a new mixed finite element for the stokes and elasticity problems the stokes problem is approximated by a mixed finite element method using a new finite el ement which has properties analogous to the finite volume methods namely the local conservation of the momentum and the mass estimates of optimal order are derived for the errors in the velocity the pressure and the gradient of the velocity this new finite element also works for the elasticity problem and all estimates are valid uniformly with respect to the compressibility finally some numerical results for the incompressible navier stokes equations are presented

numerical simulation of 3d viscoelastic flows with free surfaces a numerical model is presented for the simulation of viscoelastic flows with complex free surfaces in three space dimensions the mathematical formulation of the model is similar to that of the volume of fluid vof method but the numerical procedures are different a splitting method is used for the time discretization the prediction step consists in solving three advection problems one for the volume fraction of liquid which allows the new liquid domain to be obtained one for the velocity field one for the extra stress the correction step corresponds to solving an oldroyd b fluid flow problem without advection in the new liquid domain two different grids are used for the space discretization the three advection problems are solved on a fixed structured grid made out of small cubic cells using a forward characteristics method the oldroyd b problem without advection is solved using continuous piecewise linear stabilized finite elements on a fixed unstructured mesh of tetrahedrons efficient post processing algorithms enhance the quality of the numerical solution a hierarchical data structure reduces the memory requirements convergence of the numerical method is checked for the pure extensional flow and the filling of a tube numerical results are presented for the stretching of a filament fingering instabilities are obtained when the aspect ratio is large also results pertaining to jet buckling are reported

automata theory based on quantum logic some characterizations automata theory based on quantum logic abbr l valued automata theory may be viewed as a logical approach of quantum computation in this paper we characterize some fundamental properties of l valued automata theory and discover that some properties of the truth value lattices of the underlying logic are equivalent to certain properties of automata more specifically i the transition relations of l valued automata are extended to describe the transitions enabled by strings of input symbols and particularly these extensions depend on the distributivity of the truth value lattices proposition 3 1 ii some properties of the l valued successor and source operators and l valued subautomata are demonstrated to be equivalent to a property of the truth value lattices which is exactly equivalent to the distributive law proposition 4 3 and corollary 4 4 this is a new characterization of boolean algebras in the framework of l valued automata theory iii we verify that the intersection of two l valued subautomata is still an l valued subautomaton if and only if the multiplication is distributive over the union in the truth value lattices proposition 4 5 which is strictly weaker than the usual distributivity iv we show that some topological characterizations in terms of the l valued successor and source operators also rely on the distributivity of truth value lattices theorem 5 6 finally we address some related topics for further study

algebraic myhill nerode theorems the myhill nerode theorem states that the equivalence relation l given by a language l has finite index if and only if l is accepted by a finite automaton in this paper we give several generalizations of the theorem which are algebraic in nature in our versions a finiteness condition involving the action of a semigroup on a certain function plays the role of the finiteness of the index of l while various algebraic structures including algebras coalgebras and bialgebras play the role of the finite automaton which accepts the language we develop additional theory concerning the algebraic objects which so arise and study the minimal ones

a continuous interior penalty method for viscoelastic flows in this paper we consider a finite element discretization of the oldroyd b model of viscoelastic flows the method uses standard continuous polynomial finite element spaces for velocities pressures and stresses inf sup stability and stability for convection dominated flows are obtained by adding a term penalizing the jump of the solution gradient over element faces to increase robustness when the deborah number is high we add a nonlinear artificial viscosity of shock capturing type the method is analyzed on a linear model problem and optimal a priori error estimates are proven that are independent of the solvent viscosity eta s finally we demonstrate the performance of the method on some known benchmark cases

on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

fuzzy equivalence relations and their equivalence classes in this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice we give certain characterizations of fuzzy semi partitions and fuzzy partitions over a complete residuated lattice as well as over a linearly ordered complete heyting algebra in the latter case for a fuzzy equivalence relation over a linearly ordered complete heyting algebra we construct an algorithm for calculation of a minimal family of its equivalence classes which generates it most of the presented results are new but some of them are generalizations of known results given in a way which simplifies and clarifies them

mathematical and numerical analysis of a simplified time dependent viscoelastic flow a time dependent model corresponding to an oldroyd b viscoelastic fluid is considered the convective terms being disregarded global existence in time is proved in banach spaces provided the data are small enough using the implicit function theorem and a maximum regularity property for a three fields stokes problem a finite element discretization in space is then proposed existence of the numerical solution is proved for small data so as a priori error estimates using again an implicit function theorem

on the discrete evss method abstract this paper is a completion of a previous paper written by two of the authors m fortin r guenette r pierre numerical analysis of the modified evss method comput methods appl mech engrg 143 1997 79 95 concerning the devss method which is a discrete variant of the popular elastic viscous split stress evss method introduced by rajagopalan r a brown r c armstrong finite element methods for calculation of steady viscoelastic flow using constitutive equations with a newtonian viscosity j non newtonian fluid mech 36 1990 159 199 within the context of viscoelastic fluids the method uses the rate of deformation tensor as an additional variable in this paper it is shown that a simple modification of the theoretical framework introduced in the first paper m fortin r guenette r pierre numerical analysis of the modified evss method comput methods appl mech engrg 143 1997 79 95 allows the treatment of multi mode constitutive equations of viscoelastic flows as well as that of the velocity gradient introduced as the additional variable instead of the rate of deformation tensor moreover this general framework based on a generalized brezzi babuska theory allows different discretizations for the stress and the additional variable the paper presents a general criteria insuring the stability of the method three particular mixed finite elements satisfying this criteria are studied an error analysis is performed on stokes and viscoelastic flows

galkerkin least squares finite element methods for the three field stokes system in 3 abstract in this work two new finite element methods for solving the three field stokes system associated with viscoelastic flow problems in three dimensional space are introduced both methods are based on a galerkin least squares formulation and complete first and second order convergence proofs of the corresponding approximations are given

grammar theory based on lattice ordered monoid motivated by li and pedrycz s work on fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids and inspired by the close relationship between the automata theory and the theory of formal grammars we have established a fundamental framework of l valued grammar it is shown that the set of l valued regular languages coincides with the set of l languages recognized by nondeterministic l fuzzy finite automata and every l language recognized by a deterministic l fuzzy finite automaton is an l valued regular language

finite element methods for the linear regularized 13 moment equations describing slow rarefied gas flows abstract the paper is concerned with the numerical solution of the linear steady state regularized 13 moment equations in two space dimensions to facilitate the understanding of the specific challenges the equations are first divided into two subsystems before the full system is approached the arising problems mainly stem from the complicated saddle point structure as well as the non standard nature of the boundary conditions a continuous interior penalty method is presented and the pronounced advantages of utilizing high order basis functions in this setting are illustrated to render the presented approach more efficient a hybridization technique is presented that originates in the discontinuous galerkin method

new formulations positivity preserving discretizations and stability analysis for non newtonian flow models we propose a class of new discretization schemes for solving the rate type non newtonian constitutive equations the so called conformation tensor has been known to be symmetric and positive definite in a large class of constitutive equations preserving such a positivity property on the discrete level is believed to be crucially important but difficult high weissenberg number problems on numerical instabilities have been often associated with this issue in this paper we present various discretization schemes that preserve the positive definiteness of the conformation tensor regardless of the time and spatial resolutions moreover the robustness of the algorithm has been also demonstrated by the stability analysis using the discrete analogue of energy estimates new schemes presented in this paper are constructed based upon the newly discovered relationship between the rate type constitutive equations and the symmetric matrix riccati differential equations

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

a unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty we discuss stabilized galerkin approximations in a new framework widening the scope from the usual dichotomy of the discontinuous galerkin method on the one hand and petrov galerkin methods such as the supg method on the other the idea is to use interior penalty terms as a means of stabilizing the finite element method using conforming or nonconforming approximation thus circumventing the need of a petrov galerkin type choice of spaces this is made possible by adding a higher order penalty term giving l2 control of the jumps in the gradients between adjacent elements we consider convection diffusion reaction problems using piecewise linear approximations and prove optimal order a priori error estimates for two different finite element spaces the standard h1 conforming space of piecewise linears and the nonconforming space of piecewise linear elements where the nodes are situated at the midpoint of the element sides the crouzeix raviart element moreover we show how the formulation extends to discontinuous galerkin interior penalty methods in a natural way by domain decomposition using nitsche s method

approximation of time dependent viscoelastic fluid flow supg approximation in this article we consider the numerical approximation to the time dependent viscoelasticity equations with an oldroyd b constitutive equation the approximation is stabilized by using a streamline upwind petrov galerkin supg approximation for the constitutive equation we analyze both the semidiscrete and fully discrete numerical approximations for both discretizations we prove the existence of and derive a priori error estimates for the numerical approximations

geometric aspects of reduction of order using the differential geometry of vectorfields and forms we reinterpret and extend the traditional idea of an integrating factor for a first order differential equation with symmetry in particular we provide a simple and manifestly geometric approach to reduction of order via symmetry for ordinary differential equations which largely obviates the necessity for canonical coordinates and the associated quotient manifolds in so doing some new results which generalise the class of lie group actions which can be used to solve ordinary differential equations are developed

determining the equivalence for one way quantum finite automata two quantum finite automata are equivalent if for any input string x the two automata accept x with equal probability in this paper we first focus on determining the equivalence for one way quantum finite automata with control language cl 1qfas defined by bertoni et al and then as an application we address the equivalence problem for measure many one way quantum finite automata mm 1qfas introduced by kondacs and watrous more specifically we obtain that i two cl 1qfas a 1 and a 2 with control languages regular languages l 1 and l 2 respectively are equivalent if and only if they are c 1n 1 2 c 2n 2 2 1 equivalent where n 1 and n 2 are the numbers of states in a 1 and a 2 respectively and c 1 and c 2 are the numbers of states in the minimal dfas that recognize l 1 and l 2 respectively furthermore if l 1 and l 2 are given in the form of dfas with m 1 and m 2 states respectively then there exists a polynomial time algorithm running in time o m 1n 1 2 m 2n 2 2 4 that takes as input a 1 and a 2 and determines whether they are equivalent ii as an application of item i two mm 1qfas a 1 and a 2 with n 1 and n 2 states respectively are equivalent if and only if they are 3n 1 2 3n 2 2 1 equivalent furthermore there is a polynomial time algorithm running in time o 3n 1 2 3n 2 2 4 that takes as input a 1 and a 2 and determines whether a 1 and a 2 are equivalent

minimization of fuzzy finite automata abstract in this paper we show that a fuzzy finite automation m 1 has an equivalent minimal fuzzy finite automation m we also show that m can be chsen so that if m 2 is equivalent to m 1 then m is a homomorphic image of m 2

on fuzzy regular languages abstract we introduce the concept of a max min fuzzy language fl m and a min max fuzzy language fl m recognized by a type of fuzzy automaton m we show that if l1 and l2 are finite valued f regular languages then so are l1 l2 and l1 l2 we give a form of a fuzzified pumping lemma which we use to give a necessary and sufficient condition for fl m to be nonconstant

algebraic properties of la languages in this study we introduce the concepts of l valued regular substitution la substitution deterministic l valued regular substitution dla substitution l valued fuzzy homomorphism and its inverse images homomorphism and its inverse images for a lattice ordered monoid l we also study the properties of la languages and dla languages under the above mentioned algebraic operations the algebraic characterization of the l valued regular language is given

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

minimization algorithm of fuzzy finite automata in this paper a class of fuzzy finite automata corresponding to the mealy type of ordinary automata is formulated and also two types of statewise equivalence relations are introduced from the equivalence relations a minimal form is defined and a minimization algorithm of the mealy type of fuzzy finite automata is obtained

new symmetry solution techniques for first order non linear pdes using recent extensions of work of s lie vorlesungen uber differentialgleichungen mit bekannten infinitesimalen transformationen leipzig teubner 1891 and e cartan lecons sur les invariants integreaux hermann paris 1922 les systems differentials exterieures et leurs applications geometrique hermann paris 1945 for integrating frobenius integrable vector field distributions via symmetry we examine some symmetry techniques for finding local solutions of first order non linear partial differential equations pdes in the language of exterior differential systems we develop a technique for solving first order quasilinear pdes that is then applied to general first order non linear partial differential equations our results are significant inasmuch as we give algorithms for solving first order pdes in the presence of symmetry that are essentially mechanical in nature and done in the original coordinate system

determinization of fuzzy automata with membership values in complete residuated lattices in this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices in comparison with the previous methods developed by belohlavek r belohlavek determinism and fuzzy automata information sciences 143 2002 205 209 and li and pedrycz y m li w pedrycz fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids fuzzy sets and systems 156 2005 68 92 our method always gives a smaller automaton and in some cases when the previous methods result in infinite automata our method can result in a finite one we also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them and in particular to the concept of the nerode s fuzzy right congruence of a fuzzy automaton which we introduce and study here

weighted automata and weighted logics weighted automata are used to describe quantitative properties in various areas such as probabilistic systems image compression speech to text processing the behaviour of such an automaton is a mapping called a formal power series assigning to each word a weight in some semiring we generalize buchi s and elgot s fundamental theorems to this quantitative setting we introduce a weighted version of mso logic and prove that for commutative semirings the behaviours of weighted automata are precisely the formal power series definable with particular sentences of our weighted logic we also consider weighted first order logic and show that aperiodic series coincide with the first order definable ones if the semiring is locally finite commutative and has some aperiodicity property

fuzzy groups fuzzy functions and fuzzy equivalence relations to each fuzzy subgroup a fuzzy equivalence relation is associated and it is proved that a fuzzy subgroup is normal if and only if the operation of the group is compatible with its associated fuzzy equivalence relation in the definition of fuzzy subgroup only the subset is fuzzy whilst the group operation remains crisp in an opposite direction another structure can be constructed maintaining crisp the basic set x of the group and fuzzifying the group operation when in addition it is imposed to the fuzzy operation to be compatible with a given fuzzy equivalence relation this structure is called a vague group the results of the paper allow us to associate a vague group to every fuzzy subgroup in such a way that it can be interpreted as the fuzzy quotient group x special attention is paid to normal fuzzy groups and vague groups of the additive group r of the real numbers two examples related to triangular numbers illustrating the results of the paper are provided

pumping lemma in context free grammar theory based on complete residuated lattice valued logic residuated lattices are important algebras and have close links with various important algebras automata theory based on complete residuated lattice valued logic called l valued automata has been established by the second author in 2001 and 2002 as a continuation of automata theory based on complete residuated lattice valued logic in this paper we mainly deal with the problem concerning pumping lemma in l valued context free languages l cfls as a generalization of the notion in the theory of formal grammars the definition of l valued context free grammars l cfgs is introduced we also discuss a special case of l cfgs l right or left linear grammars and show the equivalence between l linear grammars and l regular grammars this result shows that we generalize the pumping lemma in l valued regular languages l rls more recently established by the second author

equivalence in automata theory based on complete residuated lattice valued logic automata theory based on complete residuated lattice valued logic called l valued finite automata abbr l vfas was introduced by the second author in 2001 in this paper we deal with the problems of equivalence between l valued sequential machines abbr l vsms and l vfas we define l vsms and particularly present a method for deciding the equivalence between l vsms as well an algorithm procedure for deciding the equivalence between l vsms is constructed we analyze the complexity and efficiency of the algorithm procedure and obtain the relative results to l vfas moreover the definitions of l valued languages abbr l vls and l valued regular languages abbr l vrls recognized by l vfas are given and some related properties are also discussed we show an equivalent relation between l vrls and conventional regular languages by using l valued pumping lemma we get a necessary and sufficient condition for an l vl to be nonconstant

an algebraic approach to hybrid systems we propose an algebraic model for hybrid systems and illustrate its usefulness by proving theorems in realization theory using this viewpoint by a hybrid system we mean a collection of continuous nonlinear control systems associated with a discrete finite state automaton the automaton switches between the continuous control systems and this switching is a function of the discrete input symbols that it receives

the relationships among several types of fuzzy automata we discuss the relationships among several types of fuzzy automata in which all fuzzy sets are defined by membership functions whose codomains are a lattice ordered monoid l these automata include nondeterministic l valued finite automata with l move nondeterministic l valued finite automata deterministic l valued finite automata and l valued finite state automata we consider all that come with fuzzy initial states and fuzzy final states or with crisp initial states or crisp final states some comparative results concerning the power of fuzzy automata used in the existing literature to recognize fuzzy languages are given systematically

automata theory based on complete residuated lattice valued logic pushdown automata automata theory based on complete residuated lattice valued logic called l valued automata has been proposed by qiu automata theory based on complete residuated latticed valued logic sci china ser f 44 6 2001 419 429 automata theory based on complete residuated latticed valued logic ii sci china ser f 45 6 2002 442 452 in this paper we discuss some properties of l valued context free grammars languages and pushdown automata we show that for such grammars chomsky and greibach normal forms can be equivalently constructed and we also prove that the languages accepted by final states and by empty stack in l valued pushdown automata are equivalent in particular we prove the equivalence between l valued context free grammars and l valued pushdown automata

products of fuzzy finite state machines abstract we introduce the concepts of fuzzy transformation semigroups coverings cascade and wreath products for fuzzy finite state machines in order to overcome some of the difficulties which arise from the fuzzification of these concepts we also introduce the notions of polysemigroups and weak coverings

a new discrete evss method for the viscoelastic flows in this paper we propose a new discrete elastic viscous split stress evss method for the viscoelastic flows obeying an oldroyd b type constitutive equation supposing that the velocity and pressure are approximated by the taylor hood elements and applying the orthogonal projection technique we introduce two gauss integrations as a stabilizing term in the discrete evss method compared with the popular one the new method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot but gets the same stabilized result additionally some numerical experiments are shown to verify its efficiency

a categorical approach to lattice valued fuzzy automata some uniform categorical theoretical treatment of automata and lattice valued fuzzy automata using quantale theory is studied in this paper first l relational sheaves on a monoid m and q enriched categories are introduced for quantales l and q the equivalence of the corresponding categories are proved next then lattice valued fuzzy automata are described by q enriched categories in fact lattice valued fuzzy automata are characterized by the category of generalized lattice valued automata using the notions of q bimodules finally some of the algebraic properties of behaviors of generalized lattice valued automata are studied by using the technique of gluing of q bimodules

topological properties of the class of generators of an indistinguishability operator the present paper investigates the relations between topologies in the classical sense fuzzy topologies in lowen s sense and indistinguishability operators as well as constructing topologies and fuzzy topologies by means of indistinguishability operators furthermore as a particular consequence of the results in this paper a characterization theorem for pseudo metrizable topological spaces in the classical sense is also surprisingly obtained

the algebra of fuzzy truth values the purpose of this paper is to give a straightforward mathematical treatment of algebras of fuzzy truth values for type 2 fuzzy sets

fuzzy language on free monoid in this paper we shall introduce the notion of fuzzy regular language adjunctive language and dense language and discuss their algebraic character and algebraic properties

edge stabilization for the generalized stokes problem a continuous interior penalty method in this note we introduce and analyze a stabilized finite element method for the generalized stokes equation stability is obtained by adding a least squares penalization of the gradient jumps acro

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

a stabilized cut finite element method for the three field stokes problem we propose a nitsche based fictitious domain method for the three field stokes problem in which the boundary of the domain is allowed to cross through the elements of a fixed background mesh the dependent variables of velocity pressure and extra stress tensor are discretized on the background mesh using linear finite elements this equal order approximation is stabilized using a continuous interior penalty cip method on the unfitted domain boundary dirichlet boundary conditions are weakly enforced using nitsche s method we add cip like ghost penalties in the boundary region and prove that our scheme is inf sup stable and that it has optimal convergence properties independent of how the domain boundary intersects the mesh additionally we demonstrate that the condition number of the system matrix is bounded independently of the boundary location we corroborate our theoretical findings numerically

on the recognizability of fuzzy languages ii it is shown that a fuzzy language is recognized by a finite monoid iff it has finitely many right derivatives iff it has finitely many left derivatives finally we show that the behaviors of lukasiewicz automata have the above properties

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

explicit solutions of pde via vessiot theory and solvable structures we consider the problem of computing the integrable sub distributions of the non integrable vessiot distribution of multi dimensional second order partial differential equations pdes we use vessiot theory and solvable structures to find the largest integrable distributions contained in the vessiot distribution associated to second order pdes in particular we show how the solvable symmetry structure of the original pde can be used to construct integrable sub distributions leading to group invariant solutions of the pde in two and more than two independent variables

integration of pdes by differential geometric means we use vessiot theory and exterior calculus to solve partial differential equations pdes of the type uyy f x y u ux uy uxx uxy and associated evolution equations these equations are represented by the vessiot distribution of vector fields we develop and apply an algorithm to find the largest integrable sub distributions and hence solutions of the pdes we then apply the integrating factor technique sherring and prince 1992 trans am math soc 433 453 to integrate this integrable vessiot sub distribution the method is successfully applied to a large class of linear and nonlinear pdes

solvable structures and hidden symmetries we show that some examples in the literature of non standard symmetry reductions of ordinary differential equations can be understood using the concept of a solvable structure of one forms

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

stability analysis of explicit entropy viscosity methods for non linear scalar conservation equations this material is based upon work supported by the department of homeland security under agreement 2008 dn 077 ari018 02 national science foundation grants dms 0811041 dms 0914977 dms 1015984 af office of scientific research grant fa99550 12 0358 and is partially supported by award kus c1 016 04 made by king abdullah university of science and technology kaust

automata theory based on quantum logic reversibilities and pushdown automata automata theory based on quantum logic called l valued finite automata l vfas may be viewed as a logical approach to quantum computing this work is mainly divided into two parts one part deals with reversibility of l vfas and the other establishes a basic framework of l valued pushdown automata l vpdas first we provide some preliminaries concerning quantum logic and l vfas and we prove a useful property of l valued successor and source operators then we clarify the relationships between various reversibilities closely related to quantum finite automata in the literature in particular we define a reversibility of l vfas which is termed as retrievability and we clarify the relationships between a number of different fashions regarding retrievability of l vfas we prove that some of them are equivalent but for the others to be equivalent the truth value set is required to satisfy a certain condition this is an essential difference from the classical situation afterwards we introduce l vpdas and show that the class of the languages accepted by l vpdas by empty stack coincides with that accepted by l vpdas by final state finally we provide some examples of l vfas and conclude with some remarks

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

on quotient machines of a fuzzy automaton and the minimal machine in this paper the concept of substitution property sp partition for a finite fuzzy automaton is formulated and the quotient automaton with respect to an sp partition is defined the state minimization problem for such automata by using the method of quotient machines is solved

local and nonlocal solvable structures in the reduction of odes solvable structures likewise solvable algebras of local symmetries can be used to integrate scalar ordinary differential equations odes by quadratures solvable structures however are particularly suitable for the integration of odes with a lack of local symmetries in fact under regularity assumptions any given ode always admits solvable structures even though finding them in general could be a very difficult task in practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra in this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order i e classical and higher in particular we introduce the notion of nonlocal solvable structure

congruences and homomorphisms of fuzzy automata concepts of congruences and homomorphisms of fuzzy automata are defined and homomorphism theorem is proved lattices of congruences of fuzzy automata are described and an algorithm for computing the greatest congruence contained in an equivalence of a fuzzy automaton is presented it is used for minimization procedures for both fuzzy automata with and without outputs connections with previously known minimization algorithms are discussed

minimization of states in automata theory based on finite lattice ordered monoids in this study we consider a concept of complete l fuzzy matrix define complete lattice valued finite automata clfas and study their properties the definitions of statewise equivalence relations and automata equivalence relations of a clfa are given two algorithms are aimed at the minimization of states of a clfa

automata theory based on complete residuated lattice valued logic a categorical approach automata theory based on complete residuated lattice valued logic called l valued automata l vas has been primarily established by qiu in 2001 and 2002 in this paper we consider the l vas that have l valued initial and final states we study the categorical issue of l vas the main technical contributions include 1 we investigate the relationship between the category of l vas and the category of non deterministic automata ndas also we study the relationship between the category of generalized l vas and the category of ndas 2 we prove the existence of isomorphisms between the category of l vas and the subcategory of generalized l vas and between the category of l vas and the category of sets of ndas 3 finally we further investigate some specific relationships between the output l valued subsets of generalized l vas and the output l valued subsets of ndas

minimization of lattice finite automata and its application to the decomposition of lattice languages in this paper we study the minimization of lattice valued finite automata with membership values in a distributive lattice and its relationships to the decomposition of lattice valued regular languages first we establish the equivalence of nondeterministic lattice finite automata la and deterministic lattice finite automata dla furthermore we provide some characterization of lattice valued regular languages and regular operations on family of lattice valued regular languages in the sequel we introduce some notions that help clarify the concept of minimal dlas and present an effective algorithm to obtain a minimal dla from a given la using the construction of minimal dla we introduce some simple classes of lattice valued regular languages such as l unitary and l prefix ones we demonstrate that any lattice valued regular language can be decomposed as disjoint joins of such kinds of simple languages

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

pumping lemma in automata theory based on complete residuated lattice valued logic a note abstract automata theory based on complete residuated lattice valued logic called l valued automata was established in qiu automata theory based on completed residuated lattice valued logic i science in china f 44 6 2001 419 429 qiu automata theory based on completed residuated lattice valued logic ii science in china f 45 6 2002 442 452 in this note we deal with the pumping lemma in l valued automata theory after recalling some preliminaries related to complete residuated lattices and l valued automata we define a number of l valued accepting predicates in particular the pumping lemma for l valued automata theory is set up we show that if those related l valued predicates are defined by using connective instead of then the pumping lemma may not hold again furthermore we investigate the l valued automata with e transitions and present the equivalence between the l valued automata without e transitions and those with e transitions finally a number of related questions is addressed

numerical analysis of the modified evss method abstract in this paper we present a proof of the stability of a new mixed finite element method introduced recently by the authors 9 within the context of viscoelastic fluids the mixed formulation is related to the evss elastic viscous split stress method proposed by rajagopalan et al 14 and is based on the introduction of the rate of deformation tensor as an additional unknown the proof applies to the stokes flow and some linearized constitutive equations of slow viscoelastic flows existence and uniqueness of the continuous and the discrete problems are derived from a generalized brezzi babuska theory it is shown that no additional compatibility condition is required between the various variables except the usual one for the velocity and the pressure fields this result allows to choose low order finite element for the stress several numerical experiments on the 4 1 contraction stokes flow will be presented which will confirm the improved stability obtained with this new formulation