on the directional dynamics of additive cellular automata we continue the study of cellular automata ca directional dynamics i e the behavior of the joint action of ca and shift maps this notion has been investigated for general ca in the case of expansive dynamics by boyle and lind and by sablik for sensitivity and equicontinuity in this paper we give a detailed classification for the class of additive ca providing non trivial examples for some classes of sablik s classification moreover we extend the directional dynamics studies by considering also factor languages and attractors

kolmogorov complexity and cellular automata classification we present a new approach to cellular automata ca classification based on algorithmic complexity we construct a parameter which is based only on the transition table of ca and measures the randomness of evolutions is better in a certain sense than any other parameter recursively definable on ca tables we investigate the relations between the classical topological approach and ours our parameter is compared with langton s parameter turns out to be theoretically better and also agrees with some practical evidences reported in literature finally we propose a protocol to approximate and make experiments on ca dynamical behavior

additive one dimensional cellular automata are chaotic according to devaney s definition of chaos abstract we study the chaotic behavior of a particular class of dynamical systems cellular automata we specialize the definition of chaos given by devaney for general dynamical systems to the case of cellular automata a dynamical system x f is chaotic according to devaney s definition of chaos if its transition map f is sensitive to the initial conditions topologically transitive and has dense periodic orbits on x our main result is the proof that all the additive one dimensional cellular automata defined on a finite alphabet of prime cardinality are chaotic in the sense of devaney

discrete time hybrid control in borel spaces average cost optimality criterion abstract this paper addresses an optimal hybrid control problem in discrete time with borel state and action spaces by hybrid we mean that the evolution of the state of the system may undergo deep changes according to structural modifications of the dynamic such modifications occur either by the position of the state or by means of the controller s actions the optimality criterion is of a long run ratio average or ratio ergodic type we provide the existence of optimal average policies for this hybrid control problem by analyzing an associated dynamic programming equation we also show that this problem can be translated into a standard or non hybrid optimal control problem with cost constraints besides we show that our model includes some special and important families of control problems such as those with an impulsive or switching mode finally to illustrate our results we provide an example on a pollution accumulation problem

solution of some conjectures about topological properties of linear cellular automata we study two dynamical properties of linear d dimensional cellular automata over zm namely denseness of periodic points and topological mixing for what concerns denseness of periodic points we complete the work initiated in theoret comput sci 174 1997 157 theoret comput sci 233 1 2 2000 147 14th annual symp on theoretical aspects of computer science stacs 97 lncs n 1200 springer berlin 1997 pp 427 438 by proving that a linear cellular automata has dense periodic points over the entire space of configurations if and only if it is surjective as conjectured in cattaneo et al 2000 for non surjective linear ca we give a complete characterization of the subspace where periodic points are dense for what concerns topological mixing we prove that this property is equivalent to transitivity and then easily checkable finally we classify linear cellular automata according to the definition of chaos given by devaney in an introduction to chaotic dynamical systems 2nd ed addison wesley reading ma usa 1989

nondeterministic cellular automata abstract using purely topological concepts we characterize the class of nondeterministic mappings between shift spaces that give rise to nondeterministic sliding block codes we use such topological notions to investigate basic properties of surjective and reversible nondeterministic cellular automata

stochastic hybrid control the objective of this paper is to study the stochastic version of a previous paper of the authors in which hybrid control for deterministic systems was considered the modelling is quite similar to the deterministic case we have a system whose state is composed of a continuous part and a discrete part they are affected by a continuous type control and an impulse control the dynamics is moreover perturbed by noise also a continuous and a discrete noise process the markovian character of the sate process is preserved we develop the model and show how the dynamic programming approach leads to some involved quasi variational inequality

number conserving cellular automata i decidability we prove that definitions of number conserving cellular automata found in literature are equivalent a necessary and sufficient condition for cellular automata to be number conserving is proved using this condition we give a quasi linear time algorithm to decide number conservation

on the undecidability of the limit behavior of cellular automata cellular automata ca are discrete dynamical systems and an abstract model of parallel computation the limit set of a cellular automaton is its maximal topological attractor a well known result due to kari says that all nontrivial properties of limit sets are undecidable in this paper we consider the properties of limit set dynamics i e properties of the dynamics of ca restricted to their limit sets there can be no equivalent of kari s theorem for limit set dynamics anyway we show that there is a large class of undecidable properties of limit set dynamics namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor as a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity map and whether it is closing injective expansive positively expansive and transitive

merit functions for general variational inequalities in this paper we consider some classes of merit functions for general variational inequalities using these functions we obtain error bounds for the solution of general variational inequalities under some mild conditions since the general variational inequalities include variational inequalities quasivariational inequalities and complementarity problems as special cases results proved in this paper hold for these problems in this respect results obtained in this paper represent a refinement of previously known results for classical variational inequalities

optimal stochastic scheduling of power generation systems with scheduling delays and large cost differentials the optimal scheduling or unit commitment of power generation systems to meet a random demand involves the solution of a class of dynamic programming inequalities for the optimal cost and control law we study the behavior of this optimality system in terms of two parameters i a scheduling delay e g the startup time of a generation unit and ii the relative magnitudes of the costs operating or starting of different units in the first case we show that under reasonable assumptions the optimality system has a solution for all values of the delay and as the delay approaches zero that the solutions converge uniformly to those of the corresponding system with no delays in the second case we show that as the cost of operating or starting a given machine increases relative to the costs of the other machines there is a point beyond which the expensive machine is not used except in extreme situations we give a formula for the relative costs that characterize this point moreover we show that as

on an iterative algorithm for general variational inequalities in this paper we suggest and analyze a new three step iterative algorithm for solving the general variational inequalities we also study the global convergence of the proposed method under some mild conditions since the general variational inequalities include variational inequalities quasi variational inequalities and quasi complementarity problems as special cases one can deduce similar results for these problems our results can be viewed as an improvement and refinement of the previously known and new results preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method

a complete and efficiently computable topological classification of d dimensional linear cellular automata over z m we study the dynamical behavior of d dimensional linear cellular automata over zm we provide easy to check necessary and sufficient conditions for a d dimensional linear cellular automata over zm to be sensitive to initial conditions positively expansive strongly transitive and equicontinuous as a consequence of our results we have a complete and efficiently computable topological classification of d dimensional linear cellular automata over zm according to the most important dynamical properties studied in the theory of discrete time dynamical systems

differential automata and their discrete simulators on presente la notion d automate differentiel pour la formulation d une classe de problemes aux valeurs initiales sur des champs vectoriels hysteretiques

dynamical behavior of additive cellular automata over finite abelian groups abstract we study the dynamical behavior of additive d dimensional d 1 cellular automata where the alphabet is any finite abelian group this class of discrete time dynamical systems is a generalization of the systems extensively studied by many authors among which one may list 38 44 41 among our major contributions there is the proof that topologically transitive additive d dimensional cellular automata over a finite abelian group are ergodic this result represents a solid bridge between the world of measure theory and that of topology and greatly extends previous results obtained in 12 44 for linear ca over z m z i e additive ca in which the alphabet is the cyclic group z m z and the local rules are linear combinations with coefficients in z m z in our scenario the alphabet is any finite abelian group and the global rule is any additive map this class of ca strictly contains the class of linear ca over z m z n i e with the local rule defined by n n matrices with elements in z m z which in turn strictly contains the class of linear ca over z m z in order to further emphasize that finite abelian groups are more expressive than z m z we prove that contrary to what happens in z m z there exist additive ca over suitable finite abelian groups which are roots with arbitrarily large indices of the shift map as a relevant consequence of our results we have that for additive d dimensional ca over a finite abelian group ergodic mixing weak ergodic mixing ergodicity topological mixing weak topological mixing topological total transitivity and topological transitivity are all equivalent properties as a corollary we see that invertible transitive additive ca are isomorphic to bernoulli shifts furthermore we prove that surjectivity implies openness for additive d dimensional ca over a finite abelian group hence we get that topological transitivity is equivalent to the well known devaney notion of chaos when d 1 moreover we provide a first characterization of strong transitivity for additive ca which we suspect to be true also for the general case

general variational inequalities and nonexpansive mappings in this paper we suggest and analyze some three step iterative schemes for finding the common elements of the set of the solutions of the noor variational inequalities involving two nonlinear operators and the set of the fixed points of nonexpansive mappings we also consider the convergence analysis of the suggested iterative schemes under some mild conditions since the noor variational inequalities include variational inequalities and complementarity problems as special cases results obtained in this paper continue to hold for these problems results obtained in this paper may be viewed as an refinement and improvement of the previously known results

recovery of the absorption coefficient from diffused reflected light using a discrete diffusive model an algorithm based on a discrete model for photon migration is proposed for recovering the absorption coefficient in a semi infinite slab a pulsed light source is modeled and only reflected signals are used in the reconstruction the diffusion coefficient and speed of light are assumed constant and known the algorithm is based on the result that the earliest reflected signals obtained from a particular voxel depend either in a linear or in a quadratical fashion on the square of the absorption coefficient in that voxel by solving the discrete model in the forward direction in a region where the absorption coefficient has been calculated already the absorption coefficients in the voxels on the boundary of the region are calculated using interpolation results show that simple absorptive regions can be accurately recovered

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

on the limit sets of cellular automata the limit sets of cellular automata defined by wolfram play an important role in applications of cellular automata to complex systems a number of results on limit sets are proved considering both finite and infinite configurations of cellular automata the main concern of this paper is with testing membership and essential emptiness of limit sets for linear and two dimensional cellular automata

ergodicity transitivity and regularity for linear cellular automata over z m 1 we study the dynamical behavior of d dimensional linear cellular automata over zm we provide an easy to check necessary and sufficient condition for a d dimensional linear cellular automata over zm to be ergodic and topologically transitive as a byproduct we get that for linear cellular automata ergodicity is equivalent to topological transitivity finally we prove that for 1 dimensional linear cellular automata over zm regularity denseness of periodic orbits is equivalent to surjectivity

classification of sofic projective subdynamics of multidimensional shifts of finite type motivated by hochman s notion of subdynamics of a z subshift 8 we define and examine the projective subdynamics of z shifts of finite type sfts where we restrict not only the action but also the phase space we show that any z sofic shift of positive entropy is the projective subdynamics of a z2 z sft and that there is a simple condition characterizing the class of zero entropy z sofic shifts which are not the projective subdynamics of any z2 sft we define notions of stable and unstable subdynamics in analogy with the notions of stable and unstable limit sets in cellular automata theory and discuss how our results fit into this framework one dimensional strictly sofic shifts of positive entropy admit both a stable and an unstable realization whereas a particular class of zero entropy z sofics only allows for an unstable realization finally we prove that the union of z subshifts all of which are realizable in z sfts is again realizable when it contains at least two periodic points that the projective subdynamics of z2 sfts with the uniform filling property ufp are always sofic and we exhibit a class of non sofic z subshifts which are not the subdynamics of any z sft

quasi periodic configurations and undecidable dynamics for tilings infinite words and turing machines we describe turing machines tilings and infinite words as dynamical systems and analyze some of their dynamical properties it is known that some of these systems do not always have periodic configurations we prove that they always have quasi periodic configurations and we quantify quasi periodicity we then study the decidability of dynamical properties for these systems in analogy to rice s theorem for computable functions we derive a theorem that characterizes dynamical system properties that are undecidable as an illustration of this result we prove that topological entropy is undecidable for turing machines and for tilings

a stochastic games framework for verification and control of discrete time stochastic hybrid systems we describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting in particular we consider finite horizon zero sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space and a rational adversary has the opposing objective we derive an algorithm for computing the maximal probability of achieving the control objective subject to the worst case adversary behavior from this algorithm sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst case disturbance strategies these results are then specialized to the safety problem in which the control objective is to remain within a safe set we illustrate our modeling framework and computational approach using both a tutorial example with jump markov dynamics and a practical application in the domain of air traffic management

nonlinear filtering of systems governed by ito differential equations with jump parameters abstract in this paper we present a system of coupled stochastic infinite dimensional differential equations of zakai type which describes the evolution of the unnormalized conditional density of a conditional markov process this generalizes the nonlinear filtering equation of zakai

self adaptive methods for general variational inequalities abstract it is well known that the general variational inequalities are equivalent to the fixed point problems and the wiener hopf equations in this paper we use these alternative equivalent formulations to suggest and analyze some new self adaptive iterative methods for solving the general variational inequalities our results can be viewed as a significant extension of the previously known results for variational inequalities an example is given to illustrate the efficiency of the proposed method

a combined octree delaunay method for fully automatic 3 d mesh generation fully automatic three dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations two techniques in particular the octree and delaunay approaches have been used towards this end a method that combines both approaches to fully automatic mesh generation is presented here the resulting algorithm provides the linear growth rate and divide and conquer approach of the octree method with the simplicity and optimal properties of the delaunay triangulation

advanced general purpose computational mechanics system for large scale analysis and design abstract we have been developing an advanced general purpose computational mechanics system named adventure which is designed to be able to analyze a model of arbitrary shape with a 10 100 million degrees of freedom dofs mesh and additionally to enable parametric and nonparametric shape optimization domain decomposition based parallel algorithms are implemented in pre processes domain decomposition main processes system matrix assembling and solutions and post process visualization respectively the hierarchical domain decomposition method with a pre conditioned iterative solver hddm is adopted in the main processes as one of the major solution techniques module based architecture of the system with standardized i o format and libraries are also developed and employed to attain flexibility portability extensibility and maintainability of the whole system this paper describes some key technologies employed in the system and shows some latest results including elastic stress analysis of a precise three dimensional 3d model of a nuclear reactor vessel with a 60 million dof mesh on hitachi sr2201 1024 pes and nonparametric shape optimization of a support structure for an express way with a one million dof mesh on a pc cluster 10 pes

perturbation analysis of a system of quasi variational inequalities for optimal stochastic scheduling optimal scheduling of continuously evolving dynamical systems involves the analysis of certain partial differential inequalities on solution dependent domains these are the quasi variatlonai inequalities qvi s introduced for such problems by a bensoussan and j l lions they arise naturally in such applications as inventory control and unit commitment scheduling in electric energy systems qvi s are in these contexts the analog of the dynamic programming partial differential equations of r bellman for continuous control problems analytical treatment of qvi s involves not only the solution of partial differential inequalities but also the simultaneous analysis of the free boundaries of the domain of the solution in effect the optimal return function is the solution of the inequalities and the optimal control switching policy is defined by the free boundaries this paper considers a system of two singularly perturbed second order quasi variational inequalities with a turning point in a bounded domain in r1 asymptotic approximations for the free boundaries are derived using standard perturbation analysis for boundary value problems also local regularity properties of the limit solution are obtained the results are illustrated by a parametric study of a simple model of commitment scheduling for a single unit in a power generation system

ergodic problem for optimal stochastic switching abstract we study the minimization of the long run average cost for a family of reflected diffusion processes when the control is to switch from one process to another one this leads to solving the ergodic problem for a system of quasi variational inequalities with neumann boundary conditions this problem is studied as the limit of the discounted case when the discount factor goes to zero

number conserving cellular automata ii dynamics in this second part we study the dynamics of the number conserving cellular automata we give a classification which focuses on pattern divergence and chaoticity moreover we prove that in the case of number conserving cellular automata surjectivity is equivalent to regularity as a byproduct we obtain a strong characterization of the class of cellular automata with bounded evolutions on finite configurations

controlled diffusion processes with markovian switchings for modeling dynamical engineering systems abstract in this paper the intrinsic complex nature of engineering systems under control is treated by introducing an approach based on controlled stochastic differential equations with markovian switchings in short csdems technical conditions for the existence and uniqueness of the solutions of the csdems are provided in this context it is not unusual to deal with non linear csdems that cannot be solved analytically therefore we develop a new two step predictor corrector method for finding numerical approximations to solutions of csdems this method utilizes the euler maruyama method an illustrative application to the biochemical engineering area is presented to highlight the usefulness of our approach as a simulation tool

on the dynamics and recursive properties of multidimensional symbolic systems we study the sub dynamics of multidimensional shifts of finite type and sofic shifts and the action of cellular automata on their limit sets such a subaction is always an effective dynamical system i e it is isomorphic to a subshift over the cantor set the complement of which can be written as the union of a recursive sequence of basic sets our main result is that to varying degrees this recursive theoretic condition is also sufficient we show that the class of expansive subactions of multidimensional sofic shifts is the same as the class of expansive effective systems and that a general effective system can be realized modulo a small extension as the subaction of a shift of finite type or as the action of a cellular automaton on its limit set after removing a dynamically trivial set as applications we characterize in terms of their computational properties the numbers which can occur as the entropy of cellular automata and construct sfts and cas with various interesting properties

theory of cellular automata a survey this article surveys some theoretical aspects of cellular automata ca research in particular we discuss classical and new results on reversibility conservation laws limit sets decidability questions universality and topological dynamics of ca the selection of topics is by no means comprehensive and reflects the research interests of the author the main goal is to provide a tutorial of ca theory to researchers in other branches of natural computing to give a compact collection of known results with references to their proofs and to suggest some open problems

the nilpotency problem of one dimensional cellular automata the limit set of a celullar automaton consists of all the configurations of the automaton that can appear after arbitrarily long computations it is known that the limit set is never empty it contains at least one homogeneous configuration a ca is called nilpotent if its limit set contains just one configuration the present work proves that it is algorithmically undecidable whether a given one dimensional cellular automaton is nilpotent the proof is based on a generalization of the well known result about the undecidability of the tiling problem of the plane the generalization states that the tiling problem remains undecidable even if one considers only so called nw deterministic tile sets that is tile sets in which the left and upper neighbors of each tile determine the tile uniquely the nilpotency problem is known to be undecidable for d dimensional ca for d geq 2 the result is the basis of the proof of rice s theorem for ca limit sets which states that every nontrivial property of limit set

statistical mechanics of surjective cellular automata reversible cellular automata are seen as microscopic physical models and their states of macroscopic equilibrium are described using invariant probability measures we establish a connection between the invariance of gibbs measures and the conservation of additive quantities in surjective cellular automata namely we show that the simplex of shift invariant gibbs measures associated to a hamiltonian is invariant under a surjective cellular automaton if and only if the cellular automaton conserves the hamiltonian a special case is the well known invariance of the uniform bernoulli measure under surjective cellular automata which corresponds to the conservation of the trivial hamiltonian as an application we obtain results indicating the lack of non trivial gibbs or markov invariant measures for sufficiently chaotic cellular automata we discuss the relevance of the randomization property of algebraic cellular automata to the problem of approach to macroscopic equilibrium and pose several open questions as an aside a shift invariant pre image of a gibbs measure under a pre injective factor map between shifts of finite type turns out to be always a gibbs measure we provide a sufficient condition under which the image of a gibbs measure under a pre injective factor map is not a gibbs measure we point out a potential application of pre injective factor maps as a tool in the study of phase transitions in statistical mechanical models

a second step towards complexity theoretic analogs of rice s theorem abstract rice s theorem states that every nontrivial language property of the recursively enumerable sets is undecidable borchert and stephan 1997 initiated the search for complexity theoretic analogs of rice s theorem in particular they proved that every nontrivial counting property of circuits is up hard and that a number of closely related problems are spp hard the present paper studies whether their up hardness result itself can be improved to spp hardness we show that their up hardness result cannot be strengthened to spp hardness unless unlikely complexity class containments hold nonetheless we prove that every p constructibly bi infinite counting property of circuits is spp hard we also raise their general lower bound from unambiguous nondeterminism to constant ambiguity nondeterminism

realization problems for nonuniform cellular automata given a finite set of local rules the sequences built from them give a set of nonuniform cellular automata it is known 1 that for any such set of local rules the subset of nonuniform cellular automata built from them which give a surjective global map is in fact a sofic subshift for the injective sequences this set is only automatic accepted by a buchi automaton and it is not necessarily open or closed we prove the first corresponding realization result we provide for any sft a set of local rules such that the surjective injective nonuniform cellular automata over them are precisely the sequences in the sft up to a renaming of symbols in fact we prove that sfts are exactly the subshifts which are the set of injective sequences of nonuniform cellular automata for some set of local rules we also consider surjectivity of subclasses of nonuniform cellular automata and realizability questions for other properties in particular number conservation and chain transitivity

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

the compaction of aggregates of non spherical linear viscous particles an approximate discrete element model is used to study the compaction of aggregates of non spherical linear viscous particles the numerical model is developed in which each particle is treated individually with the appropriate constitutive relations kinematic conditions contact constraints and elimination of overlap satisfied for every particle in the aggregate mesh update algorithms are generated based on mixed triangular and quadrilateral element system the algorithms are used to detect contact generate mesh modify concave elements and prevent locking the method could be used in a variety of problems that can be represented using granular media such as asphalt polymers aluminum snow food product and others a series of numerical simulations are shown to demonstrate the efficiency and accuracy of the model

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

technical communique near optimal control for a class of stochastic hybrid systems to address a computationally intractable optimal control problem for a class of stochastic hybrid systems this paper proposes a near optimal state feedback control scheme which is constructed by using a statistical prediction method based on approximate numerical solution that samples over the entire state space a numerical example illustrates the potential of the approach

automatic mesh generation of quadrilateral elements using intelligent local approach this paper describes a new automated mesh generation method named intelligent local approach ila which well controls both size and aspect ratio of quadrilateral element in a two dimensional plane the ila can be straightforwardly extended to hexahedral elements in a three dimensional solid here elements are created sequentially considering local information on geometrical constraints and user s demand on quality of elements a user can specify the following two numerical fields a a field of element size and b that of element aspect ratio a field of priority of element creation is also specified within the ila to efficiently deal with various complicated geometrical constraints for high quality quadrilateral elements a fuzzy knowledge processing technique is effectively utilized the ila is implemented using an object oriented technique fundamental performances of the ila are demonstrated in detail through generating several quadrilateral meshes

characterization and computation of infinite horizon specifications over markov processes this work is devoted to the formal verification of specifications over general discrete time markov processes with an emphasis on infinite horizon properties these properties formulated in a modal logic known as pctl can be expressed through value functions defined over the state space of the process the main goal is to understand how structural features of the model primarily the presence of absorbing sets influence the uniqueness of the solutions of corresponding bellman equations furthermore this contribution shows that the investigation of these structural features leads to new computational techniques to calculate the specifications of interest the emphasis is to derive approximation techniques with associated explicit convergence rates and formal error bounds

a computable approach to measure and integration theory we introduce a computable framework for lebesgue s measure and integration theory in the spirit of domain theory for an effectively given second countable locally compact hausdorff space and an effectively given finite borel measure on the space we define a recursive measurable set which extends the corresponding notion due to s anin for the lebesgue measure on the real line we also introduce the stronger notion of a computable measurable set where a measurable set is approximated from inside and outside by sequences of closed and open subsets respectively the more refined property of computable measurable sets give rise to the idea of partial measurable subsets which naturally form a domain for measurable subsets we then introduce interval valued measurable functions and develop the notion of recursive and computable measurable functions using interval valued simple functions this leads us to the interval versions of the main results in classical measure theory the lebesgue integral is shown to be a continuous operator on the domain of interval valued measurable functions and the interval valued lebesgue integral provides a computable framework for integration

rice s theorem for the limit sets of cellular automata abstract rice s theorem is a well known result in the theory of recursive functions a corresponding theorem for cellular automata limit sets is proved all nontrivial properties of limit sets of cellular automata cas are shown undecidable the theorem remains valid even if only one dimensional cas are considered

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided

an element free smoothed radial point interpolation method efs rpim for 2d and 3d solid mechanics problems abstract this paper presents a novel element free smoothed radial point interpolation method efs rpim for solving 2d and 3d solid mechanics problems the idea of the present technique is that field nodes and smoothing cells scs used for smoothing operations are created independently and without using a background grid which saves tedious mesh generation efforts and makes the pre process more flexible in the formulation we use the generalized smoothed galerkin gs galerkin weak form that requires only discrete values of shape functions that can be created using the rpim by varying the amount of nodes and scs as well as their ratio the accuracy can be improved and upper bound or lower bound solutions can be obtained by design the scs can be of regular or irregular polygons in this work we tested triangular quadrangle n sided polygon and tetrahedron as examples stability condition is examined and some criteria are found to avoid the presence of spurious zero energy modes this paper is the first time to create gs galerkin weak form models without using a background mesh that tied with nodes and hence the efs rpim is a true meshfree approach the proposed efs rpim is so far the only technique that can offer both upper and lower bound solutions numerical results show that the efs rpim gives accurate results and desirable convergence rate when comparing with the standard finite element method fem and the cell based smoothed fem cs fem

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods

formal languages and global cellular automaton behavior abstract a connection is made between the description of one dimensional cellular automata as dynamical systems acting on a compact metric space and as computational systems acting on strings operators are defined which determine a bijective correspondence between subshifts of infinite configurations and languages of finite strings under this correspondence families of languages give rise to families of subshifts regular languages correspond to sofic subshifts families of subshifts corresponding to context free context sensitive and recursively enumerable languages are introduced and their closure properties under forward and backward cellular automaton images studied