the steady state collision of two compressible subsonic perfect flows abstract this paper is devoted to the mathematical theory for the steady state collision of two compressible subsonic irrotational flows issuing from two infinitely long nozzles we established the existence uniqueness and asymptotic behavior of the subsonic collision flow with a smooth interface for the steady euler system in an important physical regime more precisely there exists a critical value if the summation of the incoming mass fluxes in the inlets of the nozzles is less than the critical value then there exists a unique smooth subsonic compressible collision flow and furthermore there exists a smooth interface which separates the two non miscible compressible subsonic flows in particular a key observation is that the location of the interface can be determined uniquely by the incoming mass fluxes in the inlets of the nozzles finally we showed some monotonic relationship between the location of the interface and the incoming mass fluxes

a harmonic retrieval framework for discontinuous motion estimation motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities in this paper we show that discontinuous or multiple motion estimation can be viewed as a multicomponent harmonic retrieval problem from this viewpoint a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous or multiple motion compared with existing techniques the resulting algorithm is not iterative which not only implies computational efficiency but also obviates concerns regarding convergence or local minima it also adds flexibility to spatio temporal techniques which have suffered from lack of explicit modeling of discontinuous motion experimental verification of our framework on both synthetic data as well as real image data is provided

a degenerate elliptic problem from subsonic sonic flows in general nozzles abstract this paper deals with two dimensional subsonic sonic potential flows in general nozzles which is governed by a free boundary problem of a quasilinear degenerate elliptic equation for a large class of nozzles it is shown that if the variation rate of the cross section of the nozzle is suitably small there exists a unique subsonic sonic flows in the nozzle such that the sonic curve intersects the upper wall at a fixed point and the velocity of the flow is along the normal direction at the inlet and the sonic curve furthermore the sonic curve of this flow is a free boundary where the flow is singular in the sense that the speed is only holder continuous and the acceleration blows up at the sonic state

motion estimation in the frequency domain using fuzzy c planes clustering a previous work explicitly models the discontinuous motion estimation problem in the frequency domain where the motion parameters are estimated using a harmonic retrieval approach the vertical and horizontal components of the motion are independently estimated from the locations of the peaks of respective periodogram analyses and they are paired to obtain the motion vectors using a procedure proposed by chen giannakis nandhakumar see ieee trans image processing vol 7 p 1242 56 1998 in this paper we present a more efficient method that replaces the motion component pairing task and hence eliminates the problems of the pairing method described by chen et al the method described in this paper uses the fuzzy c planes fcp clustering approach to fit planes to three dimensional 3 d frequency domain data obtained from the peaks of the periodograms experimental results are provided to demonstrate the effectiveness of the proposed method

stability of supersonic contact discontinuity for two dimensional steady compressible euler flows in a finite nozzle abstract in this paper we study the stability of supersonic contact discontinuity for the two dimensional steady compressible euler flows in a finitely long nozzle of varying cross sections we formulate the problem as an initial boundary value problem with the contact discontinuity as a free boundary to deal with the free boundary value problem we employ the lagrangian transformation to straighten the contact discontinuity and then the free boundary value problem becomes a fixed boundary value problem we develop an iteration scheme and establish some novel estimates of solutions for the first order of hyperbolic equations on a cornered domain finally by using the inverse lagrangian transformation and under the assumption that the incoming flows and the nozzle walls are smooth perturbations of the background state we prove that the original free boundary problem admits a unique weak solution which is a small perturbation of the background state and the solution consists of two smooth supersonic flows separated by a smooth contact discontinuity

further improvements of determinization methods for fuzzy finite automata in this paper we provide further improvements of determinization methods for fuzzy finite automata these methods perform better than all previous determinization methods for fuzzy finite automata developed by b lohlavek 3 li and pedrycz 38 ignjatovic et al 25 and jancic et al 33 in the sense that they produce smaller automata while require the same computation time the only exception is the brzozowski type determinization algorithm developed recently by jancic and iric 34 which produces a minimal crisp deterministic fuzzy automaton but the algorithms created here can also be used within the brzozowski type algorithm and improve its performance

fuzzy homomorphisms of algebras in this paper we consider fuzzy relations compatible with algebraic operations which are called fuzzy relational morphisms in particular we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations called uniform fuzzy relational morphisms and those which are partially uniform f functions called fuzzy homomorphisms both uniform fuzzy relations and partially uniform f functions were introduced in a recent paper by us uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras we give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms we establish certain relationships between them and fuzzy congruences and we prove homomorphism and isomorphism theorems concerning them we also point to some applications of uniform fuzzy relational morphisms

uniform fuzzy relations and fuzzy functions in this paper we introduce and study the concepts of a uniform fuzzy relation and a partially uniform f function we give various characterizations and constructions of uniform fuzzy relations and uniform f functions we show that the usual composition of fuzzy relations is not convenient for f functions so we introduce another kind of composition and we establish a mutual correspondence between uniform f functions and fuzzy equivalences we also give some applications of uniform fuzzy relations in approximate reasoning especially in fuzzy control and we show that uniform fuzzy relations are closely related to the defuzzification problem

two dimensional cavity flow in an infinitely long channel with non zero vorticity abstract the main object of this paper is to investigate the well posedness theory of the incompressible inviscid cavity flow in an infinitely long channel the flow is governed by two dimensional incompressible steady euler system the main results read that given a mass flux and a constant vorticity in the inlet of the channel firstly we establish the existence and the uniqueness of the incompressible cavity flow in an infinitely long symmetric channel which contains a smooth free surface detaching at the boundary point of the obstacle secondly some fundamental properties such as the asymptotic behaviors of the cavity flow and the free boundary in the upstream and downstream and the positivity of the horizontal velocity are also obtained finally we show that there does not exist a finite cavity or a cusped cavity in the infinitely long nozzle which gives a positive answer to the conjecture by h villat in 1913 on the non existence of a symmetric finite cusped cavity behind an obstacle

the transonic shock in a nozzle 2 d and 3 d complete euler systems abstract in this paper we study a transonic shock problem for the euler flows through a class of 2 d or 3 d nozzles the nozzle is assumed to be symmetric in the diverging or converging part if the supersonic incoming flow is symmetric near the divergent or convergent part of the nozzle then as indicated in section 147 of r courant k o friedrichs supersonic flow and shock waves interscience publ new york 1948 there exist two constant pressures p 1 and p 2 with p 1 p 2 such that for given constant exit pressure p e p 1 p 2 a symmetric transonic shock exists uniquely in the nozzle and the position and the strength of the shock are completely determined by p e moreover it is shown in this paper that such a transonic shock solution is unique under the restriction that the shock goes through the fixed point at the wall in the multidimensional setting furthermore we establish the global existence stability and the long time asymptotic behavior of an unsteady symmetric transonic shock under the exit pressure p e when the initial unsteady shock lies in the symmetric diverging part of the 2 d or 3 d nozzle on the other hand it is shown that an unsteady symmetric transonic shock is structurally unstable in a global in time sense if it lies in the symmetric converging part of the nozzle

polynomial time algorithms for computing distances of fuzzy transition systems behaviour distances to measure the resemblance of two states in a nondeterministic fuzzy transition system have been proposed recently in literature such a distance defined as a pseudo ultrametric over the state space of the model provides a quantitative analogue of bisimilarity in this paper we focus on the problem of computing these distances we first extend the definition of the pseudo ultrametric by introducing discount such that the discounting factor being equal to 1 captures the original definition we then provide polynomial time algorithms to calculate the behavioural distances in both the non discounted and the discounted setting the algorithm is strongly polynomial in the former case

weak bisimulations for fuzzy automata abstract forward and backward bisimulations have been introduced recently by ciric et al 2012 9 as a means for modeling the equivalence between states of fuzzy automata and approximating the language equivalence as well as for use in the state reduction of fuzzy automata the main aim of the present paper is to introduce two new kinds of bisimulations weak forward and backward bisimulations which provide better approximations of the language equivalence than forward and backward bisimulations and when employed in the state reduction they provide better reductions we give procedures for deciding whether there exist weak forward and backward simulations and bisimulations and for computing the greatest ones whenever they exist using weak bisimulations in conjunction with the concept of a uniform fuzzy relation we determine necessary and sufficient conditions under which two fuzzy automata are weak bisimulation equivalent we also characterize uniform weak backward and forward bisimulations between two fuzzy automata in terms of isomorphisms between their nerode and reverse nerode automata

approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures abstract for the purpose of reducing the number of states of fuzzy automata we study approximate bisimulations of fuzzy automata under fuzzy similarity measures which are induced by residuums of left continuous t norms for a real number 0 1 and a fuzzy similarity measure s we define approximate bisimulation under s between two fuzzy automata and prove that the degree of similarity between them is more than or equal to if there exists an approximate bisimulation between them furthermore we put forward the notion of surjective functional approximate bisimulations between two fuzzy automata under s using the notion of surjective functional approximate bisimulations under s the approximate bisimulations for a fuzzy automaton under s is defined as an equivalence relation with two additional properties according to an approximate bisimulation for a fuzzy automaton an aggregated fuzzy automaton has been constructed and the degree of similarity between them is also more than or equal to it is significant for us to find that there might not possess the greatest approximate bisimulation for a fuzzy automaton and we provide a polynomial time algorithm for computing all maximal approximate bisimulations finally we provide the conditions of the existence of the greatest approximate bisimulation

frequency domain motion estimation using a complex lapped transform a frequency domain algorithm for motion estimation based on overlapped transforms of the image data is developed as an alternative to block matching methods the complex lapped transform clt is first defined by extending the lapped orthogonal transform lot to have complex basis functions the clt basis functions decay smoothly to zero at their end points and overlap by 2 1 when a data sequence is transformed a method for estimating cross correlation functions in the clt domain is developed this forms the basis of a motion estimation algorithm that calculates vectors for overlapping windowed regions of data the overlapping data window used has no block edge discontinuities and results in smoother motion fields furthermore when motion compensation is performed using similar overlapping regions the algorithm gives comparable or smaller prediction errors than standard models using exhaustive search block matching and computational load is lower for larger displacement ranges and block sizes

global subsonic and subsonic sonic flows through infinitely long axially symmetric nozzles abstract in this paper we establish existence of global subsonic and subsonic sonic flows through infinitely long axially symmetric nozzles by combining variational method various elliptic estimates and a compensated compactness method more precisely it is shown that there exist global subsonic flows in nozzles for incoming mass flux less than a critical value moreover uniformly subsonic flows always approach to uniform flows at far fields when nozzle boundaries tend to be flat at far fields and flow angles for axially symmetric flows are uniformly bounded away from 2 finally when the incoming mass flux tends to the critical value subsonic sonic flows exist globally in nozzles in the weak sense by using angle estimate in conjunction with a compensated compactness framework

subsonic non isentropic euler flows with large vorticity in axisymmetric nozzles abstract in this paper we investigate the effects of vorticity for smooth subsonic non isentropic euler flows in infinitely long axisymmetric nozzles it is a sequel to b duan and z luo 2013 13 on non isentropic euler system in 13 the authors obtained the unique existence of a smooth subsonic solution with restriction on the smallness of bernoulli s function in the upstream the smallness assumption is sufficient to prevent the appearance of singularity however it leads that the vorticity is also small the purpose of this paper is to remove such restriction on the smallness of the vorticity

nondeterministic automata equivalence bisimulations and uniform relations in this paper we study the equivalence of nondeterministic automata pairing the concept of a bisimulation with the recently introduced concept of a uniform relation in this symbiosis uniform relations serve as equivalence relations which relate states of two possibly different nondeterministic automata and bisimulations ensure compatibility with the transitions initial and terminal states of these automata we define six types of bisimulations but due to the duality we discuss three of them forward backward forward and weak forward bisimulations for each of these three types of bisimulations we provide a procedure which decides whether there is a bisimulation of this type between two automata and when it exists the same procedure computes the greatest one we also show that there is a uniform forward bisimulation between two automata if and only if the factor automata with respect to the greatest forward bisimulation equivalences on these automata are isomorphic we prove a similar theorem for weak forward bisimulations using the concept of a weak forward isomorphism instead of an isomorphism we also give examples that explain the relationships between the considered types of bisimulations

an improved algorithm for determinization of weighted and fuzzy automata for a given weighted finite automaton over a strong bimonoid we construct its reduced nerode automaton which is crisp deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics we show that the reduced nerode automaton is even smaller than the nerode automaton which was previously used in determinization related to this semantics we determine necessary and sufficient conditions under which the reduced nerode automaton is finite and provide an efficient algorithm which computes the reduced nerode automaton whenever it is finite in determinization of weighted finite automata over semirings and fuzzy finite automata over lattice ordered monoids this algorithm gives smaller crisp deterministic automata than any other known determinization algorithm

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

transonic shock in a nozzle i 2d case in this paper we establish the existence and uniqueness of a transonic shock for the steady flow through a general two dimensional nozzle with variable sections the flow is governed by the inviscid potential equation and is supersonic upstream has no flow boundary conditions on the nozzle walls and an appropriate boundary condition at the exit of the exhaust section the transonic shock is a free boundary dividing two regions of c 1 1 0 flow in the nozzle the potential equation is hyperbolic upstream where the flow is supersonic and elliptic in the downstream subsonic region in particular our results show that there exists a solution to the corresponding free boundary problem such that the equation is always subsonic in the downstream region of the nozzle when the pressure in the exit of the exhaustion section is appropriately larger than that in the entry this problem is motivated by the conjecture of courant and friedrichs on the transonic phenomena in a nozzle 10 furthermore the stability of the transonic shock is also proven when the upstream supersonic flow is a small steady perturbation for the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation the main ingredients of our analysis are a generalized hodograph transformation and multiplier methods for elliptic equation with mixed boundary conditions and comer singularities

backward and forward bisimulation minimization of tree automata we improve on an existing p a abdulla j hogberg l kaati bisimulation minimization of tree automata international journal of foundations of computer science 18 4 2007 699 713 bisimulation minimization algorithm for finite state tree automata by introducing backward and forward bisimulation and developing minimization algorithms for them minimization via forward bisimulation is also effective on deterministic tree automata faster than the previous algorithm and yields the minimal equivalent deterministic tree automaton minimization via backward bisimulation generalizes the previous algorithm and can yield smaller automata but is just as fast we demonstrate implementations of these algorithms on a typical task in natural language processing

finite l fuzzy machines abstract for finite l fuzzy machines we develop behaviour reduction and minimization theory here l stands for l 0 1 where l is a totally ordered set with universal bounds 0 and 1 and the operations are join and meet the most essential results include investigating behaviour equivalence reduction and minimization problems and their algorithmical decidability

automata theory based on complete residuated lattice valued logic reduction and minimization automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by qiu recently in this paper we define a kind of mealy type of l vfas mlfas a generalization of l vfas two kinds of statewise equivalence relations are introduced and a minimal form is defined we study the existence of the minimal form of an mlfa then we show that any two states can be distinguished by some word with finite length also a minimization algorithm of the mlfas is presented in addition we obtain a minimization algorithm for l vfas as well finally we define l valued languages l vls and l valued regular languages l vrls recognized by l vfas and provide some properties of l vrls

two dimensional subsonic euler flows past a wall or a symmetric body the existence and uniqueness of two dimensional steady compressible euler flows past a wall or a symmetric body are established more precisely given positive convex horizontal velocity in the upstream there exists a critical value rho rm cr such that if the incoming density in the upstream is larger than rho rm cr then there exists a subsonic flow past a wall furthermore rho rm cr is critical in the sense that there is no such subsonic flow if the density of the incoming flow is less than rho rm cr the subsonic flows possess large vorticity and positive horizontal velocity above the wall except at the corner points on the boundary moreover the existence and uniqueness of a two dimensional subsonic euler flow past a symmetric body are also obtained when the incoming velocity field is a general small perturbation of a constant velocity field and the density of the incoming flow is larger than a critical value the asymptotic behavior of the flows is obtained with the aid of some integral estimates for the difference between the velocity field and its far field states

computation of the greatest right and left invariant fuzzy quasi orders and fuzzy equivalences abstract right invariant fuzzy quasi orders for fuzzy automata are broadly studied in the recent literature as they arise as solutions to particular systems of fuzzy relation equations and inequalities some of their applications include determinization and state reduction procedures as well as simulations and bisimulations for fuzzy automata in this paper we provide a procedure for computing the greatest right invariant fuzzy quasi order for a given fuzzy automaton over a complete residuated lattice the proposed procedure terminates in a finite number of steps whenever the underlying structure of the fuzzy automaton is locally finite when the previous condition is not satisfied we show that the greatest right invariant fuzzy quasi order can be obtained by taking the limit value of the convergent array of fuzzy quasi orders for fuzzy automata over bl algebras on the real unit interval 0 1 analogous procedures for computing the greatest left invariant fuzzy quasi order as well as the greatest right and left invariant fuzzy equivalences for a fuzzy automaton are also presented in addition the faster algorithm for computing the greatest right invariant equivalence on a nondeterministic automaton is also presented

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

epsilon bisimulation relations for fuzzy automata this paper investigates the approximate bisimulation relations for fuzzy automata in order to study the approximate minimization problem of fuzzy automata for a small positive real number epsilon we introduce the notion of epsilon bisimulation relations between two fuzzy automata and prove that the behavior of a fuzzy automaton a differs by epsilon from the behavior of a fuzzy automaton b under a epsilon bisimulation relation between them also the notion of surjective functional epsilon bisimulation relations between two fuzzy automata is defined according to surjective functional epsilon bisimulation relations we discuss epsilon bisimulation relations for a fuzzy automaton a construction of aggregated fuzzy automaton by the given epsilon bisimulation for a fuzzy automaton is given furthermore we find that there might not exist the greatest epsilon bisimulation relation for a fuzzy automaton and we novelly give an effective algorithm to construct all maximal epsilon bisimulation relations for the given fuzzy automaton finally we point out that bisimulation relations for a fuzzy automaton are also epsilon bisimulation relations the conditions for the real number epsilon to ensure the existence of the greatest epsilon bisimulation are also discussed

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

a theory of vague lattices based on many valued equivalence relations i general representation results the present work introduces a new and general theory of ordering relations and lattices based on many valued equivalence relations under the name vague ordering relations and vague lattices respectively representations and constructions of vague ordering relations and vague lattices are the main subjects of this paper and various desirable results in this direction are established furthermore algebraic characterizations of vague lattices are studied

global subsonic euler flows in an infinitely long axisymmetric nozzle abstract in this paper we consider global subsonic compressible flows through an infinitely long axisymmetric nozzle the flow is governed by the steady euler equations and has boundary conditions on the nozzle walls existence and uniqueness of global subsonic solution are established for an infinitely long axisymmetric nozzle when the variation of bernoulli s function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value the results give a strictly mathematical proof to the assertion in bers 1958 2 there exists a critical value of the incoming mass flux such that a global subsonic flow exists uniquely in a nozzle provided that the incoming mass flux is less than the critical value the existence of subsonic flow is obtained by the precisely a priori estimates for the elliptic equation of two variables with the assumptions on the nozzle in the far fields the asymptotic behavior can be derived by a blow up argument for the infinitely long nozzle finally we obtain the uniqueness of uniformly subsonic flow by energy estimate and derive the existence of the critical value of incoming mass flux

a note on trillas chc models trillas et al e trillas s cubillo e castineira on conjectures in orthocomplemented lattices artificial intelligence 117 2000 255 275 recently proposed a mathematical model for conjectures hypotheses and consequences abbr chcs and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic we demonstrate that the orthomodular condition is not necessary for holding watanabe s structure theorem of hypotheses and indeed in some orthocomplemented but not orthomodular lattices this theorem is still valid we use the chc operators to describe the theorem of deduction the theorem of contradiction and the lindenbaum theorem of classical logic and clarify their existence in the chc models a number of examples is presented and we re define the chc operators in residuated lattices and particularly reveal the essential differences between the chc operators in orthocomplemented lattices and residuated lattices

construction of fuzzy automata from fuzzy regular expressions li and pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice ordered monoid and generalize the well known results of the classical theory of formal languages in particular they have shown that a fuzzy language over an integral lattice ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton however they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression in this paper we provide such an efficient method transforming scalars appearing in a fuzzy regular expression ainto letters of the new extended alphabet we convert the fuzzy regular expression ato an ordinary regular expression a r then starting from an arbitrary nondeterministic finite automaton a that recognizes the language a r represented by the regular expression a r we construct fuzzy finite automata a a and a a r with the same or even less number of states than the automaton a which recognize the fuzzy language a represented by the fuzzy regular expression a the starting nondeterministic finite automaton a can be obtained from a r using any of the well known constructions for converting regular expressions to nondeterministic finite automata such as glushkov mcnaughton yamada s position automaton brzozowski s derivative automaton antimirov s partial derivative automaton or ilie yu s follow automaton

on two dimensional sonic subsonic flow a compensated compactness framework is established for sonic subsonic approximate solutions to the two dimensional euler equations for steady irrotational flows that may contain stagnation points only crude estimates are required for establishing compactness it follows that the set of subsonic irrotational solutions to the euler equations is compact thus flows with sonic points over an obstacle such as an airfoil may be realized as limits of sequences of strictly subsonic flows furthermore sonic subsonic flows may be constructed from approximate solutions the compactness framework is then extended to self similar solutions of the euler equations for unsteady irrotational flows

subsonic sonic limit of approximate solutions to multidimensional steady euler equations a compactness framework is established for approximate solutions to subsonic sonic flows governed by the steady full euler equations for compressible fluids in arbitrary dimension the existing compactness frameworks for the two dimensional irrotational case do not directly apply for the steady full euler equations in higher dimensions the new compactness framework we develop applies for both non homentropic and rotational flows one of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass balance and the vorticity along with the bernoulli law and the entropy relation through a more delicate analysis on the phase space as direct applications we establish two existence theorems for multidimensional subsonic sonic full euler flows through infinitely long nozzles

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

estimation of multiple time varying motions using time frequency representations and moving objects segmentation we extend existing spatiotemporal approaches to handle time varying motions estimation of multiple objects it is shown that multiple time varying motions estimation is equivalent to the instantaneous frequency estimation of superpoliteness fm sinusoids therefore we apply established signal processing tools such as time frequency representations to show that for each time instant the energy is concentrated along planes in the 3 d space spatial frequencies instantaneous frequency using fuzzy c planes we estimate indirectly the instantaneous velocities furthermore adapting existing approaches to our problem we attain the identification of the moving objects the experimental results verify the effectiveness of our methodology

formal power series and regular operations on fuzzy languages in this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet and representation of fuzzy languages by these formal power series this representation generalizes the well known representation of fuzzy languages by their cut and kernel languages we show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages we use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series

multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type we are concerned with the existence and stability of multidimensional transonic shocks for the euler equations for steady potential compressible fluids the euler equations consisting of the conservation law of mass and the bernoulli law for the velocity can be written as the following second order nonlinear equation of mixed elliptic hyperbolic type for the velocity potential r r 1 1 div d d 0 where the density function q is

steady subsonic ideal flows through an infinitely long nozzle with large vorticity in this paper the existence uniqueness and far field behavior of a class of subsonic flows with large vorticity for the steady euler equations in infinitely long nozzles are established more precisely for any given convex horizontal velocity of incoming flow in the upstream there exists a critical value mcr if the mass flux is larger than mcr then there exists a unique smooth subsonic euler flow through the infinitely long nozzle this well posedness result is proved by a new observation for the method developed in xie and xin siam j math anal 42 751 784 2010 to deal with the euler system furthermore the optimal convergence rates of the subsonic flows at far fields are obtained via the maximum principle and an elaborate choice of the comparison functions

automata theory based on complete residuated lattice valued logic turing machines automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by the second author in 2001 in view of the importance of turing machines in this paper we establish a theory of turing machines based on complete residuated lattice valued logic which is a continuation of l vfas first we give the definition of l valued nondeterministic turing machines l ntms and observe that the multitape l ntms have the same language recognizing power as the single tape l ntms we give some related properties of l valued turing machines and discuss computing with fuzzy letters via l valued turing machines second we introduce the concepts of l valued recursively enumerable languages and l valued recursive languages and obtain some equivalent relations some results concerning the characterization of n recursively enumerable sets are given and the super computing power of l valued turing machines is investigated we also prove that l valued deterministic turing machines and l ntms are not equivalent in the sense of recognizing or deciding languages finally we show that there is no universal l valued turing machine however a universal l valued turing machine exists if the membership degrees of l valued sets are restricted to a finite complete residuated lattice with universal bounds 0 and 1

existence of steady subsonic euler flows through infinitely long periodic nozzles abstract in this paper we study the global existence of steady subsonic euler flows through infinitely long nozzles which are periodic in x 1 direction with the period l it is shown that when the variation of bernoulli function at some given section is small and mass flux is in a suitable regime there exists a unique global subsonic flow in the nozzle furthermore the flow is also periodic in x 1 direction with the period l if in particular the bernoulli function is a constant we also get the existence of subsonic sonic flows when the mass flux takes the critical value

on a degenerate free boundary problem and continuous subsonic sonic flows in a convergent nozzle this paper concerns the well posedness of a boundary value problem for a quasilinear second order elliptic equation which is degenerate on a free boundary such problems arise when studying continuous subsonic sonic flows in a convergent nozzle with straight solid walls it is shown that for a given inlet being a perturbation of an arc centered at the vertex of the nozzle and a given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc there is a unique continuous subsonic sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet and the given incoming mass flux furthermore the sonic curve of this continuous subsonic sonic flow is a free boundary where the flow is singular in the sense that while the speed is c1 2 holder continuous at the sonic state the acceleration blows up at the sonic state

on incompressible oblique impinging jet flows abstract the object of this work is to investigate the fluid mechanics of oblique impinging jet flows and to this end some existence and nonexistence results are initiated first we established the existence of incompressible oblique impinging jet plane flows with two asymptotic directions more precisely given a two dimensional semi infinitely long nozzle and a wall behind the nozzle for any given mass flux in the inlet of the nozzle then there exists a smooth incompressible oblique impinging jet flow with two asymptotic directions the impinging jet develops two free streamlines which initiate smoothly at the endpoints of the semi infinitely long nozzle and the speed on free streamlines remains a constant which can be determined by the impinging jet flow itself the asymptotic behaviors of the oblique impinging jet flows at the far fields the position of the stagnation points convexity of the free boundaries and other properties are also considered on another side it is showed in this paper that there does not exist an oblique impinging jet flow with one asymptotic direction generally

three dimensional full euler flows in axisymmetric nozzles abstract in this paper we consider global subsonic compressible flows through general infinitely long nozzles the flow is governed by the steady full euler equations we find a new invariant along streamline take advantages of this we reformulate the full euler system into quasilinear second order equations of stream function with the upstream condition and the solid wall boundary condition we obtain the existence uniqueness asymptotic behavior and the critical mass flux

transonic shocks for the full compressible euler system in a general two dimensional de laval nozzle in this paper we study the transonic shock problem for the full compressible euler system in a general two dimensional de laval nozzle as proposed in courant and friedrichs supersonic flow and shock waves interscience new york 1948 given the appropriately large exit pressure pe x if the upstream flow is still supersonic behind the throat of the nozzle then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes pe x we solve this problem completely for a general class of de laval nozzles whose divergent parts are small and arbitrary perturbations of divergent angular domains for the full steady compressible euler system the problem can be reduced to solve a nonlinear free boundary value problem for a mixed hyperbolic elliptic system one of the key ingredients in the analysis is to solve a nonlinear free boundary value problem in a weighted holder space with low regularities for a second order quasilinear elliptic equation with a free parameter the position of the shock curve at one wall of the nozzle and non local terms involving the trace on the shock of the first order derivatives of the unknown function

estimation of multiple accelerated motions using chirp fourier transform and clustering motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed which however cannot handle both time varying and multiple motions extending previously published ideas we present an efficient method for estimating multiple linearly time varying motions it is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals from this viewpoint one can exploit established signal processing tools such as the chirp fourier transform it is shown that accelerated motion results in energy concentration along planes in the 4 d space spatial frequencies temporal frequency chirp rate using fuzzy c planes clustering we estimate the plane motion parameters the effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted

bisimulations for fuzzy transition systems there has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems however the comparison at this level is too coarse recently a finer behavioral measure i e bisimulation has been introduced to fuzzy finite automata however the results obtained are applicable only to finite state systems in this paper we consider bisimulation for general fuzzy systems which may be infinite state or infinite event by modeling them as fuzzy transition systems ftss to help understand and check bisimulation we characterize it in three ways by enumerating whole transitions comparing individual transitions and using a monotonic function in addition we address composition operations subsystems quotients and homomorphisms of ftss and discuss their properties connected with bisimulation the results presented here are useful to compare the behavior of general fuzzy systems in particular this makes it possible to relate an infinite fuzzy system to a finite one which is easier to analyze with the same behavior

weakly linear systems of fuzzy relation inequalities the heterogeneous case new types of systems of fuzzy relation inequalities and equations called weakly linear have been recently introduced in j ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 the mentioned paper dealt with homogeneous weakly linear systems composed of fuzzy relations on a single set and a method for computing their greatest solutions has been provided this method is based on the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations here we adapt this method for computing the greatest solutions of heterogeneous weakly linear systems where the unknown fuzzy relation relates two possibly different sets we also introduce and study quotient fuzzy relational systems and establish relationships between solutions to heterogeneous and homogeneous weakly linear systems besides we point out to applications of the obtained results in the state reduction of fuzzy automata and computing the greatest simulations and bisimulations between fuzzy automata as well as in the positional analysis of fuzzy social networks

three dimensional steady subsonic euler flows in bounded nozzles abstract the existence and uniqueness of three dimensional steady subsonic euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit if in addition the normal component of the voriticity and the variation of bernoulli s function at the entrance are both zero then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number as the magnitude of the normal component of the momentum approaches the critical number the associated flows converge to a subsonic sonic flow furthermore when the normal component of vorticity and the variation of bernoulli function are both small the existence and uniqueness of subsonic euler flows with non zero vorticity are established the proof of these results is based on a new formulation for the euler system a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions detailed study for a linear div curl system and delicate estimate for the transport equations

low mach number limit of steady flows through infinite multidimensional largely open nozzles abstract in this paper we justify of the low mach number limit of the steady irrotational euler flow through infinite multidimensional largely open nozzles firstly the existence and uniqueness of the incompressible flow are proved then the uniform estimates on the compressibility parameter e which is singular for the flows are established via a variational approach based on the compressible incompressible difference functions the limit is in the holder space and is unique moreover the convergence rate is of order e 2 including the pressure and for the compressible case the extra force influences the asymptotic behaver to the open end while the effect vanishes in the limiting process from compressible flows to the incompressible ones also for the compressible flows with general conservative forces the well posedness of subsonic solution are given which leads to the existence of subsonic sonic limit solutions

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

reduction of fuzzy automata by means of fuzzy quasi orders abstract in our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations in that paper we have also studied reductions by means of those solutions which are fuzzy equivalences in this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi orders generally fuzzy quasi orders and fuzzy equivalences are equally good in the state reduction but we show that right and left invariant fuzzy quasi orders give better reductions than right and left invariant fuzzy equivalences we also show that alternate reductions by means of fuzzy quasi orders give better results than alternate reductions by means of fuzzy equivalences furthermore we study a more general type of fuzzy quasi orders weakly right and left invariant ones and we show that they are closely related to determinization of fuzzy automatons we also demonstrate some applications of weakly left invariant fuzzy quasi orders in conflict analysis of fuzzy discrete event systems

a behavioral distance for fuzzy transition systems in contrast with the existing approaches to exact bisimulation for fuzzy systems we introduce a robust notion of behavioral distance to measure the behavioral similarity of nondeterministic fuzzy transition systems which are a generalization of fuzzy automata this behavioral distance provides a quantitative analogue of bisimilarity and is defined as the greatest fixed point of a suitable monotonic function the behavioral distance has the important property that two systems are at zero distance if and only if they are bisimilar moreover for any given threshold we find that systems with behavioral distances bounded by the threshold are equivalent in addition we show that two system combinators parallel composition and product are nonexpansive with respect to our behavioral distance which makes compositional verification possible the theory developed here is applicable to the quantitative verification approximate reduction and reliability analysis of fuzzy transition systems

steady euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles abstract we establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets entropy waves for the steady euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles we first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity or the bernoulli and entropy functions at the inlet for the smooth case then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets entropy waves by nonlinear arguments this is the first result on the global existence of solutions of the multidimensional steady compressible full euler equations with free boundaries which are not necessarily small perturbations of piecewise constant background solutions the subsonic sonic limit of the solutions is also shown finally through the incompressible limit we establish the existence and uniqueness of incompressible euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets the methods and techniques developed here will be useful for solving other problems involving similar difficulties

bisimulations for fuzzy automata bisimulations have been widely used in many areas of computer science to model equivalence between various systems and to reduce the number of states of these systems whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata we prove that a uniform fuzzy relation between fuzzy automata a and b is a forward bisimulation if and only if its kernel and co kernel are forward bisimulation fuzzy equivalence relations on a and b and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalence relations as a consequence we get that fuzzy automata a and b are ufb equivalent i e there is a uniform forward bisimulation between them if and only if there is a special isomorphism between the factor fuzzy automata of a and b with respect to their greatest forward bisimulation fuzzy equivalence relations this result reduces the problem of testing ufb equivalence to the problem of testing isomorphism of fuzzy automata which is closely related to the well known graph isomorphism problem we prove some similar results for backward forward bisimulations and we point to fundamental differences because of the duality with the studied concepts backward and forward backward bisimulations are not considered separately finally we give a comprehensive overview of various concepts on deterministic nondeterministic fuzzy and weighted automata which are related to bisimulations

fuzzy ϵ approximate regular languages and minimal deterministic fuzzy automata ϵ accepting them abstract in this paper for a real number 0 1 we put forward the notion of fuzzy approximate regular languages and study their properties especially the pumping lemma in the context of this kind of languages by comparing sets of fuzzy approximate regular languages under the order of set inclusion we get an infinite hierarchy of fuzzy languages the smallest is the set of fuzzy regular languages and the biggest is the set of fuzzy languages and the sets of approximate regular languages are different for different 0 1 2 we also investigate whether operations closed in the set of fuzzy regular languages are still closed in the set of fuzzy approximate regular languages furthermore for a fuzzy approximate regular language f approximate equivalence relations for f are characterized in order to construct deterministic fuzzy automata accepting f if a fuzzy approximate regular language f is also a fuzzy regular language and accepted by a given accessible deterministic fuzzy automaton a then we give a polynomial time algorithm to construct at least one minimal deterministic fuzzy automaton accepting f by means of a finally we point out that the number of states of minimal deterministic fuzzy automata accepting a fuzzy regular language is smaller than or equal to that of minimal deterministic fuzzy automata accepting this language

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

contact discontinuities for 3 d axisymmetric inviscid compressible flows in infinitely long cylinders abstract we prove the existence of a subsonic axisymmetric weak solution u p with u u x e x u r e r u e to steady euler system in a three dimensional infinitely long cylinder n when prescribing the values of the entropy p and angular momentum density r u at the entrance by piecewise c 2 functions with a discontinuity on a curve on the entrance of n due to the variable entropy and angular momentum density swirl conditions with a discontinuity at the entrance the corresponding solution has a nonzero vorticity nonzero swirl and contains a contact discontinuity r g d x we construct such a solution via helmholtz decomposition the key step is to decompose the rankine hugoniot conditions on the contact discontinuity via helmholtz decomposition so that the compactness of approximated solutions can be achieved then we apply the method of iteration to obtain a solution and analyze the asymptotic behavior of the solution at far field

detection and characterization of cluster substructure ii fuzzy c varieties and convex combinations thereof in part i siam j appl math 40 1981 pp 339 357 fuzzy c lines was introduced as an algorithm for detection and characterization of linearly clustered data in part ii we address two extensions of the theory in part i specifically we will first generalize the straight line prototype of a cluster developed in part i to any r dimensional linear variety of r s 0 leqq r s secondly we will consider a distance functional which utilizes convex combinations of the distance functionals developed here and in part i all of the notation and symbols used here are unchanged from part i

bisimulation relations for weighted automata bisimulation is a well known equivalence relation for discrete event systems and has been extended to probabilistic and stochastic systems this paper introduces a general definition of bisimulation which can be applied to finite automata where weights and labels are assigned to transitions it is shown that this general view contains several known bisimulations as special cases and defines naturally equivalences for different classes of models apart from the well known forward bisimulation also backward bisimulation is introduced and it is shown that both types of bisimulation preserve different types of results furthermore it is shown that forward and backward bisimulation are congruences according to commonly known composition operations for automata

estimation of time varying velocities of moving objects by time frequency representations an approach to the estimation of motion parameters of moving objects in a video sequence by using the slide subspace based line detection algorithm algorithm is considered the proposed procedure projects video frames to the coordinate axes in order to obtain synthetic images containing information about the motion parameters these synthetic images are mapped to the fm signals by using constant spl mu propagation the problem of velocity estimation is reduced to the instantaneous frequency if estimation if estimators based on time frequency tf representations are used three tf representations spectrogram spec wigner distribution wd and s method sm are used and compared to this aim a tradeoff between concentration of the tf representation velocity estimation accuracy and reduction of the cross terms possibility for estimation of the multiple objects parameters is achieved by the sm a performance analysis of the algorithm is done theoretical results are illustrated on several numerical examples

subsonic flows in a multi dimensional nozzle in this paper we study the global subsonic irrotational flows in a multi dimensional n 2 infinitely long nozzle with variable cross sections the flow is described by the inviscid potential equation which is a second order quasilinear elliptic equation when the flow is subsonic first we prove the existence of the global uniformly subsonic flow in a general infinitely long nozzle for arbitrary dimension with sufficiently small incoming mass flux and obtain the uniqueness of the global uniformly subsonic flow then we show that there exists a critical value of the incoming mass flux such that a global uniformly subsonic flow exists uniquely provided that the incoming mass flux is less than the critical value this gives a positive answer to the problem of bers on global subsonic irrotational flows in infinitely long nozzles for arbitrary dimension bers in surveys in applied mathematics vol 3 wiley new york 1958 finally under suitable asymptotic assumptions of the nozzle we obtain the asymptotic behavior of the subsonic flow in far fields by means of a blow up argument the main ingredients of our analysis are methods of calculus of variations the moser iteration techniques for the potential equation and a blow up argument for infinitely long nozzles

computation of the greatest simulations and bisimulations between fuzzy automata recently two types of simulations forward and backward simulations and four types of bisimulations forward backward forward backward and backward forward bisimulations between fuzzy automata have been introduced if there is at least one simulation bisimulation of some of these types between the given fuzzy automata it has been proved that there is the greatest simulation bisimulation of this kind in the present paper for any of the above mentioned types of simulations bisimulations we provide an efficient algorithm for deciding whether there is a simulation bisimulation of this type between the given fuzzy automata and for computing the greatest one whenever it exists the algorithms are based on the method developed in ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 which comes down to the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations

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

detection and characterization of cluster substructure i linear structure fuzzy c lines in part i a generalization of the fuzzy c means or fuzzy isodata clustering algorithms is developed necessary conditions for minimization of a generalized total weighted squared orthogonal error objective function lead to a picard iteration scheme which generates simultaneously i c fuzzy clusters in the data ii a set of c prototypical straight lines in feature space which best fit the data in a well defined sense iii a set of c prototpyical centers of mass on the c lines which characterize the core of each linear fuzzy cluster theoretical optimization is achieved using principal components of generalized within cluster fuzzy scatter matrices a convergence theorem for each algorithm in the infinite family is given the algorithms are exemplified by five numerical examples using both real and artificial data sets having essentially linear substructure in part ii the fuzzy c means and fuzzy c lines algorithms are shown to be special cases of a more general class of fuzzy algorithms the

on a degenerate mixed type boundary value problem to the 2 d steady euler equation abstract this paper is concerned with the structure of sonic supersonic solutions near sonic curves arising from the transonic channel flow problems in gas dynamics given two smooth curves one of which is a sonic curve and the other is a characteristic curve we construct a local classical supersonic solution for the two dimensional steady euler equations in the angular region a novel set of dependent and independent variables are introduced to transform the euler equations into a linear system with explicitly singularity regularity structures we use the iteration method to establish the existence and uniqueness of smooth solutions for the new system and then express the solution in terms of the original variables

steady compressible subsonic impinging flows with non zero vorticity abstract a well posedness analysis of steady state of inviscid compressible subsonic impinging flows with non zero vorticity is developed a nonlinear nonhomogeneous second order partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow specifying the horizontal velocity we first construct a subsonic solution to the impinging flow problem with special horizontal velocity and specific effluent fluxes in the outlets moreover we showed that such a subsonic impinging flow with the same asymptotic behavior in the upstream and downstreams is unique furthermore the existence uniqueness and regularity of the interface separating the two fluids with different outlets are obtained this result extends the recent result on the compressible subsonic irrotational impinging flows in 5 finally as a byproduct we obtain the existence of subsonic sonic impinging flows

existence and optimal convergence rates of multi dimensional subsonic potential flows through an infinitely long nozzle with an obstacle inside in this paper the well posedness and optimal convergence rates of subsonic irrotational flows through a three dimensional infinitely long nozzle with a smooth obstacle inside are established more precisely the global existence and uniqueness of the uniformly subsonic flow are obtained via variational formulation as long as the incoming mass flux is less than a critical value furthermore with the aid of delicate choice of weight functions we prove the optimal convergence rates of the flow at far fields via weighted energy estimates and nash moser iteration

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

characterizations of fuzzy finite automata in this paper we establish some important concepts in fuzzy finite automata ffas with bifuzzy property and clarify their essential relationships first we present a number of basic definitions and properties in ffas we then define a bifuzzy family of subautomata bifuzzy source and successor operators as well as demonstrate the bifuzzy topological characterization of ffas also we clarify the relationships between our results and previous ones and thus derive a relation figure visualizing their connections afterwards we investigate further the bifuzzy separability retrievability and homomorphism fuzzy continuous mapping and open mapping are also incorporated in particular we prove a number of equivalent characterizations for these concepts and expound the relationships amongst them this also concludes that both the bifuzzy source and successor operators are fuzzy closure operators we discover that our investigation generalizes to some extent the algebraic fuzzy automata elaborated by malik mordeson and others finally the main results obtained are summarized the potential applications are indicated and a number of related problems for further study are addressed

transonic shocks in compressible flow passing a duct for three dimensional euler systems in this paper we study the transonic shock in steady compressible flow passing a duct the flow is a given supersonic one at the entrance of the duct and becomes subsonic across a shock front which passes through a given point on the wall of the duct the flow is governed by the three dimensional steady full euler system which is purely hyperbolic ahead of the shock and is of elliptic hyperbolic composed type behind the shock the upstream flow is a uniform supersonic one with the addition of a three dimensional perturbation while the pressure of the downstream flow at the exit of the duct is assigned apart from a constant difference the problem of determining the transonic shock and the flow behind the shock is reduced to a free boundary value problem in order to solve the free boundary problem of the elliptic hyperbolic system one crucial point is to decompose the whole system to a canonical form in which the elliptic part and the hyperbolic part are separated at the level of the principal part due to the complexity of the characteristic varieties for the three dimensional euler system the calculus of symbols is employed to complete the decomposition the new ingredient of our analysis also contains the process of determining the shock front governed by a pair of partial differential equations which are coupled with the three dimensional euler system