a kleene theorem for a class of planar acyclic graphs in this paper we study planar directed ordered connected acyclic graphs in particular graphs that can be built over a finite doubly ranked alphabet by parallel and serial composition on the one hand we introduce finite automata on graphs and on the other hand rational expressions that involve union nondeterministic parallel composition serial composition and the iterations of these compositions we prove a kleene theorem linking these two characterizations of sets of graphs

decidability of equivalence for deterministic synchronized tree automata abstract synchronized tree automata allow limited communication between computations in independent subtrees of the input this enables them to verify for instance the equality of two unary subtrees of unlimited size the class of tree languages recognized by synchronized tree automata is strictly included in the context free tree languages as our main result we show that equivalence of tree languages recognized by deterministic synchronized tree automata can be effectively decided this contrasts the earlier undecidability result for the equivalence problem for nondeterministic synchronized tree automata for our decidability proof we introduce globally deterministic synchronized tree automata we establish the various inclusion relations between the deterministic globally deterministic and nondeterministic synchronized tree automata

iterated stack automata and complexity classes abstract an iterated pushdown is a pushdown of pushdowns of of pushdowns an iterated exponential function is 2 to the 2 to the to the 2 to some polynomial the main result presented here is that the nondeterministic 2 way and multi head iterated pushdown automata characterize the deterministic iterated exponential time complexity classes this is proved by investigating both nondeterministic and alternating auxiliary iterated pushdown automata for which similar characterization results are given in particular it is shown that alternation corresponds to one more iteration of pushdowns these results are applied to the 1 way iterated pushdown automata 1 they form a proper hierarchy with respect to the number of iterations and 2 their emptiness problem is complete in deterministic iterated exponential time similar results are given for iterated stack checking stack nonerasing stack nested stack checking stack pushdown automata

alternating pushdown and stack automata the classes of languages accepted by alternating pushdown automata alternating stack automata and alternating nonerasing stack automata both with and without an auxiliary space bounded worktape are characterized in terms of complexity classes defined by time bounded deterministic turing machines it is also shown that alternating 2 way finite state machines accept only regular languages

generalised cosine functions basis and regularity properties abstract we examine regularity and basis properties of the family of rescaled p cosine functions we find sharp estimates for their fourier coefficients we then determine two thresholds p 0 2 and p 1 2 such that this family is a schauder basis of l s 0 1 for all s 1 and p p 0 p 1

approximation properties of the q sine bases for graphic 1 the eigenfunctions of the nonlinear eigenvalue problem associated with the one dimensional q laplacian are known to form a riesz basis of l 2 0 1 we examine in this paper the approximation properties of this family of functions and its dual and establish a non orthogonal spectral method for the p poisson boundary value problem and its corresponding parabolic time evolution initial value problem with stochastic forcing the principal objective of our analysis is the determination of optimal values of q for which the best approximation is achieved for a given p problem 1 embed inline graphic 1 gif

structural equivalence and et0l grammars for a given context sensitive grammar g we construct et0l grammars g1 and g2 that are structurally equivalent if and only if the language generated by g is empty which implies that structural equivalence is undecidable for et0l grammars this is in contrast to the decidability result for the e0l case in fact we show that structural equivalence is undecidable for propagating et0l grammars even when the number of tables is restricted to be at most two a stronger notion of equivalence that requires the sets of syntax trees to be isomorphic is shown to be decidable for et0l grammars

parallel and two way automata on directed ordered acyclic graphs in this paper we study automata which work on directed ordered acyclic graphs in particular those graphs called derivation dags d dags which model derivations of phrase structure grammars a rather complete characterization of the relative power of the following features of automata on d dags is obtained parallel versus sequential deterministic versus nondeterministic and finite state versus a restricted type of pushdown store new results concerning trees follows as special cases closure properties of classes of d dag languages definable by various automata are studied for some basic operations characterization of general directed ordered acyclic graphs by these automata is also given contents abstract 1 introduction 2 definitions of the graphs 3 parallel dag automata 4 finite state relabeling 5 two way dag walking automata 6 comparison 7 closure properties of d dag languages 8 recognition of doags acknowledgment references

an adaptive procedure based on background cells for meshless methods in practical implementations meshless methods using moving least squares mls approximation and global galerkin formulation require a background mesh for domain integration an adaptive procedure based on background mesh is developed for meshless methods using mls it comprises a cell energy error estimate and a local domain refinement technique the error estimate differs from conventional pointwise approaches in that it evaluates error based on individual cells instead of points for each cell a computed cell energy and a reference cell energy are generated based on a same stress field by using two different integration schemes the difference between the two energy values is used as the basic measure of error estimation the advantage of this strategy is that it requires only one stress field and no reference field needs to be furnished this has significance as the stress field generated by meshless methods is already very smooth and traditional error estimates based on stress smoothing techniques for finite element methods are not applicable to achieve high efficiency in domain refinement a local technique based on the delaunay algorithm is implemented in this technique each node is assigned a scaling factor to control local nodal density refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor the numerical experiments in this paper show that the proposed adaptive procedure is simple effective and efficient the limitations of the approach are also discussed

transducers and the decidability of independence in free monoids abstract a transducer based general method is derived by which proofs of the decidability of independence of regular languages with respect to a given relation can be obtained this permits a uniform proof of the decidability of certain code properties which so far has only been obtained using separate quite different and ad hoc proofs

pushdown machines for the macro tree transducer the macro tree transducer can be considered as a system of recursive function procedures with parameters where the recursion is on a tree e g the syntax tree of a program we investigate characterizations of the class of tree tree to string translations which is induced by macro tree transducers macro tree to string transducers respectively for this purpose we define several pushdown machines of which the control is recursive without parameters or even iterative and which work on a generalized pushdown as storage because of the relevance for semantics of programming languages we stress besides the nondeterministic case the study of machines for the total deterministic macro tree to string transducer which translates every input tree into exactly one output tree string respectively finally we characterize the n fold composition of total deterministic macro tree transducers by recursive pushdown machines with an iterated pushdown as storage which is a pushdown of pushdowns of of pushdowns

composite mesh concept based fem error estimation and solution improvement abstract the use of composite finite element models where meshes with different granularities are allowed to share the same problem domain is introduced the idea of this method was taken from the mixture theory of multiphase materials where the properties of each component enter into the formulation affected by a participation factor the different behaviors of each component mesh due to differences in the model accuracy rather than to the material properties we perform estimation of local and global errors for some problems in planar domains that are drawn from engineering problems structural elastic deformations or heat and mass transfer in catalytic chemical reactors the main examples in this work are elliptic problems with boundary conditions of dirichlet neumann and mixed types the method is not restricted to 2d being also applicable to 3d problems in this paper we also develop the use of composite models with the target of improving the numerical solution of finite element models by using extrapolation like concepts improved solutions may be obtained without increasing the computational cost of the problem or requiring postprocessing of the results some examples are shown for which exact solution is available in order to validate the method

linear deterministic multi bottom up tree transducers in general top down and bottom up tree transducers lead to incomparable classes of tree transformations both for the nondeterministic and the deterministic case if deterministic top down tree transducers are extended by the capability to recognize regular tree properties and deterministic bottom up tree transducers are generalized by allowing states with arbitrary finite rank then the two devices now called deterministic top down tree transducers with regular look ahead and deterministic multi bottom up tree transducers respectively become equivalent z fulop a kuhnemann h vogler a bottom up characterization of deterministic top down tree transducers with regular look ahead inform process lett 91 2004 57 67 in this paper we focus on the class ld mbot of tree transformations which are computed by linear deterministic multi bottom up tree transducers we investigate the relationship among ld mbot and the classes of tree transformations computed by restricted deterministic bottom up tree transducers and by restricted deterministic top down tree transducers with regular look ahead in fact we show the inclusion diagram of nine such classes

l a l b decidability results from complete formal systems abstract the equivalence problem for deterministic pushdown automata is shown to be decidable we exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda m we then extend the result to deterministic pushdown transducers from a free monoid into an abelian group a general algebraic and logical framework inspired by harrison et al theoret comput sci 9 1979 173 205 conrcelle theoret comput sci 6 1978 255 279 and meitus kybernetika 5 1989 14 25 in russian is developed

complete formal systems for equivalence problems we describe four complete and recursively enumerable formal systems s0 d0 h0 b0 each one of them proves the decidability of some equivalence problem for some class of automata namely the language equivalence problem for simple automata the language equivalence problem for deterministic pushdown automata the function equivalence problem for deterministic pushdown transducers with outputs in an abelian group the bisimulation equivalence problem for loop free pushdown automata

an adaptive finite element meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems in this paper an automatic adaptive coupling procedure is proposed for the finite element method fem and the element free galerkin method efgm for linear elasticity and for problems with both material and geometrical nonlinearities in this new procedure initially the whole of the problem domain is modelled using the fem during an analysis those finite elements which violate a predefined error measure are automatically converted to an efg zone this efg zone can be further refined by adding nodes thus avoiding computationally expensive fe remeshing local maximum entropy shape functions are used in the efg zone of the problem domain for two reasons their weak kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the efg and fe regions compared to the use of moving least squares basis functions the zienkiewicz and zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the fe region of the problem domain while the chung and belytschko error estimation procedure is used in the efg region

compositions of deterministic bottom up top down and regular look ahead tree transformations we show that dtr dt ldb that ldtr ldt db and that dt ldtr h where db dt h stand for the class of deterministic bottom up tree transformations the class of deterministic top down tree transformations and the class of homomorphism tree transformations respectively the prefix l stands for the adjective linear and the superscript r stands for the regular look ahead the composition of tree transformation classes x and y is denoted by x y using these results and the composition and inclusion results of engelfriet fulop and fulop and vagvolgyi we show that the problem of determining the correct inclusion relationship between two arbitrary compositions of tree transformation classes from the set dtr ldtr dt ldt db ldb h lh can be decided in linear time

a meshless interpolation algorithm using a cell based searching procedure in this paper we propose a fast algorithm for bivariate interpolation of large scattered data sets it is based on the partition of unity method for constructing a global interpolant by blending radial basis functions as local approximants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cell based searching procedure more precisely we construct a cell structure which partitions the domain and strictly depends on the dimension of the subdomains thus providing a meaningful improvement in the searching process compared to the nearest neighbour searching techniques presented in allasia et al 2011 and cavoretto and de rossi 2010 2012 in fact this efficient algorithm and in particular the new searching procedure enable us a fast computation also in several applications where the amount of data to be interpolated is often very large up to many thousands or even millions of points analysis of computational complexity shows the high efficiency of the proposed interpolation algorithm this is also supported by numerical experiments

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a trivariate interpolation algorithm using a cube partition searching procedure in this paper we propose a fast algorithm for trivariate interpolation which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube partition searching procedure more precisely we construct a cube structure which partitions the domain and strictly depends on the size of its subdomains so that the new searching procedure and accordingly the resulting algorithm enable us to efficiently deal with a large number of nodes complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

addendum to a hilbert space of dirichlet series and systems of dilated functions in l 2 0 1 addendum to a hilbert space of dirichlet series and systems of dilated functions in l 2 0 1

storage to tree transducers with look ahead we generalize engelfriet s decomposition result stating that the class of transformations induced by top down tree transducers with regular look ahead is equal to the composition of the class of top down tree transformations and the class of linear tree homomorphisms replacing the input trees with an arbitrary storage type the top down tree transducers are turned into regular storage to tree transducers we show that the class of transformations induced by regular storage to tree transducers with positive look ahead is equal to the composition of the class of transformations induced by regular storage to tree transducers with the class of linear tree homomorphisms we also show that the classes of transformations induced by both io and oi context free storage to tree transducers are closed under positive look ahead and are closed under composition with linear tree homomorphisms

enrichment and coupling of the finite element and meshless methods a mixed hierarchical approximation based on finite elements and meshless methods is presented two cases are considered the first one couples regions where finite elements or meshless methods are used to interpolate continuity and consistency is preserved the second one enriches a finite element mesh with particles thus there is no need to remesh in adaptive refinement processes in both cases the same formulation is used convergence is studied and examples are shown copyright 2000 john wiley sons ltd

coupling finite element method with meshless finite difference method in thermomechanical problems this paper focuses on coupling two different computational approaches namely finite element method fem and meshless finite difference method mfdm in one domain the coupled approach is applied in solving thermomechanical initialboundary value problem where the heat transport in the domain is non stationary in this method the domain is divided into two subdomains for fem and mfdm respectively contrary to other coupling techniques the approach presented in this paper is defined in terms of mathematical problem formulation rather than at the approximation level in the weak form of thermomechanical initialboundary value problem variational principle the appropriate additional coupling integrals are defined a priori subsequently the fem and the mfdm approximations which may differ from each other are provided to the formulation it is assumed that there exists a very thin layer of material between the subdomains which is not spatially discretized the width of this layer may be considered the coupling parameter and it is the same for both thermal and mechanical parts similar approach is applied to essential boundary conditions e g prescribed temperature and displacements consequently the consistent formulation of the mixed problem for the coupled femmfdm method is derived the analysis is illustrated with two and three dimensional examples of mechanical and thermomechanical problems

a novel element differential method for solid mechanical problems using isoparametric triangular and tetrahedral elements abstract a novel strong form numerical method element differential method edm is developed to solve geometrically complex mechanics problems based on triangular or tetrahedral meshes the discretization of the structure under investigation has been based on lagrange isoparametric quadrilateral or hexahedral elements while applying edm in this paper a new family of isoparametric triangular and tetrahedral elements with a central node is proposed for edm a set of shape functions with analytical expressions for their first and second order partial derivatives is constructed for these triangular and tetrahedral elements respectively moreover a new element collocation scheme is proposed to establish a system of equations directly from the governing differential equations for internal nodes and traction equilibrium equations for nodes on edges of an element in this collocation scheme no variational principles or virtual energy principles are required to set up the solution scheme while no integration is needed when forming the coefficients of the system of equations numerical examples including standard patch tests and more practical problems are given to demonstrate the correctness of the constructed elements and the efficiency of the proposed element collocation method

fast slow diffusion and collapsing sandpiles we regard the limit as p of the flow governed by the p laplacian as providing a simplistic model for the collapse of an initially unstable sandpile upon rescaling to stretch out the initial layer we obtain some simple dynamics and provide fairly explicit solutions in certain cases involving nonlocal geometric curvature motion in particular we note that such models entail instantaneous mass transfer governed by monge kantorovich theory

the effective interface approach for coupling of the fe and meshless fd methods and applying essential boundary conditions the paper presents a new effective technique for coupling two computational methods with different types of discretization and approximation it is based on a concept of two adjacent subdomains which are connected with each other by means of a thin layer of material each of the subdomain may have a different discretization structure and approximation base the standard finite element method fem as well as the meshless finite difference method mfdm are applied here to be coupled however the coupling can be used for any other methods the same concept is used for applying the essential boundary conditions for both of the methods the width of the interface layer depending on discretization density is evaluated by means of several heuristic assumptions the paper is illustrated with selected two and three dimensional examples

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

some remarks on a nonhomogeneous eigenvalue problem related to generalized trigonometric functions abstract in this paper a nonhomogeneous eigenvalue problem with p laplacian is studied we first show the sturm liouville property and derive the asymptotic expansion of eigenvalues and eigenfunctions employing the derivation of the eigenfunctions we discuss the basis property related to the eigenfunctions finally we also solve two inverse problems the inverse nodal problem and ambarzumyan problem

a meshless singular boundary method for transient heat conduction problems in layered materials abstract the transient heat conduction problems in layered materials are common encountered in practical application but bring great challenge to most numerical algorithms in this study the singular boundary method sbm a meshless boundary collocation technique is first employed to numerically simulate such problems based on the time dependent fundamental solution of diffusion equation taking the boundary conditions and interface conditions into account the computing system of the sbm for layered materials is established and then is solved the proposed method fully inherits the merits of conventional boundary type methods while possessing its distinctive advantages furthermore it is simple straightforward computationally efficient and stable since it does not need to discretize temporal derivative term three numerical experiments are performed to verify the efficiency and accuracy of the proposed scheme numerical results clearly indicate the efficiency accuracy and stability of the presented sbm for solving transient heat conduction problems in layered materials

a complete classification of deterministic root to frontier tree transformation classes abstract we take seven fundamental deterministic root to frontier tree transformation classes and consider the infinite set generated by them with composition the generated set is partially ordered under inclusion we effectively give this partial ordering by displaying an inclusion diagram of the poset

weighted automata with storage abstract we consider finite state automata that are equipped with a storage moreover the transitions are weighted by elements of a unital valuation monoid a weighted automaton with storage recognizes a weighted language which is a mapping from input strings to elements of the carrier set of the unital valuation monoid for the class of weighted languages recognizable by such automata we prove closure properties a chomsky schutzenberger theorem and a buchi elgot trakhtenbrot theorem in case of idempotent locally finite and sequential unital valuation monoids the recognized weighted languages are step functions

generalized automata on infinite trees and muller mcnaughton s theorem abstract we introduce various types of top down and bottom up generalized automata on infinite trees we study the power of deterministic and nondeterministic generalized tree automata and prove that deterministic and nondeterministic bottom up automata accept the same class we prove also that nondeterministic top down and bottom up generalized automata have the same power we give various characterizations of the monadic second order theory of the tree in terms of tree automata and tree grammars we consider different types of extensions of muller mcnaughton s theorem but unfortunately not all the extensions of it are possible

a complete rewriting system for a monoid of tree transformation classes abstract we take the set s of the seven fundamental deterministic root to frontier tree transformation classes dr ldr ndr l ndr h lh and nh where dr h is the calss of all deterministic root to frontier resp homomorphism tree transformations and the prefixes l n and ln mean the linear the nondeleting and the linear nondeleting subclasses respectively we examine the monoid s generated by s with composition we give a finite complete rewriting system r over s where the elements of s are considered now as denotations of the corresponding tree transformation classes such that every element of r viewed as a formal equation is valid in s and that r presents s i e s s r with r being the thue congruence generated by r on the free monoid s moreover it is shown that the word problem of s r is decidable in linear time

on the asymptotic solutions of a differential equation with multiple singular points abstract a singularly perturbed model problem with multiple distinct regular singular points is studied the uniform approximation of wazwaz and hanson 1986 is effectively extended to many singular points thus establishing a generalized version of that theorem where the classic inner and outer expansions are not employed a leading order general asymptotic solution is correctly represented by a set of matched exponential asymptotic expansions where each approximation contains dominant and recessive terms the resonance criteria due to the influence of multiple singular points are discussed for an even number of singular points the eigenvalues were found to be positive with a minimal eigenvalue however negative eigenvalues with a maximal eigenvalue arise for an odd number of singular points the maximal and the minimal eigenvalue may not be unique and each is 0 1

on the power of tree walking automata tree walking automata twas recently received new attention in the fields of formal languages and databases to achieve a better understanding of their expressiveness we characterize them in terms of transitive closure logic formulas in normal form it is conjectured by engelfriet and hoogeboom that twas cannot define all regular tree languages or equivalently all of monadic second order logic we prove this conjecture for a restricted but powerful class of twas in particular we show that 1 bounded twas that is twas that are only allowed to traverse every edge of the input tree at most once in every direction cannot define all regular languages we then extend this result to a class of twas that can simulate first order logic fo and is capable of expressing properties not definable in fo extended with regular path expressions the latter logic being a valid abstraction of current query languages for xml and semistructured data

basis properties of the p q sine functions we improve the currently known thresholds for basisness of the family of periodically dilated p q sine functions our findings rely on a beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity we also determine refined bounds on the riesz constant associated with this family these results seal mathematical gaps in the existing literature on the subject

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

hasse diagrams for classes of deterministic bottom up tree to tree series transformations the relationship between classes of tree to tree series and o tree to tree series transformations computed by restricted deterministic bottom up weighted tree transducers is investigated essentially these transducers are deterministic bottom up tree series transducers except that the former are defined over monoids whereas the latter are defined over semirings and only use the multiplicative monoid thereof in particular the common restrictions of nondeletion linearity totality and homomorphism can equivalently be defined for deterministic bottom up weighted tree transducers using well known results of classical tree transducer theory and also new results on deterministic weighted tree transducers classes of tree to tree series and o tree to tree series transformations computed by restricted deterministic bottom up weighted tree transducers are ordered by set inclusion more precisely for every commutative monoid and all sensible combinations of the above mentioned restrictions the inclusion relation of the classes of tree to tree series and o tree to tree series transformations is completely conveyed by means of hasse diagrams

the io and oi hierarchies abstract an analysis of recursive procedures in algol 68 with finite modes shows that a denotational semantics of this language can be described on the level of program schemes using a typed calculus with fixed point operators in the first part of this paper we derive classical schematological theorems for the resulting class of level n schemes in part two we investigate the language families obtained by call by value and call by name interpretation of level n schemes over the algebra of formal languages it is proved that differentiating according to the functional level of recursion leads to two infinite hierarchies of recursive languages the io and oi hierarchies which can be characterized as canonical extensions of the regular context free and io and oi macro languages respectively sufficient conditions are derived to establish strictness of io like hierarchies finally we derive that recursion on higher types induces an infinite hierarchy of control structures by proving that level n schemes are strictly less powerful than level n 1 schemes

decay of p q fourier coefficients we show that essentially the speed of decay of the fourier sine coefficients of a function in a lebesgue space is comparable to that of the corresponding coefficients with respect to the basis form

deciding equivalence of finite tree automata it is shown that for every constant m it can be decided in polynomial time whether or not two m ambiguous finite tree automata are equivalent in general inequivalence for finite tree automata is dexptime complete with respect to logspace reductions and pspace complete with respect to logspace reductions if the automata in question are supposed to accept only finite languages for finite tree automata with weights in a field r a polynomial time algorithm is presented for deciding ambiguity equivalence provided r operations and r tests for 0 can be performed in constant time this result is used to construct an algorithm deciding ambiguity inequivalence of finite tree automata in randomized polynomial time finally for every constant m it is shown that it can be decided in polynomial time whether or not a given finite tree automaton is m ambiguous

decidability of structural equivalence of eol grammars abstract we introduce height counting tree automata that are able to recognize the syntax trees of e0l grammars the equivalence problem of height counting tree automata is shown to be decidable and using this result we solve an open problem raised by ottmann and wood 5 6 i e the decidability of structural equivalence of e0l grammars

element free galerkin methods in combination with finite element approaches element free galerkin efg methods are methods for solving partial differential equations with the help of shape functions coming from moving least squares approximation the efg method is more flexible than the finite element fe method since it requires only nodal data and no element connectivity is needed because the efg method is computationally expensive combinations of the efg method and the fe method are considered implementations based on several weak forms of the problem description are studied numerical examples in elastostatics and fracture mechanics show that the implementations are able to compute both displacement and stress fields accurately

regular languages with variables on graphs this paper presents a pattern language based on regular expressions that allows the introduction of variables that can be instantiated to portions of the path that matches the expression the paper will define a simple syntax for the language and its formal semantics it will also study a modification of finite state automata that through the introduction of actions on transitions allows the variables to be instantiated while matching the expression finally the paper will show that the problem of answering queries with variables is inherently harder than simple matching essentially because even for fairly simple expressions the size of the results can be exponential in the size of the graph the class of expressions and a class of graphs for which query answering is polynomial will be identified and a processing algorithm for these expressions based on the intersection graph will be provided and analyzed

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

higher order meshless schemes applied to the finite element method in elliptic problems abstract this paper presents selected approximation techniques typical for the meshless finite difference method mfdm although applied to the finite element method fem finite elements with standard or hierarchical shape functions are coupled with higher order meshless schemes based upon the correction terms of a simple difference operator those terms consist of higher order derivatives which are evaluated by means of the appropriate formulas composition as well as a numerical solution which corresponds to the primary interpolation order assigned to element shape functions correction terms modify the right hand sides of algebraic fe equations only yielding an iterative procedure therefore neither re generation of the stiffness matrix nor introduction of any additional nodes and or degrees of freedom is required such improved fe mfd solution approach allows for the optimal application of advantages of both methods for instance a high accuracy of the nodal fe solution and a derivatives super convergence phenomenon at arbitrary domain points typical for the meshless fdm existing and proposed higher order techniques applied in the fem are compared with each other in terms of the solution accuracy algorithm efficiency and computational complexity in order to examine the considered algorithms numerical results of several two dimensional benchmark elliptic problems are presented both the accuracy of a solution and the solution s derivatives as well as their convergence rates evaluated on irregular and structured meshes as well as arbitrarily irregular adaptive clouds of nodes are taken into account

top down tree transducers with two way tree walking look ahead abstract we consider top down tree transducers with deterministic nondeterministic and universal two way tree walking look ahead and compare the transformational powers of their deterministic and strongly deterministic versions by giving the inclusion diagram of the induced tree transformation classes we also study the closure properties of these transformation classes with respect to composition

deterministic top down tree transducers with iterated look ahead it is known that by iterating the look ahead tree languages for deterministic top down tree automata more and more powerful recognizing devices are obtained let dr0 dr where dr is the class of all tree languages recognizable by deterministic top down tree automata and let for n 1 drn be the class of all tree languages recognizable by deterministic top down tree automata with drn 1 look ahead then dr0 dr1 dr2 slutzki and vagvolgyi 1993 showed that the composition powers of the class of all deterministic top down tree transformations with deterministic top down look ahead dttdr form a proper hierarchy i e dttdr n dttdr n 1 for n 0 along the proof they studied the notion of the deterministic top down tree transducer with drn look ahead dttdrn and showed that dttdr n 1 dttdrn n 0 where dttdrn stands for the class of all tree transformations induced by dttdrn s our aim is to show the reversed inclusion i e dttdrn dttdr n 1 n 0 this implies a precise characterization dttdrn dttdr n 1 n 0 and implies that the classes dttdrn n 0 form a proper hierarchy

a complete description for a monoid of deterministic bottom up tree transformation classes we consider the set m db ldb ndb lndb h lh nh of which the elements are the class of deterministic bottom up tree transformations db the linear the nondeleting and the linear nondeleting subclasses of db ldb ndb and lndb the class of homomorphism tree transformations h the linear and the nondeleting subclasses of h lh and nh the main aim of this paper is to obtain a finite generating system of the equations of the form x1 xm y1 yn where xi yj m for 1 i m 1 j n and is the composition of tree transformation classes therefore we give a finite thue system over m where m is now considered as a seven letter alphabet such that two words x1 xm and y1 yn of the free monoid m are congruent modulo the thue congruence t generated by t over m if and only if x1 xm y1 yn moreover we give a set n of representatives for the congruence t and an inclusion diagram of the tree transformation classes of the form z1 zk where z1 zk n we also present an algorithm that to each word x1 xm m produces the unique representative z1 zk n such that x1 xm t z1 zk we prove that using this algorithm and the inclusion diagram of the tree transformation classes represented by the elements of n we can decide for any given tree transformation classes x1 xm and y1 yn obtained by composition from elements of m if x1 xm y1 yn and hence if x1 xm y1 yn

tree automata and attribute grammars the translational mechanism of attribute grammars using tree automata are investigated the pushdown tree to string transducer with a certain synchronization facility as a model to realize transformations by attribute grammars is proposed and its basic properties using tree walking finite state automata are studied to demonstrate the utility of this model it is shown that noncircular attribute grammars are equally powerful as arbitrary attribute grammars and a method is provided to show that a certain type of transformations is impossible by attribute grammars

basis properties of generalized trigonometric functions abstract some basis properties of the generalized trigonometric functions cos p q are investigated in the context of lebesgue spaces l r 0 1

compositions with superlinear deterministic top down tree transformations abstract we denote the class of deterministic top down tree transformations by dt and the class of homomorphism tree transformations by hom the sign of a class with the prefix l sl nd denotes the linear superlinear nondeleting subclass of that class we fix the set m hom sl dt l dt nd dt dt of tree transformation classes then consider the monoid m of all tree transformation classes of the form x 1 o ox m where o is the operation composition m 0 and the x i s are elements of m as the main result of the paper we give an effective description of the monoid m with respect to inclusion this means that we present an algorithm which can decide given arbitrary two elements of the monoid whether some inclusion equality or incomparability holds between them

principal abstract families of weighted tree languages abstract we introduce semiring weighted regular tree grammars with storage where the semiring is complete we show that the class of weighted tree languages generated by them is a principal abstract family of weighted tree languages provided that the semiring is commutative the rank of symbols occurring in trees is bounded by a global parameter and that the storage is finitely encoded and contains a reset instruction moreover we prove the same statement for the iterated pushdown instead of finitely encoded storage containing a reset instruction