ultraproducts of z with an application to many valued logics abstract up to categorical equivalence abelian lattice ordered groups with strong unit coincide with chang s mv algebras the lindenbaum algebras of the infinite valued ukasiewicz calculus while the property of being a strong unit is not definable even in first order logic mv algebras form an equational class on the other hand the addition operation and the translation invariant lattice order of a lattice ordered group are more amenable than the truncated addition operation of an mv algebra in this paper mv algebraic and group theoretical techniques are combined to classify and axiomatize all universal classes generated by an infinite totally ordered mv algebra a such that the quotient of a by its unique maximal ideal is finite the number of elements of this quotient and that of the largest finite subalgebra of a turns out to be a complete classifier the main tool for our results is given by order preserving embeddings of totally ordered groups g into ultrapowers of the additive group of integers that also preserve the nondivisibility properties of prescribed elements of g

exponential h stabilization of chaotic systems with time varying delay and external disturbance via intermittent control abstract this paper establishes an exponential h stabilization approach for chaotic systems with time varying delay and external disturbance via intermittent control based on the construction of a new lyapunov krasovskii functional and the employment of the free matrix based integral inequality some delay dependent and delay derivation dependent criteria to ensure the exponential h stabilization of the considered systems are derived in terms of linear matrix inequalities lmis different from previous works the obtained criteria can be handled to fast and slow time varying delay since an adjustable parameter is introduced in the lyapunov krasovskii functional and the indirect proof strategy is used to discuss the h performance and to reduce computational complexity moreover the desired controller can reduce the effect of external disturbance to a prescribed attenuation level and its gain matrix can be easily given by solving lmis finally numerical simulation is carried out to show the validity and benefits of the proposed method

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

on generalized versions of central limit theorems for if events if sets were introduced by atanassov to model imprecision which can be often met in real world applications if sets were also used for definition of if events for which probability theories were considered including if probability theory and m probability theory within these theories if observables and m observables were introduced and their properties have been studied in this paper we consider limit behavior of the row sums of triangular arrays of independent if observables and m observables we prove generalized versions of the central limit theorem clt for short for both types of observables i e the lindeberg clt and the lyapounov clt furthermore we prove the feller theorem for null arrays of if observables and m observables finally we illustrate our theoretical results by examples

right l groups geometric garside groups and solutions of the quantum yang baxter equation abstract right lattice ordered groups are introduced and studied as a general framework for garside groups and related groups without a garside element every right l group g has a two sided partially ordered subgroup n g which generalizes the quasi centre of an artin tits group the group n g splits into copies of z if g is noetherian the positive cone of a right l group is described as a structure that is known from algebraic logic a pair of left and right self similar hoops for noetherian right l groups g modularity of the lattice structure is characterized in terms of an operation on the set x g of atoms it is proved that modular garside groups are equivalent to finite projective spaces with a non degenerate labelling a concept of duality for x g is introduced and applied in the distributive case this gives a one to one correspondence between noetherian right l groups with duality and non degenerate unitary set theoretic solutions of the quantum yang baxter equation the description of garside groups via garside germs is extended to right l groups which yields a one sided enhancement and a new proof of dvurecenskij s non commutative extension of mundici s correspondence between abelian l groups and mv algebras

a family of hyperchaotic multi scroll attractors in rn abstract in this work we present a mechanism how to yield a family of hyperchaotic multi scroll systems in r n based on unstable dissipative systems this class of systems is constructed by a switching control law changing the equilibrium point of an unstable dissipative system for each equilibrium point presented in the system a scroll emerges the switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor thus if two systems display different numbers of scrolls they have different switching control laws this paper also presents a generalized theory that explains different approaches such as hysteresis and step functions from a unified viewpoint extending the concept of chaos in r 3 to hyperchaotic multi scroll systems in r n n 4 an illustrative example of synchronizing a communication system is given based on the developed theory

reduced order observer design for the synchronization of the generalized lorenz chaotic systems abstract this paper is concerned with the design of the novel observer that synchronizes with the generalized lorenz chaotic systems a simple reduced order observer scheme is proposed by including extra terms the boundedness of the state variables in the original system is not necessary for the observer design the prior knowledge on the derivative signal of the system output is not required it is also shown that by adopting lyapunov method and choosing appropriate design parameters the synchronization observation errors can converge to zero exponentially finally numerical examples are provided to illustrate the validity of the theoretical result

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

geometrical methods in wajsberg hoops abstract the aim of this paper is to show that certain geometric methods originally developed for investigating ukasiewicz many valued logics may be profitably applied to the study of classes of partially ordered residuated monoids we substantiate this claim by characterizing all free wajsberg hoops in terms of mcnaughton functions over the n cube and by giving complete axiomatizations for all varieties of wajsberg hoops

satisfiability in many valued sentential logic is np complete abstract cook s np completeness theorem is extended to all many valued sentential logics including the infinite valued calculus of ukasiewicz

equational characterization of all varieties of mv algebras abstract it is known that all subvarieties of mv algebras are finitely axiomatizable in the literature one can find equational characterizations of certain subvarieties such as mv n algebras in this paper we write down equational bases for all mv varieties and prove a representation theorem for each subvariety

on the semisimple tensor product of mv algebras abstract in this note we show how the mv algebraic tensor product can be used to define natural adjunctions between the algebraic structures of ukasiewicz logic with product in order to do this we define the semisimple tensor pmv algebra of a semisimple mv algebra

on the entropy of dynamical systems in product mv algebras recently the so called product mv algebras have been introduced and the entropy of partitions in these algebras have been studied in this paper the previous results are applied to dynamical systems

mv observables and mv algebras we introduce mv observables an analogue of observables for mv algebras as homomorphisms from the borel tribe generated by the borel sets of r and constant functions from 0 1 into an mv algebra m we show that it is possible to define such observables only for weakly divisible mv algebras we present a representation as well as a so called calculus of mv observables which enables us to construct e g the sum or product of mv observables

locally compact group actions on c algebras and compact subgroups be a compact subgroup in this paper we shall give necessary and sufficient conditions in order that the crossed product g x a be simple or prime our conditions are in terms of the dual 2 of the com pact subgroup k the paper is organized as follows in the second section we summarize some preliminary definitions and results about continuous banach representations of compact groups the same section contains the definitions of the subspaces of spherical functions sn nl l 7 n e e those of the algebras s i and the relations between these subspaces section 3 contains a study of saturated actions of g on a in terms of the ideals s s we mention that for compact groups the notion of saturated action has been defined by rieffel see 19 chap 73 the same section contains conditions in order that the crossed product be simple for compact abelian groups g our result reduces to the following g x

stone duality for dedekind σ complete l groups with order unit abstract building on the goodearl handelman lawrence functional representation theorem we provide a purely topological representation specifically a categorical duality for a large class of dedekind complete l groups g with order unit u including all g where u has a finite index of nilpotence our duality is a far reaching generalization of the well known stone duality between complete boolean algebras and basically disconnected compact hausdorff spaces

bases of admissible rules of proper axiomatic extensions of ukasiewicz logic in this paper we give a base of admissible rules for every proper axiomatic extension of the infinite valued ukasiewicz logic we first prove that single conclusion admissible rules of any proper axiomatic extension are finitely based the proof strongly relies on the characterization of least v quasivarieties given in 11

on injectivity of semimodules over additively idempotent division semirings and chain mv semirings abstract in this paper we give a characterization of injective semimodules over additively idempotent semirings consequently we provide a complete description of injective semimodules over the semifield of tropical integers and give an explicit construction of the injective hulls of semimodules over chain division semirings we also give a criterion for self injective mv semirings with an atomic boolean center and describe the structure of finitely generated injective semimodules over finite mv semirings as well as we show that every complete mv semiring with an atomic boolean center is an exact semiring which is defined by a hahn banach type separation property on semimodules arising in the tropical case from the phenomenon of tropical matrix duality moreover we show that complete boolean algebras are precisely the mv semirings in which every principal ideal is injective

hulls of ordered algebras projectability strong projectability and lateral completeness abstract there has been compelling evidence during the past decade that lattice ordered groups l groups play a far more significant role in the study of algebras of logic than it had been previously anticipated their key role has emerged on two fronts first a number of research articles have established that some of the most prominent classes of algebras of logic may be viewed as l groups with a modal operator second and perhaps more importantly recent research has demonstrated that the foundations of the conrad program for l groups can be profitably extended to a much wider class of algebras namely the variety of e cyclic residuated lattices that is residuated lattices that satisfy the identity x e e x here the term conrad program refers to paul conrad s approach to the study of l groups that analyzes the structure of individual or classes of l groups by primarily focusing on their lattices of convex l subgroups the present article building on the aforementioned works studies existence and uniqueness of the laterally complete projectable and strongly projectable hulls of e cyclic residuated lattices while these hulls first made their appearance in the context of functional analysis and in particular the theory of riesz spaces their introduction into the study of algebras of logic adds new tools and techniques in the area and opens up possibilities for a deep exploration of their logical counterparts

finitely presented lattice ordered abelian groups with order unit abstract let g be an l group which is short for lattice ordered abelian group baker and beynon proved that g is finitely presented iff it is finitely generated and projective in the category u of unital l groups those l groups having a distinguished order unit u only the direction holds in general we show that a unital l group g u is finitely presented iff it has a basis a large class of projectives is constructed from bases having special properties

word problems in elliott monoids abstract algorithmic issues concerning elliott local semigroups are seldom considered in the literature although these combinatorial structures completely classify af algebras in general the addition operation of an elliott local semigroup is partial but for every af algebra b whose murray von neumann order of projections is a lattice this operation is uniquely extendible to the addition of an involutive monoid e b let m 1 be the farey af algebra introduced by the present author in 1988 and rediscovered by f boca in 2008 the freeness properties of the involutive monoid e m 1 yield a natural word problem for every af algebra b with singly generated e b because b is automatically a quotient of m 1 given two formulas and in the language of involutive monoids the problem asks to decide whether and code the same equivalence of projections of b this mimics the classical definition of the word problem of a group presented by generators and relations we show that the word problem of m 1 is solvable in polynomial time and so is the word problem of the behncke leptin algebras a n k and of the effros shen algebras f for 0 1 q a real algebraic number or 1 e we construct a quotient of m 1 having a godel incomplete word problem and show that no primitive quotient of m 1 is godel incomplete

farey stellar subdivisions ultrasimplicial groups and k0 of af c algebras abstract the theory will i believe admit of being extended to solid reticulations formed by the intersections of three systems of equidistant parallel planes determinants of the third order between the three coordinates of successive points replacing the pq p q of the plane theory

amalgamation and interpolation in ordered algebras the first part of this paper provides a comprehensive and self contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations in particular proofs are given of known equivalences between the amalgamation property and the robinson property the congruence extension property and the extension property and the flat amalgamation property and the deductive interpolation property as well as various dependencies between these properties these relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice ordered abelian groups and mv algebras and to determine important subvarieties of residuated lattices where these properties hold or fail in particular a full description is given of all subvarieties of commutative gmv algebras possessing the amalgamation property

stochastic independence for probability mv algebras we propose a notion of stochastic independence for probability mv algebras addressing an open problem posed by riecan and mundici furthermore we prove a representation theorem for probability mv algebras and we get mv algebraic versions of the holder inequality and the hausdorff moment problem

fuzzy implicative and boolean ideals of mv algebras abstract we show how to obtain results in mv algebras by considering their fuzzy ideals in particular we prove the following theorem let be a fuzzy ideal of an mv algebra x then the folllowing are equivalent 1 x x 0 for all x x 2 x n x for all x x and all n 1 3 x x is a boolean algebra 4 is fuzzy implicative if i is an ideal of x and we take i then we obtain corresponding results for the ideal i and x we show how to extend fuzzy prime and fuzzy implicative ideals various fuzzy radicals are considered and related to the corresponding radicals of the algebra and we show how they live in the spectrum of the algebra

splittings in gbl algebras ii the representable case abstract in this paper we continue our investigations on splitting algebras in varieties of residuated semi lattices carried out in 2 and 3 the focus is on representable varieties of gbl algebras i e varieties generated by their totally ordered members in this context several characterizations of splitting algebras are obtained

maximal subalgebras of c algebras associated with periodic flows we find necessary and sufficient conditions for the subalgebra of analytic elements associated with a periodic c dynamical system to be a maximal norm closed subalgebra our conditions are in terms of the arveson spectrum of the action we also describe equivalent properties of the system in terms of the strong connes spectrum and the simplicity of the crossed product c 2012 elsevier inc all rights reserved

topological characterization of filter topological mv algebras abstract motivated by the study of c topology on lattice ordered groups luan and yang introduced the concept of filter topology on mv algebras in a recent paper in order to have a better perception of this concept we study some basic facts and notable examples including the standard mv algebra and chang s algebra in this paper using the fact that an isomorphism between mv algebras admits a topological isomorphism between filter topological mv algebras we show that every filter topology on a finite linearly ordered finite simple mv algebra is discrete in addition we completely describe the shape of open sets in filter topology generated by a proper filter further the description is applied to present the basic topological properties of a large class of filter topologies as an application we characterize an algebraic property of mv algebras an mv algebra is bipartite if and only if it has a proper filter which generates a filter topology with exactly four open sets

synchronization analysis in an array of asymmetric neural networks with time varying delays and nonlinear coupling in this paper the global exponential synchronization is investigated for an array of asymmetric neural networks with time varying delays and nonlinear coupling assuming neither the differentiability for time varying delays nor the symmetry for the inner coupling matrices by employing a new lyapunov krasovskii functional applying the theory of kronecker product of matrices and the technique of linear matrix inequality lmi a delay dependent sufficient condition in lmis form for checking global exponential synchronization is obtained the proposed result generalizes and improves the earlier publications an example with chaotic nodes is given to show the effectiveness of the obtained result

every state on semisimple mv algebra is integral integral representation theorem will be established for finitely additive probability measures states on semisimple mv algebras this result generalizes the well known theorem of butnariu and klement in case of order continuous states on tribes of fuzzy sets precisely it will be demonstrated that every state on a separating clan of continuous fuzzy sets arises as an integral with respect to a unique borel probability measure the key technique leading to this result exploits the geometrical topological properties of the state space the set of all states on every mv algebra forms a bauer simplex

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

generalized bosbach and riecan states based on relative negations in residuated lattices bosbach and riecan states on residuated lattices both are generalizations of probability measures on boolean algebras recently two types of generalized bosbach states on residuated lattices were introduced by georgescu and muresan through replacing the standard mv algebra in the original definition with arbitrary residuated lattices as codomains however several interesting problems there remain still open the first part of the present paper gives positive answers to these open problems it is proved that every generalized bosbach state of type ii is of type i and the similarity cauchy completion of a residuated lattice endowed with an order preserving generalized bosbach state of type i is unique up to homomorphisms preserving similarities where the codomain of the type i state is assumed to be cauchy complete consequently many existing results about generalized bosbach states can be further strengthened the second part of the paper introduces the notion of relative negation with respect to a given element called relative element in residuated lattices and then many issues with the canonical negation such as glivenko property semi divisibility generalized riecan state of residuated lattices can be extended to the context of such relative negations in particular several necessary and sufficient conditions for the set of all relatively regular elements of a residuated lattice to be special residuated lattices are given of which one extends the well known glivenko theorem and it is also proved that relatively generalized riecan states vanishing at the relative element are uniquely determined by their restrictions on the mv algebra consisting of all relatively regular elements when the domain of the states is relatively semi divisible and the codomain is involutive

on non associative generalizations of mv algebras and lattice ordered commutative loops the aim of the paper is to describe the connections between lattice ordered commutative loops and certain basic algebras which are a non associative generalization of mv algebras and are related to commutative semicopulas this extends the well known equivalence between lattice ordered abelian groups with strong order unit and mv algebras

h synchronization of time delayed chaotic systems abstract this paper considers h synchronization of a class of time delayed chaotic systems with external disturbance based on lyapunov theory and linear matrix inequality lmi formulation the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems but also reduce the effect of external disturbance to an h norm constraint then a criterion for existence of the controller is given in terms of lmis finally a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme

adaptive control of chaotic continuous time systems with delay a simple delay system governed by a first order differential delay equation may behave chaotically but the conditions for the system to have such behaviors have not been well recognized in this paper a set of rules is postulated first for the conditions for the delay system to display chaos a model reference adaptive control scheme is then proposed to control the chaotic system state to converge to an arbitrarily given reference trajectory with certain and uncertain system parameters numerical examples are given to analyze the chaotic behaviors of the delay system and to demonstrate the effectiveness of the proposed adaptive control scheme

generalized fuzzy connectives onmv algebras w x the theory of mv algebras developed by c c chang 8 9 first w x appeared in 1958 several years later zadeh 14 published his fundamental paper on fuzzy set theory the two theories had independent motivations mv algebras were developed to provide an algebraic proof of the completeness theorem for ukasiewicz infinite valued propositional logic fuzzy set theory was proposed to provide a mathematical basis for sets where in reality set membership was vague the logic of ukasiewicz includes in some sense two valued classical logic fuzzy set theory includes the usual two valued characteristic functions thus both theories are extensions of classical logic both of the above theories use as a basis of interpretation the real unit w x w x interval 0 1 the basic mv algebraic operations on 0 1 are a b s u min 1 a q b a b s max 0 a q b y 1 and a s 1 y a the basic fuzzy w x theoretic operations on 0 1 suggested by zadeh are a k b s max a b u a n b s min a b and a s 1 y a now the operations k and n can be defined in terms of and u thus the ukasiewicz operations are more general and include the basic fuzzy operations by pointwise extension we obtain given an arbitrary set x b two w x x u algebraic structures on 0 1 say a determined by and a 1 2 determined by k n a is an mv algebra and is often referred to as 1 the bold algebra of fuzzy subsets of x a is the basic algebra of fuzzy 2 subsets of x by the remark above that k n can be defined in terms of u we see that a is some type of substructure of a 2 1

least v quasivarieties of mv algebras this paper is a contribution to the study of the lattice of all quasivarieties of mv algebras given a variety v of mv algebras we say that a quasivariety is a v quasivariety provided that it generates v as a variety it turns out that every variety has a least v quasivariety denoted by q v moreover it is generated as a quasivariety by its free algebra over an infinite set of generators we obtain a komori s type characterization of q v for every proper subvariety of mv algebras we investigate the order structure of the poset of least v quasivarieties and we find all minimal quasivarieties among all quasivarieties of mv algebras different from the class of boolean algebras finally we make some remarks on the logical interpretation of least v quasivarieties of mv algebras as structurally complete extensions of the infinite valued ukasiewicz logic

riesz mcnaughton functions and riesz mv algebras of nonlinear functions abstract we focus on riesz mv algebras which are mv algebras equipped with a multiplication by numbers in the real interval 0 1 we consider for every integer n the riesz mv algebra of all continuous functions from the n th power of 0 1 to 0 1 and the riesz mv subalgebras thereof in particular we study the riesz mv subalgebras isomorphic to free riesz mv algebras with finitely many generators possibly different from the usual linear models given by what we call riesz mcnaughton functions and which generalize mcnaughton functions used in the case of mv algebras in doing this we characterize zerosets of riesz mcnaughton functions by means of polyhedra and we extend to riesz mv algebras a duality for mv algebras exposed in a paper by marra and spada

the annihilator of fuzzy subgroups abstract we implement the notion of annihilator into fuzzy subgroups of an abelian group there are different uses for the term annihilator in algebraic contexts that have been used fuzzy systems in this paper we refer to another type of annihilator which is essential in classical duality theory and extends the widely applied notion of orthogonal complement in euclidean spaces we find that in the natural algebraic duality of a group a fuzzy subgroup can be recovered after taking the inverse annihilator of its annihilator we also study the behavior of annihilators with respect to unions and intersections some illustrative examples of annihilators of fuzzy subgroups are shown both with finite and infinite rank

exponential h synchronization and state estimation for chaotic systems via a unified model in this paper h synchronization and state estimation problems are considered for different types of chaotic systems a unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems such as hopfield neural networks cellular neural networks chua s circuits unified chaotic systems qi systems chaotic recurrent multilayer perceptrons etc based on the h performance analysis of this unified model using the linear matrix inequality approach novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the state estimation problem is then studied for the same unified model where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level the parameters of these controllers and filters are obtained by solving the eigenvalue problem most chaotic systems can be transformed into this unified model and h synchronization controllers and state estimators for these systems are designed in a unified way three numerical examples are provided to show the usefulness of the proposed h synchronization and state estimation conditions

on limit theorems in fuzzy quantum spaces two kinds of fuzzy connectives are used for constructing two models of quantum mechanics in the framework some versions of the weak law of large numbers and the central limit theorem are presented

extensions for af algebras and dimension groups let a c be approximately finite dimensional af c algebras with a nonunital and c unital suppose that either i a is the algebra of compact operators or ii both a c are simple the classification of extensions of a by c is studied here by means of elliott s dimension groups in case i the weak ext group of c is shown to be extz ko c z and the strong ext group is an extension of a cyclic group by the weak ext group conditions under which either ext group is trivial are determined in case ii there is an unnatural and complicated group structure on the classes of extensions when a has only finitely many pure finite traces and somewhat more generally our motivating theme is to consider extensions of c algebras by other than the algebra of compact operators because af algebras are describable in terms of partially ordered groups they seem particularly suitable for this extension theory as the ordered groups arising from simple af algebras are fairly well understood it turns out that one can solve completely the problem of classifying simple by simple af algebras when the finite trace space of the bottom af algebra has finite dimensional dual in the course of doing this we establish formulae for the usual strong and weak ext groups of af algebras our homological approach to this differs from the computational viewpoint of pimsner and popa 14 15 we consider short exact sequences extensions of c algebras a b c with b an af algebra there is a translation to extensions within a class of partially ordered abelian groups and distinguished subset known as dimension groups with interval via the functor ko0 this translation is reversible owing to a recent result of l brown that an extension of an af algebra by an af algebra is af so all c extensions are represented as dimension group extensions with the appropriate notion of equivalence extending strong equivalence as defined in 3 p 268 when a is the algebra of compact operators on a separable hilbert space the equivalence classes admit a limited additive operation often forming a disjoint union of groups a single group results if for example both a and c are simple with a unitless but not necessarily stable 1 deals with the appropriate definitions of extensions dimension groups equivalence and the translation between af algebras and dimension groups much of this is well known in the second section it is shown that if a is simple stable and c is received by the editors december 11 1979 and in revised form march 25 1981 1980 mathematics subject classification primary 46l35 secondary 54a22 16a54 16a56 06f20 supported in part by an operating grant from nserc of canada d1982 american mathematical society 0002 9947 82 0000 1 059 09 75

sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances abstract this paper investigates two classes of synchronization problems of multiple chaotic systems with unknown uncertainties and disturbances by employing sliding mode control modified projective synchronization and transmission synchronization are discussed here for the modified projective synchronization problem sliding mode controllers are designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances for the transmission synchronization problem based on adaptive sliding mode control an integral sliding surface is selected and the adaptive laws are derived to tackle unknown uncertainties and disturbances for such systems a class of nonlinear adaptive sliding mode controllers is developed to guarantee asymptotical stability of the error systems so that all chaotic systems can synchronize with each other simulation results are given to illustrate the effectiveness of the proposed schemes by comparing with the existing methods

loomis sikorski representation of monotone σ complete effect algebras we show that monotone s complete effect algebras with the riesz decomposition property are s homomorphic images of effect tribes with the riesz decomposition property which are effect algebras of fuzzy sets closed under pointwise limits of nondecreasing fuzzy sets

free products in the category of abelian l groups with strong unit abstract we examine the structure of free products in the category a 1 of abelian l groups with strong unit we give several examples of free product computations with particular regard to l groups in a 1 corresponding via the functor k0 to af c algebras considered by glimm bratteli elliott pimsner voiculescu effros and others

h synchronization of chaotic systems using output feedback control design this article investigates the h synchronization problem for a general class of chaotic systems based on lyapunov theory linear matrix inequality lmi and linear matrix equality lme formulation the output feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an h norm constraint two illustrative examples are provided to demonstrate the effectiveness of the developed theoretical results

algebraic structures in fuzzy logic abstract common features in various fuzzy logical systems are investigated it turns out that adjoint couples and residuated lattices are very often present though not always explicitly expressed some minor new results are also proved

fuzzy maximal ideals of bci and mv algebras abstract we consider fuzzy maximal ideals of bci bck and mv algebras and show that such fuzzy ideals take only the values 0 1 and have level ideals which are maximal ideals of the algebra it is shown that fuzzy maximal ideals of commutative bck algebras are fuzzy prime we establish a correspondence between ideals and fuzzy ideals in a bounded bck algebra this correspondence is one to one between maximal ideals and fuzzy maximal ideals we also show how to construct fuzzy ideals which are not characteristic functions of ideals of an mv algebra

adaptive variable structure control for chaos suppression of unified chaotic systems this paper investigates the chaos suppression problem for a class of unified chaotic systems subject to uncertainties and control input with dead zone nonlinearity using the variable structure control technique a robust adaptive control law is established to suppress chaos in a class of unified chaotic systems even with unknown uncertainties and dead zone nonlinearity in input in particular a switching surface is newly proposed to simplify the task of ensuring the stability of the closed loop system in the sliding mode numerical results validate the effectiveness of the proposed adaptive control scheme

l algebras self similarity and l groups abstract every set x with a binary operation satisfying x y x z y x y z corresponds to a solution of the quantum yang baxter equation if the left multiplication is bijective w rump a decomposition theorem for square free unitary solutions of the quantum yang baxter equation adv math 193 2005 40 55 the same equation becomes a true statement of propositional logic if the binary operation is interpreted as implication in the present paper l algebras essentially defined by the mentioned equation are introduced and studied for example hilbert algebras locales left hoops pseudo mv algebras and l group cones are l algebras the main result states that every l algebra admits a self similar closure in a further step a structure group g x is associated to any l algebra x one more equation implies that the structure group g x is lattice ordered as an application we characterize the l algebras with a natural embedding into the negative cone of an l group in particular this implies mundici s equivalence between mv algebras and unital abelian l groups and dvurecenskij s non commutative generalization

observables on perfect mv algebras abstract an observable on an mv algebra is any homomorphism from the borel algebra b r into the mv algebra which maps a sequence of disjoint borel sets onto summable elements of the mv algebra we establish that there is a one to one correspondence between observables on rad dedekind complete perfect mv algebras with principal radicals and their spectral resolutions it means that we show that our partial information on an observable known only on all intervals of the form t is sufficient to determine the whole information about the observable in addition this correspondence allows us to define the olson order which is a partial order on the set o m of all observables on an mv algebra m as well as we can define a sum of observables so that o m becomes a lattice ordered semigroup

quadratic optimal synchronization of uncertain chaotic systems abstract this paper investigates the quadratic optimal synchronization of uncertain chaotic systems with parameter mismatch parametric perturbations and external disturbances on both master and slave systems a robust control scheme based on lyapunov stability theory and quadratic optimal control approach is derived to realize chaotic synchronization the sufficient criterion for stability condition is formulated in a linear matrix inequality lmi form the effect of uncertain parameters and external disturbance is suppressed to an h norm constraint an adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena the simulation results for synchronization of the chua s circuit system and the lorenz system demonstrate the effectiveness of the proposed scheme

exponential rm h _ infty synchronization of general discrete time chaotic neural networks with or without time delays this brief studies exponential h synchronization of a class of general discrete time chaotic neural networks with external disturbance on the basis of the drive response concept and h control theory and using lyapunov krasovskii or lyapunov functional state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays but also reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities most discrete time chaotic systems with or without time delays such as hopfield neural networks cellular neural networks bidirectional associative memory networks recurrent multilayer perceptrons cohen grossberg neural networks chua s circuits etc can be transformed into this general chaotic neural network to be h synchronization controller designed in a unified way finally some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods

effectible residuated lattices and n th roots in this paper conditions are given on residuated lattices and on girard algebras in order for them to be generalized effect algebras and effect algebras respectively a new class of such effectible residuated lattices essentially enlarging mv algebras is defined of particular interest are pre radicable residuated lattices having all n th roots generalizing hohle s square roots to an arbitrary order n the existence of partial n th roots on effectible residuated lattices and girard algebras is related with the concept of divisible effect algebras

fuzzy ideals of bci and mv algebras abstract using fuzzy ideals it is shown that every ideal of a bci algebra is weakly implicative for a fuzzy ideal of an mv algebra it is shown that it satisfies x v y x y x y for all x y if it is fuzzy implicative and fuzzy prime then it also satisfies x y x y x x 1 and x x 0 for all x and y and in fact im 0 1

weakly divisible mv algebras and product abstract we introduce weakly divisible mv algebras and we show that every weakly divisible complete mv algebra is isomorphic to the system of all continuous fuzzy functions defined on some compact hausdorff space which generalizes a result of di nola and sesse in non classical logics and their application to fuzzy subsets kluwer academic dordrecht to appear this enables us to define an associative and commutative product on weakly divisible complete mv algebras with a multiplicative unity 1 as an application we show that any system of observables on this mv algebra admits a joint observable with respect to this product

stone duality above dimension zero axiomatising the algebraic theory of c x abstract it has been known since the work of duskin and pelletier four decades ago that k op the opposite of the category of compact hausdorff spaces and continuous maps is monadic over the category of sets it follows that k op is equivalent to a possibly infinitary variety of algebras in the sense of slominski and linton isbell showed in 1982 that the lawvere linton algebraic theory of can be generated using a finite number of finitary operations together with a single operation of countably infinite arity in 1983 banaschewski and rosick independently proved a conjecture of bankston establishing a strong negative result on the axiomatisability of k op in particular is not a finitary variety isbell s result is best possible the problem of axiomatising by equations has remained open using the theory of chang s mv algebras as a key tool along with isbell s fundamental insight on the semantic nature of the infinitary operation we provide a finite axiomatisation of

states on semi divisible generalized residuated lattices reduce to states on mv algebras a semi divisible residuated lattice is a residuated lattice l satisfying an additional condition weaker than that of divisibility such structures are related to mathematical fuzzy logic as well as to extended probability theory by the fact that the subset of complemented elements induces an mv algebra we define generalized residuated lattices by omitting commutativity of the corresponding monoidal operation and study semi divisibility in such structures we show that given a good generalized residuated lattice l the set of complemented elements of l denoted by mv l forms a pseudo mv algebra if and only if l is semi divisible maximal filters on a semi divisible generalized residuated lattice l are in one to one correspondence with maximal filters on mv l we study states on semi divisible generalized residuated lattices riecan states on a semi divisible generalized residuated lattice l are determined by riecan states on mv l the same holds true for bosbach states whenever l is a good divisible generalized residuated lattice extremal riecan states on a semi divisible generalized residuated lattice l are in one to one correspondence with maximal and semi normal filters on l

representing continuous t norms in quantum computation with mixed states a model of quantum computation is discussed in aharanov et al 1997 proc 13th annual acm symp on theory of computation stoc pp 20 30 and tarasov 2002 j phys a math gen 35 5207 35 in which quantum gates are represented by quantum operations acting on mixed states it allows one to use a quantum computational model in which connectives of a four valued logic can be realized as quantum gates in this model we give a representation of certain functions known as t norms menger 1942 proc natl acad sci usa 37 57 60 that generalize the triangle inequality for the probability distribution valued metrics as a consequence an interpretation of the standard operations associated with the basic fuzzy logic hajek 1998 metamathematics of fuzzy logic trends in logic vol 4 dordrecht kluwer is provided in the frame of quantum computation

on the geometric theory of local mv algebras abstract we investigate the geometric theory of local mv algebras and its quotients axiomatizing the local mv algebras in a given proper variety of mv algebras we show that whilst the theory of local mv algebras is not of presheaf type each of these quotients is a theory of presheaf type which is morita equivalent to an expansion of the theory of lattice ordered abelian groups di nola lettieri s equivalence is recovered from the morita equivalence for the quotient axiomatizing the local mv algebras in chang s variety that is the perfect mv algebras we establish along the way a number of results of independent interest including a constructive treatment of the radical for mv algebras in a fixed proper variety of mv algebras and a representation theorem for the finitely presentable algebras in such a variety as finite products of local mv algebras

closure operations on mv algebras abstract closure operations on posets have been investigated and applied extensively to lattices of congruences of various algebraic structures in this paper we initiate the study of closure operations on mv algebras and star operations on mv modules the connections between closure star operations studied here and those of semirings as well as those of lattice ordered rings are also investigated we provide several examples of these closure operations and star operations and also study some of their main properties

an extension of stone duality to fuzzy topologies and mv algebras abstract in this paper we introduce the concept of mv topology a special class of fuzzy topological spaces and prove a proper extension of stone duality to the categories of limit cut complete mv algebras and stone mv spaces namely zero dimensional compact hausdorff mv topological spaces then we describe the category of limit cut complete mv algebras and show that it is a completion namely a reflective subcategory with faithful reflection of the category of semisimple mv algebra last we compose our duality with other known ones thus obtaining new categorical equivalences and dualities involving categories of mv algebras

coproductmv algebras nonstandard reals and riesz spaces abstract up to categorical equivalence mv algebras are unit intervals of abelian lattice ordered groups for short l groups with strong unit while the property of being a strong unit is not even definable in first order logic mv algebras are definable by a few simple equations accordingly such notions as ideals and coproducts are definable for anymv algebraaas particular cases of the general algebraic notions the radical rad ais the intersection of all maximal ideals ofa anmv algebraais said to be local iff it has a unique maximal ideal then by hoelder s theorem the quotienta rad ais isomorphic to a subalgebra of the real unit interval 0 1 using nonstandard real numbers we give a concrete representation of those totally orderedmv algebrasawhich are isomorphic to the coproduct ofa rad aand rad a the latter denoting the subalgebra ofagenerated by its radical as an application using several categorical equivalences we describe themv algebraic counterparts of riesz spaces also known as vector lattices