holomorphic discrete series for hyperboloids of hermitian type abstract in the present paper we study the holomorphic discrete series h d s for hyperboloids of hermitian type they are the spacesg hwhereg so0 p 2 h so0 p 1 we find some complex hullsy ofg h they correspond to minimalg invariant cones in the lie algebra ofg consider the hardy spacesh2 y and give explicit expressions for the corresponding cauchy szego kernels earlier these expressions were known forp 2 gelfand gindikin andp 1 molchanov we compute the projectionse of thel2 g h onto the images of the hardy spaces the differenceq e e is most interesting it is an analogue of the hilbert transform we study the relations between the h d s forgand the h d s forg h it turns out that forp 2 there is a finite number of representations of the h d s forg hwhich are not representations of the h d s ofg we give explicit expressions for the kernels of the projections on the subspaces of the hardy spaces where the h d s forgacts

coarse stability and bifurcation analysis using time steppers a reaction diffusion example evolutionary pattern forming partial differential equations pdes are often derived as limiting descriptions of microscopic kinetic theory based models of molecular processes e g reaction and diffusion the pde dynamic behavior can be probed through direct simulation time integration or more systematically through stability bifurcation calculations time stepper based approaches like the recursive projection method shroff g m keller h b 1993 siam j numer anal 30 1099 1120 provide an attractive framework for the latter we demonstrate an adaptation of this approach that allows for a direct effective coarse bifurcation analysis of microscopic kinetic based models this is illustrated through a comparative study of the fitzhugh nagumo pde and of a corresponding lattice boltzmann model

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

an inner amenable group whose von neumann algebra does not have property gamma we construct inner amenable groups g with infinite conjugacy classes and such that the associated ii1 factor has no non trivial asymptotically central elements i e does not have property gamma of murray and von neumann this solves a problem posed by effros in 1975

sampled data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements abstract in this paper the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation pde systems via sampled data fuzzy control approach initially the nonlinear pde system is accurately represented by the takagi sugeno t s fuzzy pde model then based on the t s fuzzy pde model a novel time dependent lyapunov functional is used to design a sampled data fuzzy controller under spatially point measurements such that the closed loop fuzzy pde system is exponentially stable with a given decay rate the stabilization conditions are presented in terms of a set of linear matrix inequalities lmis finally simulation results on the control of the diffusion equation and the fitzhugh nagumo fhn equation to illustrate the effectiveness of the proposed design method

on a family of almost commuting endomorphisms abstract if g i is a central sequence of unitaries in a ii 1 factor we show that under certain circumstances lim n ad n i 1 g i is an automorphism examples come naturally from solutions of the yang baxter equation with a spectral parameter and the study of endomorphisms of the cuntz algebra

robust h control of uncertain fuzzy systems under time varying sampling robust h sampled data control for uncertain fuzzy systems is discussed in many practical situations a system is modeled as a continuous time fuzzy system while the control input is the zero order hold which can be represented as a piecewise continuous delay here we take a delay system approach to the h sampled data control problem the closed loop system with a sampled data state feedback controller becomes a system with time varying delay first h performance conditions for the closed loop system are given in terms of linear matrix inequalities lmis such conditions are derived by using the leibniz newton formula and free weighting matrix method for fuzzy time delay systems under the assumption that sampling time is not greater than some prescribed number then a design method for a robust h sampled data state feedback controller for uncertain fuzzy systems is proposed numerical examples are given to illustrate our robust h sampled data state feedback control design

cocycle conjugacy classes of shifts on the hyperfinite ii1 factor abstract we study a class of endomorphisms of subfactor index 2 called binary shifts on the hyperfinite ii1 factor invariants are identified for cocycle conjugacy and strong cocycle conjugacy classes in particular there is a connection between the bratteli diagram associated with a binary shift and strong cocycle conjugacy

normalizers and permutative endomorphisms of the 2 adic ring c algebra abstract a complete description is provided for the unitary normalizer of the diagonal cartan subalgebra d 2 in the 2 adic ring c algebra q 2 which generalizes and unifies analogous results for cuntz and bunce deddens algebras furthermore the inclusion o 2 q 2 is proved not to be regular finally countably many novel permutative endomorphisms of q 2 are exhibited with prescribed images of the generator u

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

technical communique stability and stabilization of nonuniform sampling systems this paper is concerned with nonuniform sampling systems where the sampling interval is time varying within a certain known bound the system is transformed into a time varying discrete time system where time varying parts due to the sampling interval variation are treated as norm bounded uncertainties using robust control techniques to reduce conservatism arising from modeling time varying parts as a single uncertainty the time varying parts are modeled as n uncertainties with larger n a less conservative stability condition is derived at sacrifice of more computation it is shown through a numerical example that the proposed stability condition is better than existing stability conditions

on endomorphisms of the cuntz algebra which preserve the canonical uhf subalgebra ii abstract it was shown recently by conti rordam and szymanski that there exist endomorphisms u of the cuntz algebra o n such that u f n f n but u f n and a question was raised if for such a u there must always exist a unitary v f n with u f n v f n in the present paper we answer this question to the negative to this end we analyze the structure of such endomorphisms u for which the relative commutant u f n f n is finite dimensional

non inner amenability of the thompson groups t and v abstract in this paper we prove that the thompson groups t and v are not inner amenable in particular their group von neumann algebras do not have property moreover we prove that if the reduced group c algebra of t is simple then the thompson group f is non amenable furthermore we give a few new equivalent characterizations of amenability of f

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

endomorphisms of graph algebras abstract we initiate a systematic investigation of endomorphisms of graph c algebras c e extending several known results on endomorphisms of the cuntz algebras o n most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal masa d e of c e our results pertain both automorphisms and proper endomorphisms firstly the weyl group and the restricted weyl group of a graph c algebra are introduced and investigated in particular criteria of outerness for automorphisms in the restricted weyl group are found we also show that the restriction to the diagonal masa of an automorphism which globally preserves both d e and the core af subalgebra eventually commutes with the corresponding one sided shift secondly we exhibit several properties of proper endomorphisms investigate invertibility of localized endomorphisms both on c e and in restriction to d e and develop a combinatorial approach to analysis of permutative endomorphisms

causal compactification and hardy spaces let m g h be a irreducible symmetric space of cayley type then m is diffeomorphic to an open and dense g orbit in the shilov boundary of g k x g k this compactification of m is causal and can be used to give answers to questions in harmonic analysis on m in particular we relate the hardy space of m to the classical hardy space on the bounded symmetric domain g k x g k this gives a new formula for the cauchy szego kernel for m

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

on conjugacy of masas and the outer automorphism group of the cuntz algebra we investigate the structure of the outer automorphism group of the cuntz algebra and closely related with this problem of conjugacy of masaa in on in particular we exhibit an uncountable family of masas conjugate to the standard masa dn via bogolubov automorphisms that are not inner conjugate to dn

the weyl group of the cuntz algebra abstract the weyl group of the cuntz algebra o n is investigated this is isomorphic to the group of polynomial automorphisms u of o n namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries s i and their adjoints a necessary and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism u restricts to an automorphism of the canonical diagonal masa some steps towards a general criterion for invertibility of u on the whole of o n are also taken a condition for verifying invertibility of a certain subclass of polynomial endomorphisms is given first examples of polynomial automorphisms of o n not inner related to those induced by unitaries from the core uhf subalgebra are exhibited for every n 2 in particular the image of the weyl group in the outer automorphism group of o n is strictly larger than the image of the restricted weyl group analyzed in previous papers results about the action of the weyl group on the spectrum of the diagonal are also included

endomorphisms of o n which preserve the canonical uhf subalgebra abstract unital endomorphisms of the cuntz algebra o n which preserve the canonical uhf subalgebra f n o n are investigated we give examples of such endomorphisms u for which the associated unitary element u in o n which satisfies s j u s j for all j does not belong to f n one such example in the case where n 2 arises from a construction of a unital endomorphism on o 2 which preserves the canonical uhf subalgebra and where the relative commutant of its image in o 2 contains a copy of o 2

invariant convex cones and causality in semisimple lie algebras and groups the convex cones in a simple lie algebra g invariant under the adjoint group g of g are studied using a earlier abstract classification of such cones we find explicit algebraic presentations of such cones in all the classical hermitian symmetric lie algebras nontrivial such cones exist only in these cases the g orbits in such cones are listed the notion of a temporal action of a lie group with an invariant causal orientation upon a causally oriented manifold is defined the canonical actions of such classical groups g as above on the shilov boundaries of the associated tube type hermitian symmetric spaces are shown to be temporal actions corollaries are 1 the existence of nontrivial lie semigroups s in the infinite sheeted coverings g of g which are invariant under conjugation by g and satisfy s s 1 e and 2 the global causality i e no closed time like curves of such covering groups g

brief paper input to state stability for networked control systems via an improved impulsive system approach this paper presents a novel impulsive system approach to input to state stability iss analysis of networked control systems ncss with time varying sampling intervals and delays this approach is based upon the new idea that an ncs can be viewed as an interconnected hybrid system composed of an impulsive subsystem and an input delay subsystem a new type of time varying discontinuous lyapunov krasovskii functional which makes full use of the information on the piecewise constant input and the bounds of the network delays is introduced to analyze the iss property of ncss linear matrix inequality based sufficient conditions are derived for iss of ncss with respect to external disturbances when applied to the approximate tracking problem for ncss the derived iss result provides bounds on the steady state tracking error numerical examples are provided to show the efficiency of the proposed approach

finite dimensional guaranteed cost sampled data fuzzy control for a class of nonlinear distributed parameter systems in this paper a finite dimensional guaranteed cost sampled data fuzzy control gcsdfc problem is addressed for a class of nonlinear parabolic partial differential equation pde systems initially applying the galerkin s method to the pde system a nonlinear ordinary differential equation ode system is derived the resulting nonlinear ode system can accurately describe the dominant dynamics of the pde system which is subsequently expressed by the takagi sugeno t s fuzzy model then a guaranteed cost sampled data fuzzy controller is developed to stabilize exponentially the closed loop slow fuzzy system while providing an upper bound for the quadratic cost function a novel time dependent functional is constructed to derive the condition for the existence of the proposed controller which is presented by bilinear matrix inequalities bmis moreover a suboptimal gcsdfc problem to minimize the cost bound can be formulated as a bmi optimization problem a local optimization algorithm that views the bmi as a double linear matrix inequality lmi is given to solve this bmi optimization problem in which a latin hypercube sampling lhs method is proposed to find an initially feasible solution for starting the algorithm furthermore it is shown that the proposed controller can ensure the exponential stability of the closed loop pde system finally simulation results on the fisher equation and the temperature profile of a catalytic rod show that the proposed design strategy is effective

brief analysis and control of parabolic pde systems with input constraints this paper develops a general framework for the analysis and control of parabolic partial differential equations pde systems with input constraints initially galerkin s method is used for the derivation of ordinary differential equation ode system that capture the dominant dynamics of the pde system this ode systems are then used as the basis for the synthesis via lyapunov techniques of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed loop stability in the presence of constraints precise conditions that guarantee stability of the constrained closed loop parabolic pde system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator the theoretical results are used to stabilize an unstable steady state of a diffusion reaction process using constrained control action

sampled data fuzzy control with guaranteed cost for nonlinear parabolic pde systems via static output feedback this article introduces a sampled data sd static output feedback fuzzy control fc with guaranteed cost for nonlinear parabolic partial differential equation pde systems first a takagi sugeno t s fuzzy parabolic pde model is employed to represent the nonlinear pde system second with the aid of the t s fuzzy pde model a sd fc design with guaranteed cost under spatially averaged measurements is developed in the formulation of linear matrix inequalities by utilizing a time dependent lyapunov functional and inequality techniques which can stabilize exponentially the pde system while providing an optimized upper bound on the cost function the membership functions of the proposed controller are determined by the measurement output and independent of the fuzzy pde plant model finally simulation results are presented to control the diffusion equation and the fitzhugh nagumo equation for demonstrating the effectiveness of the proposed method

robust stabilization design of nonlinear stochastic partial differential systems fuzzy approach abstract in this paper we address the robust stabilization design problem for nonlinear stochastic partial differential systems nspdss in the presence of random external disturbances and measurement noise in the spatio temporal domain we propose a fuzzy stochastic partial differential system to approximate the nspdss based on fuzzy interpolation approach next we develop a fuzzy stochastic spatial state space model to represent the fuzzy stochastic partial differential system by employing a semi discretization finite difference scheme based on this model we propose a robust fuzzy estimator based stabilization controller to stabilize the nspdss furthermore robust stochastic h stabilization design is suggested to attenuate the effects of random external disturbances and measurement noise in the spatio temporal domain from the area energy point of view the lmi technique is applied to solve the issue of control gains and estimator gains of the controller by using a systematic control design procedure finally a simulation is presented as an example to illustrate the design procedure and to confirm the performance of the proposed robust fuzzy estimator based stabilization design for the nspdss

c simplicity of free products with amalgamation and radical classes of groups abstract we give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group c algebra and provide a concrete example of an amalgam with trivial kernel such that its reduced group c algebra has a unique tracial state but is not simple moreover we show that there is a radical class of groups for which the reduced group c algebra of any group is simple precisely when the group has a trivial radical corresponding to this class

symmetry in the cuntz algebra on two generators abstract we investigate the structure of the automorphism of o 2 which exchanges the two canonical isometries our main observation is that the fixed point c subalgebra for this action is isomorphic to o 2 and we detail the relationship between the crossed product and fixed point subalgebra

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

uniqueness of invariant means for measure preserving transformations for some compact abelian groups x e g t n 2 and hii 1 z2 the group g of topological automorphisms of x has the haar integral as the unique g invariant mean on l x ax this gives a new characterization of lebesgue measure on the bounded lebesgue measurable subsets 8 of rn n 3 it is the unique normalized positive finitely additive measure on 8 which is invariant under isometries and the transformation of rn xi xn xi x2 x2 i x other examples of as well as necessary and sufficient conditions for the uniqueness of a mean on l q x 3 p which is invariant by some group of measure preserving transformations of the probability space x 3 p are described 0 introduction let 8 be the ring of bounded lebesgue measurable sets in rn or in sn the n dimensional unit sphere in rn and let xn be the lebesgue measure on 8 normalized by xn j 1 where j 0 1 or by xn sn 1 respectively the classical characterization by lebesgue of is that it is the unique positive real valued functionf on 8 which satisfies these three conditions a f jn 1 orf sn 1 respectively b f is invariant under isometries c f is countably additive in 1923 banach 1 studied the question of ruziewicz as to whetherf is still unique when c is replaced by c0 f is finitely additive banach gave a negative answer to this question for r 1 r2 and s1 but for r n 3 or sn n 2 this question is still unanswered in this paper we will prove a theorem which comes close to a solution of this problem for rn n 3 theorem 3 10 if f satisfies a b and c0 and if f is invariant under the transformation of r n n 3 given by xi x2 x f xi x2 x2 9 xn then f xn our method of proof will give several other theorems similar to this one in theorem 3 10 we do not need the full strength of b we need only know that f is absolutely continuous with respect to x i e for n e 3 f n 0 whenever n 0 the fact that for rn n 3 or sn n 2 a b and c0 imply this absolute continuity of f is an observation of tarski which is proved like this received by the editors march 3 1980 presented to the society january 10 1981 ams mos subject classifications 1970 primary 28a70 43a07 43a40 1981 american mathematical society 0002 9947 81 0000 0268 04 50

classification of outer actions of zn on o2 abstract we will show that any two outer actions of z n on o 2 are cocycle conjugate

causal compactification of compactly causal spaces we give a classification of causal compactifications of compactly causal spaces introduced by olafsson and orsted for a compactly causal space g h these compactifications are given by g orbits in the bergman silov boundary of g 1 k 1 with g c g 1 and g 1 k 1 a hermitian symmetric space of tube type for the classical spaces an explicit construction is presented

sampled data fuzzy control of chaotic systems based on a t s fuzzy model in this paper a sampled data fuzzy controller is designed to stabilize a class of chaotic systems a takagi sugeno t s fuzzy model is employed to represent the chaotic systems based on this general model the exponential stability issue of the closed loop systems with an input constraint is first investigated by a novel time dependent lyapunov functional which is positive definite at sampling times but not necessary between the sampling times then two sufficient conditions are developed for sampled data fuzzy controller synthesis of the underlying t s fuzzy model with or without input constraint all the proposed results in this paper depend on both the upper and lower bounds on a sampling interval and the available information about the actual sampling pattern is fully utilized the proposed sampled data fuzzy control scheme is successfully applied to the chaotic lorenz system which is shown to be effective and less conservative compared with existing results

sampled data fuzzy control with space varying gains for nonlinear time delay parabolic pde systems abstract this paper introduces a sampled data fuzzy control sdfc with space varying gains for nonlinear time delay parabolic partial differential equation pde systems first a takagi sugeno t s fuzzy time delay parabolic pde model is employed to represent the nonlinear time delay pde system second with the aid of the t s fuzzy time delay pde model a sdfc design with space varying gains is developed in the formulation of space dependent linear matrix inequalities lmis by constructing an appropriate lyapunov functional which can stabilize exponentially the time delay pde system these stabilization conditions can be applied to either slowing varying time delay or fast varying one finally simulation results on two examples are presented to demonstrate the effectiveness of the proposed method

finite group actions on c algebras with the rohlin property i basic properties of finite group actions with the rohlin property on unital c algebras are investigated a characterization of finite group actions with the rohlin property on the cuntz algebra 02 is given in terms of central sequences which may be considered as an equivariant version of e kirchberg and n c phillips s characterization of 02 a large class of symmetries on 02 are classified in terms of the fixed point algebras for conjugacy and the crossed products for cocycle conjugacy model actions of symmetries of 02 are constructed for given k theoretical invariants

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

brief paper stability and stabilization of aperiodic sampled data control systems using robust linear matrix inequalities stability analysis of an aperiodic sampled data control system is considered for application to networked and embedded control the stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals although this condition is numerically intractable a tractable sufficient condition can be constructed with the mean value theorem special attention is paid to tightness of the sufficient condition for less conservative stability analysis a region dividing technique for the reduction of conservatism and generalization to stabilization are also discussed an example demonstrates the efficacy of the approach

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

a duality for endomorphisms of von neumann algebras we consider endomorphisms of von neumann algebras let m be a von neumann algebra represented on a hilbert space h and let m be the corresponding commutant let end m be given and suppose m has a cyclic vector in h such that the corresponding state leaves invariant then there is a dual completely positive mapping on m which we find and describe each of the two and has an associated spectral group and we show that the group for is contained in that for we consider the following three restrictions on i is a shift on m ii is strongly ergodic and iii is ergodic we give spectral theoretic conditions on using the two groups described above to fall into each of the three classes we also show that the two groups are conjugacy invariants and we discuss the case of cocycle conjugacy

the 2 adic ring c algebra of the integers and its representations abstract we study the 2 adic version of the ring c algebra of the integers first we work out the precise relation between the cuntz algebra o 2 and our 2 adic ring c algebra in terms of representations secondly we prove a 2 adic duality theorem identifying the crossed product arising from 2 adic affine transformations on the 2 adic numbers with the analogous crossed product algebra over the real numbers and finally as an outcome of this duality result we construct an explicit imprimitivity bimodule and prove that it transports one canonical representation into the other

homology for operator algebras abstract a 4 cycle algebra is a finite dimensional digraph algebra csl algebra whose reduced digraph is a 4 cycle a rigid embedding between such algebras is a direct sum of certain nondegenerate multiplicity one star extendible embeddings a complete classification is obtained for the regular isomorphism classes of direct systems a of 4 cycle algebras with rigid embeddings the critical invariant is a binary relation in k 0 a h 1 a generalising the scale of the k 0 group called the joint scale the joint scale encapsulates other invariants and compatibility conditions of regular isomorphism these include the scale of h 1 a the scale of h 0 a h 1 a sign compatibility congruence compatibility and h 0 h 1 coupling classes these invariants are also important for lifting k 0 h 1 isomorphisms to algebra isomorphisms we resolve this lifting problem for various classes of 4 cycle algebra direct systems

labeled trees and localized automorphisms of the cuntz algebras we initiate a detailed and systematic study of automorphisms of the cuntz algebras on which preserve both the diagonal and the core uhf subalgebra a general criterion of invertibility of endomorphisms yielding such automorphisms is given combinatorial investigations of endomorphisms related to permutation matrices are presented key objects entering this analysis are labeled rooted trees equipped with additional data our analysis provides insight into the structure of aut on and leads to numerous new examples in particular we completely classify all such automorphisms of o2 for the permutation unitaries in 4 m2 we show that the subgroup of out o2 generated by these automorphisms contains a copy of the infinite dihedral group z z2 msc 2000 46l40 46l05 37b10

the restricted weyl group of the cuntz algebra and shift endomorphisms it is shown that modulo the automorphisms which fix the canonical diagonal masa point wise the group of those automorphisms of on which globally preserve both the diagonal and the core uhf subalgebra is isomorphic via restriction with the group of those homeomorphisms of the full one sided n shift space which eventually commute along with their inverses with the shift transformation the image of this group in the outer automorphism group of on can be embedded into the quotient of the automorphism group of the full two sided n shift by its center generated by the shift if n is prime then this embedding is an isomorphism msc 2010 46l40 37b10

fuzzy state space modeling and robust observer based control design for nonlinear partial differential systems in this paper a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems npdss based on galerkin s method a takagi sugeno t s fuzzy pds is first proposed to model an npds then the t s fuzzy pds can be represented by a finite dimensional t s fuzzy subsystem in controlled mode and a coupled infinite dimensional t s fuzzy subsystem in residual mode therefore the npds can be partitioned into a finite dimensional t s fuzzy slow state space subsystem to be controlled and a coupled infinite dimensional fast residual subsystem to be tolerated based on the small gain theorem a robust fuzzy observer based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the npds furthermore based on the dissipative theory an hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of npdss the matlab linear matrix inequality toolbox can be employed to efficiently solve the optimal hinfin fuzzy observer based control design problem of npdss finally a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer based control method for the perturbative npdss

automorphisms of the dimension group and gyration numbers o introduction 1 the sign gyration compatibility condition 2 gyration and orbit sign numbers 3 construction of sgcc a m 4 application of sgcc a summary let aut o a denote the group of automorphisms of a subshift of finite type xa o a built from a primitive matrix a we show that the sign gyrationcompatibility condition homomorphism sgcc a m defined on aut 0 a factors through the group aut s a of automorphisms of the dimension group this is used to find a mixing subshift of finite type with a permutation of fixed points that cannot be lifted to an automorphism of the shift we also give an example of a mixing subshift of finite type where the dimension group representation is not surjective this example is used in kr3 to give examples of subshifts of finite type reducible with two mixing components that are shift equivalent but not strong shift equivalent over the nonnegative integers o introduction

h stabilization criterion with less complexity for nonuniform sampling fuzzy systems abstract this paper investigates the problem of h stabilization for nonuniform sampling fuzzy systems a method to design a fuzzy controller is proposed by taking the variation ranges of membership functions within sampling intervals into consideration to reduce the computational complexity jensen s integral inequality method is employed based on a well known inequality a convex combination technique is developed to deal with nonlinear time varying coefficients derived from jensen s integral inequality combining with capturing the characteristic of sampled data systems with a novel piecewise lyapunov krasovskii functional lkf a less complex and less conservative h stabilization criterion is formulated as linear matrix inequalities lmis which can be easily checked by using standard numerical software some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

finite group actions on c algebras with the rohlin property ii abstract we classify finite group actions on some classes of c algebras with the rohlin property in terms of the k groups a group cohomological obstruction is obtained for the k groups of a c algebra allowing such an action for example the tate cohomology groups with the k groups as the coefficient modules must vanish model actions with the rohlin property are constructed for given k theoretical invariants quasi free actions of finite cyclic groups on the cuntz algebras and their dual actions are investigated from the view point of the rohlin property

periodic points and automorphisms of the shift on etudie le groupe d automorphisme d un decalage de markov topologique a l aide des points periodiques et des ensembles instables

distributed control design for parabolic evolution equations application to compressor stall control we present a theoretical study of distributed control design for semilinear parabolic nonlocal evolution equations with an application to axial compressor stall control using air injection by taking advantage of the spatial invariance of the equations a linear controller is constructed following bamieh et al via linear quadratic control of each fourier mode we derive sufficient conditions for the linear controller to stabilize the full nonlinear system concepts such as controller decentralization finite dimensional implementation inverse optimality and beneficial nonlinearities are discussed in the second part of this paper these developments are applied to a model of axial compressor control with air injection the unactuated model is derived following the work of moore and greitzer and the model coupled with air injection actuation follows the works of behnken et al and weigl et al a numerical study of the control designs is pursued and the comparison of controller performance is discussed the techniques presented here are expected to be useful for distributed control design of a much broader class of nonlinear reaction diffusion systems

c simplicity and representations of topological full groups of groupoids abstract given an ample groupoid g with compact unit space we study the canonical representation of the topological full group g in the full groupoid c algebra c g in particular we show that the image of this representation generates c g if and only if c g admits no tracial state the techniques that we use include the notion of groups covering groupoids as an application we provide sufficient conditions for c simplicity of certain topological full groups including those associated with topologically free and minimal actions of non amenable and countable groups on the cantor set

the holomorphic discrete series for affine symmetric spaces i abstract let x g h be an affine symmetric space we study part of the discrete spectrum of l2 x for x of hermitian type a notion we define in analogy with the group case in particular we find intertwining operators from the scalar holomorphic discrete series of g which is automatically of hermitian type into l2 x the multiplicity of this series is then shown to be one by a uniqueness result for the intertwining operators finally we investigate the complexification x c of x and show that the discrete series in question admits holomorphic continuation into a certain domain in x c