frequency domain approach to optimally robust residual generation and evaluation for model based fault diagnosis methods of residual generation and evaluation for model based fault diagnosis in uncertain linear dynamic systems are investigated with the aid of frequency domain approaches and h optimization techniques based on the factorization technique the construction of residual generators in terms of a parametrization concept is proposed with its help the fault detection and isolation problem with perfect model uncertainty decoupling is studied and moreover by its optimal approximation the problem of optimally robust residual generation is treated the optimization problem is solved by h techniques to increase the robustness of residual evaluation a frequency domain residual evaluation index is introduced and optimal input adaptive fault thresholds are derived with respect to the frequency domain evaluation index the results are illustrated in terms of an inverted pendulum example

lie bialgebra structures on the twisted heisenberg virasoro algebra abstract in this paper we investigate lie bialgebra structures on the twisted heisenberg virasoro algebra with the determination of certain lie bialgebra structures on the virasoro algebra we determine certain structures on the twisted heisenberg virasoro algebra moreover some general and useful results are obtained with our methods and results we also can easily determine certain structures on some lie algebras related to the twisted heisenberg virasoro algebra

a spinor like representation of the contact superconformal algebra k 4 in this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra k 4 into the lie superalgebra of pseudodifferential symbols on the supercircle s1 2 associated with this embedding is a one parameter family of spinor like tiny irreducible representations of k 4 realized just on 4 fields instead of the usual 16

embedding of the lie superalgebra d 2 1 α into the lie superalgebra of pseudodifferential symbols on s1 2 we obtain an embedding of the one parameter family of exceptional simple lie superalgebras d 2 1 into the lie superalgebra of pseudodifferential symbols on the supercircle s1 2 correspondingly there is an embedding of d 2 1 into a nontrivial central extension of the derived contact superconformal algebra k 4 realized in terms of 4 4 matrices over a weyl algebra

efficient recursive algorithms for detection of abrupt changes in signals and control systems this paper addresses a number of open problems concerning the generalized likelihood ratio glr rules for online detection of faults and parameter changes in control systems it is shown that with an appropriate choice of the threshold and window size these glr rules are asymptotically optimal the rules are also extended to non likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing gaussian approximations to these statistics when the window size is chosen suitably recursive algorithms are developed for practical implementation of the procedure and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate

factoriality of boejko speicher von neumann algebras we study the von neumann algebra generated by q deformed gaussian elements li l i where operators li fulfill the q deformed canonical commutation relations lil j ql jli ij for 1 q 1 we show that if the number of generators is finite greater than some constant depending on q it is a ii1 factor which does not have the property our technique can be used for proving factoriality of many examples of von neumann algebras arising from some generalized brownian motions both for the type ii1 and type iii case

simple associative conformal algebras of linear growth abstract we describe simple finitely generated associative conformal algebras of gel fand kirillov dimension one

magic squares and matrix models of lie algebras this paper is concerned with the description of exceptional simple lie algebras as octonionic analogues of the classical matrix lie algebras we review the tits freudenthal construction of the magic square which includes the exceptional lie algebras as the octonionic case of a construction in terms of a jordan algebra of hermitian 3 3 matrices tits or various plane and other geometries freudenthal we present alternative constructions of the magic square which explain its symmetry and show explicitly how the use of split composition algebras leads to analogues of the matrix lie algebras su 3 sl 3 and sp 6 we adapt the magic square construction to include analogues of su 2 sl 2 and sp 4 for all real division algebras

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

associative conformal algebras with finite faithful representation abstract the classification of irreducible subalgebras of the associative conformal algebra cend n is presented in this paper the structure theory of associative conformal algebras with finite faithful representation is developed

brief paper an integrated trade off design of observer based fault detection systems in this paper problems related to the integrated design of observer based fault detection systems are addressed in the context of norm based residual evaluation a trade off between false alarm rate far and fault detection rate fdr is first formulated aiming at minimizing far under given fdr an approach is then presented for the design of observer based fault detection systems for this purpose the well established factorization technique is applied finally study is devoted to the comparison between the existing methods and the proposed one

semiprime prime and simple jordan superpairs covered by grids in this paper we continue the investigation of jordan superpairs covered by a grid which have recently been described by the second author e neher j algebra 269 2003 28 73 for such a jordan superpair we characterize semiprimeness primeness and simplicity in terms of its associated supercoordinate system

finite conformal modules over n 2 3 4 superconformal algebras in this paper we continue the study of representation theory of formal distribution lie superalgebras initiated by cheng and kac asian j math 1 181 193 1997 2 153 156 1998 erratum we study finite verma type conformal modules over the n 2 n 3 and the two n 4 superconformal algebras and also find explicitly all singular vectors in these modules from our analysis of these modules we obtain a complete list of finite irreducible conformal modules over the n 2 n 3 and the two n 4 superconformal algebras

the tetrahedron algebra the onsager algebra and the sl2 loop algebra let k denote a field with characteristic 0 and let t denote an indeterminate we give a presentation for the three point loop algebra sl2 k t t 1 t 1 1 via generators and relations this presentation displays s4 symmetry using this presentation we obtain a decomposition of the above loop algebra into a direct sum of three subalgebras each of which is isomorphic to the onsager algebra

q gaussian processes non commutative and classical aspects we examine for 1 q 1 q gaussian processes i e families of operators non commutative random variables where the a t fulfill the q commutation relations for some covariance function equipped with the vacuum expectation state we show that there is a q analogue of the gaussian functor of second quantization behind these processes and that this structure can be used to translate questions on q gaussian processes into corresponding and much simpler questions in the underlying hilbert space in particular we use this idea to show that a large class of q gaussian processes possesses a non commutative kind of markov property which ensures that there exist classical versions of these non commutative processes this answers an old question of frisch and bourret fb

triality exceptional lie algebras and deligne dimension formulas abstract we give a computer free proof of the deligne cohen and de man formulas for the dimensions of the irreducible g modules appearing in g k k 4 where g ranges over the exceptional complex simple lie algebras we give additional dimension formulas for the exceptional series as well as uniform dimension formulas for other representations distinguished by freudenthal along the rows of his magic chart our proofs use the triality model of the magic square which we review and present a simplified proof of its validity we conclude with some general remarks about obtaining series of lie algebras in the spirit of deligne and vogel

an lmi approach to minimum sensitivity analysis with application to fault detection this paper systematically studies the minimum input sensitivity analysis problem the lowest level of sensitivity of system outputs to system inputs is defined as an h index a full characterization of the h index is given first in terms of matrix equalities and inequalities and then in terms of linear matrix inequalities lmis as a dual of the bounded real lemma a related problem of input observability is also studied with new necessary and sufficient conditions given which are necessary for a fault detection system to have a nonzero worst case fault sensitivity the above results are applied to the problem of fault detection filter analysis with numerical examples given to show the effectiveness of the proposed approaches

exceptional n 6 superconformal algebra we realize the exceptional n 6 superconformal algebra spanned by 32 fields inside the lie superalgebra of pseudodifferential symbols on the supercircle s1 3 correspondingly we obtain two nonisomorphic one parameter families of irreducible representations of this superconformal algebra in a superspace spanned by 8 fields

representations of simple noncommutative jordan superalgebras i abstract in this article we begin the study of representations of simple finite dimensional noncommutative jordan superalgebras in the case of degree 3 we show that any finite dimensional representation is completely reducible and depending on the superalgebra quasiassociative or jordan then we study representations of superalgebras d t and k 3 and prove the kronecker factorization theorem for superalgebras d t in the last section we use a new approach to study noncommutative jordan representations of simple jordan superalgebras

a new n 6 superconformal algebra in this paper we construct a newn 6 superconformal algebra which extends the virasoro algebra by theso 6 current algebra by 6 odd primary fields of conformal weight 3 2 and by 10 odd primary fields of conformal weight 1 2 the commutation relations of this algebra which we will refer to asck 6 are represented by short distance operator product expansions ope we constructck 6 as a subalgebra of theso 6 superconformal algebra k6 thus giving it a natural representation as first order differential operators on the circle withn 6 extended symmetry we show thatck 6 has no nontrivial central extensions

conservative algebras of 2 dimensional algebras abstract in 1990 kantor introduced the conservative algebra w n of all algebras i e bilinear maps on the n dimensional vector space in case n 1 the algebra w n does not belong to well known classes of algebras such as associative lie jordan leibniz algebras we describe the algebra of all derivations of w 2 and subalgebras of w 2 of codimension one we also study similar problems for the algebra w 2 of all commutative algebras on the two dimensional vector space and the algebra s 2 of all commutative algebras with trace zero multiplication on the two dimensional space

a matrix factorization solution to the h h fault detection problem in this paper we give a matrix factorization solution to the h h fault detection fd problem for linear time invariant dynamic systems an h h fd filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults more specifically it minimizes the largest singular value over the extended imaginary axis of the transfer matrix from the disturbance to the residual signal vectors subject to the constraint that the singular values of the transfer matrix from the fault to the residual vectors are larger than or equal to 1 we show through the use of matrix function factorizations and completions that the problem reduces to a nonstandard model matching problem which is then solved under a mild assumption concerning the rank of a matrix function we also give an illustrative example

lie superalgebras graded by p n and q n abstract in this article we study lie superalgebras graded by the root systems p n and q n

quadratic jordan superpairs covered by grids abstract in this paper we are proposing a theory of jordan superpairs defined over super commutative superrings our framework has two novelties we allow scalars of even and odd parity and we do not assume that 1 2 lies in our base superring to demonstrate that it is possible to work in this generality we classify jordan superpairs covered by a grid

classification of linearly compact simple jordan and generalized poisson superalgebras abstract we classify all linearly compact simple jordan superalgebras over an algebraically closed field of characteristic zero as a corollary we deduce the classification of all linearly compact unital simple generalized poisson superalgebras

free monotone transport by solving a free analog of the monge ampere equation we prove a non commutative analog of brenier s monotone transport theorem if an n tuple of self adjoint non commutative random variables z 1 z n satisfies a regularity condition its conjugate variables 1 n should be analytic in z 1 z n and j should be close to z j in a certain analytic norm then there exist invertible non commutative functions f j of an n tuple of semicircular variables s 1 s n so that z j f j s 1 s n moreover f j can be chosen to be monotone in the sense that and g is a non commutative function with a positive definite hessian in particular we can deduce that c z 1 z n c s 1 s n and w z 1 dots z n cong l mathbb f n thus our condition is a useful way to recognize when an n tuple of operators generate a free group factor we obtain as a consequence that the q deformed free group factors vargamma q mathbb r n are isomorphic for sufficiently small q with bound depending on n to free group factors we also partially prove a conjecture of voiculescu by showing that free gibbs states which are small perturbations of a semicircle law generate free group factors lastly we show that entrywise monotone transport maps for certain gibbs measure on matrices are well approximated by the matricial transport maps given by free monotone transport

quadratic conformal superalgebras abstract in this paper we shall classify quadratic conformal superalgebras by certain compatible pairs of a lie superalgebra and a novikov superalgebra four general constructions of such pairs are given moreover we shall classify such pairs related to simple novikov algebras

superconformal algebras and transitive group actions on quadrics a classification of physical superconformal algebras is given the list consists of seven algebras the virasoro algebra the neveu schwarz algebra then 2 3 and 4 algebras the superalgebra of all vector fields on then 2 supercircle and a new algebrack6 constructed in 3 the proof relies heavily on the classification of all connected subgroups ofson c which act transitively on the quadric v v 1

symmetric composition algebras abstract a construction of all the okubo algebras over fields of characteristic 3 is provided and the complete classification of the composition algebras with associative norm over fields is finished

singular dimensions of the n 2 superconformal algebras i verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1 following a method developed for the virasoro algebra by kent we introduce the concept of adapted orderings on superconformal algebras we prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space we apply this method to the topological n 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological verma modules 0 1 2 or 3 depending on the type of verma module and the type of singular vector as a consequence we prove the conjecture of gato rivera and rosado on the possible existing types of topological singular vectors 4 in chiral verma modules and 29 in complete verma modules interestingly we have found two dimensional spaces of singular vectors at level 1 finally by using the topological twists and the spectral flows we also obtain the maximal dimensions of the singular vector spaces for the neveu schwarz n 2 algebra 0 1 or 2 and for the ramond n 2 algebra 0 1 2 or 3

on the hochschild cohomologies of associative conformal algebras with a finite faithful representation associative conformal algebras of conformal endomorphisms are of essential importance for the study of finite representations of conformal lie algebras lie vertex algebras we describe all semisimple algebras of conformal endomorphisms which have the trivial second hochschild cohomology group with coefficients in every conformal bimodule as a consequence we state a complete solution of the radical splitting problem in the class of associative conformal algebras with a finite faithful representation

symmetric triality relations and structurable algebras in this paper some properties of algebras satisfying local symmetric triality relations have been studied including both generalized symmetric composition algebras and the conjugate algebras of any structurable algebras we also discuss a general method of constructing lie algebras from such a system which can permit a construction of the magic square

derivations of the cheng kac jordan superalgebras abstract the derivations of the cheng kac jordan superalgebras are studied it is shown that assuming 1 is a square in the ground field the lie superalgebra of derivations of a cheng kac jordan superalgebra is isomorphic to the lie superalgebra obtained from a simpler jordan superalgebra a kantor double superalgebra of vector type by means of the tits kantor koecher construction this is done by exploiting the s 4 symmetry of the cheng kac jordan superalgebra

structurable superalgebras of cartan type abstract we describe the simple lie superalgebras arising from the unital structurable superalgebras of characteristic 0 and construct four series of the unital simple structurable superalgebras of cartan type we give a classification of simple structurable superalgebras of cartan type over an algebraically closed field f of characteristic 0 together with the faulkner theorem on the classification of classical such superalgebras it gives a classification of the simple structurable superalgebras over f

triality of structurable and pre structurable algebras abstract we introduce a notion of pre structurable algebras based on the structurable algebra of allison as well as lie algebras that satisfy triality

a numerical algorithm for inner outer factorizations of real rational matrices abstract in this paper reliable algorithms are developed to perform the inner outer factorization of a strictly wide real rational matrix the derivations are based on a right coprime factorization of a certain right inverse of the given transfer matrix where the denominator factor is inner the implementation of the algorithms can be carried out efficiently using real matrix operations

exactness of the fock space representation of the q commutation relations we show that for all q in the interval 1 1 the fock representation of the q commutation relations can be unitarily embedded into the fock representation of the extended cuntz algebra in particular this implies that the c algebra generated by the fock representation of the q commutation relations is exact an immediate consequence is that the q gaussian von neumann algebra is weakly exact for all q in the interval 1 1

lie algebras with s4 action and structurable algebras abstract the normal symmetric triality algebras sta s and the normal lie related triple algebras lrta s have been recently introduced by the second author in connection with the principle of triality it turns out that the unital normal lrta s are precisely the structurable algebras extensively studied by allison it will be shown that the normal sta s respectively lrta s are the algebras that coordinatize those lie algebras whose automorphism group contains a copy of the alternating respectively symmetric group of degree 4

factoriality of q gaussian von neumann algebras we prove that the von neumann algebras generated by n q gaussian elements are factors for n 2

jordan bimodules over the superalgebras p n and q n we extend the jacobson s coordinatization theorem to jordan superalgebras using it we classify jordan bimodules over superalgebras of types q n and jp n n 3 then we use the tits kantor koecher construction and representation theory of lie superalgebras to treat the remaining case q 2

non injectivity of the q deformed von neumann algebra in this paper we prove that the von neumann algebra generated by q gaussians is not injective as soon as the dimension of the underlying hilbert space is greater than 1 our approach is based on a suitable vector valued khintchine type inequality for wick products the same proof also works for the more general setting of a yang baxter deformation our techniques can also be extended to the so called q araki woods von neumann algebras recently introduced by hiai in this latter case we obtain the non injectivity under some asssumption on the spectral set of the positive operator associated with the deformation

computation of general inner outer and spectral factorizations in this paper we solve two problems in linear systems theory the computation of the inner outer and spectral factorizations of a continuous time system considered in the most general setting we show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic riccati equation of order usually much smaller than the mcmillan degree of the transfer function matrix of the system the proposed procedures are completely general being applicable for a polynomial proper improper system whose transfer function matrix could be rank deficient and could have poles zeros on the imaginary axis or at infinity as an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix numerical refinements and examples illustrating the proposed approach are discussed in detail

local triality and some related algebras abstract eight dimensional symmetric composition algebras give very nice formulae for triality and local triality these latter formulae will be extended to any algebra in a suitable variety the simple algebras in this variety will be shown to be precisely the symmetric composition algebras over fields while the prime algebras are central orders in the simple ones

classification of modules of the intermediate series over ramond n 2 superconformal algebras in this paper we first discuss the structure of the ramond n 2 superconformal algebras then we classify the modules of the intermediate series over ramond n 2 superconformal algebra