fault detection and isolation based on fuzzy automata fuzzy automata are proposed for fault diagnosis the output of the monitored system is partitioned into linear segments which in turn are assigned to pattern classes templates with the use of membership functions a sequence of templates is generated and becomes input to fuzzy automata which have transitions that correspond to the templates of the properly functioning system if the automata reach their final states i e the input sequence is accepted by the automata with a membership degree that exceeds a certain threshold then normal operation is deduced otherwise a failure is diagnosed fault diagnosis of a dc motor and detection of abnormalities in the ecg signal are used as case studies

marching on in degree solver of time domain finite element boundary integral method for transient electromagnetic analysis a marching on in degree solver of time domain finite element boundary integral method is proposed for the analysis of transient electromagnetic scattering from inhomogeneous objects weighted laguerre polynomials are employed as temporal basis functions and testing functions in the proposed algorithm which leads to a recursive matrix equation without time variable and it can be solved degree by degree then the time domain response can be obtained by post processing furthermore a hybrid algorithm using both direct method and iterative method is introduced to accelerate the convergence in the solving of matrix equation numerical results are presented to demonstrate the accuracy stability and effectiveness of the proposed method

electromagnetic scattering from 3 d curved dielectric bodies using time domain integral equations a boundary integral equation bie approach is developed to calculate transient scattering from dielectric bodies the treatment is directly in terms of the e and h fields rather than magnetic and electric currents it employs curvilinear quadratic modeling which allows accurate representation of arbitrarily shaped curved bodies the treatment is isoparametric with the same quadratic representation of the spatial field variation and with the temporal variation modeled by similar quadratic elements integration employs high order gaussian quadrature with special treatment of the singular and hypersingular integrals that arise the treatment is implicit requiring the solution of a sparse matrix equation at each timestep this adds only trivially to the cost at each timestep and by freeing the timestep from the constraint that it be smaller than the smallest nodal spacing can greatly reduce the number of timesteps that must be employed additionally it produces stable results without resort to the averaging processes proposed elsewhere example calculations of scattering from a sphere a cube and an almond are presented and compared with earlier published transient results and with results from a frequency domain treatment good agreement and improved accuracy is found

numerical solution of the space fractional fokker planck equation the traditional second order fokker planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of brownian motion densities of stable type have been used to describe the probability distribution of these motions the resulting governing equation of these motions is similar to the traditional fokker planck equation except that the order of the highest derivative is fractional in this paper a space fractional fokker planck equation sffpe with instantaneous source is considered a numerical scheme for solving sffpe is presented using the riemann liouville and grunwald letnikov definitions of fractional derivatives the sffpe is transformed into a system of ordinary differential equations ode then the ode system is solved by a method of lines numerical results for sffpe with a constant diffusion coefficient are evaluated for comparison with the known analytical solution the numerical approximation of sffpe with a time dependent diffusion coefficient is also used to simulate levy motion with stable densities we will show that the numerical method of sffpe is able to more accurately model these heavy tailed motions

diagnosability of fuzzy discrete event systems in this paper discrete event systems dess are reformulated as fuzzy discrete event systems fdess and fuzzy discrete event dynamical systems fdedss these frameworks include fuzzy states events and if then rules in these frameworks all events occur at the same time with different membership degrees fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems such as fault diagnosis applications to measure a diagnoser s fault discrimination ability a fuzzy diagnosability degree is proposed if the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system for any degree less than one researchers should not devote their time to distinguish all possible fault types correctly thus two different diagnosability definitions fdeds and fdes are introduced due to the specialized fuzzy rule base embedded in the fdeds it is capable of representing a class of non linear dynamic system computationally speaking the framework of diagnosability of the fdeds is structurally similar to the framework of diagnosability of a non linear system the crisp des diagnosability has been turned into the term fuzzy diagnosability for the fdes the newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non linear systems in addition a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development finally the potential applications of the proposed method are discussed

diagnosability of stochastic discrete event systems we investigate diagnosability of stochastic discrete event systems we define the notions of a and aa diagnosability for stochastic automata these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by sampath et al through the construction of a stochastic diagnoser we determine offline conditions necessary and sufficient to guarantee a diagnosability and sufficient to guarantee aa diagnosability we also show how the stochastic diagnoser can be used for on line diagnosis of failure events we illustrate the results through two examples from hvac systems

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

finite difference methods for two dimensional fractional dispersion equation fractional order partial differential equations as generalizations of classical integer order partial differential equations are increasingly used to model problems in fluid flow finance and other areas of application in this paper we discuss a practical alternating directions implicit method to solve a class of two dimensional initial boundary value fractional partial differential equations with variable coefficients on a finite domain first order consistency unconditional stability and therefore first order convergence of the method are proven using a novel shifted version of the classical grunwald finite difference approximation for the fractional derivatives a numerical example with known exact solution is also presented and the behavior of the error is examined to verify the order of convergence

an ellam scheme for advection diffusion equations in two dimensions we develop an eulerian lagrangian localized adjoint method ellam to solve two dimensional advection diffusion equations with all combinations of inflow and outflow dirichlet neumann and flux boundary conditions the ellam formalism provides a systematic framework for implementation of general boundary conditions leading to mass conservative numerical schemes the computational advantages of the ellam approximation have been demonstrated for a number of one dimensional transport systems practical implementations of ellam schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper extensive numerical results are presented to compare the ellam scheme with many widely used numerical methods and to demonstrate the strength of the ellam scheme

numerical approximation of a time dependent nonlinear space fractional diffusion equation in this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a nonlocal quadratic nonlinearity the analysis is performed for a general fractional order diffusion operator the nonlinear term studied is a product of the unknown function and a convolution operator of order 0 convergence of the approximation and a priori error estimates are given numerical computations are included which confirm the theoretical predictions

fuzzy automata with fuzzy relief this paper shows a definition of a fuzzy automaton which has the state input and output sets as fuzzy sets the state transition function is defined as moving on a fuzzy relief with fuzzy peak states and boundaries between different membership functions after the definition of fuzzy automaton with fuzzy relief the paper deals with a generalization simulation and realization of such a fuzzy automaton the paper links the defined fuzzy automaton to an existing fuzzy jk memory cell and to well known fuzzy automata defined on the basis of crisp sets

theory of generalized fuzzy discrete event systems there exist a large number of systems whose state variables are continuous signals and transit based on event driven mechanisms to model the transitions of these state variables the theory of extended fuzzy discrete event systems efdess was developed by extending the fuzzy discrete event system fdes theory however the efdes theory remains limited in modeling these event driven systems a primary reason for this is that the efdes theory allows every event to be characterized by one variable only and thus every event can be modeled by a fuzzy set fs only although the efdes theory provides the steps for computing the next states of the state variables how to compute their next states remains unknown when any event is modeled by multiple fss to overcome this limitation this paper will present the theory of generalized fuzzy discrete event systems gfdess by generalizing the efdes theory in the proposed gfdes theory events are characterized by their multiple attributes which may determine the transitions of the state variables and are modeled by representing each of their attributes using one fs to establish the gfdes theory models for gfdess will be presented by extending the concepts of efdess to make this theory complete the procedures for computing the next states of the state variables will also be provided in addition numerical examples will be presented to further illustrate the proposed gfdes theory

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

fast upwind and eulerian lagrangian control volume schemes for time dependent directional space fractional advection dispersion equations abstract we develop control volume methods for two dimensional time dependent advection dominated directional space fractional advection dispersion equations with the directional space fractional derivative weighted in all the directions by a probability measure in the unit circle which are used to model the anisotropic superdiffusive transport of solutes in groundwater moving through subsurface heterogeneous porous media we develop a fast upwind control volume method for the governing equation to eliminate the spurious numerical oscillations that often occur in space centered numerical discretizations of advection term which are relatively straightforward to implement we also develop a eulerian lagrangian control volume method for the governing equation which symmetrizes the governing equation by combining the time derivative term and the advection term into a material derivative term along characteristic curves both methods are locally mass conservative which are essential in these applications due to the nonlocal nature of the directional space fractional differential operators corresponding numerical discretizations usually generate full stiffness matrices conventional direct solvers tend to require o n 2 memory requirement and have o n 3 computational complexity per time step where n is the number of spatial unknowns which is computationally significantly more expensive than the numerical approximations of integer order advection diffusion equations based on the analysis of the structure of stiffness matrix we propose a fast krylov subspace iterative solver to accelerate the numerical approximations of both the upwind and eulerian lagrangian control volume methods which reduce computational complexity from o n 3 by a direct solver to o n log n per krylov subspace iteration per time step and a memory requirement from o n 2 to o n numerical results are presented to show the utility of the methods

observability of discrete event dynamic systems a finite state automaton is adopted as a model for discrete event dynamic systems deds observations are assumed to be a subset of the event alphabet observability is defined as having perfect knowledge of the current state at points in time separated by bounded numbers of transitions a polynomial test for observability is given it is shown that an observer may be constructed and implemented in polynomial time and space a bound on the cardinality of the observer state space is also presented a notion of resiliency is defined for observers and a test for resilient observability and a procedure for the construction of a resilient observer are presented

a stabilized marching on in degree scheme for the transient solution of the electric field integral equation time domain electric integral equation methods td efie suffer from the numerical stability problem numerous schemes have been proposed over the years for the purpose of taking care of this instability among them the marching on in degree mod method is one of the newly proposed algorithms for calculating the various transient responses the mod solver employs a set of associated laguerre functions and incorporates exact temporal galerkin testing although the mod scheme is assumed to be more stable when compared with marching on in time mot there are few numerical or theoretical investigations on the stability of the various numerical recursive operations for the mod methodology it has been shown that the time domain magnetic field integral equation td mfie using the mod method can be stabilized by using a filon type quadrature formula to accurately integrate the highly oscillatory laguerre functions which has caused instability for the mod solvers using a higher degree of approximation on the other hand the analytical expression of temporal derivatives used in the mod scheme is strongly affected by an unbounded initial value of the transient current in this paper a novel filon type radial integration method and a sequential constraint term for td efie mod are proposed which make the stabilized mod solver accurate and stable for the arbitrary degree of the laguerre polynomials some numerical results are presented to illustrate the validity of the stabilized mod solution of td efie for transient scattering problems

multidimensional advection and fractional dispersion extension of the fractional diffusion equation to two or three dimensions is not as simple as extension of the second order equation this is revealed by the solutions of the equations unlike the gaussian the most general stable vector cannot be generated with an atomistic measure on the coordinate axes a random combination of maximally skewed stable variables on the unit sphere generates a stable vector that is a general model of a diffusing particle subsets are symmetric stable vectors that have previously appeared in the literature and the well known multidimensional brownian motion a multidimensional fractional differential operator is defined in the process

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

a fast finite difference method for three dimensional time dependent space fractional diffusion equations and its efficient implementation fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by second order diffusion equations because of the non local property of fractional differential operators numerical methods for space fractional diffusion equations generate dense or even full coefficient matrices with complicated structures traditionally these methods were solved with gaussian elimination which requires computational work of o n 3 per time step and o n 2 of memory to store where n is the number of spatial grid points in the discretization the significant computational work and memory requirement of these methods makes a numerical simulation of three dimensional space fractional diffusion equations computationally prohibitively expensive in this paper we develop an efficient and faithful solution method for the implicit finite difference discretization of time dependent space fractional diffusion equations in three space dimensions by carefully analyzing the structure of the coefficient matrix of the finite difference method and delicately decomposing the coefficient matrix into a combination of sparse and structured dense matrices the fast method has a computational work count of o nlogn per iteration and a memory requirement of o n while retaining the same accuracy as the underlying finite difference method solved with gaussian elimination numerical experiments of a three dimensional space fractional diffusion equation show the utility of the fast method

from classic observability to a simple fuzzy observability for fuzzy discrete event systems in order to determine uncertainties from restricted available information fuzzy discrete event systems fdess or fuzzy discrete event dynamic systems fdedss were recently proposed these frameworks include fuzzy states and events occurring simultaneously with different membership degrees fuzzy states and events have been used to describe uncertainties that occur often in practical problems such as treatment planning for hiv aids patients sensory information processing for robotic control and fault diagnosis problems in order to measure information associated with fdess or fdedss the classical discrete event system des observability has been turned into fuzzy observability for fdess or fdedss the newly proposed method allows ease of defining degrees of observability so that uncertainties in fdess or fdedss can be dealt with effectively this gives an opportunity to design better decision making systems to calculate the observability degree a simple fuzzy observability checking method is introduced and two examples are elaborated upon to illustrate the presented method finally the newly proposed method is tested on a heating ventilating and air conditioning hvac system

safe diagnosability of fuzzy discrete event systems and a polynomial time verification since fuzzy discrete event systems fdess were significantly brought forward the study of fdess has received increasing attention recently this paper addresses the safe diagnosability under the framework of fdess the contributions are threefold first the notion of safe diagnosability for fuzzy systems is formalized a safe diagnosable fdes means that not only each failure can be detected in terms of fuzziness as well as the detection must be completed before any unsafe operation is executed then a necessary and sufficient condition of safe diagnosability of fdess is proposed by constructing the safe diagnoser finally we present an algorithm for verifying the safe diagnosability of fdess based on a constructive nondeterministic automaton namely verifier it is worth noting that both constructing the verifier and verifying the safe diagnosability of fdess can be realized with a polynomial complexity

a fast finite difference method for two dimensional space fractional diffusion equations fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by second order diffusion equations because of the nonlocal property of fractional differential operators numerical methods for space fractional diffusion equations generate complicated dense or full coefficient matrices consequently these numerical methods were traditionally solved by gaussian elimination which requires computational work of o n 3 per time step and o n 2 of memory where n is the number of spatial grid points in the discretization the significant computational work and memory requirement of the numerical methods impose a serious challenge for the numerical simulation of two and especially three dimensional space fractional diffusion equations we develop a fast and yet accurate solution method for the implicit finite difference discretization of space fractional diffusion equations in two space dimensions by carefully analyzing the structure of the coefficient ma

analysis of transient scattering from composite arbitrarily shaped complex structures a time domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures the solution method is based on the method of moments mom and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions an implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain the usual late time instabilities associated with the time domain integral equations are avoided by using an implicit scheme detailed mathematical steps are included along with representative numerical results

computational aspects of fem approximation of fractional advection dispersion equations on bounded domains in r 2 in this paper we investigate the numerical approximation of the variational solution to the fractional advection dispersion equation fade on bounded domains in r2 more specifically we investigate the computational aspects of the galerkin approximation using continuous piecewise polynomial basis functions on a regular triangulation of the domain the computational challenges of approximating the solution to fractional differential equations using the finite element method stem from the fact that a fractional differential operator is a non local operator several numerical examples are given which demonstrate approximations to fades

a direct o nlog2n finite difference method for fractional diffusion equations fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second order diffusion equations because of the nonlocal property of fractional differential operators the numerical methods have full coefficient matrices which require storage of o n 2 and computational cost of o n 3 where n is the number of grid points in this paper we develop a fast finite difference method for fractional diffusion equations which only requires storage of o n and computational cost of o nlog 2n while retaining the same accuracy and approximation property as the regular finite difference method numerical experiments are presented to show the utility of the method

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

a fourth order scheme for space fractional diffusion equations abstract a weighted and shifted difference formula is constructed based on the lubich operators which gives a forth order and unconditionally stable difference scheme for the cauchy problem of space fractional diffusion equations the novelty of the proposed method here is that only four weighted parameters are required compared to eight parameters used in the previous work to achieve the fourth order accuracy and to ensure the stability at the same time to verify the efficiency of the proposed scheme several numerical experiments for both one dimensional and two dimensional fractional diffusion problems are provided

a characteristics mixed finite element method for advection dominated transport problems we define a new finite element method called the characteristics mixed method for approximating the solution to an advection dominated transport problem the method is based on a space time variational form of the advection diffusion equation our test functions are piecewise constant in space and in time they approximately follow the characteristics of the advective i e hyperbolic part of the equation thus the scheme uses a characteristic approximation to handle advection in time this is combined with a low order mixed finite element spatial approximation of the equation boundary conditions are incorporated in a natural and mass conservative fashion the scheme is completely locally conservative in fact on the discrete level fluid is transported along the approximate characteristics a postprocessing step is included in the scheme in which the approximation to the scalar unknown is improved by utilizing the approximate vector flux this has the effect of improving the rate of convergence of

a fast finite element method for space fractional dispersion equations on bounded domains in mathbb r 2 we develop a fast and accurate finite element method for space fractional dispersion equations in two space dimensions which are expressed in terms of fractional directional derivatives in all the directions that are integrated with respect to a probability measure on the unit circle the fast method significantly reduces the computational work of solving the discrete linear algebraic systems from o n 3 by a direct solver to o n log n per iteration and a memory requirement from o n 2 to o n furthermore the fast method reduces the evaluation of the stiffness matrix which often constitutes a large portion of the cpu time from o n 2 to o n the developed preconditioned fast krylov subspace iterative solver significantly reduces the number of iterations in a krylov subspace iterative method and may improve the convergence behavior of the solver numerical results show the utility of the method

space fractional advection dispersion equations with variable parameters diverse formulas numerical solutions and application to the macrodispersion experiment site data 1 to model the observed local variation of transport speed an extension of the homogeneous space fractional advection dispersion equation fade to more general cases with space dependent coefficients drift velocity v and dispersion coefficient d has been suggested to provide a rigorous evaluation of this extension we explore the underlying physical meanings of two proposed and one other possible form of the fade by using the generalized mass balance law proposed by meerschaert et al 2006 when the classical fick s law is replaced by its generalized form in the first order mass conversation law the original fade with constant parameters extends to the advection dispersion equation ade with fractional flux denoted as ff ade when the net inflow of dispersive flux is from nonlocal concentration gradients following a fractional divergence we get the ade with fractional divergence fd ade when the total net inflow from both nonlocal advection and nonlocal concentration gradients follows a fractional form the fade contains fully fractional divergence ffd ade these three fades with constant parameters can also be obtained by proper choice of the two memory kernels in the nonlocal dispersive constitutive theory proposed by cushman et al 1994 while the space variable fades correspond to the conditional nonlocal theory proposed by neuman 1993 after specifying the general levy type functional form of the random distribution the corresponding langevin markov models can be found in many cases where the lagrangian stochastic processes can be conditioned directly on local aquifer properties at any practical measurable level and resolution the resulting lagrangian random walk particle tracking methods along with previous numerical solutions using implicit euler finite differences distinguish and elucidate the plume behavior described by these fades the fractional models are applied to fit the tritium plumes measured at the macrodispersion experiment test site when the local parameters gleaned from the hydraulic conductivity k distribution are varied even slightly i e a two zone model allowing the use of observed hydraulic conditions at the site the model fits are well within the variability of the data the extended fades describe the fast and space dependent leading edges of measured plumes in the regional scale alluvial system which was underestimated and could not be fully captured by the original fade with constant parameters applications also favor the fd ade model because of the ease of implementation and consistency with previous analysis of the k statistics

fast parareal iterations for fractional diffusion equations abstract numerical methods for fractional pdes is a hot topic recently this work is concerned with the parareal algorithm for system of odes u t a u t f that arising from semi discretizations of time dependent fractional diffusion equations with nonsymmetric riemann liouville fractional derivatives the spatial semi discretization of this kind of fractional derivatives often results in a coefficient matrix a with spectrum a satisfying a s c r where 0 is a measure of dissipativity of the differential equations to accelerate the parareal algorithm we propose a scaled model u t 1 a u t f with 0 to serve the coarse grid correction which is an important component of our parareal algorithm given and we derive a sharp bound of the convergence factor of the parareal iterations moreover by minimizing such a bound we get optimized scaling factor opt it is shown that compared to 1 i e the classical implementation pattern of the coarse grid correction the optimized scaling factor significantly improves the convergence rate numerical examples are presented to support the theoretical finding

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

transient electromagnetic scattering from dielectric objects using the electric field integral equation with laguerre polynomials as temporal basis functions in this paper we propose a time domain electric field integral equation td efie formulation for analyzing the transient electromagnetic response from three dimensional 3 d dielectric bodies the solution method in this paper is based on the galerkin s method that involves separate spatial and temporal testing procedures triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3 d dielectric structures the time domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthonormal basis function that is derived from the laguerre functions these basis functions are also used as the temporal testing functions use of the laguerre polynomials as expansion functions for the transient portion of response enables one not only to handle the time derivative terms in the integral equation in an analytic fashion but also completely separates the space and the time variables thus the time variable along with the courant condition can be eliminated in a galerkin formulation using this procedure we also propose an alternative formulation using a different expansion of the magnetic current the total computational cost for this new method is similar to that of an implicit marching on in time mot efie scheme even though at each step this procedure requires more computations numerical results involving equivalent currents and far fields computed by the two proposed methods are presented and compared

a framework for state attraction of discrete event systems under partial observation state attraction for discrete event systems des addresses the problem of reaching a desired subset of the plant state space after a bounded number of event occurrences the problem of state attraction arises for example in fault tolerant supervisory control or in the control of reconfigurable manufacturing systems and is also applicable to systems biological problems such as the control of gene regulatory networks state attraction is investigated with the assumption of full event observation in the existing literature this paper extends the concept of state attraction to the case of partial observation the notion of weak attraction under partial observation wapo is introduced and necessary and sufficient conditions for the existence of a supervisor under partial observation that achieves wapo are derived furthermore a solution algorithm is proposed that finds such supervisor whenever it exists it is shown that such supervisor can always be realized as a subautomaton of the observer automaton of the des plant an application example from systems biology illustrates the obtained results

fuzzy discrete event systems under fuzzy observability and a test algorithm in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently notably fdess have been applied to biomedical control for human immunodeficiency virus hiv acquired immune deficiency syndrome aids treatment planning and sensory information processing for robotic control qiu independently developed supervisory control theory of fdess we note that the controllability of events in qiu s work is fuzzy but the observability of events is crisp and the observability of events in cao and ying s work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in this paper we establish the supervisory control theory of fdess with partial observations in which both the observability and controllability of events are fuzzy instead we formalize the notions of fuzzy controllability condition and fuzzy observability condition in addition controllability and observability theorem of fdess is set up in a more generic framework in particular we present a detailed computing flow to verify whether the controllability and observability conditions hold thus this result can decide the existence of supervisors also we use this computing method to check the existence of supervisors in the controllability and observability theorem of classical discrete event systems dess which is a new method and different from classical case a number of examples are elaborated on to illustrate the presented results

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

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

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

observability and decentralized control of fuzzy discrete event systems fuzzy discrete event systems as a generalization of crisp discrete event systems have been introduced in order that it is possible to effectively represent uncertainty imprecision and vagueness arising from the dynamic of systems a fuzzy discrete event system has been modeled by a fuzzy automaton its behavior is described in terms of the fuzzy language generated by the automaton in this paper we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation observability normality and co observability of crisp languages are extended to fuzzy languages it is shown that the observability together with controllability of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor when a decentralized solution is desired it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co observable moreover the infimal controllable and observable fuzzy superlanguage and the supremal controllable and normal fuzzy sublanguage are also discussed simple examples are provided to illustrate the theoretical development

convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics abstract a nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium conservation of mass for the mixture leads to an elliptic equation for pressure and conservation for the displacing fluid yields a convectiondominated parabolic equation for the concentration of that fluid a sequential implicit time stepping procedure is defined in which the pressure and darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the concentration is approximated by a combination of a galerkin finite element method and the method of characteristics optimal order convergence in l2 is proved time truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the concentration equation temporal and spatial errors are lessened by direct computation of the velocity in the mixed method as opposed to differentiation of the pressure several extensions of these results are outlined

an approximation to miscible fluid flows in porous media with point sources and sinks by an eulerian lagrangian localized adjoint method and mixed finite element methods we develop an eulerian lagrangian localized adjoint method ellam mixed finite element method mfem solution technique for accurate numerical simulation of coupled systems of partial differential equations pdes which describe complex fluid flow processes in porous media an ellam which was shown previously to outperform many widely used methods in the context of linear convection diffusion pdes is presented to solve the transport equation for concentration since accurate fluid velocities are crucial in numerical simulations an mfem is used to solve the pressure equation for the pressure and darcy velocity this minimizes the numerical difficulties occurring in standard methods for approximating velocities caused by differentiation of the pressure and then multiplication by rough coefficients the ellam mfem solution technique significantly reduces temporal errors symmetrizes the governing transport equation eliminates nonphysical oscillation and or excessive numerical dispersion in many simulators conserves mass and treats boundary conditions accurately numerical experiments show that the ellam mfem solution technique simulates miscible displacements of incompressible fluid flows in porous media accurately with fairly coarse spatial grids and very large time steps which are one or two orders of magnitude larger than the time steps used in many methods moreover the ellam mfem solution technique can treat large mobility ratios discontinuous permeabilities and porosities anisotropic dispersion in tensor form and point sources and sinks