continuous feedback approach for controlling chaos we show that the continuous feedback approach is highly effective for controlling chaotic systems the control design for the lorenz system is presented as an example to demonstrate the strength of this approach the proposed control is able to eliminate chaos and bring the system toward any of the three steady states two different control input locations are considered only one system variable is used in the feedback the control scheme can tolerate both measurement noise and modeling uncertainty as long as they are bounded

non linear oscillations of a rotor in active magnetic bearings abstract the non linear response of a rotor supported by active magnetic bearings is investigated and both primary and internal resonances are considered the method of multiple scales is used to obtain four first order ordinary differential equations that describe the modulation of the amplitudes and phases of vibrations in the horizontal and vertical directions the steady state response and the stability of the solutions are determined numerically from the reduced system it is shown that the steady state solutions lose their stability by either saddle node bifurcation or hopf bifurcation in the regime of multiple coexisting solutions two stable solutions are found the effect of imbalance eccentricity as well as the effect of the proportional and derivative gains of the controller on the non linear response of the system are studied finally numerical simulations are performed to verify the analytical predictions

fuzzy equivalence relations and their equivalence classes in this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice we give certain characterizations of fuzzy semi partitions and fuzzy partitions over a complete residuated lattice as well as over a linearly ordered complete heyting algebra in the latter case for a fuzzy equivalence relation over a linearly ordered complete heyting algebra we construct an algorithm for calculation of a minimal family of its equivalence classes which generates it most of the presented results are new but some of them are generalizations of known results given in a way which simplifies and clarifies them

sup t norm and inf residuum are one type of relational product unifying framework and consequences we present a simple framework which enables us to consider the well known sup t norm and inf residuum products of relations as two particular cases of a single more general type of product we present basic properties of the framework and consequences for the theory of fuzzy relations informally the paper implies that in many cases of fuzzy relational modeling such as in solving fuzzy relational equations there is no need to develop the methods for sup t norm and inf residuum products separately because these methods are just two particular instances of a single method

the liapunov dimension of strange attractors abstract many papers have been published recently on studies of dynamical processes in which the attracting sets appear quite strange in this paper the question of estimating the dimension of the attractor is addressed while more general conjectures are made here particular attention is paid to the idea that if the jacobian determinant of a map is greater than one and a ball is mapped into itself then generically the attractor will have positive two dimensional measure and most of this paper is devoted to presenting cases with such jacobians for which the attractors are proved to have non empty interior

chaotic and non linear dynamic analysis of a two axis rate gyro with feedback control mounted on a space vehicle abstract an analysis is presented in this paper for a two axis rate gyro subjected to linear feedback control mounted on a space vehicle which is spinning with uncertain angular velocity z t about its spin of the gyro for the autonomous case in which z t is steady the stability analysis of the system is studied by routh hurwitz theory for the non autonomous case in which z t is sinusoidal function this system is a strongly non linear damped system subjected to parametric excitation by varying the amplitude of sinusoidal motion periodic and chaotic responses of this parametrically excited non linear system are investigated using the numerical simulation some observations on symmetry breaking bifurcations period doubling bifurcations and chaotic behavior of the system are investigated by various numerical techniques such as phase portraits poincare maps average power spectra and lyapunov exponents in addition some discussions about chaotic motions of this system can be suppressed and changed into regular motions by a suitable constant motor torque are included

the equivalence of certain heat kernel and green function bounds abstract we show that certain upper and lower bounds on the green function and heat kernel of a second order elliptic operator in a bounded region are equivalent and imply a number of apparently stronger bounds we also show that these bounds are equivalent to the harnack inequality except for peculiar regions and are therefore almost always valid

nonexistence of global solutions of a nonlinear hyperbolic system consider the initial value problem utt au ivip vtt av u q x e r t t o u x 0 f x v x 0 h x ut x 0 g x vt x 0 x with 1 0 we show that there exists a bound b n oo such that if 1 pq b n all nontrivial solutions with compact support blow up in finite time

necessary and sufficient conditions for generalized uniform fuzzy partitions abstract the fundamental concept in the theory of fuzzy transform f transform is the fuzzy partition which is a generalization of the classical concept of partition the original definition assumes that every two normal fuzzy subsets in a partition overlap in such a way that the sum of the membership degrees at each point is equal to 1 this condition can be generalized by relaxing the assumption of normality for fuzzy sets the result is a denser fuzzy partition that may improve the approximation properties and the smoothness of the inverse f transform a fuzzy partition with this property will be referred to as general the problem is how a general fuzzy partition can be effectively constructed if we use a generating function with special properties then it is not immediately clear whether it defines a general fuzzy partition in this paper we find a necessary and sufficient condition that will enable the optimal generalized fuzzy partition to be designed more easily which is important in various practical applications of the f transform for example image processing time series analysis and solving differential equations with boundary conditions

l fuzzy closure systems this paper studies the generalization of fuzzy closure operators and fuzzy closure systems introduced by belohlavek in 2001 and introduces the concepts of strong l fuzzy closure systems and strong l fuzzy closure operators it is shown that a strong l fuzzy closure system is precisely the fuzzy system in opposition to the crisp system and a strong l fuzzy closure operator is a suitable closure operator that has a close relation to a strong l fuzzy closure system it is also shown that there is a galois correspondence between the category of strong l fuzzy closure system spaces and that of strong l fuzzy closure spaces

lattice type fuzzy order is uniquely given by its 1 cut proof and consequences a 1 cut of a fuzzy relation sometimes called a core does not contain all the information that is represented by the fuzzy relation particularly a fuzzy order on a universe x equipped with an fuzzy equality is not uniquely determined by its 1 cut 1 x y x y 1 that is there are in general several fuzzy orders with a common 1 cut we show that if the fuzzy order obeys in addition the lattice structure which many natural examples of fuzzy orders do it is uniquely determined by its 1 cut moreover we discuss consequences of this result for the so called fuzzy concept lattices and formal concept analysis

fuzzy sets and sheaves part ii this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete w valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

the fujita exponent for the cauchy problem in the hyperbolic space abstract it is well known that the heat kernel in the hyperbolic space has a different behavior for large times than the one in the euclidean space the main purpose of this paper is to study its effect on the positive solutions of cauchy problems with power nonlinearities existence and non existence results for local solutions are derived emphasis is put on their long time behavior and on fujita s phenomenon to have the same situation as for the cauchy problem in r n namely finite time blow up for all solutions if the exponent is smaller than a critical value and existence of global solutions only for powers above the critical exponent we must introduce a weight depending exponentially on the time in this respect the situation is similar to problems in bounded domains with dirichlet boundary conditions important tools are estimates for the heat kernel in the hyperbolic space and comparison principles

non linear dynamics and chaos control of a damped satellite with partially filled liquid the dynamic behaviors of a damped satellite with partially filled liquid which is subjected to external disturbance are studied in this paper the lyapunov direct method is used to obtain conditions of stability of the equilibrium point of the system a co dimension one bifurcation analysis for the autonomous system is carried out near the degenerate point it is found that hopf bifurcation occurs in the system by center manifold theory by applying numerical results phase diagrams power spectrum poincare maps and lyapunov exponents are presented to observe periodic and chaotic motions the effect of the parameter changes in the system can be found in the bifurcation and parametric diagrams for global analysis the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping micm method finally several methods the delayed feedback control the addition of constant motor torque the addition of periodic force and adaptive control algorithm are used to control chaos effectively

fuzzy homomorphisms of algebras in this paper we consider fuzzy relations compatible with algebraic operations which are called fuzzy relational morphisms in particular we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations called uniform fuzzy relational morphisms and those which are partially uniform f functions called fuzzy homomorphisms both uniform fuzzy relations and partially uniform f functions were introduced in a recent paper by us uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras we give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms we establish certain relationships between them and fuzzy congruences and we prove homomorphism and isomorphism theorems concerning them we also point to some applications of uniform fuzzy relational morphisms

pointed semi quantales and lattice valued topological spaces in a way more general than variable basis approach to lattice valued topological spaces the present paper introduces an alternative approach to lattice valued topological spaces direct product representation spaces extending the notion of quantal spaces in the sense of mulvey and pelletier to semi quantales recently proposed by rodabaugh this paper aims to give an answer to the main question whether there exists a categorical connection possibly a categorical equivalence between direct product representation spaces and variable basis lattice valued topological spaces small sources in the category of semi quantales which are called pointed semi quantales can be identified with direct product representation spaces for this reason the main problem will be handled in terms of pointed semi quantales generalized quasi lattice valued topological spaces extending variable basis quasi topological spaces into the present setting are introduced to be a suitable topological counterpart of pointed semi quantales to formalize and to solve the main problem categories of pointed semi quantales and of generalized quasi lattice valued topological spaces are constructed and the relations between these categories providing a satisfactory answer to the main problem are established in this paper

uniform fuzzy relations and fuzzy functions in this paper we introduce and study the concepts of a uniform fuzzy relation and a partially uniform f function we give various characterizations and constructions of uniform fuzzy relations and uniform f functions we show that the usual composition of fuzzy relations is not convenient for f functions so we introduce another kind of composition and we establish a mutual correspondence between uniform f functions and fuzzy equivalences we also give some applications of uniform fuzzy relations in approximate reasoning especially in fuzzy control and we show that uniform fuzzy relations are closely related to the defuzzification problem

products of elements in vague semigroups and their implementations in vague arithmetic vague arithmetic different from the present literature of fuzzy arithmetic has been proposed in demirci internat j uncertainty fuzziness and knowledge based systems 10 1 2002 25 internat j general systems 32 2 2003 157 177 to model vaguely defined arithmetic operations resulting from the indistinguishability of real numbers the main motivating problem of this paper is to introduce the notion of vague product sum of a finite number of real numbers in vague arithmetic and to point out their fundamental properties from a more abstract mathematical point of view the vague product sum of a finite number of real numbers in vague arithmetic and their properties can be considered as the vague product of a finite number of elements in vague semigroups and their relevant properties for this reason a large part of this paper is devoted to the vague product of a finite number of elements in vague semigroups and their elementary properties as a direct implementation of the present results it is shown that the vague product sum of a finite number of real numbers in vague arithmetic can be easily evaluated in terms of the underlying many valued equivalence relations furthermore various non trivial examples for the vague product sum of a finite number of real numbers in vague arithmetic are designed and a simple technique for the construction of such non trivial examples is stated

bifurcation behavior of a rotor supported by active magnetic bearings abstract the non linear dynamics of a rigid rotor levitated by active magnetic bearings is investigated the vibrations in the horizontal and vertical directions are analyzed on the center manifold near the double zero degenerate point by using normal form method the resulting normal forms in the horizontal and vertical directions are different due to the effect of rotor weight it is shown that the vibratory behavior in the vertical direction can be reduced on the center manifold to the bogdanov takens form for the autonomous case there exist saddle node bifurcation and hopf bifurcation for local analysis and a saddle connection bifurcation for global analysis for non autonomous case the melnikov technique is used to determine the critical parameter at which the homoclinic orbits intersect transversally for the vibrations in the horizontal direction the essential non linear terms of the truncated normal form are third order the behaviors of zero solutions are given finally numerical simulations are performed to verify the analytical predictions

stabilization and positioning control of a rolling disk by using the bogdanov takens bifurcation abstract on the basis of bogdanov takens bifurcation we obtain two nonlinear control laws for stabilization and positioning of a rolling disk on a horizontal plane at a desired set point the first control law is applied to reach a set of predetermined points from previously calculated initial conditions which unavoidably implies a small position error to overcome this problem a second procedure based on a nonlinear inverse control law is examined by using adequate leaning tilting and rolling moments the system satisfies nonholonomic constraints it is underactuated and the analysis of the bogdanov takens bifurcation provides the admissible parameter values to reach the desired set point our analysis allows stabilization and positioning of the rolling disk through small control torques neglecting the internal servomechanism dynamics with adequate reaction forces satisfying the nonholonomic conditions the results of the analytical calculations are verified by full numerical simulations

chaos control of new mathieu van der pol systems with new mathieu duffing systems as functional system by gyc partial region stability theory abstract in this paper a new strategy by using gyc partial region stability theory is proposed to achieve chaos control using the gyc partial region stability theory the new lyapunov function used is a simple linear homogeneous function of error states and the lower order controllers are much more simple and introduce less simulation error numerical simulations are given for new mathieu van der pol system and new mathieu duffing system to show the effectiveness of this strategy

global existence and finite time blow up for a parabolic system on hyperbolic space in this paper we study the global existence and finite time blow up of positive solutions for a parabolic system on hyperbolic space using the heat semigroup and constructing subsolutions and supersolutions we obtain the fujita type results in the case of a critical exponent the critical exponent is not a blow up exponent

tuning of a pid controlled gyro by using the bifurcation theory this paper concerns the control design of a pid controlled gimbals suspension gyro whose parameters are determined by using bifurcation theory the non linear mathematical model of the gyro is deduced by using the nutation theory of gyroscopes considering a pid controller with constrained integral action it is shown that depending on different values of the maximum allowed integral action a poincare andronov hopf bifurcation may appear the analysis of the stability or instability of this bifurcation from the first lyapunov value gives a procedure to adjust the parameters of the pid controller the developed control methodology is evaluated through numerical simulations 2007 elsevier b v all rights reserved

a note on semilinear heat equation in hyperbolic space abstract bandle et al 1 obtained a quite interesting result about a semilinear heat equation that the fujita exponent relative to the whole hyperbolic space is just the same as that relative to bounded domain in euclidean space and in addition the properties of solutions are different in the critical exponent case our purpose is to answer an open problem proposed by bandle et al for the critical exponent case and it together with the one obtained by them shows that the critical exponent case does belong to the non blow up case which is completely different from the case in euclidean space

existence and nonexistence of global solutions forut δu a x upinrd abstract we study nonnegative solutions of the equation u t 2 u a x u p in r d t 0 under the assumption that a x 0 is on the order x m for m 2 or that 0 a x c x 2 extending the classical result of fujita and more recent results of bandle and levine and of levine and meier we find a critical exponent p p m d such that if 1 p p then there exist no solutions that are global in time while if p p then there exist both global and nonglobal solutions

fuzzy sets and sheaves part ii sheaf theoretic foundations of fuzzy set theory with applications to algebra and topology this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

the normal form of a granular fuzzy function we consider here a particular kind of fuzzy relations f x y on x y such that the cut f is an ordinary function for each 0 1 from the underlying level granular structure on x to that on y which are determined by a given pair of similarity relations x x x and y y y on x and y respectively this type of fuzzy relations have a close connection with rough sets and functions between them and are called here granular fuzzy functions we show that each granular fuzzy function f x y has a unique normal form f x y f x y which preserves the values f x for each 0 1 where x is the equivalence class of x at the level for x the normal form functions f x y are in many ways more well behaved than the non normal forms in terms of function composition unique inverse function etc

eq algebras from the point of view of generalized algebras with fuzzy equalities eq algebras introduced by novak are algebras of truth values for a higher order fuzzy logic fuzzy type theory in this paper the compatibility of multiplication w r t the fuzzy equality in an arbitrary eq algebra is examined particularly an example indicates that the compatibility axiom does not always hold and then a class of eq algebras satisfying the compatibility axiom is characterized by introducing a residuated integral meet semilattice ordered monoid valued fuzzy algebra called a generalized algebra with a fuzzy equality

simplification and independence of axioms of fuzzy logic systems imtl and nm monoidal t norm based logic mtl is the common formalization of all fuzzy logic of left continuous t norms and their residua this system has two important schematic extensions involutive monoidal t norm based logic imtl and nilpotent minimum logic nm in this paper we discuss simplification and independence of axioms of imtl and nm the shorter axioms of both logics and an independent axioms of the system imtl are given

regular and chaotic dynamic analysis and control of chaos of an elliptical pendulum on a vibrating basement the dynamic behavior of an elliptical pendulum subjected to external disturbance is studied in this paper the lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system by applying numerical results phase diagrams power spectrum period t maps and lyapunov exponents are presented to observe periodic and chaotic motions the effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams for global analysis the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping micm method finally several methods the delayed feedback control the addition of constant torque the addition of periodic force adaptive control algorithm and bang bang control are used to control chaos effectively

double degeneracy and chaos in a rate gyro with feedback control the analysis of a single axis rate gyro subjected to feedback control mounted on a space vehicle that is spinning with uncertain angular velocity zabout its spin of the gyro is presented for the autonomous case in which zis steady we examine the dynamics of the resulting system on the center manifold near the double zero degenerate point by using center manifold and normal form methods there exist a few kinds of bifurcations in the autonomous case such as pitchfork and hopf bifurcations for local bifurcation analyses and a saddle connection bifurcation for global analyses as singular velocity zof the space vehicle is harmonic the melnikov technique was used to give criteria for the existence of chaos in the gyro motion the numerical simulations are performed to verify the analytical results in the form of phase portraits bifurcation diagrams and lyapunov exponents in addition chaotic motions of this system can be changed into regular motions by a small parametric perturbation with lyapunov exponent calculations

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

stability and hopf bifurcation of a magnetic bearing system with time delays the effect of time delays occurring in the feedback control loop on the linear stability of a simple magnetic bearing system is investigated by analyzing the associated characteristic transcendental equation it is found that a hopf bifurcation can take place when time delays pass certain values the direction and stability of the hopf bifurcation are determined by constructing a center manifold and by applying the normal form method it is also found that a codimension two bifurcation can occur through a hopf and a steady state bifurcation interaction finally numerical simulations are performed to verify the analytical predictions

join completions of l ordered sets in this paper we build and characterize the join completions of an l ordered set which generalizes the join completions of a crisp poset the universal property of join completions is studied a categorical characterization of the dedekind macneille completion for an l ordered set is presented

generalized t norm structures abstract this is a continuation of the work in drossos and navara eufit 96 aachen germany 1996 in this paper we investigate the possibility of defining a quantitative structure non idempotent on the top of a usual qualitative structure these generalized monoidal structures are very much related to the notion of t norms and t conorms defined on the closed interval 0 1 we would then like to define an appropriate generalization of the notion of t norm as a generalized monoidal structure which will reflect a minimum of properties of t norms defined on 0 1 considered as absolutely basic

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

a natural interpretation of fuzzy sets and fuzzy relations we present a new and natural interpretation of fuzzy sets and fuzzy relations where the basic notions and operations have quite natural meanings we interpret fuzzy sets and fuzzy relations in a cumulative heyting valued model for intuitionistic set theory and define the basic notions and operations naturally in the model as far as fuzzy sets and fuzzy relations are considered as extensions of crisp sets and relations this interpretation seems to be most natural in the interpretation the canonical embedding from the class of all sets into the model plays an important role we distinguish generalized fuzzy sets fuzzy subsets of crisp sets and membership functions of fuzzy sets on crisp sets thus we present a foundation for developing a general theory of fuzzy sets where fuzzy subsets of different sets can be treated in a natural and uniform way

global existence and nonexistence for some degenerate and quasilinear parabolic systems abstract the author discusses the degenerate and quasilinear parabolic system u t u v u a u p v q and v t u v v b u r v s with dirichlet boundary conditions in a bounded domain and shows that the global existence depends crucially on the sign of the difference q r 1 p 1 s and the domain

fuzzy complete lattices in this paper based on l fuzzy posets previously introduced by the third author l fuzzy complete lattices are defined which are generalizations of usual complete lattices and coincide with wagner s complete and cocomplete w categories enriched over the frame l and are consequently a special kind of complete w lattices defined by lai and zhang however tarski fixed point theorem for the l fuzzy complete lattices is proved in a different way from that by lai and zhang furthermore some fuzzy powerset operators are suggested they are not only generalizations of ordinary powerset operators but also generalizations of l valued zadeh powerset operators and their properties are discussed

traffic signal control on similarity logic reasoning the main intention in this study is to tie fuzzy reasoning to many valued logic framework a lukasiewicz many valued logic similarity based fuzzy control algorithm is introduced and tested in three realistic traffic signal control systems the results are compared to fuzzy control systems where the inference is based on standard matlab fuzzy logic toobox s mamdani style system the compared traffic signal control modes are signalized pedestrian crossing and multi phase signal control with phase selection the statistical significance in differences of expectations obtained by different control schemes has been tested by two sided approximate students test on significance level 0 01 simulations made by hutsim traffic signal simulator show that the performances of the new control algorithm and that of standard mamdani style algorithm are almost equal however if traffic density is high then the new algorithm gives significantly better statistical results moreover a stronger mathematical approach offers a natural smoothness test

topological and lattice structures of l fuzzy rough sets determined by lower and upper sets this paper builds the topological and lattice structures of l fuzzy rough sets by introducing lower and upper sets in particular it is shown that when the l relation is reflexive the upper resp lower set is equivalent to the lower resp upper l fuzzy approximation set then by the upper resp lower set it is indicated that an l preorder is the equivalence condition under which the set of all the lower resp upper l fuzzy approximation sets and the alexandrov l topology are identical however associating with an l preorder the equivalence condition that l interior resp closure operator accords with the lower resp upper l fuzzy approximation operator is investigated at last it is proven that the set of all the lower resp upper l fuzzy approximation sets forms a complete lattice when the l relation is reflexive

control of stochastic chaos using sliding mode method stabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper the stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a wiener process which eventually generates an ito differential equation it is also assumed that the chaotic system being studied has some model uncertainties which are not random the sliding mode controller with some modifications is used for stochastic chaos suppression it is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero as some case studies the stabilization of 1 cycle and 2 cycle orbits of chaotic duffing and f 6 van der pol systems is investigated by applying the proposed method to their corresponding stochastically perturbed systems simulation results show the effectiveness of the method and the accuracy of the statements proved in the paper

fuzzy sets and formal logics the paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics our focus is on the historical side of these developments

stability and bifurcation of rotor motion in a magnetic bearing abstract the equations of motion of a two degrees of freedom mass in a magnetic bearing are non linear in displacement with geometric coupling of the magnetic bearing coupling the horizontal and vertical components of rotor motion the non linear forced response is studied in two ways 1 using imbalance force 2 using non imbalance harmonic force in the forced response only periodic motion is investigated here stable periodic motion is obtained by numerical integration and by the approximate method of trigonometric collocation where unstable motion coexists with stable motion after a bifurcation of periodic motion the unstable motion is obtained by the collocation method the periodic motions local stability and bifurcation behavior are obtained by floquet theory the parameters i e rotor speed imbalance eccentricity forcing amplitude rotor weight and geometric coupling are investigated to find regimes of non linear behavior such as jumps and subharmonic motion

critical exponent for parabolic system with time weighted sources in bounded domain abstract this paper considers the time weighted parabolic system u t u e t v p v t v e t u q in bounded domain with r and p q 0 subject to null dirichlet boundary condition the critical fujita curve is determined as p q c 1 max p q 0 1 where 1 is the first eigenvalue of the laplacian as an extension it is observed for another coupled system u t u m u v p v t v n v u q with p q 1 that there is the fujita critical coefficient max m n 1 namely any nontrivial solution blows up in finite time if and only if max m n 1 the studies of critical curves for coupled systems in the current literature are all heavenly relying upon jensen s inequality and the kaplan method for which one has to deal with complicated discussions on the exponents p q being greater or less than 1 differently in the present framework the heat semigroup is introduced to study critical curves for coupled systems where various superlinear and sublinear cases can be treated uniformly by estimates involved this greatly simplifies the arguments for establishing fujita type theorems

on the critical exponent for reaction diffusion equations in this paper we study the initial boundary value problem for u t u h t u p with homogeneous dirichlet boundary conditions where h t t q for large t let s sup s positive solutions w of u t u such that mathop lim sup limits t to infty t s parallel w cdot t parallel infty infty then for p 1 q 1 s we show if p p there are global positive solutions that decay to zero uniformly for t if 1 p p then all nontrivial solutions blow up in finite time we determine p for some conical domains in r 2 and r 3 a similar result is derived for a bounded domain if h t e t for large t

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

boundedness and blow up for a semilinear reaction diffusion system abstract we consider the semilinear parabolic system s u t u p t u q where x rnn 1 t 0 and p q are positive real numbers at t 0 nonnegative continuous and bounded initial values u0 v0 x are prescribed the corresponding cauchy problem then has a nonnegative classical and bounded solution u t x v t x in some strip st 0 t r n 0 t sup t 0 u v remain bounded in s t we show in this paper that if 0 t so that solutions can be continued for all positive times when pq 1 and 1 pq 1 n 2 with max p q one has t for every nontrivial solution u v t is then called the blow up time of the solution under consideration finally if 1 pq 1 n 2 both situations coexist since some nontrivial solutions remain bounded in any strip s while others exhibit finite blow up times

stability analysis via the concept of lyapunov exponents a case study in optimal controlled biped standing balancing control is important for biped standing in spite of large efforts it is very difficult to design balancing control strategies satisfying three requirements simultaneously maintaining postural stability improving energy efficiency and satisfying the constraints between the biped feet and the ground in this article a proportional derivative pd controller is proposed for a standing biped which is simplified as a two link inverted pendulum with one additional rigid foot link the genetic algorithm ga is used to search for the control gain meeting all three requirements the stability analysis of such a deterministic biped control system is carried out using the concept of lyapunov exponents les based on which the system stability where the disturbance comes from the initial states and the structural stability where the disturbance comes from the pd gains are examined quantitively in terms of stability region this article contributes to the biped balancing control more significan

algebras with fuzzy equalities an algebra with fuzzy equality is a set with operations on it that is equipped with similarity i e a fuzzy equivalence relation such that each operation f is compatible with described verbally compatibility says that each f yields similar results if applied to pairwise similar arguments on the one hand algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic and have been studied from this point of view before on the other hand they are the formal counterpart to the intuitive idea of having functions that are not allowed to map similar objects to dissimilar ones the present paper aims at developing fundamental points of algebras with fuzzy equalities we introduce the notion of an algebra with fuzzy equality present natural examples compare the notion with other approaches and introduce and develop basic structural notions subalgebras morphisms products direct unions in a follow up paper vychodil direct limits and reduced products of algebras with fuzzy equalities submitted for publication we deal with advanced topics in algebras with fuzzy equalities direct limits reduced products

hopf bifurcation control a new approach in this paper we find conditions to control a hopf bifurcation in a class of nonlinear systems whose linear approximation has two eigenvalues on the imaginary axis without assuming that the system is controllable we use the center manifold theorem to project the dynamics on a two dimensional manifold and design a controller that permits us to decide the stability and direction of the emerging periodic solution

global chaos control of non autonomous systems this study describes a global approach of controlling chaos to reduce tedious waiting time caused by using conventional local controllers with euler s method a non autonomous system is approximated by a non linear difference system and then an approximate global poincare map function is derived from the difference system by iterating one or more periods of a periodic excitation based on the map function unstable periodic orbits embedded in a chaotic motion can be detected and a global controller for a targeted unstable periodic orbit is designed the global controller makes all the unstable periodic orbits vanish except a targeted periodic orbit furthermore a lyapunov s direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit for practical applications system models are usually unknown to obtain a mathematical model non linear system identification based on the harmonic balance principle is applied to an unknown chaotic system of a noisy environment simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit

on the category set jcpos category set jcpos of lattice valued subsets of sets is introduced and studied we prove that it is topological over setxjcpos and show its natural coalgebraic subcategory

the dedekind macneille completions for fuzzy posets in this paper the dedekind macneille completion for an l fuzzy poset previously introduced by the authors is built and characterized which generalizes the dedekind macneille completion for an ordinary poset the relationship between the l fuzzy complete lattices defined by the authors and belohlavek s completely lattice l ordered sets is discussed

similarity relations and bk relational products bk relational products and their role in the analysis and synthesis of complex systems has been discussed by bandler and kohout in a series of papers we show that bk products preserve similarity of the relations in that if r1 r2 and s1 s2 are similar then r1 s1 and r2 s2 are also similar for any type of bk products applications of the results are discussed

computing the lattice of all fixpoints of a fuzzy closure operator we present a fast bottom up algorithm to compute all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees along with the partial order on the set of all fixpoints fuzzy closure operators appear in several areas of fuzzy logic and its applications including formal concept analysis fca that we use as a reference area of application in this paper several problems in fca such as computing all formal concepts from data with graded attributes or computing non redundant bases of all attribute dependencies can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data the development of a general algorithm that is applicable in particular to these problems is the ultimate purpose of this paper we present the algorithm its theoretical foundations and experimental evaluation

the hopf bifurcation and limit cycle by the incremental harmonic balance method abstract it is well recognized that periodic solutions and their stabilities under small perturbations play a very important role in the study of nonlinear dynamic systems these problems have been investigated by various perturbation methods which are however subjected to the limitation of weak nonlinearity moreover a perturbation method cannot define the parameter range within which a correct solution or a satisfactory approximation can be obtained by the method this situation may lead to totally incorrect results when the parameter is out of a certain range by introducing a variable parameter the incremental harmonic balance method which can treat strongly nonlinear dynamic problems can be used to perform parametric studies on the hopf bifurcation and limit cycle problems this method is ideally suited for parametric studies giving solution diagrams in this paper it is applied to study the van der pol oscillator and coupled oscillators examples show that beyond a certain limit the standard perturbation methods will give incorrect results

completely lattice l ordered sets with and without l equality a relationship between l order based on an l equality and l order based on crisp equality is explored in detail this enables to clarify some properties of completely lattice l ordered sets and generalize some related assertions namely belohlavek s main theorem of fuzzy concept lattices is generalized as well as his theorem dealing with dedekind macneille completion analogously completion of an l ordered set via completely lattice l ordered set of all down l sets is described

fuzzy closure operators closure operators and closure systems play a significant role in both pure and applied mathematics in the framework of fuzzy set theory several particular examples of closure operators and systems have been considered e g so called fuzzy subalgebras fuzzy congruences fuzzy topology etc recently fuzzy closure operators and fuzzy closure systems themselves i e operators which map fuzzy sets to fuzzy sets and the corresponding systems of closed fuzzy sets have been studied by gerla et al see e g 3 4 6 7 as a matter of fact a fuzzy set a is usually defined as a mapping from a universe set x into the real interval 0 1 in the above mentioned works therefore the structure of truth values of the logic behind is fixed to 0 1 equipped usually with minimum as the operation corresponding to logical conjunction as it appeared recently in the investigations of fuzzy logic in narrow sense 9 10 i e fuzzy logic as a many valued logical calculus there are several logical calculi formalizing the intuitive idea of fuzzy reasoning which are complete with respect to the semantics over special structures of truth values among these structures the most general one is that of a residuated lattice it is worth noticing that residuated lattices introduced originally in 12 as an abstraction in the study of ideal systems of rings have been proposed as a suitable structure of truth values by goguen in 8 from this point of view the need for a general notion of a fuzzy closure concept becomes apparent the aim of this paper is to outline a general theory of fuzzy closure operators and fuzzy closure systems in the next section we introduce the necessary concepts in section 3 fuzzy closure operators and systems are

triangular norm based measures and their markov kernel representation abstract we approach the problem whether left continuous triangular norm based valuations called t measures or t probability measures defined on triangular normbased tribes of the unit cube can be disintegrated by markov kernels we prove that each t measure based on a fundamental triangular norm these triangular norms t together with their corresponding triangular conorms s satisfy the functional equation t x y s x y x y can be uniquely represented as a sum of a disintegrable t measure and a hard core which is either identically zero or which is monotonically irreducible i e cannot be disintegrated

a note on the extension principle it is shown that a function obtained by zadeh s extension principle preserves similarity as a consequence if using the extension principle for building models of systems the exact description of phenomena by means of fuzzy sets does not matter

nonlinear feedback for controlling the lorenz equation this work presents a nonlinear feedback approach for controlling the lorenz equation the derivation of the feedback is based on linearizing an input output dynamic of the system which leads to large regions of asymptotic stability here the input signal to the lorenz equation is the applied heat via the rayleigh number the performance of the nonlinear feedback is tested via the stabilization of equilibrium points and periodic orbits

non linear dynamics and chaos control of a physical pendulum with vibrating and rotating support the dynamic behavior of a physical pendulum system of which the support is subjected to both rotation and vertical vibration are studied in this paper both analytical and computational results are employed to obtain the characteristics of the system by using lyapunov s direct method the conditions of stability of the relative equilibrium position can be determined melnikov s method is applied to identify the existence of chaotic motion the incremental harmonic balance method is used to find the stable and unstable periodic solutions for the strong non linear system by applying various numerical results such as phase portrait pioncare map time history and power spectrum analysis a variety of the periodic solutions and the phenomena of the chaotic motion can be presented the effects of the changes of parameters in the system could be found in the bifurcation and parametric diagrams further chaotic motion can be verified by using lyapunov exponent and lyapunov dimension the global analysis of basin boundary and fractal structure are observed by the modified interpolated cell mapping method besides non feedback control delayed feedback control adaptive control and variable structure control are used to control the chaos effectively

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow