finite elastic solid reinforced by two distinct stiff fibre families the fibre tensions are assumed decoupled and uniaxial at out set the associated energy conjugate fibre stretch rates are shown to be uniaxial by duality the natively displacement dependent fibre tension fibre stretch pairs are replaced by auxiliary independent variables the complementary displacement based stresses and energy conjugate strain rates become tensionless and stretch rate less in the two fibre directions respectively by construction an additively decoupled hyperelastic strain energy ansatz in terms of the fibre stretches and a novel apparently doubly stretchless cauchy green tensor is used the displacement based part of the formulation is set in an apparently inextensible fibre metric space the proposed uniaxial fibre tension description is statically exact for the fully constrained problem and the novel doubly stretchless cauchy green tensor is conditionally kinematically admissible in its vicinity the formulation is realised as a five field mixed finite element method admitting separate higher order approximations in h 1 for the displacement and in l 2 for the energy conjugate fibre tensions and stretches respectively the convergence and correctness of the implementation is verified by numerical and analytical examples

a new nystrom type method for fredholm integral equations of the second kind a new nystrom type method is proposed in the paper to solve linear fredholm integral equations of the second kind convergence and error analysis of the numerical solution are made a practical and simple algorithm is given to obtain the approximation solution a numerical example is given to verify the proposed method and compare with the known existing ones

numerical solution of non linear fredholm integral equations by using multiwavelets in the petrov galerkin method in this paper we use the wavelet petrov galerkin wpg method for solving one of the most important cases in non linear fredholm integral equations which is called hammerstein equations we suppose that the trial space and the test space that are used in this method to be piecewise polynomials space also we use alpert s multiwavelets as the bases for these spaces such that the wavelet basis for the test space constructed from lower degree polynomials than the trial space finally for showing efficiency of this method we use some numerical examples

mechanization for solving spp by reducing order method in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of reduction of order approximation method for solving singular perturbation problems was established a new maple procedure redordproc was established too the procedure redordproc give not only the approximate analytic solutions but also the numerical solutions of the kinetics problems some examples are presented to illustrate the implementation of the program

a new algorithm for integral of trigonometric functions with mechanization in this paper by using the theories of mathematical analysis the authors systematically studied the problem of integrating of trigonometric functions utilizing omnipotence expressions tan x2 t a new integral algorithm for the integral of trigonometric functions was established and a new maple program trigint for the calculation mechanizing for the integral of trigonometric functions was established trigint could evaluate not only the integral of trigonometric functions utilizing omnipotence expresssions correctly but also all the other kinds of functions the results indicated that the algorithm established in this paper had advantages of simple idea excellent property for operation and powerful competence this would be useful for some calculating problems of engineering mathematics

balances for fixed points of primitive substitutions an infinite word defined over a finite alphabet a is balanced if for any pair of factors of the same length and for any letter a in the alphabet a a 1 where a denotes the number of occurrences of the letter a in the word in this paper we generalize this notion and introduce a measure of balance for an infinite sequence in the case of fixed points of primitive substitutions we show that the asymptotic behaviour of this measure is in part ruled by the spectrum of the incidence matrix associated with the substitution connections with frequencies of letters and other balance properties are also discussed

spectral structure of digit sets of self similar tiles on mathbb r 1 we study the structure of the digit sets d for the integral selfsimilar tiles t b d we call such a d a tile digit set with respect to b so far the only available classes of such tile digit sets are the complete residue sets and the product forms our investigation here is based on the spectrum of the mask polynomial pd i e the zeros of pd on the unit circle by using the fourier criteria of self similar tiles of kenyon and protasov as well as the algebraic techniques of cyclotomic polynomials we characterize the tile digit sets through some product of cyclotomic polynomials kernel polynomials which is a generalization of the product form to higher order

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

computations of multi resultant with mechanization abstract resultant is a classical algebraic tool for determining whether or not a polynomial systems have a common root without explicitly solving for the roots but the complexity of resultants can be very high in practice in this paper by using the theories and methods of computer algebra two reliable algorithms for computing multi resultant problems dixon resultant and macaulay resultant were established two new maple procedures dixonres and macaulayres were established too some examples are presented to illustrate the implementations of the programs this would be useful for solving a system of polynomial equations

numerical solution of linear fredholm integral equation by using hybrid taylor and block pulse functions in this paper we use a combination of taylor and block pulse functions on the interval 0 1 that is called hybrid functions to estimate the solution of a linear fredholm integral equation of the second kind we convert the integral equation to a system of linear equations and by using numerical examples we show our estimation have a good degree of accuracy

a 3 field formulation for strongly transversely isotropic compressible finite hyperelasticity abstract a hu washizu type 3 field virtual work principle for strongly transversely isotropic compressible finite hyperelasticity is developed implemented and verified the independent variables are the stretch its energy conjugate uniaxial tension and the displacement the formulation is based on a new decomposition of the deformation gradient into a simply stretchless part and a lateral contraction free uniaxial extension in the fully constrained limit the formulation provides the constraint manifold setting of hyperelasticity with the simple internal kinematic constraint of inextensibility the finite element formulation is implemented in an hp adaptive code providing the proper flexible environment for finite elements with variable order and mixed interpolation a study using a semi inverse analytical solution corroborates the convergence characteristics for h refinements and p enrichments of the 3 field implementation the case of isostatic loading of a circular cylinder reinforced with a single family of fibres and the pressurisation of a saccular aneurysm like configuration with circumferential fibre reinforcement are used for verification and illustration a posteriori residual discretisation error estimation is used for making mesh refinements in the latter case typical applications are found in soft tissue biomechanics

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

conjugacies for tiling dynamical systems we consider tiling dynamical systems and topological conjugacies between them we prove that the criterion of being of finite type is invariant under topological conjugacy for substitution tiling systems under rather general conditions including the penrose and pinwheel systems we show that substitutions are invertible and that conjugacies are generalized sliding block codes

an analysis of thep version of the finite element method for nearly incompressible materials in this paper we analyze the behavior of the so calledp version of the finite element method when applied to the equations of plane strain linear elasticity we establish optimal rate error estimates that are uniformly valid independent of the value of the poisson ratio v in the interval 0 1 2 this shows that thep versiondoes not exhibit the degeneracy phenomenon which has led to the use of various only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material

two dimensional iterated morphisms and discrete planes iterated morphisms of the free monoid are very simple combinatorial objects which produce infinite sequences by replacing iteratively letters by words the aim of this paper is to introduce a formalism for a notion of two dimensional morphisms we show that they can be iterated by using local rules and that they generate two dimensional patterns related to discrete approximations of irrational planes with algebraic parameters we associate such a two dimensional morphism with any usual pisot unimodular one dimensional iterated morphism over a three letter alphabet

languages d0l systems sets of curves and surface automorphisms we introduce extend and apply some relationships between formal language theory and surface theory first we show how boundaries of languages topologized with the cantor metric can be mapped to sets of curves on surfaces namely laminations second we present how and when endomorphisms of free monoids i e substitutions can be mapped to automorphisms of surfaces so that d0l systems correspond to iterations of these automorphisms third we apply these ideas to construct sets of non periodic irreducible automorphisms of surfaces following 14 35 43 so that the involved proofs do not use any differential or algebraic tools but accordingly substitution and d0l system theory of 11 12 31 32 37 mainly the decidability for a d0l language 12 to be strongly repetitive or not this construction also yields effective symbolic descriptions of the stable sets of curves associated with these automorphisms

on critical exponents in fixed points of non erasing morphisms let s be an alphabet of size t let f s s be a non erasing morphism let w be an infinite fixed point of f and let e w be the critical exponent of w we prove that if e w is finite then for a uniform f it is rational and for a non uniform f it lies in the field extension q r l 1 l where r l 1 l are the eigenvalues of the incidence matrix of f in particular e w is algebraic of degree at most t under certain conditions our proof implies an algorithm for computing e w