binary 18 11 2 codes do not exist nor do 64 53 2 codes a binary linear block code c with block length n and dimension n is commonly denoted by n k or if its minimum distance is d by n k d the code s covering radius r c can be defined as the smallest number r such that any binary column vector of length n k can be written as a sum of r or fewer columns of a parity check matrix of c an n k code with covering radius r is denoted by n k r r a brualdi et al 1989 showed that l m r is defined to be the smallest n such that an n n m r code exists l m 2 is known for m or 6 while it is shown by brualdi et al that 17 or l

robust stability of uncertain linear systems with saturating actuators we consider the robust stability of uncertain linear systems with saturating actuators and present two sufficient conditions to guarantee the stability of the closed loop system we assume that the bound of the initial state is known and that the uncertainty is unstructured the obtained results meet our intuition that the lower bound of initial state and the higher bound of saturation level make it easy to design a controller finally we show the usefulness by an example

stability of a strongly stabilizing control for systems with a skew adjoint operator in hilbert space the stabilization problem of systems with a skew adjoint operator in a hilbert space is considered we prove that an one dimensional stabilizing feedback control allows a wide class of perturbations such that the system under consideration is strongly stabilizable with the aim of the perturbed controls

highest weight representations for gl m n and gl m n it is shown how vector coherent state vcs theory enlightens the simultaneous discussion of representation theory for classical lie algebras and superalgebras and provides an optimal framework for the explanation of the noted similarities and dissimilarities of their representations reducibility atypicality and the positive definitiveness of inner products in vcs representation spaces are discussed the discussion is exemplified through the parallel and explicit construction of highest weight ladder representations of the lie algebra gl m n and superalgebra gl m n in gl m gl n bases

a separation principle for bilinear systems with dissipative drift input output stabilization of a class of bilinear systems using a nonlinear stabilizing feedback control law together with an observer is studied in some cases it can be proved that the result is a globally asymptotically stable system

an improvement of the van wee bound for binary linear covering codes the van wee bound gives a lower bound on the cardinality of block codes with a prescribed covering radius the author presents an improvement of this bound for binary linear codes and compares the results with other bounds mentioned in the literature almost all reported bounds can be obtained via the present bound as well moreover the present authors obtain a number of new lower bounds

affine kac moody algebras and semi infinite flag manifolds we study representations of affine kac moody algebras from a geometric point of view it is shown that wakimoto modules introduced in 18 which are important in conformal field theory correspond to certain sheaves on a semi infinite flag manifold with support on its schhubert cells this manifold is equipped with a remarkable semi infinite structure which is discussed in particular the semi infinite homology of this manifold is computed the cousin grothendieck resolution of an invertible sheaf on a semi infinite flag manifold gives a two sided resolution of an irreducible representation of an affine algebras consisting of wakimoto modules this is just the brst complex as a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent lie algebra

modified bounds for covering codes the covering radius of binary codes is studied bounds on k n r the minimum cardinality of any binary code of length n and covering radius r are found modifications of the van wee lower bounds are proved for k n r the minimal number of codewords in any binary code of length n and covering radius r the first of the two van wee bounds is based on studying the hamming spheres of radius 1 centered at the points which have distance r to the code c the points covered by more than one codeword are divided into several classes and better estimates for some of these classes are obtained using a suitable averaging process the lower bound for k n r when r or 2 is improved the second van wee bound studies spheres of radius 2 centered at the points which have distance r 1 or r to the code c these points are divided essentially into two classes the points that are covered by only one codeword of c and the points that are covered by more than one codeword

stabilization of uncertain distributed parameter systems the stabilization of uncertain systems governed by an evolution equation in a real hilbert space is studied the uncertain systems under consideration are described by state equations in which both the state and input operators depend upon uncertain parameters exponential stability is achieved by the suitable choice of state feedback control the proofs are based upon perturbation analysis of semigroup and lyapunov theory a number of examples are given to illustrate the approach

on the structure of linear codes with covering radius two and three we obtain new bounds on l m r the minimum length of a linear code with codimension m and covering radius r all bounds are derived in a uniform way we employ results from coding theory some earlier results on covering codes and combinatorial arguments we prove the following bounds l 6 2 13 l 7 2 19 l 8 2 spl ges 25 l 9 2 spl ges 34 l 2m l 2 spl ges 2 sup m 1 for m spl ges 3 l 14 2 spl ges 182 l 16 2 spl ges 363 l 18 2 spl ges 725 l 20 2 spl ges 1449 l 22 2 spl ges 2897 l 24 2 spl ges 5794 l 9 3 spl ges 17 l 10 3 spl ges 21 l 12 3 spl ges 31 l 13 3 spl ges 38

vector coherent state representation theory a vector coherent state theory is formulated as a natural extension of standard coherent state theory it is shown that the godement representations and the coherent state representations of the sp n r groups of rowe and of deenen and quesne are special cases of this more general theory

short codes with a given covering radius the covering radius r of a code is the maximum distance from any vector in the space containing the code to the nearest codeword the authors introduce a new function l m r called the length function which equals the smallest length of a binary code of codimension m and covering radius r they investigate basic properties of the length function projective geometries over larger fields are used to construct families of codes which improve significantly the upper bound for l m 2 obtained by amalgamation of hamming codes general methods are developed for ruling out the existence of codes of covering radius 2 with a given codimension and length resulting in lower bounds for l m 2 a table is presented which gives the best results now known for l m r with m

on the covering radius of codes the covering radius r of a code is the maximal distance of any vector from the code this work gives a number of new results concerning t n k the minimal covering radius of any binary code of length n and dimension k for example t n 4 and t n 5 are determined exactly and reasonably tight bounds on t n k are obtained for any k when n is large these results are found by using several new constructions for codes with small covering radius one construction the amalgamated direct sum involves a quantity called the norm of a code codes with norm leq 2 r 1 are called normal and may be combined efficiently the paper concludes with a table giving bounds on t n k for n leq 64

vector coherent state theory as a theory of induced representations a general definition is given of vector coherent state vcs representation theory it is shown that the theory is more general than suggested by previous applications and that it incorporates the standard theories of induced representations as special cases the associated k matrix theory is also given a fuller treatment than hitherto and shown to provide a rather general algorithm both for projecting vcs representations from larger representations in which they are embedded and for determining the hermitian form with respect to which an isometric equivalent representation is in fact isometric

a separation principle for distributed dissipative bilinear systems the problem of input output stabilization is generalized from finite dimensional bilinear systems to a class of distributed bilinear systems the solution is based on the nonlinear feedback stabilization results given previously by the authors 1999 with the observers presented by the same authors 1997 in another work

linear inequalities for covering codes ii triple covering inequalities the lower bounds on k n r minimum number of codewords of any binary code of length n and covering radius r are improved a new technique combining the hamming association scheme and the results of a classic problem of covering pairs by k tuples is introduced the new lower bounds are obtained by studying various linear inequalities satisfied by covering codes and such an inequality is derived the lower bounds for k n r are studied for some special values of n and r which serve as examples showing how the methods developed are applied to concrete cases

bounded feedback stabilization and global separation principle of distributed parameter systems we show that the infinite dimensional system spl sigma x spl dot t ax t bu t x sub 0 spl epsiv h is globally strongly asymptotically stabilizable by an arbitrarily small smooth feedback here the operator a is the infinitesimal generator of a c sub 0 semigroup of contractions e sup ta on real hilbert space h and b is a bounded linear operator mapping a hilbert space of controls u into h an explicit smooth feedback control law is given further we identify the class of perturbations for which the system is still stabilizable by the same feedback law as for the nominal system based on these results and some differential lyapunov operator equations we then establish a global separation principle for the system spl sigma with a kalman like observer finally these results are illustrated via an example dealing with the wave equation

improved sphere bounds on the covering radius of codes the sphere bound is a trivial lower bound on k n r the minimal cardinality of any binary code of length n and with covering radius r by simple arguments it is considerably improved to k n 1 or 2 sup n n for n even a table of lower and upper bounds on k n r for n

lower bounds on t n k from linear inequalities the linear inequality method for covering codes is used to improve the lower bounds of t n k the smallest covering radius of any n k binary linear code to make better use of the strength of this method the relation between the covering radius of a code and the minimum distance of its dual code is studied the authors obtained 65 improved lower bounds for t n k within the range of n

inequalities for covering codes any code c with covering radius r must satisfy a set of linear inequalities that involve the lloyd polynomial l sub r x these generalize the sphere bound syndrome graphs associated with a linear code c are introduced to help keep track of low weight vectors in the same coset of c if there are too many such vectors c cannot exist illustrations show that t 17 10 3 and t 23 15 3 where t n k is the smallest covering radius of any n k code

vector coherent state realization of representations of the affine superalgebra a 1 0 1 the method of vector coherent states is generalized to study the representations of the affine superalgebra a 1 0 1 a new realization of all the irreducible highest weight representations of this affine superalgebra is obtained in terms of holomorphic superdifferential operators in infinitely many grassmannian and bosonic variables

stabilization of some distributed parameter systems the question of stabilization of perturbed or uncertain infinite dimensional systems is considered one class of perturbations for which the system remains stabilizable by the same feedback law as for the nominal system is identified sufficient conditions are presented that generate strong stabilizability of the perturbed system given that the unperturbed system has similar properties it is also shown that for deterministic as well as stochastic systems exponential stability can be achieved by choice of a suitable feedback controller the theoretical results are illustrated by some numerical examples

the minimal covering radius t 15 6 of a six dimensional binary linear code of length 15 is equal to 4 the nonexistence of a binary linear 15 6 code with covering radius 3 is proved by geometrically based arguments the author also considers the wider application of the techniques

new lower bounds for covering codes some new lower bounds on mod c mod for a binary linear n k r code c with n 1 t r 1 r 0 2 odd or with n 1 t r 1 1 t 2 even are obtained these bounds improve the sphere covering bound considerably and give several new values and lower bounds for the function t n k the smallest covering radius of any n k code

an extension of the borel weil construction to the quantum group u q n the borel weil bw construction for unitary irreps of a compact lie group is extended to a construction of all unitary irreps of the quantum groupu q n thisq bw construction uses a recursion procedure foru q n in which the fiber of the bundle carries an irrep ofu q n 1 u q 1 with sections that are holomorphic functions in the homogeneous spaceu q n u q n 1 u q 1 explicit results are obtained for theu q n irreps and for the related isomorphism of quantum group algebras

vector coherent state representations induced representations and geometric quantization i scalar coherent state representations coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model i classical realizations which are the starting point for geometric quantization ii induced unitary representations corresponding to prequantization and iii irreducible unitary representations obtained in geometric quantization by choice of a polarization these representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations

an improved sphere covering bound for the codes with n 3r 2 let c be a binary code not necessarily linear with covering radius r and length n 3r 2 the sphere covering bound on the cardinality of c is improved considerably provided c has minimal distance d 2 some new results on the function t n k the smallest covering radius of any binary linear code with length n and dimension k t 38 6 or 13 t 47 7 or 16 t 59 8 or 20 are given

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

vector coherent state theory of the noncompact orthosymplectic superalgebras i general theory vector coherent states are defined for the positive discrete series irreducible representations of the non compact orthosymplectic superalgebras osp p 2n r where p 2m or 2m 1 an orthonormal bargmann berezin basis symmetry adapted to osp p 2n r so p sp 2n r so p u n is constructed and used to develop the k matrix theory for osp p 2n r a general method is provided for determining the conditions of existence of star representations and of grade star representations in the osp 2 2n r case and the branching rule for their decomposition into a direct sum of so p sp 2n r irreducible representations as a by product it also enables the matrix elements of the odd generators between basis states of lowest weight so p u n irreducible representations to be calculated in a straightforward way

vector coherent state realization of representations of the affine lie algebra the method of vector coherent states is generalized to study representations of the affine lie algebra a large class of highest weight irreps is explicitly constructed which contains the integrable highest weight irreps as special cases

feedback stabilization of a class of distributed parameter systems with control constraints abstract the feedback stabilization problem for a class of infinite dimensional linear systems with control constraints is investigated the approach is developed using a state space system framework which is based on a semigroup formulation in contrast to the previous works in this direction it is not assumed that the c 0 semigroup we deal with is a semigroup of contractions the main result links the problem with the positive invariance of appropriate polyhedral sets verifiable necessary and sufficient conditions for this latter property are stated

structural stabilization of uncertain systems necessity of the matching condition this paper investigates one aspect of the problem of stabilizing an uncertain linear system that is the systems under consideration contain uncertain parameters which are unknown but bounded the question arises as to whether such a system can be stabilized via feedback control in some of the previous papers in this area the system is assumed to satisfy a so called matching condition this type of assumption is used to assure that the uncertain system can be stabilized it is known however that the matching condition is not a necessary condition for stabilizability this paper introduces a strengthened notion of stabilizability referred to as structural stabilizability via a nominally determined quadratic lyapunov function it is then shown that if a system is to have this stronger property the matching condition must necessarily be satisfied