relative observability and coobservability of timed discrete event systems we study supervisory control of timed discrete event systems tdes under partial observation and propose new observability concepts effective for supervisor synthesis first we consider monolithic centralized supervisory control and introduce timed relative observability and timed relative weak observability the former concept extends our previous work to the timed case while the latter exploits choices of forcible events to preempt the clock event tick we prove that timed relative respectively weak observability is stronger than timed respectively weak observability weaker than normality and closed under set union hence there exists the supremal relatively respectively weakly observable sublanguage of a given language

nonexistence of self similar singularities in the ideal magnetohydrodynamics in this paper we exclude the scenario of the apparition of finite time singularity in the form of self similar singularities in the ideal magnetohydrodynamic equations assuming suitable integrability conditions on the vorticity and the magnetic field we also consider the more refined possibility of asymptotically self similar singularities where the local classical solution converges to the self similar profile as we approach the possible time of singularity the scenario of asymptotically self similar singularity is also excluded under suitable conditions on the profile in the two dimensional magnetohydrodynamics the magnetic field evolution equations reduce to a divergence free transport equation for a scalar stream function this helps us to improve the above nonexistence theorems on the self similar singularities in the sense that we require merely weaker integrability conditions on the profile in order to prove the results

an algebraic model for performance evaluation of timed event multigraphs this note demonstrated that a certain class of petri nets called timed event multigraphs can be represented as a set of linear equations by using a novel dioid with this new algebra some properties are presented in the text an example is discussed in the end and an interesting result is computed

euler s equations and the maximum principle in this paper we use maximum principle in the far field region for the time dependent self similar euler equations to exclude discretely self similar blow up for the euler equations of the incompressible fluid flows our decay conditions near spatial infinity of the blow up profile are given explicitly in terms the coefficient in the equations we also deduce triviality of the discretely self similar solution to the magnetohydrodynamic system under suitable decay conditions near spatial infinity than the previous one applying similar argument directly to the euler equations we obtain a priori estimate of the vorticity in the far field region

a linear system theoretic view of discrete event processes and its use for performance evaluation in manufacturing a discrete event system is a system whose behavior can be described by means of a set of time consuming activities performed according to a prescribed ordering events correspond to starting or ending some activity an analogy between linear systems and a class of discrete event systems is developed following this analogy such discrete event systems can be viewed as linear in the sense of an appropriate algebra the periodical behavior of closed discrete event systems i e involving a set of repeatedly performed activities can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra this problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph the potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized the case of a flowshop like production process is analyzed in detail

on the euler equations of incompressible fluids euler equations of incompressible fluids use and enrich many branches of mathematics from integrable systems to geometric analysis they present important open physical and mathematical problems examples include the stable statistical behavior of ill posed free surface problems such as the rayleightaylor and kelvin helmholtz instabilities the paper describes some of the open problems related to the incompressible euler equations with emphasis on the blowup problem the inviscid limit and anomalous dissipation some of the recent results on the quasigeostrophic model are also mentioned

liouville type theorems for the forced euler equations and the navier stokes equations in this paper we study the liouville type properties for solutions to the steady incompressible euler equations with forces in mathbb r n if we assume single signedness condition on the force then we can show that a c 1 mathbb r n solution v p with v 2 p in l frac q 2 mathbb r n q in frac 3n n 1 infty is trivial v 0 for the solution of the steady navier stokes equations satisfying v x to 0 as x to infty the condition int mathbb r 3 delta v frac 6 5 dx infty which is stronger than the important d condition int mathbb r 3 nabla v 2 dx infty but both having the same scaling property implies that v 0 in the appendix we reprove theorem 1 1 chae commun math phys 273 203 215 2007 using the self similar euler equations directly

on formation of a locally self similar collapse in the incompressible euler equations the paper addresses the question of the existence of a locally self similar blow up for the incompressible euler equations several exclusion results are proved based on the l p condition for velocity or vorticity and for a range of scaling exponents in particular in n dimensions if in self similar variables u in l p and u sim frac 1 t alpha 1 alpha then the blow up does not occur provided alpha n 2 or 1 alpha leq n p this includes the l 3 case natural for the navier stokes equations for alpha n 2 we exclude profiles with asymptotic power bounds of the form y n 1 delta lesssim u y lesssim y 1 delta solutions homogeneous near infinity are eliminated as well except when homogeneity is scaling invariant

nonexistence of self similar singularities for the 3d incompressible euler equations we prove that there exists no self similar finite time blowing up solution to the 3d incompressible euler equations if the vorticity decays sufficiently fast near infinity in mathbb r 3 by a similar method we also show nonexistence of self similar blowing up solutions to the divergence free transport equation in mathbb r n this result has direct applications to the density dependent euler equations the boussinesq system and the quasi geostrophic equations for which we also show nonexistence of self similar blowing up solutions

unique continuation type theorem for the self similar euler equations abstract we prove a unique continuation type theorem for the self similar euler equations in r 3 assuming the time periodicity namely if a time periodic solution v y s of the time dependent self similar euler equations has the property that v 0 s 0 for all s 0 s 0 where s 0 is the time period and y 0 is a local extremal point of v y s near the origin then v y s 0 for all y s r 3 0 s 0 a similar result holds for more general system with arbitrary coefficients and also for the inviscid incompressible magnetohydrodynamic mhd system as a consequence we obtain new criteria for the absence of the discretely self similar singularities for the 3d euler equations and the inviscid 3d mhd

supervisory control of timed discrete event systems the ramadge wonham framework for control of discrete event systems is augmented with timing features by use of ostroff s semantics for timed transition models it is shown that the rw concept of controllability and the existence of maximally permissive supervisory controls can be suitably generalized the enhanced setting admits subsystem composition and the concept of forcible event as an event that preempts the tick of a global clock an example of a simple manufacturing cell illustrates how the new framework can be used to solve synthesis problems which may include logic based temporal and quantitative optimality specifications

brief paper input signal design for identification of max plus linear systems max plus linear systems efficiently describe the dynamics of event time sequences of a class of discrete event systems the present contribution addresses the problem of designing adequate input signals for state space identification of max plus linear systems it is shown that the input signal design problem can be rewritten as a set of upper bound constraints and therefore solved using an existing algorithm this input signal design method allows to incorporate additional objectives and constraints e g minimum or maximum input event separation time order constraints etc which are desirable or even required for the input signals and the resulting process behavior

on leray s self similar solutions of the navier stokes equations satisfying local energy estimates this paper proves that leray s self similar solutions of the three dimensional navier stokes equations must be trivial under very general assumptions for example if they satisfy local energy estimates

a characterization of realizable behavior in supervisory control of timed event graphs abstract we study supervisory control of timed event graphs in the max algebra framework desirable behavior is assumed to be specified as a set of firing time sequences of transitions we address a control problem which requires that behavior of the supervised system equal the specification set a necessary and sufficient condition for the existence of a control input set to solve our problem is presented we call the condition the strong controllability condition however the given specification is not necessarily strongly controllable we then obtain its supremal strongly controllable subset moreover we derive a necessary and sufficient condition for the supremal strongly controllable subset to be nonempty under the assumption that desirable behavior is specified by the upper time bound sequence

supervisory control of real time discrete event systems using lattice theory the behaviour of timed discrete event systems des s can be described by sequences of event occurrence times these sequences can be ordered to form a lattice since logical untimed des behaviours described by regular languages also form a lattice questions of controllability for timed des s may be treated in much the same manner as they are for untimed systems in this paper we establish conditions for the controllability of timed des performance specification which are expressed as inequations on the lattice of sequences these specifications may take the form of sets of acceptable event occurrence times maximum or minimum occurrence times or limits on the separation times between events optimal behaviours are found as extremal solutions to these inequations using fixed point results for lattices

nonexistence of singular pseudo self similar solutions of the navier stokes system we show that there are no singular pseudo self similar solutions of the navier stokes system with finite energy

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

formulas for the extremal controllable sequences in timed event graphs this paper studies controllable sequences in the max algebra model of timed event graphs we present a formula for the supremal controllable sequence when a desirable behavior is specified as a single sequence as a result the supremal sequence can be computed without iterative computation a formula for the infimal controllable sequence is also obtained under some assumptions

a conley index study of the evolution of the lorenz strange set abstract in this paper we study the lorenz equations using the perspective of the conley index theory more specifically we examine the evolution of the strange set that these equations posses throughout the different values of the parameter we also analyze some natural morse decompositions of the global attractor of the system and the role of the strange set in these decompositions we calculate the corresponding morse equations and study their change along the successive bifurcations we see how the main features of the evolution of the lorenz system are explained by properties of the dynamics of the global attractor in addition we formulate and prove some theorems which are applicable in more general situations these theorems refer to poincare andronov hopf bifurcations of arbitrary codimension bifurcations with two homoclinic loops and a study of the role of the traveling repellers in the transformation of repeller attractor pairs into attractor repeller ones

formulas for calculating supremal controllable and normal sublanguages abstract supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis in this paper we discuss the computation of supremal controllable and normal sublanguages we derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed as a result those languages can be computed without applying recursive algorithms we also discuss those aspects of these formulas