a quintic b spline finite elements scheme for the kdvb equation abstract an algorithm for solving the korteweg de vries burgers kdvb equation based on the collocation method with quintic b spline finite elements is set up to simulate the solutions of the kdv burgers and the kdvb equations the migration of solitary waves and temporal evolution of a maxwellian initial pulse are studied for the kdv equation burgers equation is solved for different values of reynolds number the time evaluation of the solutions of the kdvb equation with different values for the diffusion and dispersion coefficients is studied invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm a linear stability analysis shows the scheme to be unconditionally stable

ditopological texture spaces and fuzzy topology i basic concepts this is the first of three papers which develop various fundamental aspects of the theory of ditopological texture spaces in a categorical setting and present important links with the theory of l topological spaces the authors begin by defining the notion of q sets which together with the p sets considered earlier enable the formulation of a powerful concept of duality this plays an important role in the theory of direlations and difunctions which is described here in detail difunctions are then taken as the morphisms of a category dftex whose objects are texture spaces several important subcategories are defined and the closely related construct ftex defined some properties of the functors between these categories are obtained

one point compactifications of ditopological texture spaces in this paper a one point compactification of a ditopological texture space is defined and a concept of local compactness introduced and shown to be additive in the class of ditopological texture spaces an application to hutton spaces is given here a compact extension of an hutton space is obtained and a notion of local compactness is defined and shown to be productive in the class of l topological spaces where l is a hutton algebra

numerical solution of burgers equation by lattice boltzmann method in this paper a lattice boltzmann model for burgers equation is proposed through selecting equilibrium distribution function properly the model has been verified by three test examples the numerical results are found in good agreement with analytical solutions and numerical solutions reported in previous studies the advantages of the resulting method are algorithmic simplicity parallel computation easy handling of complicated boundary conditions so it is very easy to implement and deal with more complex problems

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

modular feedback logic for discrete event systems we examine a modular approach to the synthesis of state feedback controls for the problem of maintaining a predicate on the state set of a discrete dynamic system invariant dynamical systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions the basic problem of interest is to ensure by appropriate control action that a given predicate on the state set of the process remains invariantly true whenever it is initially satisfied assuming the predicate can be decomposed into the conjunction or disjunction of component predicates we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion

a fourth order numerical scheme for solving the modified burgers equation a finite difference scheme based on fourth order rational approximants to the matrix exponential term in a two time level recurrence relation is proposed for the numerical solution of the modified burgers equation the resulting nonlinear system which is analyzed for stability is solved using an already known modified predictor corrector scheme the results arising from the experiments are compared with the corresponding ones known from the available literature

aggregation and multi level control in discrete event dynamic systems abstract in this paper we consider the problem of higher level aggregate modeling and control of discrete event dynamic systems deds modeled as finite state automata in which some events are controllable some are observed and some represent events to be tracked the higher level models considered correspond to associating specified sequences of events in the original system to single macroscopic events in the higher level model we also consider the problem of designing a compensator that can be used to restrict microscopic behavior so that the system will only produce strings of these primitive sequences or tasks with this lower level control in place we can construct higher level models which typically have many fewer states and events than the original system the use of these higher level models allow us to decrease the computational complexity of problems involving complex interconnected deds

a moving petrov galerkin method for transport equations a time dependent transport equation is solved numerically by using a petrov galerkin technique on a time dependent grid a piecewise linear trial solution and piecewise hermite cubic test functions are used the same method is also applied to a time independent problem in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid generation techniques several numerical examples are given

generalized detectability for discrete event systems in our previous work we investigated detectability of discrete event systems which is defined as the ability to determine the current and subsequent states of a system based on observation for different applications we defined four types of detectabilities weak detectability strong detectability weak periodic detectability and strong periodic detectability in this paper we extend our results in three aspects 1 we extend detectability from deterministic systems to nondeterministic systems such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems 2 we develop polynomial algorithms to check strong detectability the previous algorithms are based on observer whose construction is of exponential complexity while the new algorithms are based on a new automaton called detector 3 we extend detectability to d detectability while detectability requires determining the exact state of a system d detectability relaxes this requirement by asking only to distinguish certain pairs of states with these extensions the theory on detectability of discrete event systems becomes more applicable in solving many practical problems

galerkin method for the numerical solution of the rlw equation using quintic b splines the regularized long wave equation rlw is solved numerically by using the quintic b spline galerkin finite element method the same method is applied to the time split rlw equation comparison is made with both analytical solutions and some previous results propagation of solitary waves interaction of two solitons are studied

feedback stabilization of some event graph models the authors introduce several notions of stability for event graph models timed or not the stability is similar to the boundedness notion for petri nets the event graph models can be controlled by an output feedback which takes information from some observable transitions and can disable some controllable transitions the controller itself is composed of an event graph in this framework the authors solve the corresponding stabilization problems i e they wonder if such a controller may prevent the explosion of the number of tokens

some tractable supervisory control problems for discrete event systems modeled by buchi automata discrete event systems des are modeled by buchi automata together with a means of online control in this setting the concept of a controllable language is extended to infinite strings and conditions for the existence of a supervisor controller to implement a prescribed closed loop behavior are derived the focus is on a class of des called product systems these are des composed of a finite set of asynchronous components a control problem for such a system typically requires the synthesis of an online controller so as to achieve some prescribed coordinated behavior of the component subsystems one of the principal difficulties in this task is that the size of the state space increases exponentially with the number of components it is shown that despite this fact several interesting control synthesis problems for such systems are computationally feasible and algorithms are developed for solution

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

on the numerical solution of nonlinear burgers type equations using meshless method of lines abstract in this paper a meshless method of lines mmol is proposed for the numerical solution of nonlinear burgers type equations this technique does not require a mesh in the problem domain and only a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions rbfs the scheme is tested for various examples the results obtained by this method are compared with the exact solutions and some earlier work

quartic b spline galerkin approach to the numerical solution of the kdvb equation the nonlinear korteweg de vries burgers equation is solved numerically by method of galerkin using quartic b splines as both shape and weight functions over the finite intervals five test problems are studied to demonstrate the accuracy and efficiency of the proposed method a comparison of numerical results of both algorithm and some published articles is done in computational section the numerical results are found in good agreement with exact solutions

on observability with delay antitheses and syntheses the idea of observability with delay for discrete event dynamic systems in a finite state machine framework has been proposed ozveren and wilsky 1990 this note points out some shortcomings in the existing definitions and proposes an alternative one it also derives necessary and sufficient conditions for the above property that can be tested for easily

a novel numerical scheme for solving burgers equation abstract in this paper we propose a novel numerical scheme for solving burgers equation the scheme is based on a cubic spline quasi interpolant and multi node higher order expansion which make the algorithm simple and easy to implement the numerical experiments show that the proposed method produces high accurate results

some results on fuzzy compact spaces abstract in this paper we examine first the relation between the fuzzy compactness of a fuzzy topology on a fuzzy lattice l and the compactness of two topological spaces m u m v defined on the set m of molecules of l we then investigate the relation between fuzzy compactness and the joint compactness of the bitopological space m u v

control of vector discrete event systems i the base model a vector discrete event system vdes is a discrete event system model in which the system state is represented by a vector with integer components and state transitions by integer vector addition the authors investigate such structures from the viewpoint of control theory the objective is to specialize to vdes the general automation based control theory of p j ramadge and w m wonham 1987 and w m wonham and p j ramadge 1988 it is shown that within the vdes framework a useful class of control systems can be compactly modeled and some of the associated control problems of ramadge and wonham can be more efficiently solved

on supervisor reduction in discrete event systems abstract a supervisory controller supervisor s for a discrete event system can be modelled on a recognizer r for the language corresponding to the supervisory task to be accomplished it is shown that simpler reduced supervisors can be constructed by the use of covers of the state set of r and that any mildly restricted supervisor is a reduction of r in this sense the reduction procedure is time exponential with respect to the size of the state set of r

numerical solution of burgers fisher equation by cubic b spline quasi interpolation abstract in this paper numerical solution of the burgers equation is presented based on the cubic b spline quasi interpolation at first the cubic b spline quasi interpolation is introduced moreover the numerical scheme is presented by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable the accuracy of the proposed method is demonstrated by some test problems the numerical results are found in good agreement with exact solutions the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

a non separable solution of the diffusion equation based on the galerkin s method using cubic splines abstract the two dimensional diffusion equation of the form 2 u x 2 2 u y 2 1 d u t is considered in this paper we try a bi cubic spline function of the form i j 0 n n c i j t b i x b j y as its solution the initial coefficients c i j 0 are computed simply by applying a collocation method c i j f x i y j where f x y u x y 0 is the given initial condition then the coefficients c i j t are computed by x t e tq x 0 where x t c 0 1 c 0 1 c 0 2 c 0 n c 1 0 c n n is a one dimensional array and the square matrix q is derived from applying the galerkin s method to the diffusion equation note that this expression provides a solution that is not necessarily separable in space coordinates x y the results of sample calculations for a few example problems along with the calculation results of approximation errors for a problem with known analytical solution are included

output stabilizability of discrete event dynamic systems the authors investigate the problem of designing stabilizing feedback compensators for discrete event dynamic systems deds modeled as finite state automata in which some transition events are controllable and some events are observed the problem of output stabilization is defined as the construction of a compensator such that all state trajectories in the closed loop system go through a given set e infinitely often the authors also define a stronger notion of output stabilizability which requires that the state not only pass through e infinitely often but that the set of instants when the state is in e and one knows it is in e is also infinite necessary and sufficient conditions are presented for both notions the authors also introduce and characterize a notion of resiliency that corresponds to the system being able to recover from observation errors in addition they provide some general bounds for the algorithms considered and discuss several conditions under which far smaller bounds can be achieved

paracompactness and full normality in ditopological texture spaces in this paper the authors lay the foundation for a theory of dicovers of ditopological texture spaces and use this to define notions of paracompactness and full normality some applications to fuzzy topology are also mentioned

numerical solutions of the burgers equation by the least squares quadratic b spline finite element method in this study a least squares quadratic b spline finite element method for calculating the numerical solutions of the one dimensional burgers like equations with appropriate boundary and initial conditions is presented three test problems have been studied to demonstrate the accuracy of the present method results obtained by the method have been compared with the exact solution of each problem and are found to be in good agreement with each other a fourier stability analysis of the method is also investigated

numerical solution of one dimesional burgers equation explicit and exact explicit finite difference methods this paper presents finite difference solution and analytical solution of the finite difference approximations based on the standard explicit method to the one dimensional burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics results obtained by these ways for some modest values of viscosity have been compared with the exact fourier one it is shown that they are in good agreement with each other

the generalized boundary element approach to burgers equation the generalized boundary element method is presented for the numerical solution of burgers equation the new method is based on the set of boundary integral equations derived for each subdomain by using the fundamental solution for the linearized differential operator of the equation the resulting system of quasi non linear equations is solved implicitly with use of a simple iterative procedure the adaptability and the accuracy of the proposed method are demonstrated by three examples and a comparison of the numerical results with the exact solution or other existing solutions is shown for the first example

fuzzy sets as textures spaces ii subtextures and quotient textures in this paper the authors introduce the notions of subtexture and quotient texture of a complemented texture space conditions ensuring the existence of such textures are discussed and applied to show that certain natural subtextures of product textures may be defined these are used in particular to give representations of product l fuzzy sets and a representation involving quotient textures is also examined

connectedness in ditopological texture spaces abstract the notion of a texture space under the name of fuzzy structure was introduced by brown 1993 as a means of representing a lattice of fuzzy sets as a lattice of crisp subsets of some base set corresponding to a fuzzy topology we then have the concept of a ditopology and in this paper connectedness in ditopological texture spaces is defined and some of its basic properties are obtained in particular it is shown that connectedness is productive in the context of ditopological texture spaces zero dimensionality and strong zero dimensionality are defined and it is shown that in stable zero dimensional ditopological texture spaces the component of a point coincides with the quasi component finally it is shown that a fuzzy topological space is c 5 connected if and only if the corresponding ditopological texture space is connected

stability and stabilizability of discrete event dynamic systems a finite state automaton is adopted as a model for discrete event dynamic systems deds stabdity is defined as wslting a given set e mtinitely often stabilizability is defined as choosing state feedback such that the closed loop system is stable these notions are proposed as properties of resiliency or error recovery an important ingredient in stability is shown to be a notion of transition function invariance relations between our notions of stability and invariance and the notions of safety fairness hvelock deadlock etc in computer science literature are pointed out connections are established between our notions of invariance and the classical notions of a invariance and a 11 invariance of linear systems polynomial algorithms for testing stability and stabilizabdity and for constructing a stabilizing control law are also presented

modular implementation of robust supervisory controllers for discrete event systems in this paper the problem of designing robust supervisory controllers for uncertain discrete event systems is studied it is assumed that both the plant behavior and the design specifications can be represented by regular languages it is also assumed that the unknown model of the uncertain plant belongs to a finite set of possibilities to solve the problem a modular approach based on a general recursive robust control scheme is developed the contribution of the present paper consists in deriving a maximally permissive modular robust supervisory controller for the case of prefix closed languages having the advantage of linear complexity in the number of models as opposed to the exponential complexity of the worst case scenario in the direct implementation of standard supervisors for augmented systems

a numerical solution of the burgers equation using cubic b splines in the present paper numerical solutions of the one dimensional burgers equation are obtained by a method based on collocation of cubic b splines over finite elements the accuracy of the proposed method is demonstrated by three test problems the numerical results are found in good agreement with exact solutions time space integration of the burgers equation yields a system of difference equation which is shown to be unconditionally stable

the stability of a class of discrete event systems using markov chains this paper presents a stability concept of a class of discrete event systems dess using markov chains the dess under consideration are modelled as state machines adopted from ramadge wonham which represent the hybrid dynamic models of constrained motion systems by identifying the probability of firing enabled events of the des p convergence is proposed some properties of p convergence are investigated including the fact that p convergence is a generalization of the convergence proposed by brave and heymann yet it is less restrictive the application of p convergence is shown for a robotic assembly des

b spline galerkin methods for numerical solutions of the burgers equation the first order splitting method is applied to the burgers equation and two numerical algorithms are set up for this time splitted burgers equation using both quadratic and cubic b spline galerkin finite element techniques the unknowns in the equation is resolved with the b splines in space and standart crank nicolson differencing schemes is used to advance solution in time results of three numerical test problems are used to compare each schemes with available some results

separation axioms in fuzzy topology characterized by bitopologies abstract in this paper we associate a bitopological space with a fuzzy topological space and examine the relation between various fuzzy and bitopological separation axioms

l topological spaces as spaces of points the main background of this paper is a functor from the category of l topological spaces to the category of topological spaces which is defined by means of an attachment a notion recently introduced in the lattice l and has very nice properties under the assumption of spatiality the pu liu s quasi coincidence relation largely used to study 0 1 topological spaces is determined by a suitable attachment in 0 1 so the results described here apply to that situation this functor allows to import topological concepts into the fuzzy setting directly from the classical context meanwhile this provides an evaluation of the relevance and of the consistency of basic notions in fuzzy topology as well as a critical view on how these have been introduced and treated up to now an overview of the relationship between spatial attachments and textures is outlined in the last part of the paper