hierarchies of tree series transformations we study bottom up and top down tree series transducers over a semiring a and denote the tree series transformation classes computed by them by bott ts a and topt ts a respectively we present the inclusion diagram of the classes p bott tsn a p topt tsn a p botn 1t ts a and p topn 1t ts a and prove its correctness where a is a commutative izz semiring izz idempotent zero divisor free and zero sum free and the prefix p stands for polynomial this inclusion diagram implies the properness of the following four hierarchies p topt ts a p top2t ts a p top3t ts a p bott ts a p bot2t ts a p bot3t ts a p topt ts a p bot2t ts a p top3t ts a p bot4t ts a p bott ts a p top2t ts a p bot3t ts a p top4t ts a where the first hierarchy generalizes the famous top down tree transformation hierarchy of engelfriet math systems theory 15 1982 92 125 as the second main result we prove that the first two hierarchies are proper even for arbitrary i e not necessarily commutative izz semirings

error estimates for a semi explicit numerical scheme for stefan type problems a parabolic problem of the following form is considered 1 frac partial partial t left a vartheta w right delta vartheta f 2 w varepsilon lambda vartheta wherea is a positive constant f is a datum and is a maximal monotone graph this system contains the weak formulation of the stefan problem as a particular case here the problem 1 2 is approximated by coupling 1 with therelaxed equation 3 varepsilon frac partial w partial t lambda 1 w mathrel backepsilon vartheta varepsilon constant 0 the problem 1 3 is then discretized in time by thesemi explicit scheme 4 a frac vartheta n vartheta n 1 tau frac w n w n 1 tau delta vartheta n f n 5 varepsilon frac w n w n 1 tau lambda 1 w n mathrel backepsilon vartheta n 1 a finite element space discretization and quadrature formulae are then introduced thus at each time step 5 is replaced by a finite number ofindependent algebraic equations which can be solved with respect to the barycentral values ofw n then 4 is reduced to alinear system of algebraic equations having as unknowns the nodal values of n assuming the condition e a the fully discrete scheme is stable and its solution converges to that of 1 2 error estimates are proved the results of some numerical experiments are discussed they show that the present method is faster than other classical procedures

weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data for the purpose of forecasting key macroeconomic or financial variables from a panel of time series variables we adopt the dynamic factor model and propose a weighted likelihood based method for parameter estimation the loglikelihood function is split into two parts that are weighted differently the first part is associated with the key variables while the second part is associated with the related variables which may contribute to the forecasting of key variables we derive asymptotic properties including consistency and asymptotic normality of the weighted maximum likelihood estimator we show that this estimator outperforms the standard likelihood based estimator in approximating the true unknown distribution of the data as well as in out of sample forecasting accuracy we verify the new estimation method in a monte carlo study and investigate the role of different weights in different settings in the context of forecasting gross domestic product growth this key variable is typically observed at a low quarterly frequency while the supporting variables are observed at a high monthly frequency we adopt a low frequency representation of the mixed frequency dynamic factor model and discuss the computational efficiencies of this approach in our empirical study for the u s economy we present improvements in nowcasting and forecasting accuracy when the weighted likelihood based estimation procedure is adopted

automatic average case analysis of algorithms abstract many probabilistic properties of elementary discrete combinatorial structures of interest for the average case analysis of algorithms prove to be decidable this paper presents a general framework in which such decision procedures can be developed it is based on a combination of generating function techniques for counting and complex analysis techniques for asymptotic estimations we expose here the theory of exact analysis in terms of generating functions for four different domains the iterative recursive and unlabelled labelled data type domains we then present some major components of the associated asymptotic theory and exhibit a class of naturally arising functions that can be automatically analyzed a fair fragment of this theory is also incorporated into a system called lambda upsilon omega in this way using computer algebra one can produce automatically non trivial average case analyses of algorithms operating over a variety of decomposable combinatorial structures at a fundamental level this paper is part of a global attempt at understanding why so many elementary combinatorial problems tend to have elementary asymptotic solutions in several cases it proves possible to relate entire classes of elementary combinatorial problems whose structure is well defined with classes of elementary special functions and classes of asymptotic forms relative to counting probabilities or average case complexity

approximate minimization of weighted tree automata abstract this paper studies the following approximate minimization problem given a minimal weighted tree automaton a with n states recognizing a weighted tree language f can we construct a smaller automaton a with n n states recognizing a language f that is a good approximation of f the corresponding problem for weighted automata on strings was recently studied by balle et al 16 15 where the authors introduced a new canonical form for weighted automata called singular value automata inspired by spectral methods and showed that truncating such canonical form yields a solution for the problem satisfying a certain approximation criteria in this paper we take a similar approach and show that in the tree case one can obtain an analogous canonical form that we call singular value tree automata and use it to study the approximate minimization problem for weighted tree automata we first establish the existence of this canonical form for weighted tree automata and then provide bounds on the quality of the resulting approximation method based on truncation we also study the problem of computing the canonical form given a minimal weighted tree automaton and show that in the tree case this task is considerably more complicated than in the string case in particular computing the canonical form reduces to solving a system of polynomial equations by further reducing this problem to the computation of generalized partition functions for weighted tree automata we propose and analyze two methods for computing the canonical form based on iterative methods fixed point iteration and newton s method our analysis of newton s method unveils a connection between iterative methods and sequences of sets of trees satisfying a certain technical condition that might be of independent interest

large time asymptotics in contaminant transport in porous media in this paper we derive large time solutions of the partial differential equations modelling contaminant transport in porous media for initial data with bounded support while the main emphasis is on two space dimensions for the sake of completeness we give a brief summary of the corresponding results for one space dimension the philosophy behind the paper is to compare the results of a formal asymptotic analysis of the governing equations as t to infty with numerical solutions of the complete initial value problem the analytic results are obtained using the method of dominant balance which identifies the dominant terms in the model equations determining the behaviour of the solution in the large time limit these are found in terms of time scaled space similarity variables and the procedure results in a reduction of the number of independent variables in the original partial differential equation this generates what we call a reduced equation the solution of which depends crucially on the value

equational tree transformations we define an equational relation as the union of some components of the least solution of a system of equations of tree transformations in a pair of algebras we focus on equational tree transformations which are equational relations obtained by considering the least solutions of such systems in pairs of term algebras we characterize equational tree transformations in terms of tree transformations defined by different bimorphisms to demonstrate the robustness of equational tree transformations we give equational definitions of some well known tree transformation classes for which bimorphism characterizations also exist these are the class of alphabetic tree transformations the class of linear and nondeleting extended top down tree transformations and the class of bottom up tree transformations and its linear and linear and nondeleting subclasses finally we prove that a relation is equational if and only if it is the morphic image of an equational tree transformation

positive tree representations and applications to tree automata an effective classification of tree automata costed over the semirings r and n and more generally of positive tree representations ptr is achieved by means of a global behavior theory reducibility and minimality of ptrs is also investigated

characterizing weighted mso for trees by branching transitive closure logics we introduce the branching transitive closure operator on progressing weighted monadic second order logic formulas where the branching corresponds in a natural way to the branching inherent in trees for arbitrary commutative semirings we prove that weighted monadic second order logics on trees is equivalent to the definability by formulas which start with one of the following operators i a branching transitive closure or ii one existential second order quantifier followed by one universal first order quantifier in both cases the operator is applied to step formulas over a boolean first order logic enriched by modulo counting or b boolean monadic second order logic

analysis of an upwind mixed finite element method for nonlinear contaminant transport equations in this paper the numerical approximation of a nonlinear diffusion equation arising in contaminant transport is studied the equation is characterized by advection diffusion and adsorption assuming the adsorption term is modeled by a freundlich isotherm it can be nonlinear in concentration and nondifferentiable as the concentration approaches zero we consider the approximation of this equation by a method which upwinds the advection and incorporates diffusion using a mixed finite element method error estimates for a semidiscrete formulation are derived and numerical results for a fully discrete formulation are given

finite element approximation of the transport of reactive solutes in porous media part 1 error estimates for nonequilibrium adsorption processes in this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration backward euler time discretization and possibly regularization of the following degenerate parabolic system arising in a model of reactive solute transport in porous media find u x t v x t such that begin eqnarray partial t u partial t v delta u f quad mbox in omega times 0 t qquad u 0 quad mbox on partial omega times 0 t partial tv k varphi u v quad mbox in omega times 0 t u cdot 0 g 1 cdot quad v cdot 0 g 2 cdot quad mbox in omega subset real d quad 1 le d le 3 end eqnarray for given data k in real f g 1 g 2 and a monotonically increasing varphi in c 0 real cap c 1 infty 0 cup 0 infty satisfying varphi 0 0 which is only locally holder continuous with exponent p in 0 1 at the origin e g varphi s equiv s p this lack of lipschitz continuity at the origin limits the regularity of the unique solution u v and leads to difficulties in the finite element error analysis

merging multiple longitudinal studies with study specific missing covariates a joint estimating function approach merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power this article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics such as different follow up schedules and study specific missing covariates e g covariates observed in some studies but missing in other studies the presence of study specific missing covariates presents great statistical methodology challenge in data merging and analysis we propose a joint estimating function approach to addressing this challenge in which a novel nonparametric estimating function constructed via splines based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates under mild regularity conditions we show that the proposed estimator is consistent and asymptotically normal we evaluate finite sample performances of the proposed method through simulation studies in comparison to the conventional multiple imputation approach our method exhibits smaller estimation bias we provide an illustrative data analysis using longitudinal cohorts collected in mexico city to assess the effect of lead exposures on children s somatic growth

a note on cut worthiness of recognizable tree series the topic of this short note is tree series over semirings with partially ordered carrier set thus tree series become poset valued fuzzy sets starting with a collection of recognizable tree languages we construct a tree series recognizable over any semiring such that the carrier set is a poset generated by the collection in the framework of fuzzy structures the starting collection becomes a subset of the collection of the corresponding cut sets under some stricter conditions it is even equal to this collection we also partially solve an open problem which was posed in borchardt et al cut sets as recognizable tree languages fuzzy sets and systems 157 2006 1560 1571 namely we show that if f is a given tree series over a partially ordered locally finite semiring a then f is recognizable if and only if there are finitely many cut sets of f and every cut set is a recognizable tree language

a degenerate elliptic parabolic system arising in competitive contaminant transport abstract the objective of this work is to study a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater we show that this system admits a unique weak solution provided the nonlinear adsorption isotherm associated with the reaction process satisfies certain physically reasonable structural conditions by addressing a more general problem in addition we conclude that the solute concentrations stay non negative if the source term is componentwise non negative and investigate numerically the finite speed of propagation of compactly supported initial concentrations in a two component test case

solution of degenerate convection diffusion problems by the method of characteristics a new approximation scheme is proposed to solve nonlinear degenerate convection diffusion problems the method is based on a relaxation scheme developed for degenerate parabolic problems in w jager and j kacur numer math 60 1991 pp 407 427 m2an math model numer anal 29 1995 pp 605 627 and on the method of characteristics j douglas and t i russell siam j numer anal 19 1982 pp 871 885 o pironneau numer math 38 1982 pp 309 332

weighted monadic datalog based on monadic datalog we introduce the concept of weighted monadic datalog over unranked trees this provides a query language that can be used to extract quantitative information from semi structured databases where the quantities are taken from some semiring s we show that weighted monadic datalog is as expressive as weighted tree automata on unranked trees moreover we prove that a query can be evaluated efficiently on an unranked tree provided that i s is commutative and the underlying datalog program is non circular or ii s is a finite and commutative w cpo semiring

godunov mixed methods for advection diffusion equations in multidimensions time split methods for multidimensional advection diffusion equations are considered in these methods advection is approximated by a godunov type procedure and diffusion is approximated by a low

representing ordered structures by fuzzy sets an overview we present a survey on representations of ordered structures by fuzzy sets any poset satisfying some finiteness condition semilattice lattice belonging to a special class e g distributive noetherian complete and others can be represented by a single function i e by a fuzzy set its domain and co domain are particular subsets of the same structure and consist of irreducible elements the representation is minimal in the sense that another representation could not be obtained by replacing the domain of the former by its proper subset by this approach the structure itself is uniquely represented by the collection of cuts ordered dually to inclusion

confidence distributions and a unifying framework for meta analysis this article develops a unifying framework as well as robust meta analysis approaches for combining studies from independent sources the device used in this combination is a confidence distribution cd which uses a distribution function instead of a point point estimator or an interval confidence interval to estimate a parameter of interest a cd function contains a wealth of information for inferences and it is a useful device for combining studies from different sources the proposed combining framework not only unifies most existing meta analysis approaches but also leads to development of new approaches we illustrate in this article that this combining framework can include both the classical methods of combining p values and modern model based meta analysis approaches we also develop under the unifying framework two new robust meta analysis approaches with supporting asymptotic theory in one approach each study size goes to infinity and in the other approach the number of studies

solution of parabolic equations by backward euler mixed finite element methods on a dynamically changing mesh we develop and analyze methods based on combining the lowest order mixed finite element method with backward euler time discretization for the solution of diffusion problems on dynamically changing meshes the methods developed are shown to preserve the optimal rate error estimates that are well known for static meshes the novel aspect of the scheme is the construction of a linear approximation to the solution which is used in projecting the solution from one mesh to another extensions to advection diffusion equations are discussed where the advection is handled by upwinding numerical results validating the theory are also presented

on the uniqueness of l fuzzy sets in the representation of families of sets abstract this paper deals with the uniqueness of l fuzzy sets in the representation of a given family of subsets of a nonempty set it first shows a formula of the number of l fuzzy sets whose collection of cuts coincides with a given family of subsets of a nonempty set and then provides a necessary and sufficient condition under which such l fuzzy set is unique

asymptotic profiles for covection diffusion equations with variable diffusion abstract we investigate the large time behavior of solutions of the convection diffusion equation u t div a x u d u q 1 u d r n in 0 r n with integrable initial data u0 x we take a x 1 b x 0 with b smooth and decaying to zero fast enough as x when q 1 1 n it is known that the solutions behave in a first approximation like the solutions of the head equation taking the same initial data as t we show here the influence of the nonlinear term and the variable diffusion in the large time behavior by obtaining the second term in the asymptotic development of solutions as t

on lattice valued up sets and down sets isotone and anti isotone mappings from a poset into a complete lattice are investigated as lattice valued up sets and down sets respectively cuts of these are shown to be analogue crisp sub posets of the domain up set or semi filters and down sets or semi ideals the collection of all lattice valued up sets down sets of a poset is a complete lattice under the order inherited from the lattice among other results for a collection of crisp up sets down sets of a poset necessary and sufficient conditions are given under which this collection consists of cuts of a lattice valued up set down sets a generalization in the sense of closed fuzzy sets with respect to fuzzy relations is also carried out

algebraic aspects of families of fuzzy languages we study operations on fuzzy languages such as union concatenation kleene intersection with regular fuzzy languages and several kinds of iterated fuzzy substitution then we consider families of fuzzy languages closed under a fixed collection of these operations which results in the concept of full abstract family of fuzzy languages or full affl this algebraic structure is the fuzzy counterpart of the notion of full abstract family of languages that has been encountered frequently in investigating families of crisp i e non fuzzy languages some simpler and more complicated algebraic structures such as full substitution closed affl full super affl full hyper affl will be considered as well in the second part of the paper we focus our attention to full affls closed under iterated parallel fuzzy substitution where the iterating process is prescribed by given crisp control languages proceeding inductively over the family of these control languages yields an infinite sequence of full affl structures with increasingly stronger closure properties

pushdown tree automata algebraic tree systems and algebraic tree series the results of i guessarian 1983 math systems theory16 237 263 are generalized to formal tree series the following mechanisms are of equal power i algebraic tree systems ii pushdown tree automata iii restricted pushdown tree automata

context free series on trees we investigate context free cf series on trees with coefficients on a semiring they are obtained as components of the least solutions of systems of equations having polynomials on their right hand sides the relationship between cf series on trees and cf tree grammars and recursive program schemes is also examined polypodes a new algebraic structure are introduced in order to study in common series on trees and words and applications are given

solution of nonlinear convection diffusion problems by a conservative galerkin characteristics method we consider a scheme for nonlinear degenerate convection dominant diffusion problems that arise in contaminant transport in porous media with equilibrium adsorption isotherm this scheme is based on a regularization relaxation scheme that has been introduced by jager and kacur numer math 60 407 427 1991 m2an math model numer anal 29 n5 605 627 1995 with a type of numerical integration by bermejo siam j numer anal 32 425 455 1995 to the modified method of characteristics with adjusted advection mmocaa that was recently developed by douglas et al numer math 83 3 353 369 1999 comput geosci 1 155 190 1997 we present another variant of adjusting advection method the convergence of the scheme is proved an error estimate of the approximated scheme is derived computational experiments are carried out to illustrate the capability of the scheme to conserve the mass

solution to an integrodifferential equation with integral condition in this paper we are concerned with the application of rothe time discretization scheme to find an approximate solution of degenerate parabolic integrodifferential equation with initial neumann and nonlocal integral conditions existence and uniqueness of weak solution as well as some regularity results are obtained

solute transport in porous media with equilibrium and non equilibrium multiple site adsorption travelling waves we study travelling wave solutions of a model describing solute transport through porous media where the chemical species undergoes absorption i e a retention release reaction with the surface of the porous sceleton processes of this type are of fundamental importance in different fields we do not consider the process at the microscopic scale of single grains and pores but at the microscopic scale appropriate for the measurement of the phenomena described above

patterns and pattern matching in trees an analysis this paper presents general results on the probabilities of occurrences of patterns in trees which serve to analyze a commonly used pattern matching algorithm on trees it appears that for a wide class of statistics on trees pattern matching has a linear expected time complexity in contrast to a quadratic worst case behaviour the methods used are both combinatorial and analytic and prove useful in the evaluation of a wide class of tree algorithms

a kleene theorem for weighted tree automata over tree valuation monoids abstract we investigate weighted tree automata over cauchy tree valuation monoids a new type of weight structure which includes all commutative semirings and in addition average and discounted computations of weights for trees we define rational tree series over these weight structures and we prove kleene s classical theorem for this setting a tree series over a cauchy tree valuation monoid is recognizable by a weighted tree automaton if and only if it is rational the proof works via direct automata theoretic constructions along the way our results yield a new characterization of weighted tree automata over commutative semirings by rational expressions

fuzzy tree automata in this paper we map an arbitrary algebra to a completely distributive lattice and define algebras of fuzzy sets when the algebra is a term algebra we obtain fuzzy tree languages after defining fuzzy equational sets fuzzy rational sets and fuzzy recognizable tree languages we derive a kleene theorem for fuzzy tree languages

varieties of recognizable tree series over fields we introduce varieties of recognizable s tree series k s vts for short over a field k and a ranked alphabet s our variety theorem establishes a bijective correspondence between these k s vtss and the varieties of finite dimensional k s algebras k s vfda for short a k s algebra is a k vector space equipped with multilinear s operations the link between k s vtss and k s vfdas is provided by the syntactic k s algebras of tree series the most immediate predecessors of this study are berstel s and reutenauer s 1982 2 work on tree series over fields reutenauer s 1980 27 theory of varieties of string series bozapalidis and his associates 1983 1989 1991 8 5 4 work on syntactic k s algebras steinby s 1979 1992 30 31 theory of varieties of tree languages and our previous work 2009 on series of general algebras and their syntactic k s algebras

effective constructors the formal series of trees french abstract in this paper we exhibit two different effective constructions of the syntactic algebra u s associated with a recognizable tree series s in order to make the first construction we only need a natural number n satisfying dim u s n the second way to obtain u s is by minimization of a given realization of s we finally describe effectively a minimal matrix representation of s

local likelihood based on kernel censoring by drawing an analogy with likelihood for censored data a local likelihood function is proposed which gives more weight to observations near a region of interest in the sample space resulting methods can be used for assessing local departures from a parametric model and for semiparametric density estimation some theory and three examples is given

finite element solution of nonlinear diffusion problems abstract in this paper we describe the rothe finite element numerical scheme to find an approximate solution of a nonlinear diffusion problem modeled as a parabolic partial differential equation of even order this scheme is based on the rothe s approximation in time and on the finite element method fem approximation in the spatial discretization a proof of convergence of the approximate solution is given and error estimates are shown

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

systems of partial differential equations in porous medium abstract we investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media taking advantage of the inherent structure of the system that allows to deduce a scalar generalized porous medium equation for the sum of the solute concentrations we show existence of a unique weak solution to the coupled system and derive regularity estimates we also prove that the system supports solutions propagating with finite speed thus giving rise to free boundaries and interaction of compactly supported initial concentrations of different species

cut sets as recognizable tree languages a tree series over a semiring with partially ordered carrier set can be considered as a fuzzy set we investigate conditions under which it can also be understood as a fuzzified recognizable tree language in this sense sufficient conditions are presented which when imposed ensure that every cut set i e the pre image of a prime filter of the carrier set is a recognizable tree language moreover such conditions are also presented for cut sets of recognizable tree series

an effective linear scheme to solve nonlinear degenerate parabolic differential equations abstract in this paper we consider the approximate solution of the following problem given r n 1 n 3 find u x t such that t b u u p e u 0 in q 0 t u 0 on 0 t u x 0 u 0 x x where the function b s is a monotonically increasing function satisfying 0 b to solve this problem we introduce a new nonstandard time discretization scheme we prove stability and convergence results

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

selecting likelihood weights by cross validation the relevance weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision unlike its classical counterpart the weighted likelihood combines all relevant information while inheriting many of its desirable features including good asymptotic properties however in order to be effective the weights involved in its construction need to be judiciously chosen choosing those weights is the subject of this article in which we demonstrate the use of cross validation we prove the resulting weighted likelihood estimator wle to be weakly consistent and asymptotically normal an application to disease mapping data is demonstrated

recognizable formal power series on trees trees are a very basic object in computer science they intervene in nearly a ly domain and they are studied for their own or used to represent conveniently a given situation there are at least three directions where investigations on trees themselves are motivated and this for different reasons first the notion of tree is the basis of algebraic semantics nivat 19 rosen 2 2 etc in this context the study of special languages of trees i e forests their classification and their behaviour under various types of transformations are of great importance arnold fl dauchet 8 j l ilin 1161 mongy 18 by essence work in this area is an extension of the algebraic theory of languages trees and ianguages are in fact directly related via the derivation trees of an algebraic grammar thatcher 25 a second topic heavily related to trees concerns dzra structures trees mainly binary trees and its variants constitute one of the most widely known data structures see e g hlnuth 15 the analysis of the worst cale expected or average running time t ehzvgrr nfi certain algorithms requires sometimes long and delicate computations flajolet lo kemp 14 flajolet and steyaert 12 finally trees occupy a distinguished place in the enumeration of graphs and maps both because of the simplicity of their structure and for the relationship between their el lcodings and aigebraic languages the nature of the enumerating series and especially the question whether they are algebraic or not is one of the central problems in this domain cori 7 chottin 4 we propose here a theory of formal power series on trees and present some of their basic properties together with various examples of applications which as we hope will show the interest of its development within the framework we just sketched a formal power series on trees is a function which gssociates a number to esch tree thus we could also have called them tree functions ii in analogy with the term word function used by several authors paz and salomaa zo cobham 5 as an equivalent denomination for formal power series on words the main goal of a formal power series is to count or to represent the result of some computation on

the rank of a formal tree power series we prove that a tree series s t k k a field is recognizable iff dim vs iff dim fs where vs resp fs is the subspace if kp resp kt generated by the vectors t 1 s p s t t t p and where t is the set of all trees over and p is the free monoid of all pruned trees over we finally give a myhill like criterion for tree recognizability

completion of ordered structures by cuts of fuzzy sets an overview the aim of the paper is to present a role of fuzzy sets in the theory of ordered structures main algebraic properties of cuts of fuzzy sets are given and a completion of partially ordered sets to complete lattices is described it turns out that this completion is equivalent with the famous dedekind macneille completion but the algorithm presented here is much simpler

myhill nerode type theory for fuzzy languages and automata the myhill nerode theory is a branch of the algebraic theory of languages and automata in which formal languages and deterministic automata are studied through right congruences and congruences on a free monoid in this paper we develop a general myhill nerode type theory for fuzzy languages with membership values in an arbitrary set with two distinguished elements 0 and 1 which are needed to take crisp languages in consideration we establish connections between extensionality of fuzzy languages w r t right congruences and congruences on a free monoid and recognition of fuzzy languages by deterministic automata and monoids and we prove the myhill nerode type theorem for fuzzy languages we also prove that each fuzzy language possess a minimal deterministic automaton recognizing it we give a construction of this automaton using the concept of a derivative automaton of a fuzzy language and we give a method for minimization of deterministic fuzzy recognizers in the second part of the paper we introduce and study nerode s and myhill s automata assigned to a fuzzy automaton with membership values in a complete residuated lattice the obtained results establish nice relationships between fuzzy languages fuzzy automata and deterministic automata

weighted finite automata over strong bimonoids we investigate weighted finite automata over strings and strong bimonoids such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold we define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions moreover we show that in this case the given weighted automata can be determinized

on a generalization of fuzzy algebras and congruences abstract partially ordered fuzzy algebras are mappings from an algebra to a partially ordered set with the property that every level subset is an ordinary subalgebra similar definitions are induced for p valued congruences and weak congruences necessary and sufficient conditions under which an arbitrary collection of subalgebras congruences enables construction of a p valued fuzzy subalgebra congruence are given any p valued weak congruence uniquely determines a p valued subalgebra of the same algebra finally any collection of subalgebras or congruences of a given algebra can be used for the construction of a relational valued fuzzy algebra or congruence this seems to be the most general way to obtain a fuzzy algebra congruence out of the collection of the ordinary subalgebras congruences

on lindenmayerian algebraic power series abstract we define lindenmayerian algebraic power series and study their properties these series generalize both algebraic series and etol languages

determinism and fuzzy automata the concept of a fuzzy automaton as studied in the literature is a direct generalization of the classical concept of a non deterministic automaton in this paper we consider the question of whether there is a deterministic counterpart to the notion of a fuzzy automaton we propose a definition of deterministic fuzzy automata and show that they are equally powerful as fuzzy automata compared to the classical notion of a deterministic automaton the deterministic fuzzy automaton defined in our paper differs essentially only in that the final states form a fuzzy set moreover we show that deterministic fuzzy automata are equally powerful as nested systems of deterministic automata

solution of nonlinear transport diffusion problems by linearization we construct and analyze a fully discretization scheme for approximating the solution of a class of nonlinear degenerate parabolic problems with a nonlinear neumann boundary conditions the method is based on rothe type discretization in time and on wavelet galerkin discretization in space a proof of convergence of the approximate solution is given and error estimates are proved

semiparametric regression in likelihood based models abstract a weighted likelihood is used to estimate the parameters in a semiparametric model involving two covariates and allowing an association between the covariates the development is for arbitrary but specified densities of the observations the estimators are consistent and asymptotically normal hypothesis testing of the parametric component can be performed using a wald test simulations and analysis of data with bernoulli observations demonstrate the estimators application speckman developed kernel estimators where the conditional density of the observations is normal with p parametric covariates speckman s estimators and the new estimators are asymptotically equivalent with the bias of speckman s estimators being smaller as an example we study the relationship between a binary response indicating the occurrence of an intraoperative cardiac complication icc in vascular surgery patients and two risk factors duration of the operation or and asa score which is an evaluation of the patien

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

galerkin wavelet methods for two point boundary value problems anti derivatives of wavelets are used for the numerical solution of differential equations optimal error estimates are obtained in the applications to two point boundary value problems of second order the orthogonal property of the wavelets is used to construct efficient iterative methods for the solution of the resultant linear algebraic systems numerical examples are given