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

contractions nijenhuis and saletan tensors for general algebraic structures we study generalizations in many directions of the contraction procedure for lie algebras introduced by saletan we consider products of an arbitrary nature not necessarily lie brackets and we generalize to infinite dimension considering a modification of the approach by nijenhuis tensors to bilinear operations on sections of finite dimensional vector bundles we apply our general procedure to lie algebras lie algebroids and poisson brackets we also present results on contractions of n ary products and coproducts

the deformed lie algebra of differential operators of order at most one in this paper we study the algebraic properties of the deformed lie algebra l of differential operators of order at most one we determine all the derivations central extensions and automorphism group of l furthermore the reducibility criterion for the verma modules of the universal central extension of l is achieved through a study of the shapovalov form

n ary algebras a review with applications this paper reviews the properties and applications of certain n ary generalizations of lie algebras in a self contained and unified way these generalizations are algebraic structures in which the two entries lie bracket has been replaced by a bracket with n entries each type of n ary bracket satisfies a specific characteristic identity which plays the role of the jacobi identity for lie algebras particular attention will be paid to generalized lie algebras which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized jacobi identity and to filippov or n lie algebras which are defined by fully antisymmetric n brackets that satisfy the filippov identity three lie algebras have surfaced recently in multi brane theory in the context of the bagger lambert gustavsson model because of this filippov algebras will be discussed at length including the cohomology complexes that govern their central extensions and their deformations it turns out that whitehead s lemma extends to all semisimple n lie algebras when the skewsymmetry of the lie or n lie algebra bracket is relaxed one is led to a more general type of n algebras the n leibniz algebras these will be discussed as well since they underlie the cohomological properties of n lie algebras the standard poisson structure may also be extended to the n ary case we shall review here the even generalized poisson structures whose generalized jacobi identity reproduces the pattern of the generalized lie algebras and the nambu poisson structures which satisfy the filippov identity and determine filippov algebras finally the recent work of bagger lambert and gustavsson on superconformal chern simons theory will be briefly discussed emphasis will be made on the appearance of the 3 lie algebra structure and on why the a4 model may be formulated in terms of an ordinary lie algebra and on its nambu bracket generalization

unified products for leibniz algebras applications abstract let g be a leibniz algebra and e a vector space containing g as a subspace all leibniz algebra structures on e containing g as a subalgebra are explicitly described and classified by two non abelian cohomological type objects hl g 2 v g provides the classification up to an isomorphism that stabilizes g and hl 2 v g will classify all such structures from the view point of the extension problem here v is a complement of g in e a general product called the unified product is introduced as a tool for our approach the crossed resp bicrossed products between two leibniz algebras are introduced as special cases of the unified product the first one is responsible for the extension problem while the bicrossed product is responsible for the factorization problem the description and the classification of all complements of a given extension g e of leibniz algebras are given as a converse of the factorization problem they are classified by another cohomological object denoted by ha 2 h g where is the canonical matched pair associated to a given complement h several examples are worked out in details

controllability cost of conservative systems resolvent condition and transmutation abstract this article concerns the exact controllability of unitary groups on hilbert spaces with unbounded control operator it provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality by the transmutation of controls in some time l for the corresponding second order conservative system it is proved that the cost of controls in time t for the unitary group grows at most like exp l 2 t as t tends to 0 in the application to the cost of fast controls for the schrodinger equation l is the length of the longest ray of geometric optics which does not intersect the control region this article also provides observability resolvent estimates implying fast smoothing effect controllability at low cost and underscores that the controllability cost of a system is not changed by taking its tensor product with a conservative system

on an infinite dimensional lie algebra of virasoro type in this paper we study an infinite dimensional lie algebra of virasoro type which is realized as an affinization of a two dimensional novikov algebra it is a special deformation of the lie algebra of differential operators on a circle of order at most 1 there is an explicit construction of a vertex algebra associated with the lie algebra we determine all derivations of this lie algebra in terms of some derivations and centroids of the corresponding novikov algebra the universal central extension of this lie algebra is also determined

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

on a type of commutative algebras abstract we introduce some basic concepts for jacobi jordan algebras such as representations crossed products or frobenius metabelian co flag objects a new family of solutions for the quantum yang baxter equation is constructed arising from any 3 step nilpotent jacobi jordan algebra crossed products are used to construct the classifying object for the extension problem in its global form for a given jacobi jordan algebra a and a given vector space v of dimension c a global non abelian cohomological object g h 2 a v is constructed it classifies from the view point of the extension problem all jacobi jordan algebras that have a surjective algebra map on a with kernel of dimension c the object g h 2 a k responsible for the classification of co flag algebras is computed all 1 dim a dimensional jacobi jordan algebras that have an algebra surjective map on a are classified and the automorphism groups of these algebras is determined several examples involving special sets of matrices and symmetric bilinear forms as well as equivalence relations between them generalizing the isometry relation are provided

n dimensional filiform leibniz algebras of length n 1 and their derivations abstract in this work n dimensional filiform leibniz algebras admitting a gradation of length n 1 are classified derivations of such algebras are also described

leibniz algebroid associated with a nambu poisson structure the notion of a leibniz algebroid is introduced and it is shown that each nambu poisson manifold has associated a canonical leibniz algebroid this fact permits one to define the modular class of a nambu poisson manifold as an appropriate cohomology class extending the well known modular class of poisson manifolds

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

p filiform leibniz algebras of maximum length we complete the description of 3 filiform leibniz algebras of maximum length moreover using the good structure of algebras of maximum length we study some of their cohomological properties our main tools are the previous results by cabezas and pastor 1 the construction of an appropriate homogeneous basis in the considered connected gradation and the computational support provided by two programs implemented in mathematica

homologies of algebraic structures via braidings and quantum shuffles abstract in this paper we construct structural pre braidings characterizing different algebraic structures a rack an associative algebra a leibniz algebra and their representations some of these pre braidings seem original on the other hand we propose a general homology theory for pre braided vector spaces and braided modules based on the quantum co shuffle comultiplication applied to the structural pre braidings above it gives a generalization and a unification of many known homology theories all the constructions are categorified resulting in particular in their super and co versions loday s hyper boundaries as well as certain homology operations are efficiently treated using the shuffle tools

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

nonparametric control algorithms for nonlinear fading memory systems we develop an algorithm to control an unknown nonlinear fading memory discrete time system our approach is based on nonparametric regression techniques rather than traditional feedback control we discuss a procedure that given a desired periodic output and a tolerance produces an acceptable output from any system in a wide class the algorithm uses as data past inputs which are selected by the algorithm and corresponding possibly noisy output observations and needs no extra parametric knowledge or restrictions on the system we also present an algorithm that produces an output that converges to the desired output when stricter conditions are imposed on the system our approach in its current form however cannot be used to control open loop unstable systems

deformations of 3 algebras we phrase deformations of n leibniz algebras in terms of the cohomology theory of the associated leibniz algebra we do the same for n lie algebras and for the metric versions of n leibniz and n lie algebras we place particular emphasis on the case of n 3 and explore the deformations of 3 algebras of relevance to three dimensional superconformal chern simons theories with matter

a rigid leibniz algebra with non trivial hl2 abstract in this article we generalize richardson s example of a rigid lie algebra with non trivial h 2 to the leibniz setting namely we consider the hemisemidirect product h of a semidirect product lie algebra m k g of a simple lie algebra g with some non trivial irreducible g module m k with a non trivial irreducible g module i l then for g s l 2 c we take m k resp i l to be the standard irreducible s l 2 c module of dimension k 1 resp l 1 assume k 2 5 is an odd integer and l 2 is odd then we show that the leibniz algebra h is geometrically rigid and has non trivial h l 2 with adjoint coefficients we close the article with an appendix where we record further results on the question whether h 2 g g 0 implies h l 2 g g 0

dynamic system identification with order statistics systems consisting of linear dynamic and memory less nonlinear subsystems are identified the paper deals with systems in which the nonlinear element is followed by a linear element as well as systems in which the subsystems are connected in parallel the goal of the identification is to recover the nonlinearity from noisy input output observations of the whole system signals interconnecting the elements are not measured observed values of the input signal are rearranged in increasing order and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way two algorithms are presented and their mean integrated square error is examined conditions for pointwise convergence are also established for the nonlinearity satisfying the lipschitz condition the error converges to zero the rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal results of numerical simulation are also presented

on a class of n leibniz deformations of the simple filippov algebras we study the problem of infinitesimal deformations of all real simple finite dimensional filippov or n lie algebras considered as a class of n leibniz algebras characterized by having an n bracket skewsymmetric in its n 1 first arguments we prove that all n 3 simple finite dimensional filippov algebras fas are rigid as n leibniz algebras of this class this rigidity also holds for the leibniz deformations of the semisimple n 2 filippov i e lie algebras the n 3 simple fas however admit a nontrivial one parameter infinitesimal 3 leibniz algebra deformation we also show that the n 3 simple filippov algebras do not admit nontrivial central extensions as n leibniz algebras of the above class

leibniz h pseudoalgebras abstract we define a leibniz h pseudoalgebra over a cocommutative hopf algebra h and a tensor product of leibniz h pseudoalgebras and prove that every leibniz h pseudoalgebra of free rank one over h is a lie h pseudoalgebra to characterize simple leibniz h pseudoalgebras we define the leibniz cohomology of leibniz h pseudoalgebras and determine some simple leibniz h pseudoalgebras by calculating leibniz cohomological groups of finite simple lie h pseudoalgebras defined in 2

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

a structure theorem for leibniz homology abstract presented is a structure theorem for the leibniz homology hl of an abelian extension of a simple real lie algebra g as applications results are stated for affine extensions of the classical lie algebras sl n r so n r and sp n r furthermore hl h is calculated when h is the lie algebra of the poincare group as well as the lie algebra of the affine lorentz group the structure theorem identifies all of these in terms of g invariants

the complexity of model classes and smoothing noisy data abstract we consider the problem of smoothing a sequence of noisy observations using a fixed class of models via a deterministic analysis we obtain necessary and sufficient conditions on the noise sequence and model class that ensure that a class of natural estimators gives near optimal smoothing in the case of i i d random noise we show that the accuracy of these estimators depends on a measure of complexity of the model class involving covering numbers our formulation and results are quite general and are related to a number of problems in learning prediction and estimation as a special case we consider an application to output smoothing for certain classes of linear and nonlinear systems the performance of output smoothing is given in terms of natural complexity parameters of the model class such as bounds on the order of linear systems the l1 norm of the impulse response of stable linear systems or the memory of a lipschitz nonlinear system satisfying a fading memory condition

nonparametric output prediction for nonlinear fading memory systems the authors construct a class of elementary nonparametric output predictors of an unknown discrete time nonlinear fading memory system their algorithms predict asymptotically well for every bounded input sequence every disturbance sequence in certain classes and every linear or nonlinear system that is continuous and asymptotically time invariant causal and with fading memory the predictor is based on k sub n nearest neighbor estimators from nonparametric statistics it uses only previous input and noisy output data of the system without any knowledge of the structure of the unknown system the bounds on the input or the properties of noise under additional smoothness conditions the authors provide rates of convergence for the time average errors of their scheme finally they apply their results to the special case of stable linear time invariant lti systems

hnn extensions of leibniz algebras abstract in this paper we construct hnn extensions of diassociative algebras and leibniz algebras and prove that every leibniz algebra embeds into any of its hnn extensions we also prove that every leibniz algebra with at most countable dimension embeds into a two generator leibniz algebra

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

nonparametric identification of wiener systems by orthogonal series a wiener system i e a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade is identified both the input signal and disturbance are random white and gaussian the unknown nonlinear characteristic is strictly monotonous and differentiable and therefore the problem of its recovering from input output observations of the whole system is nonparametric it is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed the estimates apply the trigonometric legendre and hermite orthogonal functions pointwise consistency of all the algorithms is shown under some additional smoothness restrictions the rates of their convergence are examined and compared an algorithm to identify the impulse response of the linear subsystem is proposed

obstruction theory in action accessible categories abstract we show that in semi abelian action accessible categories such as the categories of groups lie algebras rings associative algebras and poisson algebras the obstruction to the existence of extensions is classified by the second cohomology group in the sense of bourn moreover we describe explicitly the obstruction to the existence of extensions in the case of leibniz algebras comparing bourn cohomology with loday pirashvili cohomology of leibniz algebras

exponential stability of an abstract nondissipative linear system in this paper we consider an abstract linear system with perturbation of the form frac dy dt ay varepsilon by on a hilbert space cal h where a is skew adjoint b is bounded and varepsilon is a positive parameter motivated by a work of freitas and zuazua on the one dimensional wave equation with indefinite viscous damping p freitas and e zuazua j differential equations 132 1996 pp 338 352 we obtain a sufficient condition for exponential stability of the above system when b is not a dissipative operator we also obtain a hautus type criterion for exact controllability of system a g where g is a bounded linear operator from another hilbert space to cal h our result about the stability is then applied to establish the exponential stability of several elastic systems with indefinite viscous damping as well as the exponential stabilization of the elastic systems with noncolocated observation and control

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

extension theory and the calculus of butterflies abstract this paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions the first uses weak monoidal functors the second classifies extensions by means of suitable h 2 actions we develop our theory formally by making explicit a connection between non abelian g torsors and fibrations then we apply our general framework to the classification of extensions in a semi abelian context by means of butterflies 1 between internal crossed modules as a main result we get an internal version of dedecker s theorem on the classification of extensions of a group by a crossed module in the semi abelian context bourn s intrinsic schreier mac lane extension theorem 13 turns out to be an instance of our theorem 6 3 actually even just in the case of groups our approach reveals a result slightly more general than classical schreier mac lane theorem

leibniz algebra deformations of a lie algebra in this note we compute leibniz algebra deformations of the three dimensional heisenberg lie algebra n3 and compare it to its lie deformations it turns out that there are three extra leibniz deformations we also describe a versal leibniz deformation of n3 with the versal base

on the definitions of nucleus for dialgebras abstract malcev dialgebras were introduced recently by bremner peresi and sanchez ortega in the present paper we continue their study by introducing the notion of the generalized alternative dinucleus of a 0 dialgebra a general conjecture about the speciality of malcev dialgebras in terms of this dinucleus is formulated in the last section we introduce the appropriate generalization of the associative nucleus for dialgebras and prove an analogue of kleinfeld s theorem for the setting of dialgebras

learning by canonical smooth estimation ii learning and choice of model complexity this paper analyzes the properties of a procedure for learning from examples this canonical learner is based on a canonical error estimator developed in part i in learning problems one can observe data that consists of labeled sample points and the goal is to find a model or hypothesis from a set of candidates that will accurately predict the labels of new sample points the expected mismatch between a hypothesis prediction and the actual label of a new sample point is called the hypothesis generalization error we compare the canonical learner with the traditional technique of finding hypotheses that minimize the relative frequency based empirical error estimate it is shown that for a broad class of learning problems the set of cases for which such empirical error minimization works is a proper subset of the cases for which the canonical learner works we derive bounds to show that the number of samples required by these two methods is comparable we also address the issue of how to determine the appropriate complexity for the class of candidate hypotheses

second cohomology of q deformed witt superalgebras the purpose of this paper is to compute the second adjoint cohomology group of q deformed witt superalgebras they are hom lie superalgebras obtained by q deformation of witt lie superalgebra that is one considers derivations instead of classical derivations

steinberg leibniz algebras and superalgebras as a universal central extension of the special linear lie algebra sl n a over a unital associative algebra a the steinberg algebras st n a and stl n a were studied in several papers in this paper we mainly study the steinberg leibniz algebra stl n d defined over a dialgebra d we prove that it is the universal central extension of the special linear leibniz algebra sl n d with kernel hhs1 d the quotient of the first hochschild homology group hh1 d of the dialgebra d by the ideal generated by a b c a b c for all a b c d we also obtain a similar theorem for the steinberg leibniz superalgebra stl m n d this research plays a key role in studying the leibniz algebras superalgebras graded by finite root systems and is also connected with leibniz k theory

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

on estimation of a class of nonlinear systems by the kernel regression estimate the estimation of a multiple input single output discrete hammerstein system is studied such a system contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem the impulse response of the dynamic linear subsystem is obtained by the correlation method the main results concern the estimation of the nonlinear memoryless subsystem no conditions are imposed on the functional form of the nonlinear subsystem and the nonlinearity is recovered using the kernel regression estimate the distribution free pointwise and global convergence of the estimate is demonstrated that is no conditions are imposed on the input distribution and convergence is proven for virtually all nonlinearities the rates of pointwise as well as global convergence are obtained for all input distributions and for lipschitz type nonlinearities

nilpotent sabinin algebras abstract in this paper we establish several basic properties of nilpotent sabinin algebras namely we show that nilpotent sabinin algebras 1 can be integrated to produce nilpotent loops 2 satisfy an analogue of the ado theorem 3 have nilpotent lie envelopes we also give a new set of axioms for sabinin algebras these axioms reflect the fact that a complementary subspace to a lie subalgebra in a lie algebra is a sabinin algebra finally we note that the non associative version of the jennings theorem produces a version of the ado theorem for loops whose commutator associator filtration is of finite length

optimal asymptotic identification under bounded disturbances the intrinsic limitation of worst case identification of linear time invariant systems using data corrupted by bounded disturbances when the unknown plant is known to belong to a given model set is studied this is done by analyzing the optimal worst case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm it is shown that under some topological conditions on the model set there is an identification algorithm which is asymptotically optimal for any input and the optimal asymptotic error is characterized as a function of the inputs these results which hold for any error metric and disturbance norm are applied to three specific identification problems identification of stable systems in the l sub 1 norm identification of stable rational systems in the h sub infinity norm and identification of unstable rational systems in the gap metric for each of these problems the general characterization of optimal asymptotic error is used to find near optimal inputs to minimize the error

a note on metric dimension and feedback in discrete time the notions of a in dimension and in entropy were introduced into feedback theory of g zames 1976 1979 who proposed them as measures of the complexity of identification and the effectiveness of feedback in reducing identification costs the 1979 paper was concerned mainly with continuous time systems but also included a summary of discrete time results which contained certain errata the authors elaborate the discrete time case supply some omitted proofs and correct the errata

non antisymmetric versions of nambu poisson and algebroid brackets we show that we can skip the skew symmetry assumption in the definition of nambu poisson brackets in other words an n ary bracket on the algebra of smooth functions which satisfies the leibniz rule and an n ary version of the jacobi identity must be skew symmetric a similar result holds for a non antisymmetric version of lie algebroids

on stability equivalence between dynamic output feedback and static output feedback for a class of second order infinite dimensional systems we consider stabilization for a class of abstract second order infinite dimensional systems with collocated control and observation we show that the closed loop system under a proportional direct output feedback control is asymptotically stable if and only if the closed loop system under some dynamic output feedback control is asymptotically stable a hautus test is developed to ensure the asymptotic stability two types of dynamic output feedback controls are investigated the results are applied to some coupled wave heat equations where the heat system is considered as a controller of the wave system this study provides a different view in the study of the coupled systems described by partial differential equations

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

on the cohomology of leibniz conformal algebras we construct a new cohomology complex of leibniz conformal algebras with coefficients in a representation instead of a module the low dimensional cohomology groups of this complex are computed meanwhile we construct a leibniz algebra from a leibniz conformal algebra and prove that the category of leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution leibniz algebras

locally distributed control for a model of fluid structure interaction we consider the equations modeling the coupled vibrations of a fluid solid system the control acts in a subset of a domain occupied by the fluid our main result asserts that we have exact controllability and exponential stabilizability provided that the support of the control contains a neighborhood of the solid and a neighborhood of the exterior boundary this improves the existing exact controllability results which require a control which is active in the whole fluid domain the proof is based on a frequency domain approach combined with the use of appropriate multipliers moreover we show that the strong stabilizability property holds for any open control region

a nonparametric algorithm for identification of linear dynamic siso systems of unknown order a new nonparametric algorithm is presented for estimation of the weighting function of linear dynamic single input single output systems the behavior of the mean squared error of the proposed estimate is examined finally the optimal parameter is found for the best speed of uniform mean squared consistency

on system identification by nonparametric function fitting a new nonparametric algorithm for function fitting is proposed and its application to a broad class of system identification problems is discussed

test for leibniz n algebra structure abstract for a given basis of a vector space l over a field k and a multiplication table which is defined by a multilinear map l n l we present an algorithm and develop a computer program on mathematica in order to test if the given multiplication table corresponds to a lie n algebra or a non lie leibniz n algebra or neither the algorithm is based on the computation of a grobner basis of the ideal which is used in the construction of the universal enveloping algebra of the leibniz algebra provided by the daletskii takhtajan functor by means of the ncalgebra package which permits the construction of grobner bases in noncommutative associative algebras

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

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

exact observability square functions and spectral theory in the first part of this article we introduce the notion of a backward forward conditioning bfc system that generalises the notion of zero class admissibility introduced in xu et al 2008 30 we can show that unless the spectrum contains a half plane the bfc property occurs only in situations where the underlying semigroup extends to a group in a second part we present a sufficient condition for exact and final state observability in banach spaces that is designed for infinite dimensional output spaces and general strongly continuous semigroups to obtain this we make use of certain weighted square function estimates specialising to the hilbert space situation we obtain a result for contraction semigroups without an analyticity condition on the semigroup

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

duality and modular class of a nambu poisson structure in this paper we introduce cohomology and homology theories for nambu poisson manifolds also we study the relation between the existence of a duality for these theories and the vanishing of a particular nambu poisson cohomology class the modular class the case of a regular nambu poisson structure and some singular examples are discussed

leibniz algebras with small derived ideal abstract a nilpotent leibniz algebra l is called extra special if dim z l dim l 2 1 in this paper the structure the second homology and the capability of extra special leibniz algebras are completely determined

andre quillen cohomology of algebras over an operad abstract we study the andre quillen cohomology with coefficients of an algebra over an operad using resolutions of algebras coming from the koszul duality theory we make this cohomology theory explicit and we give a lie theoretic interpretation for which operads is the associated andre quillen cohomology equal to an ext functor we give several criteria based on the cotangent complex to characterize this property we apply it to homotopy algebras which gives a new homotopy stable property for algebras over cofibrant operads

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

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

steinberg unitary leibniz algebras abstract in this paper we mainly study the steinberg unitary leibniz algebra stul n d defined over a unital dialgebra d we consider its universal central extension and obtain some results as in the steinberg unitary lie algebra case

quantum koszul complexes for majid s braided lie algebras a yang baxter operator was canonically associated to any cocommutative braided lie algebra as defined by majid applying previous results we construct quantum koszul complexes for braided lie algebras with respect to this operator in the usual case the complexes reduce to the chevalley eilenberg complexes for classical lie algebras

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

necessary condition of linear distributed parameter systems with exact controllability abstract in this paper we studied the necessary condition of distributed parameter system with exact controllability let 0 t be the control mapping we introduce new a class of control operators that is called the i class control which satisfy r 0 t r t t is closed set for t 0 if the system is exactly controllable in finite time then the semigroup t t must have closed range in particular if the generator of t t has compact resolvent its spectra distribute in a strip parallel to imaginary axis as an application we assert that the systems associated with the immediately norm continuous semigroups are never exact controllable for zero class or i class controls

the embedding tensor leibniz loday algebras and their higher gauge theories we show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a leibniz algebra with one of its induced quotient lie algebras embedded into a rigid symmetry lie algebra that provides an additional representation constraint every leibniz algebra gives rise to a lie n algebra in a canonical way for every n in mathbb n cup infty it is the gauging of this l infty algebra that explains the tensor hierarchy of the bosonic sector of gauged supergravity theories the tower of p from gauge fields corresponds to lyndon words of the universal enveloping algebra of the free lie algebra of an odd vector space in this construction truncation to some n yields the reduced field content needed in a concrete spacetime dimension

state reconstruction of a distributed parameter system with exact observability abstract we study the problem of state reconstruction for exactly observable systems here we present two approaches for state reconstruction the riesz basis approach and the dual hilbert uniqueness method hum based on an iteration algorithm the riesz basis approach gives an explicit representation of the initial state of the system whereas the hum dual method gives an efficient approximation of the initial state

some remarks on semisimple leibniz algebras abstract from levi s theorem it is known that every finite dimensional lie algebra over a field of characteristic zero is decomposed into semidirect sum of its solvable radical and semisimple subalgebra moreover semisimple part is the direct sum of simple ideals in barnes preprint 6 levi s theorem is extended to the case of leibniz algebras in the present paper we investigate the semisimple leibniz algebras and we show that the splitting theorem for semisimple leibniz algebras is not true moreover we consider some special classes of the semisimple leibniz algebras and we find a condition under which they decompose into direct sum of simple ideals

learning dynamical systems in a stationary environment abstract we consider the problem of learning the input output relation of a dynamical system from noisy data our method rests on the use of a smooth simultaneous estimator which generalizes the standard empirical estimator in a stationary environment our algorithm is shown to select a model which exhibits the probably approximately correct pac property under very mild conditions this contribution should be thought of as a first attempt to extend concepts developed in learning theory to the field of system identification where due to the presence of the system dynamics the typical i i d assumption on the data made in learning theory is not satisfied

on the higher order generalizations of poisson structures the characterization of the nambu poisson n tensors as a subfamily of the generalized poisson ones recently introduced and here extended to the odd order case is discussed the homology and cohomology complexes of both structures are compared and some physical considerations are made

worst case identification of nonlinear fading memory systems abstract in this paper the problem of asymptotic identification for fading memory systems in the presence of bounded noise is studied for any experiment the worst case error is characterized in terms of the diameter of the worst case uncertainty set optimal inputs that minimize the radius of uncertainty are studied and characterized finally a convergent algorithm that does not require knowledge of the noise upper bound is furnished the algorithm is based on interpolating data with spline functions which are shown to be well suited for identification in the presence of bounded noise more so than other basis functions such as polynomials