strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

on askey scheme and d orthogonality i a characterization theorem this is the first in a series of papers dealing with generalized hypergeometric d orthogonal polynomials extending the polynomial families in the askey scheme in this paper we give a characterization theorem to introduce new examples of generalized hypergeometricd orthogonal polynomials to be studied in the forthcoming works for d 1 we obtain an unification of some known characterization theorems in the orthogonal polynomials theory

fixed modes in parametrized systems several necessary graph theoretic conditions are presented for a parametrized system nut to have structurally fixed modus under output feedback of some arbitrarily specified pattern the criteria are formulated by the aid of a new graph which represents the couplings inherent in the system as well as the admissible feedback pattern for the special class of structured systems the conditions turn out to be also sufficient

asymptotics of multiple orthogonal polynomials associated with the modified bessel functions of the first kind we consider polynomials which are orthogonal with respect to weight functions which are defined in terms of the modified bessel functions i and i 1 these multiple orthogonal polynomials pn c of type ii were introduced earlier by the authors the aim of this paper is to study some asymptotics of these polynomials such as plancherel rotach asymptotics as a consequence of these results we obtain the accumulation set of the scaled zeros of pn c we also give a mehler heine type formula for these polynomials which is valid on compact subsets of c hence we obtain a more precise result about the asymptotic behavior of the small zeros of pn c

d orthogonality of little q laguerre type polynomials abstract in this paper we solve a characterization problem in the context of the d orthogonality that allows us on one hand to provide a q analog for the d orthogonal polynomials of laguerre type introduced by the first author and douak and on the other hand to derive new l q classical d orthogonal polynomials generalizing the little q laguerre polynomials various properties of the resulting basic hypergeometric polynomials are singled out for d 1 we obtain a characterization theorem involving as far as we know new l q classical orthogonal polynomials for which we give the recurrence relation and the difference equation

partial state observability recovering for linear systems by additional sensor implementation this paper deals with the problem of additional sensor location in order to recover the observability of any given part of the state for structured linear systems the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure we first provide new graphical necessary and sufficient conditions for the generic partial observability then we study the location of additional sensors in order to satisfy the latter conditions we provide necessary and sufficient requirements to be satisfied by these additional sensors and all their possible locations the proposed solution is simple to implement because it is based on well known algorithms usually used for finding successors and predecessors of vertex subsets or on computation of maximal linkings in a digraph all the used algorithms have polynomial complexity orders

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

the generic number of invariant zeros of a structured linear system in this paper we consider a structured linear system represented by means of a directed graph we present a graph theoretic method to compute the generic number of invariant zeros of the corresponding rosenbrock matrix the method is based on a fundamental decomposition of the directed graph representing the structured system the generic number of invariant zeros is important in generic versions of problems involving controllability and pole placement

d orthogonality of hermite type polynomials abstract in this paper we state a characterization theorem for d orthogonal polynomials of hermite type as application we solve two characterization problems related to gould hopper polynomials and charlier type polynomials various properties of the resulting generalized hypergeometric polynomials are singled out in particularly we derive the d dimensional functional vectors ensuring the d orthogonality of these polynomials the obtained weight functions are reduced to the well known weight functions of charlier and hermite polynomials for d 1 we also explicitly express the d dimensional functional vector associated with polynomials of laguerre type which are related to the obtained hermite type polynomials

griess algebras generated by 3 ising vectors of central 2a type abstract we study the griess algebra generated by three ising vectors e f and g in a cft type vertex operator algebra v with v 1 0 such that e f e g 1 32 we call such a configuration of central 2 a type under this assumption we show that there are only 5 possible structures of griess algebras and they correspond exactly to the griess algebras g v b n x of the five voa v b n x n x 1 a 2 b 3 a 4 b 2 c constructed by hohn lam yamauchi

multiple orthogonal polynomials for classical weights a new set of special functions which has a wide range of applications from number theory to integrability of nonlinear dynamical systems is described we study multiple orthogonal polynomials with respect to p 1 weights satisfying pearson s equation in particular we give a classification of multiple orthogonal polynomials with respect to classical weights which is based on properties of the corresponding rodrigues operators we show that the multiple orthogonal polynomials in our classification satisfy a linear differential equation of order p 1 we also obtain explicit formulas and recurrence relations for these polynomials

some discrete multiple orthogonal polynomials in this paper we extend the theory of discrete orthogonal polynomials on a linear lattice to polynomials satisfying orthogonality conditions with respect to r positive discrete measures first we recall the known results of the classical orthogonal polynomials of charlier meixner kravchuk and hahn t s chihara an introduction to orthogonal polynomials gordon and breach new york 1978 r koekoek and r f swarttouw reports of the faculty of technical mathematics and informatics no 98 17 delft 1998 a f nikiforov et al classical orthogonal polynomials of a discrete variable springer berlin 1991 these polynomials have a lowering and raising operator which give rise to a rodrigues formula a second order difference equation and an explicit expression from which the coefficients of the three term recurrence relation can be obtained then we consider r positive discrete measures and define two types of multiple orthogonal polynomials the continuous case jacobi laguerre hermite etc was studied by van assche and coussement j comput appl math 127 2001 317 347 and aptekarev et al multiple orthogonal polynomials for classical weights manuscript the families of multiple orthogonal polynomials of type ii that we will study have a raising operator and hence a rodrigues formula this will give us an explicit formula for the polynomials finally there also exists a recurrence relation of order r 1 for these multiple orthogonal polynomials of type ii we compute the coefficients of the recurrence relation explicitly when r 2

multiple orthogonal polynomials results on multiple orthogonal polynomials will be surveyed multiple orthogonal polynomials are intimately related to hermite pade approximants and often they are also called hermite pade polynomials special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials referred to as angelesco and nikishin systems among the applications the number theory special functions and spectral analysis of nonsymmetric band operators will be highlighted in the analytic theory results and methods for the study of multiple orthogonal polynomials asymptotics will be reviewed new results on strong asymptotics of multiple orthogonal polynomials for nikishin system will be presented

observer design for general linear time invariant systems it is noted that for both explicit and implicit linear systems several observer design problems including system inversion for systems with or without unknown inputs can all be formulated as a single problem involving descriptor systems the method used for solving this problem is based on recursively applying the reduction operation which consists of identifying and discarding equations that do not provide useful information for the estimation problem the reduction algorithm produces a reduced dimension system for which standard observers can be constructed the method presented can be implemented using numerically robust algorithms one such algorithm is presented

vertex operator algebras extended e_8 diagram and mckay s observation on the monster simple group we study mckay s observation on the monster simple group which relates the 2a involutions of the monster simple group to the extended e 8 diagram using the theory of vertex operator algebras voas we first consider the sublattices l of the e 8 lattice obtained by removing one node from the extended eg diagram at each time we then construct a certain coset or commutant subalgebra u associated with l in the lattice voa v 2e8 there are two natural conformal vectors of central charge 1 2 in u such that their inner product is exactly the value predicted by conway 1985 the griess algebra of u coincides with the algebra described in his table 3 there is a canonical automorphism of u of order e 8 l such an automorphism can be extended to the leech lattice voa v a and it is in fact a product of two miyamoto involutions in the sequel 2005 to this article the properties of u will be discussed in detail it is expected that if u is actually contained in the moonshine voa v 1 the product of two miyamoto involutions is in the desired conjugacy class of the monster simple group

d orthogonality of humbert and jacobi type polynomials in this paper we treat three questions related to the d orthogonality of the humbert polynomials the first one consists to determinate the explicit expression of the d dimensional functional vector for which the d orthogonality holds the second one is the investigation of the components of humbert polynomial sequence that allows us to introduce as far as we know new d orthogonal polynomials generalizing the classical jacobi ones the third one consists to solve a characterization problem related to a generalized hypergeometric representation of the humbert polynomials

some generalized hypergeometric d orthogonal polynomial sets in this paper we characterize the d orthogonal polynomial sets given by their explicit expressions in a specific basis as application we consider the generalized hypergeometric case to characterize d orthogonal polynomial sets of laguerre type meixner type meixner pollaczek type krawtchouk type continuous dual hahn type and dual hahn type for d 1 we obtain a unification of some characterization theorems in the orthogonal polynomials theory

binary codes and vertex operator super algebras abstract we study a vertex operator algebra whose virasoro element is a sum of pairwise orthogonal rational conformal vectors with central charge 1 2 the most important example is the moonshine modulev in particular we construct a series of vertex operator algebras whose full automorphism groups are finite namely we construct vertex operator algebrasmd i 0 md ifrom even linear binary coded z n2and prove that if the minimum weight ofdis greater than 2 then md 1 0 and the full automorphism group ofmdis finite from the viewpoint of finite group theory the construction of a vertex operator algebra has one advantage we can expect not only automorphisms ofd but also another one indeed ifdcontains a 8 4 4 hamming subcodec thencdefines a nontrivial involutive automorphism ofmd which is not induced from the automorphism group ofd in particular we have a finite group extension of aut d z n2 d

vector orthogonal relations vector qd algorithm vector pade approximants to a function f f 1 f d from to d have been defined uniquely without any auxiliary choice than the degrees of the numerator and the denominator the same for all the components f i as in the scalar case 1 5 the denominators are associated to polynomials p r s which are given by vector orthogonal properties r and which satisfy for each s recurrence relations of order d 1 i e with d 2 terms called relations d we study here consequences of r and d first we prove an algorithm similar to the generalized mna al gorithm then we define a vector qd algorithm which links two diagonals p r s r and p r s 1 r conversely if a family p r s r 0 verifying d is given it is possible to build p r s r 0 s 0 and d linear functionals c a a 1 d such that p r 0 p r and p r s verify the orthogonal relations r with respect to the c a

the relation of the d orthogonal polynomials to the appell polynomials abstract we are dealing with the concept of d dimensional orthogonal abbreviated d orthogonal polynomials that is to say polynomials verifying one standard recurrence relation of order d 1 among the d orthogonal polynomials one singles out the natural generalizations of certain classical orthogonal polynomials in particular we are concerned in the present paper with the solution of the following problem p find all polynomial sequences which are at the same time appell polynomials and d orthogonal the resulting polynomials are a natural extension of the hermite polynomials a sequence of these polynomials is obtained all the elements of its d 1 order recurrence are explicitly determined a generating function a d 1 order differential equation satisfied by each polynomial and a characterization of this sequence through a vectorial functional equation are also given among such polynomials one singles out the d symmetrical ones definition 1 7 which are the d orthogonal polynomials analogous to the hermite classical ones when d 1 ordinary orthogonality we meet again the classical orthogonal polynomials of hermite

brief paper state and input observability recovering by additional sensor implementation a graph theoretic approach this paper deals with the problem of additional sensor location in order to recover the state and input observability for structured linear systems the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure it allows one to provide the minimal number of the required sensors and either their pertinent location or a necessary and sufficient condition which allows one to check if a sensor location is adequate or not we obtain a sensor placement procedure based on classical and well known graph theory algorithms which have polynomial complexity orders

on mathbb z _p z p orbifold constructions of the moonshine vertex operator algebra for p 3 5 7 13 we consider a mathbb z p orbifold construction of the moonshine vertex operator algebra v natural we show that the vertex operator algebra obtained by the mathbb z p orbifold construction on the leech lattice vertex operator algebra v lambda and a lift of a fixed point free isometry of order p is isomorphic to the moonshine vertex operator algebra v natural we also describe the relationship between those mathbb z p orbifold constructions and the mathbb z 2 orbifold construction in a uniform manner in appendix we give a characterization of the moonshine vertex operator algebra v natural by the existence of an orthogonal pair of ising vectors

d orthogonality via generating functions in this paper starting from a suitable generating function of a polynomial set we show how to decide whether the considered polynomial set is d orthogonal and if it is so how to determine the corresponding d dimensional functional vector then we apply the obtained results to some known and new d orthogonal polynomial sets for the known ones we give new proofs for some already obtained results

some discrete d orthogonal polynomial sets in this paper we characterize all polynomial sets which are at the same time d orthogonal and appell the resulting polynomials reduce to charlier polynomials for d 1 1 various properties of the obtained polynomials are singled out generating function recurrence relation of order d 1 and a difference equation of order d 1 we also explicitly express the d dimensional functional for which the d orthogonality holds