fuzzy regular languages over finite and infinite words we consider finite automata over semirings and quemirings accepting finite and infinite words respectively we obtain kleene theorems for fuzzy languages consisting of finite and infinite words furthermore we introduce regular fuzzy grammars and linear fuzzy systems and we show that both of them specify the class of recognizable fuzzy languages consisting of finite and infinite words

the two dimensional euler equations on singular exterior domains this paper is a follow up of gerard varet and lacave arch ration mech anal 209 1 131 170 2013 on the existence of global weak solutions to the two dimensional euler equations in singular domains in gerard varet and lacave arch ration mech anal 209 1 131 170 2013 we have established the existence of weak solutions for a large class of bounded domains with initial vorticity in lp p 1 for unbounded domains we have proved a similar result only when the initial vorticity is in l p c p 2 and when the domain is the exterior of a single obstacle the goal here is to retrieve these two restrictions we consider general initial vorticity in l 1 cap l p p 1 outside an arbitrary number of obstacles not reduced to points

the structure of qualitatively determinate relationships this paper presents the necessary and sufficient conditions for determining the signs of the solution variables of a system of linear equations based only upon a knowledge of the signs of the coefficient matrix and the signs of the right hand side variables this problem was initially formulated in economics due to the idea that the signs of an equation s derivatives might have a stronger empirical basis than that of a particular functional form a new interest in qualitative problems has arisen in connection with the need to develop analytic measures in order to better manage the understanding and use of large computer based mathematical systems the conditions for the qualitative determinancy of nonhomogeneous systems are developed in terms of a small number of necessary conditions which are jointly sufficient algorithmic approaches are given for testing a given system for qualitative determinancy for nonhomogeneous systems algorithms are given for constructing all possible qualitatively determinate systems of a given size for the homogeneous case conditions are also given for the qualitative invertibility of the irreducible coefficient matrix these conditions are then related to the problem of partially qualitatively determinate systems and the signs in the qualitative inverse of a matrix

characterizations of complete residuated lattice valued finite tree automata this paper deals with the concept of complete residuated lattice valued referred to as l valued finite tree automata in this regard we first define an l valued regular tree language and then we prove a necessary and sufficient condition for the regularity of an l valued tree language furthermore we generalize the pumping lemma for l valued finite tree automata l fta afterwards the behavior of l fta is addressed and some theorems are provided moreover the existence of the minimal form of an l fta is considered finally a minimization algorithm of the l fta is presented and its time complexity is analyzed

hardy spaces and the two dimensional euler equations with nonnegative vorticity we prove that certain quadratic expressions involving the gradient of a weakly superharmonic function in r belong to a local hardy space as an application we provide a new proof of j m delort s convergence theorem for solutions of the two dimensional euler equations with vorticities of one sign department of mathematics university of california berkeley california 94720 sfb 256 institut fur angewandte mathematik beringstrasse 4 d5300 bonn 1 ger many this content downloaded from 207 46 13 101 on sat 08 oct 2016 05 44 35 utc all use subject to http about jstor org terms

vortex sheets with reflection symmetry in exterior domains abstract in this paper we prove the existence of a weak solution of the incompressible 2d euler equations in the exterior of a reflection symmetric smooth bluff body with symmetric initial flow corresponding to vortex sheet type data whose vorticity is of distinguished sign on each side of the symmetry axis this work extends the results proved for full plane flow by the authors in m c lopes filho h j nussenzveig lopes z xin existence of vortex sheets with reflection symmetry in two space dimensions arch ration mech anal 158 3 2001 235 257

algebras of fuzzy sets in this paper we investigate two kinds of algebras of fuzzy sets which are obtained by using zadeh s extension principle we give conditions under which a homomorphism between two algebras induces a homomorphism between corresponding algebras of fuzzy sets we prove that if the structure of truth values is a complete residuated lattice the induced algebra of a subalgebra of an algebra a can be embedded into the induced algebra of fuzzy sets of a for direct products we give conditions under which the direct product of algebras of fuzzy sets could be embedded into the algebra of fuzzy sets of the direct product in the case of homomorphisms and direct products the two kinds of algebras of fuzzy sets behave in different ways

on the recognition of s systems abstract a sequence a1 an of nonempty subsets of r m is an s system if for each choice of a1 a1 an an the nullspace of the matrix a1 an is a line that penetrates the strictly positive orthant of r n for the case in which each aj is a sign cone s systems are basic to the study of the sign solvability of systems of linear equations in that case they can be recognized in time o m2 the present paper provides several characterizations of general s systems and describes a polynomial time algorithm based on linear programming for the recognition of such systems when the aj are arbitrary finitely presented convex cones

a criterion for the equivalence of the birkhoff rott and euler descriptions of vortex sheet evolution in this article we consider the evolution of vortex sheets in the plane both as a weak solution of the two dimensional incompressible euler equations and as a weak solution of the birkhoff rott equations we begin by discussing the classical birkhoff rott equations with respect to arbitrary parametrizations of the sheet we introduce a notion of weak solution to the birkhoff rott system and we prove consistency of this notion with the classical formulation of the equations our main purpose in this paper is to present a sharp criterion for the equivalence of the weak euler and weak birkhoff rott descriptions of vortex sheet dynamics

linear stability of compressible vortex sheets in two dimensional elastodynamics abstract the linear stability of rectilinear compressible vortex sheets is studied for two dimensional isentropic elastic flows this problem has a free boundary and the boundary is characteristic a necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets more precisely it is shown that besides the stable supersonic zone the elasticity exerts an additional stable subsonic zone we also find that there is a class of states in the interior of subsonic zone where the stability of such states is weaker than the stability of other states in the sense that there is an extra loss of tangential derivatives with respect to the source terms this is a new feature that the euler flow does not possess one of the difficulties for the elastic flow is that the non differentiable points of the eigenvalues may coincide with the roots of the lopatinskii determinant as a result the kreiss symmetrization cannot be applied directly instead we perform an upper triangularization of the system to separate only the outgoing modes at all points in the frequency space so that an exact estimate of the outgoing modes can be obtained moreover all the outgoing modes are shown to be zero due to the l 2 regularity of solutions the estimates for the incoming modes can be derived directly from the lopatinskii determinant this new approach avoids the lengthy computation and estimates for the outgoing modes when kreiss symmetrization is applied this method can also be applied to the euler flow and mhd flow

pointwise blow up of sequences bounded in l1 abstract given a sequence of functions bounded in l1 0 1 is it possible to extract a subsequence that is pointwise bounded almost everywhere the main objective of this note is to present an example showing that this is not possible in general we will also prove a pair of positive results we show that if the sequence of functions consists of multiples of characteristic functions of measurable sets the answer is yes we also show that it is always possible to extract a subsequence that is pointwise bounded on a countable dense set of points

fuzzy tree language recognizability a fuzzy tree language with membership grades in an arbitrary set is syntactically recognizable s recognizable if its syntactic algebra is finite the equality problem for such languages is decidable and their syntactic algebra can be effectively constructed provided that they are s recognizable linear but non arbitrary tree homomorphisms preserve s recognizability tree automata whose transitions are weighted over the unit interval and whose behavior is computed with respect to a pair made of a t norm distributive over a t conorm have the syntactic recognition power and thus their equivalence problem is decidable however s recognizability is more powerful when dealing with non distributive pairs of such operations

large time behavior for vortex evolution in the half plane in this article we study the long time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering our main result is that certain asymptotic states for half plane vortex dynamics decompose naturally into a nonlinear superposition of soliton like states our approach is to combine techniques developed in the study of vortex confinement with weak convergence tools in order to study the asymptotic behavior of a self similar rescaling of a solution of the incompressible 2d euler equations on a half plane with compactly supported nonnegative initial vorticity

existence of vortex sheets with reflection symmetry in two space dimensions the main purpose of this work is to establish the existence of a weak solution to the incompressible 2d euler equations with initial vorticity consisting of a radon measure with distinguished sign in h 1 compactly supported in the closed right half plane superimposed on its odd reflection in the left half plane we make use of a new a priori estimate to control the interaction between positive and negative vorticity at the symmetry axis we prove that a weak limit of a sequence of approximations obtained by either regularizing the initial data or by using the vanishing viscosity method is a weak solution of the incompressible 2d euler equations we also establish the equivalence at the level of weak solutions between mirror symmetric flows in the full plane and flows in the half plane finally we extend our existence result to odd l 1 perturbations without distinguished sign of our original initial vorticity

infinite fuzzy computations we consider buchi automata weighted over the fuzzy semiring f 0 1 max min 0 1 a buchi theorem for the class of w recognizable series with coefficients in f i e for behaviors of buchi automata over f is established furthermore we show that an infinitary language is buchi recognizable iff its characteristic series is w recognizable

reduced hausdorff dimension and concentration cancellation for two dimensional incompressible flow where v t v1 v2 is the fluid velocity p is the scalar pressure dv dt av at v v v and vo is an initial incompressible velocity field i e div vo 0 in this paper we study the detailed limiting behavior of approximate solution sequences for 2 d euler with vortex sheet initial data a sequence of smooth velocity fields v8 x t is an approximate solution sequence for 2 d euler provided that v is incompressible i e div v 0 and satisfies the following properties 1 the velocity fields v6 have uniformly bounded local kinetic energy i e

existence and uniqueness of global solution of the hasegawa mima equation the hasegawa mima equation is the simplest nonlinear model to investigate drift waves and drift wave turbulence in this article we establish the existence and uniqueness of a global weak solution for the cauchy problem of the two dimensional hasegawa mima equation moreover if the background particle density is homogeneous in the x direction there is a unique global regular solution

syntactic recognizability of graphs with fuzzy attributes abstract we present a syntactic recognition theory for graphs with fuzzy edges and fuzzy nodes by employing the algebraic structure of magmoids several examples are illustrated and it is proved that the cut of a recognizable set of fuzzy graphs is not always recognizable as a set of crisp graphs the described theory is then applied for the recognition of fuzzy cognitive maps and the recognizability of interesting examples of sets of fuzzy cognitive maps is examined

nondeterministic fuzzy automata to handle fuzzy uncertainty in system modeling nondeterministic finite automata have been generalized into fuzzy automata after a reexamination of the notions of fuzzy automata in the literature we ascertain that the fundamental property nondeterminism in nondeterministic finite automata has not been well embodied in the generalization in order to reflect nondeterminism in fuzzy automata we introduce nondeterministic fuzzy automata with or without e moves and fuzzy languages recognized by them like nondeterministic finite automata nondeterministic fuzzy automata provide a mathematical representation of nondeterministic dynamic fuzzy systems moreover we show that deterministic fuzzy automata nondeterministic fuzzy automata and nondeterministic fuzzy automata with e moves are all equivalent in the sense that they recognize the same class of fuzzy languages which is an extension of the well known equivalence among finite automata nondeterministic finite automata and nondeterministic finite automata with e moves

qualitative comparative statics and audits of model performance abstract it is often difficult to determine if large computer based models actually conform to the mathematical descriptions given in their documentation one way to study this problem is through a sensitivity or comparative statics analysis of the model at issue is the degree to which characteristics of the jacobian matrix associated with a solution to the model can be shown to imply characteristics of the inverse jacobian matrix any necessary characteristics of the inverse jacobian can be tested for via comparative statics sign nonsingularity of the jacobian provides an opportunity to audit a model s mathematical documentation through a comparative statics analysis prototype software was developed that tested for sign nonsingularity and applied to the jacobian matrix corresponding to the u s department of energy s oil market simulation model it was found that the signs of all of the elements of the inverse jacobian matrix could be found this

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

a remark on vorticity maximal function in this note the following inequality is proved for any nonnegative measure h 1 r2 x r2 and 0 r 1 there holds 1 b x r c ln1r 12 h 1 where c is a positive constant using 1 an estimate for the vorticity maximal function similar to the estimate in majda a majda remarks on weak solutions for vortex sheets with a distinguished sign indiana univ math j 42 1993 921 939 is established without assuming the initial vorticity having compact support from this a more simple proof of the delort s celebrated theorem j m delort existence de mappes de fourbillon en dimension deux j amer math soc 4 1991 553 586 is presented

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

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