characteristic of left invertible semigroups and admissibility of observation operators in this paper we discuss the characteristic property of the left invertible semigroups on general banach spaces and admissibility of the observation operators for such semigroups we obtain a sufficient and necessary condition about their generators further for the left invertible and exponentially stable semigroup in hilbert space we show that there is an equivalent norm under which it is contractive based on these results we prove that for any observation operator satisfying the resolvent condition is admissible for the left invertible semigroup if its range is finite dimensional in addition we prove that any observation operator satisfying the resolvent condition can be approximated by the admissible observation operators finally we give a sufficient condition of exact observability of the left invertible semigroup

infinite time exact observability of volterra systems in hilbert spaces abstract we study infinite time exact observability of volterra systems in hilbert spaces sufficient conditions are established under which infinite time exact observability of a volterra system follows from that of the corresponding cauchy system without convolution term this is done by combining the composition operator method with a result about bounded below composition operators on the hardy space

dual closure operators and their applications abstract departing from a suitable categorical description of closure operators this paper dualizes this notion and introduces some basic properties of dual closure operators usually these operators act on quotients rather than subobjects and much attention is being paid here to their key examples in algebra and topology which include the formation of monotone quotients eilenberg whyburn and concordant quotients collins in fair categorical generality these constructions are shown to be factors of the fundamental correspondence that relates connectednesses and disconnectednesses in topology as well as torsion classes and torsion free classes in algebra depending on a given cogenerator the paper also establishes a non trivial correspondence between closure operators and dual closure operators in the category of r modules dual closure operators must be carefully distinguished from interior operators that have been studied by other authors

ditopological texture spaces and fuzzy topology i basic concepts this is the first of three papers which develop various fundamental aspects of the theory of ditopological texture spaces in a categorical setting and present important links with the theory of l topological spaces the authors begin by defining the notion of q sets which together with the p sets considered earlier enable the formulation of a powerful concept of duality this plays an important role in the theory of direlations and difunctions which is described here in detail difunctions are then taken as the morphisms of a category dftex whose objects are texture spaces several important subcategories are defined and the closely related construct ftex defined some properties of the functors between these categories are obtained

on the admissibility of observation for perturbed c0 semigroups on banach spaces abstract this paper concerns linear infinite dimensional systems with unbounded observation operators we study the invariance of admissibility for observation operators under some unbounded perturbations of the generator we give also some relations between the extensions of such observation operators with respect to the original generator and the perturbed generator our results are applied to functional differential linear systems

symbolic reachability analysis and maximally permissive entrance control for globally synchronized templates abstract this paper studies the symbolic reachability relations of a class of parameterized systems in the framework of regular model checking the modules of each system are instantiated from a globally synchronized template and each globally synchronized template is represented by a finite state automaton whose event set consists of global events and local events it is shown that the symbolic reachability relations of these systems are effectively iteration closed star languages and for any iteration closed star language there exists a template with only global events that realizes it application of the symbolic reachability analysis to computing the entrance control functions that enforce deadlock freeness and blocking freeness is then illustrated for systems with idle modules in particular we show that the maximally permissive entrance control functions can be encoded using finite state automata

controllability and observability for non autonomous evolution equations the averaged hautus test abstract we consider the observability problem for non autonomous evolution systems i e the operators governing the system depend on time we introduce an averaged hautus condition and prove that for skew adjoint operators it characterizes exact observability next we extend this to more general class of operators under a growth condition on the associated evolution family we give an application to the schrodinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient

one point compactifications of ditopological texture spaces in this paper a one point compactification of a ditopological texture space is defined and a concept of local compactness introduced and shown to be additive in the class of ditopological texture spaces an application to hutton spaces is given here a compact extension of an hutton space is obtained and a notion of local compactness is defined and shown to be productive in the class of l topological spaces where l is a hutton algebra

sufficient conditions for admissibility sufficient conditions for the finite and infinite time admissibility of an observation operator are given it is shown that the estimates of weiss are close to being sufficient if the semigroup is surjective then the estimate is sufficient

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

fuzzy closure spaces abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems but many results can be extended to what are called fuzzy closure spaces or fcs s for short the notions of a subspace a sum and a product are extended to fcs s the hereditary additivity and productivity behaviour of compactness in fcs s is investigated and some weak forms of compactness and fuzzy continuous functions in fcs s are introduced the interaction between fuzzy proximity spaces and fcs s is investigated a necessary background is included for completeness

α admissibility of the right shift semigroup on l2 r abstract it is shown that the right shift semigroup on l 2 r does not satisfy the weighted weiss conjecture for 0 1 in other words admissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition this result is in contrast to the unweighted case where 0 admissibility can be characterised by a simple growth bound the result is proved by providing a link between discrete and continuous admissibility and then translating a counterexample for the unilateral shift on h 2 d to continuous time systems

equivalent conditions for stabilizability of infinite dimensional systems with admissible control operators in this paper we study the optimizability of infinite dimensional systems with admissible control operators we show that under a weak condition such a system is optimizable if and only if the system can be split into an exponentially stable subsystem and an unstable subsystem that is exactly controllable in finite time the state space of the unstable subsystem equals the span of all unstable generalized eigenvectors of the original system this subsystem can be infinite dimensional furthermore the unstable poles satisfy a summability condition the state space of the exponentially stable subsystem is given by all vectors for which the action of the original c0 semigroup is stable

on invariance of p admissibility of control and observation operators to q type of perturbations of generator of c0 semigroup abstract in this paper it is proved in general setting that p admissibilities of control operators and observation operators are invariant to any q type of perturbations of generator of c 0 semigroups on banach space moreover some relations between the extensions of observation operators with respect to the original generator and the perturbed generator are also characterized so that the output can be expressed in the mild sense as an application the admissibility as well as the mild expressibility of output of a class of observation systems with time delay in state is deduced

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

resolvent conditions for the control of parabolic equations abstract since the seminal work of russell and weiss in 1994 resolvent conditions for various notions of admissibility observability and controllability and for various notions of linear evolution equations have been investigated intensively sometimes under the name of infinite dimensional hautus test this paper sets out resolvent conditions for null controllability in arbitrary time necessary for general semigroups sufficient for analytic normal semigroups for a positive self adjoint operator a it gives a sufficient condition for the null controllability of the semigroup generated by a which is only logarithmically stronger than the usual condition for the unitary group generated by ia this condition is sharp when the observation operator is bounded the proof combines the so called control transmutation method and a new version of the direct lebeau robbiano strategy the improvement of this strategy also yields interior null controllability of new logarithmic anomalous diffusions

relative group completions abstract we extend arbitrary group completions to the category of pairs g n where g is a group and n is a normal subgroup of g relative localizations are special cases our construction is a group theoretical analogue of fibrewise completion and fibrewise localization in homotopy theory and generalizes earlier work of hilton and others on relative localization at primes we use our approach to find conditions under which factoring out group radicals preserves exactness this has implications in the study of the effect of plus constructions on homotopy fibre sequences

admissibility of control operators for solution families to volterra integral equations we reduce the admissibility of finite dimensional control operators for an evolution system satisfying certain mild regularity conditions to that for a semigroup control system for which there are plenty of results available in the literature one such necessary and sufficient condition is the carleson measure criterion we prove this condition explicitly for evolution systems without the regularity assumption mentioned above we also look at some examples which show that our respective hypotheses are necessary

survey paper well posed systems the lti case and beyond this survey is an introduction to well posed linear time invariant lti systems for non specialists we recall the more general concept of a system node classical and generalized solutions of system equations criteria for well posedness the subclass of regular linear systems some of the available linear feedback theory motivated by physical examples we recall the concepts of impedance passive and scattering passive systems conservative systems and systems with a special structure that belong to these classes we illustrate this theory by examples of systems governed by heat and wave equations we develop local and global well posedness results for lti systems with nonlinear in particular bilinear feedback by extracting the abstract idea behind various proofs in the literature we apply these abstract results to derive well posedness results for the burgers and navier stokes equations

interpolation by vector valued analytic functions with applications to controllability in this paper norm estimates are obtained for the problem of minimal norm tangential interpolation by vector valued analytic functions expressed in terms of the carleson constants of related scalar measures applications are given to the controllability properties of linear semigroup systems with a riesz basis of eigenvectors

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

generalization of l closure spaces abstract this paper introduces the concepts of l closure spaces and the convergence in l closure spaces in the variable basis setting of such closure spaces continuous generalized order homomorphisms are characterized by the convergence theory of nets filters and ideals furthermore in the fixed basis setting of such closure spaces some constructions on l closure spaces such as the subspace of an l cs the sum l cs the product of l cs and the induced l cs of a crisp closure space are investigated we obtain an important result that the category l closure is a topological category over set w r t the forgetful functor from l closure to set we obtain another important result that there is an adjunction between the category of crisp closure spaces and the full subcategory of those l closure spaces which are induced by some crisp closure space

carleson measures for hilbert spaces of analytic functions on the complex half plane the notion of a carleson measure was introduced by lennart carleson in his proof of the corona theorem for h d in this paper we will define it for certain type of reproducing kernel hilbert spaces of analytic functions of the complex half plane c which will include hardy bergman and dirichlet spaces we will obtain several necessary or sufficient conditions for a positive borel measure to be carleson by preforming tests on reproducing kernels weighted bergman kernels and studying the tree model obtained from a decomposition of the complex half plane the dirichlet space will be investigated in detail as a special case finally we will present a control theory application of carleson measures in determining admissibility of controls in well posed linear evolution equations

new blow up rates for fast controls of schrodinger and heat equations abstract we consider the null controllability problem for the schrodinger and heat equations with boundary control we concentrate on short time or fast controls we improve recent estimates see l miller geometric bounds on the growth rate of null controllability cost for the heat equation in small time j differential equations 204 2004 202 226 l miller how violent are fast controls for schrodinger and plate vibrations arch ration mech anal 172 2004 429 456 l miller controllability cost of conservative systems resolvent condition and transmutation j funct anal 218 2005 425 444 l miller the control transmutation method and the cost of fast controls siam j control optim 45 2006 762 772 on the norm of the operator associating to any initial state the minimal norm control driving the system to zero our main results concern the schrodinger and heat equations in one space dimension they yield new estimates concerning window problems for series of exponentials as described in t i seidman the coefficient map for certain exponential sums nederl akad wetensch indag math 48 1986 463 478 and in t i seidman s a avdonin s a ivanov the window problem for series of complex exponentials j fourier anal appl 6 2000 233 254 these results are used following l miller the control transmutation method and the cost of fast controls siam j control optim 45 2006 762 772 to deal with the case of several space dimensions

admissible input elements for systems in hilbert space and a carleson measure criterion we study the control system dot x ax bu quad x in x quad u text scalar where a generates a semigroup on the hilbert space x but in general the control input element b notin x many boundary value control systems point control force situations etc can be studied in this context we define and analyze admissible input elements b and develop sufficient conditions for b to be admissible in terms of the carleson measure theorem of h p theory

hautus condition on the exact controllability of conservative systems we consider the exact controllability of a linear conservative system a b associated with hilbert spaces h and u we get a necessary and sufficient controllability condition this condition is related to the hautus lemma from the finite dimensional systems theory it is an estimate in terms of operators a and b alone

semi localizations of semi abelian categories abstract a semi localization of a category is a full reflective subcategory with the property that the reflector is semi left exact there are many interesting examples of semi localizations as for instance any torsion free subcategory of a semi abelian category by specializing a result due to s mantovani we first characterize the categories which are semi localizations of exact mal tsev categories we then prove a new characterization of protomodular categories in terms of binary relations allowing us to obtain an abstract characterization of the semi localizations of exact protomodular categories this result is very useful to study the hereditarily torsion free subcategories of semi abelian categories some examples are considered in detail in the categories of groups crossed modules commutative rings and topological groups we finally explain how these results extend the corresponding ones obtained in the abelian context by w rump

admissibility in input elements for diagonal semigroups on l 2 abstract we characterize the admissible unbounded input elements for diagonal semigroups on l 2 the result verifies the necessity of a condition whose sufficience was previously established by l f ho and d l russell

on the existence of exotic banach lie groups let x be a real or complex banach space and let g be a topological group by a representation of g in x we mean a homomorphism of g into gl x the group of all automorphisms ofx a representation t g g l x is called weakly resp strongly uniformly continuous when it is continuous in the weak resp strong uniform topology on gl x a representation t g g l x is called unitary when x is a hilbert space and all the operators t g g g are unitary for unitary representations the notions of weak and strong continuity coincide in this paper we shall frequently treat vector spaces as additive groups and topological vector spaces especially normed spaces as additive topological groups thus for example if e is a normed space we shall speak of the topological group e of a subgroup k c e or of a topological quotient group e k without special explanations an abelian topological group is called exotic if it does not admit any nontrivial strongly continuous unitary representations and strongly exotic if it does not admit any non trivial weakly continuous representations in hilbert spaces an example of an exotic group was given by herer and christensen in 4 the group in the mentioned example was a polish vector space in the present paper we exhibit the existence of strongly exotic banach lie groups more precisely our aim is to prove the following fact

interior and closure operators on texture spaces i basic concepts and cech closure operators this paper is the first of a series of three papers on the theory of interior and closure operators here the theory is discussed from the textural point of view first the interior and closure operators on texture spaces are defined and some basic properties are given in terms of neighbourhoods and coneigbourhoods then the category dfic whose objects are interior closure spaces and the morphisms are bicontinuous difunctions is shown to be topological over the ground category dftex of textures and difunctions further considering the closure operator on hutton algebras known as fuzzy lattices in the sense of c ech the category hutcl of hutton closure spaces and continuous mappings is defined finally the category cdfic of complemented bicontinuous difunctions and complemented interior closure texture spaces and the opposite category of hutcl are shown to be equivalent

semigroup generation and stabilization by a r bounded feedback perturbations abstract let a be a generator of a strongly continuous semigroup of operators and assume that c and h are operators such that a ch generates a strongly continuous semigroup sh t on x let 0 be a real number in the resolvent set of a and let 1 1 then there are some fairly unrestrictive conditions under which a 0 a ch 0 a also generates a strongly continuous semigroup sk t on x which has the same exponential growth rate as sh t given an input operator b we can use this to identify a class of feedback perturbations k such that a bk generates a strongly continuous semigroup we can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system for example we show that if the control on a cantilever beam in the state space h02 0 1 l2 0 1 is a moment force on the free end then we cannot stabilize the beam with an a 1 2 bounded feedback but we can find an a e 1 4 bounded feedback for any e 0 which does stabilize the beam

a general necessary condition for exact observability suppose a generates an exponentially stable strongly continuous semigroup on the hilbert space x y is another hilbert space and c d a rightarrow y is an admissible observation operator for this semigroup this means that to any initial state in x we can associate an output function in l 2 0 infty y this paper gives a necessary condition for the exact observability of the system defined by a and c this condition called bf e is related to the hautus lemma from finite dimensional systems theory it is an estimate in terms of the operators a and c alone in particular it makes no reference to the semigroup this paper shows that bf e implies approximate observability and if a is bounded it implies exact observability this paper conjectures that bf e is in fact equivalent to exact observability the paper also shows that for diagonal semigroups bf e takes on a very simple form and applies the results to sequences of complex exponential functions

weak admissibility does not imply admissibility for analytic semigroups two conjectures on admissible control operators by george weiss are disproved in this paper one conjecture says that an operator b defined on an infinite dimensional hilbert space u is an admissible control operator if for every element u in u the vector bu defines an admissible control operator the other conjecture says that b is an admissible control operator if a certain resolvent estimate is satisfied the examples given in this paper show that even for analytic semigroups the conjectures do not hold in the last section we construct a semigroup example showing that the first estimate in the hille yosida theorem is not sufficient to conclude boundedness of the semigroup

textures and c spaces in this paper we point out that textures simple textures and plain textures are respectively isomorphic to c spaces sober c spaces and partially ordered sets using the isomorphism between textures and c spaces we show that subtextures quotient textures sums and products of textures can be identified as subspaces quotient spaces sums and products of c spaces furthermore it is shown that textures except discrete textures do not satisfy any separation axioms t 1 t 4 other than t 0 and so they are not pseudometrizable then we also give four useful characterizations of the complete distributivity condition of textures

interior and closure operators on texture spaces ii dikranjan giuli closure operators and hutton algebras in this work we discuss interior and closure operators on textures in the sense of dikranjan giuli first we define the category dficl of interior closure spaces and bicontinuous difunctions and show that it is topological over dftex whose objects are textures and morphisms are difunctions the category l closure of l closure spaces and zadeh type powerset operators and the counterparts of the lowen functors have been presented by wu neng zhou in a fixed basis setting we consider the closure operators on a hutton algebra l and in a natural way we define the category hcl of hutton closure spaces taking the morphisms of the opposite category of hutalg the category of hutton algebras fuzzy lattices and the mappings preserving arbitrary meets joins and involution in this case the categories l closure and h the category of hutton spaces and the morphisms in the sense of definition 2 1 can be considered as a subcategory and a full subcategory of hcl respectively using the fact that dficl and hcl o p are equivalent categories we guarantee the existence of products and sums in hcl finally we show that the generalized lowen functor can be also given in a textural framework for 0 1

necessary conditions for exact controllability with a finite dimensional input space we derive necessary conditions for exact controllability of infinite dimensional systems described by x ax bu where the generator a has a riesz basis of eigenvectors and the input space is finite dimensional these conditions are in terms of the eigenvalues of a and the degree of unboundedness of b but no further information about b is needed our results easily imply lack of exact controllability for a wide range of distributed parameter systems it is known from partial differential equation pde examples that the addition of damping into an exactly controllable second order system can destroy exact controllability we discuss the effect of damping on such systems using our general conditions we also give simple new proofs for results about the lack of exact controllability of hyperbolic systems in more than one space dimension

the operator carleson measure criterion for admissibility of control operators for diagonal semigroups on 1 2 abstract suppose a control system is described by a diagonal semigroup on the state space l 2 and by an unbounded control operator b defined on the input space l 2 we formulate a condition called the operator carleson measure criterion and show that this condition is necessary for the admissibility of b if the semigroup is analytic or invertible then the condition is sufficient as well our results extend the ones of ho russell and weiss concerning the case where the input space is one dimensional

a wallman type compactification of texture spaces abstract a texturing on a set s is a point separating complete completely distributive lattice s of subsets of s with respect to inclusion which contains s and for which arbitrary meet coincides with intersection and finite joins coincide with union the pair s s is known as a texture space in this paper the authors present the concept of embedding for texture spaces and define the notion of difilter on a texture space then a wallman type compactification is discussed for a class of ditopological texture spaces in terms of so called difunctions introduced by brown and his team and it is expressed in the class of molecular weakly bi r 1 hutton spaces

boundary control of a linear thermoelastic beam abstract we show in this paper that the motions of a linear thermoelastic beam may be controlled exactly to zero in a finite time by a single boundary control that acts on one end of the beam the optimal time of controllability depends upon the moment of inertia parameter of the beam and becomes arbitrarily small if this parameter is omitted as in the euler bernoulli beam theory

p admissible control elements for diagonal semigroups on l r spaces for linear systems described by dot x t a x t bu t where a is a diagonal operator on the state space l r for some 1 leq r infty we develop necessary and sufficient conditions for b to be p admissible this extends results by ho russell and weiss to the case r neq 2

torsion theories in homological categories we introduce and study the notion of torsion theory in the non abelian context of homological categories and we investigate the properties of the corresponding closure operator we then consider several new examples of torsion theories in the category of topological groups and more generally in any category of topological semi abelian algebras we finally characterize the hereditary torsion theories and we analyse a new example in the homological category of crossed modules c 2006 elsevier inc all rights reserved

torsion theories and radicals in normal categories we introduce a relativized notion of semi normalcy for categories that come equipped with a proper stable factorization system and we use radicals in the sense of module theory and normal closure operators in order to study torsion theories in such categories our results generalize and complement recent studies in the realm of semi abelian and in part homological categories in particular we characterize both torsion free and torsion classes in terms of their closure under extensions we pay particular attention to the homological and for our purposes more importantly normal categories of topological algebra such as the category of topological groups but our applications go far beyond the realm of these types of categories as they include for example the normal but non homological category of pointed topological spaces which is in fact a rich supplier for radicals of topological groups

necessary conditions for the exact observability of systems on hilbert spaces abstract in this paper we introduce the zero class of admissible observation operators for which the norm of the output map tends to zero as the time tends to zero we show that for such an observation operator exact observability implies that the semigroup of the system is bounded from below in addition if the semigroup generator has no residual spectrum then the semigroup can be extended to a c 0 group

ditopological texture spaces and fuzzy topology iii separation axioms this is the third of three papers which develop various fundamental aspects of the theory of ditopological texture spaces and relate this work with the theory of fuzzy topological spaces in this paper the authors define and study basic separation axioms in general ditopological texture spaces relating these to known separation axioms for bitopological and topological spaces and to the point free separation axioms of b hutton and i reilly for fuzzy topological spaces

blocking in fully connected networks of arbitrary size the problem of checking blocking properties is studied for networks consisting of arbitrary numbers of finite state discrete event subsystems the topology of the networks is that of a fully connected graph any subsystem can potentially interact with any other two types of blocking are studied component blocking whereby a subsystem is potentially prevented from entering its set of marker states and network blocking whereby the subsystems are potentially unable to occupy marker states simultaneously it is shown that if the subsystems are all identical and broadcast actions are permitted both types of blocking properties are undecidable but in the absence of broadcast actions they become decidable if the subsystems are not necessarily identical but only isomorphic then blocking properties are in general undecidable however a template is proposed for ensuring adequate structure for decidability it is claimed that this template is sufficiently general to admit many realistic examples

exact observability of diagonal systems with a finite dimensional output operator in this paper equivalent conditions for exact observability of diagonal systems with a finite dimensional output operator are given one of these equivalent conditions is the conjecture of russell and weiss siam j control opt 32 1 1994 1 23 the other conditions are in terms of the eigenvalues and the lyapunov solutions of finite dimensional subsystems

on the reflective and coreflective subcategory of stratified l cech closure spaces abstract in this paper it is shown that the category of cech closure spaces can be embedded in the category of stratified l cech closure spaces as a coreflective full subcategory furthermore if the underlying lattice of the complete residuated lattice l is completely distributive the embedding is also reflective finally some related commutative diagrams are obtained

on the cost of fast controls for some families of dispersive or parabolic equations in one space dimension in this paper we consider the cost of fast controls for a large class of linear equations of parabolic or dispersive type in one space dimension in small time by extending the work of tenenbaum and tucsnak j differential equations 243 2007 pp 70 100 we are able to give precise upper bounds on the time dependance of the cost of fast controls when the time of control t tends to 0 we also give a lower bound of the cost of fast controls for the same class of equations which proves the optimality of the power of t involved in the cost of the control these general results are then applied to treat notably the case of linear kdv equations and fractional heat or schrodinger equations

paracompactness and full normality in ditopological texture spaces in this paper the authors lay the foundation for a theory of dicovers of ditopological texture spaces and use this to define notions of paracompactness and full normality some applications to fuzzy topology are also mentioned

on continuity of solutions for parabolic control systems and input to state stability abstract we study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions this question naturally appears when working with boundary controlled linear partial differential equations here we focus on parabolic equations which allow for operator theoretic methods such as the holomorphic functional calculus moreover we investigate stronger conditions than continuity leading to input to state stability with respect to orlicz spaces this also implies that the notions of input to state stability and integral input to state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite dimensional

zero class admissibility of observation operators abstract an admissible observation operator is zero class admissible if the norm of the output map tends to zero as the time tends to zero sufficient and necessary conditions for zero class admissibility of observation operators are developed and a modified weiss condition is studied it is shown that the modified weiss condition is in general necessary but not sufficient for zero class admissibility for several important classes of c 0 semigroups it is proved that the modified weiss condition is indeed equivalent to zero class admissibility the methods are illustrated by certain pde examples

ditopological texture spaces and fuzzy topology ii topological considerations this is the second of three papers which develop various fundamental aspects of the theory of ditopological texture spaces in a categorical setting and present important links with the theory of l topological spaces in the first paper in this series subtitled basic concepts the authors presented the notions of direlation and difunction between textures and introduced the category dftex the construct ftex and several related categories in this paper the category dfditop of ditopological texture spaces and bicontinuous difunctions is defined and the forgetful functor u dfditop dftex shown to be topological several properties are discussed including the existence of products and coproducts an equivalence with the category of classical hutton spaces is presented and the paper ends with a consideration of l valued sets and topologies from the viewpoint of ditopological texture spaces

spectral conditions implied by observability it is well known that a finite dimensional output space implies limitations on the systems properties like observability and detectability in this paper we extend this result for infinite dimensional output spaces under the condition that the output operator is relatively compact we show that if this holds and the system is exactly observable in finite time then the inverse of the infinitesimal generator must be compact by means of an example we show that this result does not hold for exact observability in infinite time using the hautus test we obtain spectral properties of the generator for this case a consequence of this result is that if the system is exponentially detectable then the unstable part of the spectrum consists of only point spectrum with finite multiplicity

connectedness in ditopological texture spaces abstract the notion of a texture space under the name of fuzzy structure was introduced by brown 1993 as a means of representing a lattice of fuzzy sets as a lattice of crisp subsets of some base set corresponding to a fuzzy topology we then have the concept of a ditopology and in this paper connectedness in ditopological texture spaces is defined and some of its basic properties are obtained in particular it is shown that connectedness is productive in the context of ditopological texture spaces zero dimensionality and strong zero dimensionality are defined and it is shown that in stable zero dimensional ditopological texture spaces the component of a point coincides with the quasi component finally it is shown that a fuzzy topological space is c 5 connected if and only if the corresponding ditopological texture space is connected

topological semi abelian algebras given an algebraic theory t whose category of models is semi abelian we study the category top t of topological models of t and generalize to it most classical results on topological groups in particular top t is homological which includes barr regularity and forces the mal cev property every open subalgebra is closed and every quotient map is open we devote special attention to the hausdorff compact locally compact connected totally disconnected and profinite t algebras c 2004 elsevier inc all rights reserved

a categorical approach to commutator theory abstract we define a notion of commutator for equivalence relations in a mal cev category and show that it verifies a universal property

fundamental group functors in descent exact homological categories abstract we study the notion of a fundamental group in the framework of descent exact homological categories this setting is sufficiently large to include several categories of algebraic nature such as almost abelian categories semi abelian categories and categories of topological semi abelian algebras for many adjunctions in this context we describe the fundamental groups by generalised brown ellis hopf formulae for the integral homology of groups

resolvent tests for similarity to a normal operator the main result of this paper is the resolvent similarity criterion which says that linear growth of the resolvent towards the spectrum is sufficient for a hilbert space contraction with finite rank defect operators and spectrum not covering the unit disc to be similar to a normal operator similar results are proved for operators having a spectral set bounded by a dini smooth jordan curve in particular a dissipative operator with finite rank imaginary part is similar to a normal operator if and only if its resolvent grows linearly towards the spectrum relevant results on the insufficiency of linear resolvent growth not accompanied by smallness of defect operators are presented also it is proved that there is no restriction on the spectrum other than finiteness which together with linear resolvent growth implies similarity to a normal operator the construction of corresponding examples depends on a characterization of well known ahlfors curves as curves of linear length growth with respect to linear fractional transformations

textures and covering based rough sets this paper introduces the relations between covering and dicovering in the framework of rough sets the natural counterpart of a covering in textures is given by a family of pairs of sets which is called a dicovering this leads us to two dual concepts which are called star and co star of a set respectively here we define dicovering approximation space and we discuss on covering and dicovering based rough sets in this context star corresponds to the upper approximation operator defined by zakowski and co star corresponds to the lower approximation operator studied by pomykala yao and zhu and wang

observability of polynomially stable systems abstract for finite dimensional systems the hautus test is a well known and easily checkable condition for observability russell and weiss a general necessary condition for exact observability siam j control optim 32 1994 1 23 suggested an infinite dimensional version of the hautus test which is necessary for exact infinite time observability and sufficient for approximate infinite time observability of exponentially stable systems in this paper the notion of observability is studied for polynomially stable systems several known results for exponentially stable systems are extended to the setting of polynomially stable systems by means of an example the obtained results are illustrated

on distributed and parameterized supervisor synthesis problems it is shown that the problem whether an arbitrary regular language has a non empty decomposable sublanguage with respect to a fixed distribution is decidable if and only if the independence relation induced by the distribution is transitive a sufficient condition on the distributed control architecture is then derived under which there exist some fixed non blocking local generators such that the distributed supervisor synthesis problem is undecidable we also show that a natural formulation of the parameterized supervisor synthesis problem is undecidable for a fixed non blocking generator template so long as the template alphabet has at least two private events and one global event that are controllable in particular all the undecidability results are still valid even if star free specification languages are considered

textural approach to generalized rough sets based on relations this paper presents a discussion on rough set theory from the textural point of view a texturing is a family of subsets of a given universal set u satisfying certain conditions which are generally basic properties of the power set the suitable morphisms between texture spaces are given by direlations defined as pairs r r where r is a relation and r is a corelation it is observed that the presections are natural generalizations for rough sets more precisely if r r is a complemented direlation then the inverse of the relation r the corelation r is actually a lower approximation operator an upper approximation operator

counterexamples concerning observation operators for c0 semigroups this paper concerns systems of the form dot x t ax t y t cx t where a generates a c 0 semigroup two conjectures which were posed in 1991 and 1994 are shown not to hold the first conjecture by g weiss states that if the range of c is one dimensional then c is admissible if and only if a certain resolvent estimate holds the second conjecture by d russell and g weiss states that a system is exactly observable if and only if a test similar to the hautus test for finite dimensional systems holds the c 0 semigroup in both counterexamples is analytic and possesses a basis of eigenfunctions using the a c pair from the second counterexample we construct a generator a e on a hilbert space such that si a e is uniformly left invertible but its semigroup does not have this property

generalized sampled data stabilization of well posed linear infinite dimensional systems we consider well posed linear infinite dimensional systems the outputs of which are sampled in a generalized sense using a suitable weighting function under certain natural assump tions on the system the weighting function and the sampling period we show that there exists a generalized hold function such that unity sampled data feedback renders the closed loop system exponentially stable in the state space sense as well as l 2 stable in the input output sense to illustrate our main result we describe an application to a structurally damped euler bernoulli beam

counterexamples to the discrete and continuous weighted weiss conjectures counterexamples are presented to weighted forms of the weiss conjecture in discrete and continuous time in particular for certain ranges of alpha operators are constructed that satisfy a given resolvent estimate but fail to be alpha admissible for alpha in 1 0 the operators constructed are normal while for alpha in 0 1 the operator is the unilateral shift on the hardy space h 2 mathbb d

3 3 lemma and protomodularity abstract the classical 3 3 lemma and snake lemma valid in any abelian category still hold in any quasi pointed the map 0 1 is a mono regular and protomodular category some applications are given in this abstract context concerning the denormalization of kernel maps and the normalization of internals groupoids i e associated crossed modules

applications of laplace carleson embeddings to admissibility and controllability it is shown how results on carleson embeddings induced by the laplace transform can be used to derive new and more general results concerning the weighted infinite time admissibility of control and observation operators for linear semigroup systems with q riesz bases of eigenvectors as an example the heat equation is considered next a new carleson embedding result is proved which gives further results on weighted admissibility for analytic semigroups finally controllability by smoother inputs is characterized by means of a new result about weighted interpolation

on t 0 and t 1 fuzzy closure spaces abstract in this paper we introduce subspace of a fuzzy closure space sum of a family of pairwise disjoint fuzzy closure spaces and product of a family of fuzzy closure spaces for the fuzzy closure spaces defined in srivastava et al 1994 we also introduce the notion of a t1 fuzzy closure space we have studied here t0 introduced earlier in srivastava et al 1994 and t1 fuzzy closure spaces in detail several results have been proved which establish the appropriateness of the definitions in particular we observe that t0 and t1 satisfy the hereditary productive and projective properties and in addition both are good extensions of the corresponding concepts in a closure space

resolutions higher extensions and the relative mal tsev axiom abstract we study how the concept of higher dimensional extension which comes from categorical galois theory relates to simplicial resolutions for instance an augmented simplicial object is a resolution if and only if its truncation in every dimension gives a higher extension in which sense resolutions are infinite dimensional extensions or higher extensions are finite dimensional resolutions we also relate certain stability conditions of extensions to the kan property for simplicial objects this gives a new proof of the fact that a regular category is mal tsev if and only if every simplicial object is kan using a relative setting of extensions