comments on hastings additivity counterexamples hastings 12 recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy in this paper we present an expanded version of hastings proof in addition to a careful elucidation of the details of the proof we also present bounds for the minimal dimensions needed to obtain a counterexample

presymplectic geometry and fermat s principle for anisotropic media the tools of presymplectic geometry are used to study light ray trajectories in anisotropic media

a necessary and sufficient condition for the positive definiteness of interval symmetric matrices a necessary and sufficient condition for the positive definiteness of interval symmetric matrices is obtained and a useful application is shown

sufficient conditions for the asymptotic stability of interval matrices jiang 1987 gave a sufficient condition for the asymptotic stability of interval matrices we shall show here that his results can be derived in a trivial way using the lyapunov equation an extension of his results and a similar result for discrete systems is stated

a sufficient condition for stability of a polytope of matrices abstract in this paper we study the stability of interval dynamical systems a sufficient condition for the stability of a polytope of matrices which is shown to be necessary and sufficient for a certain class of matrices is obtained the results developed can also be applied to the stability of a positive cone of matrices and sufficient conditions for the stability of interval dynamical systems are obtained a relationship between real parts of eigenvalues and matrix measures is also presented

discrete vakonomic mechanics discretizations of vakonomic mechanics are developed by using the methodology of variational integrators the resulting algorithms are symplectic in some sense that we will explain and preserve the momentum map associated with a lie group of symmetries a specific example illustrating the theory is tested numerically

an analysis of completely positive trace preserving maps on m2 abstract we give a useful new characterization of the set of all completely positive trace preserving maps m 2 m 2 from which one can easily check any trace preserving map for complete positivity we also determine explicitly all extreme points of this set and give a useful parameterization after reduction to a certain canonical form this allows a detailed examination of an important class of non unital extreme points that can be characterized as having exactly two images on the bloch sphere we also discuss a number of related issues about the images and the geometry of the set of stochastic maps and show that any stochastic map on m 2 can be written as a convex combination of two generalized extreme points

robust stability for linear discrete time systems with structured perturbations the robust stability problems of linear discrete time systems with structured perturbations are considered the necessary and sufficient condition of interval stability is given and the maximal bound of robust stability is presented for systems with a non negative or non positive nominal system matrix further it is shown that the given necessary and sufficient condition and the given maximal robust bound are still valid for time varying perturbations and nonlinear perturbations

lagrangian systems with constraints a geometric approach to the method of lagrange multipliers a geometric approach to the method of lagrange multipliers is presented using the framework of the tangent bundle geometry the nonholonomic systems with constraint functions linear in the velocities are studied in the first place and then and using this study of the nonholonomic mechanical systems as a previous result the holonomic systems are considered the lagrangian inverse problem is also analysed and finally the theory is illustrated with several examples

maximal unidirectional perturbation bounds for stability of polynomials and matrices abstract given a stable polynomial or matrix we consider a class of unidirectional perturbations in this note we provide a closed form for the maximal perturbation bounds under which stability is preserved the results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial

exact maximum singular value calculation of an interval matrix in this note we present a method for calculating the maximum singular value of an interval matrix first we provide an algorithm for calculating the maximum singular value of a square interval matrix then based on this algorithm we extend the result to non square interval matrix case and to the case of computing the minimum singular value through numerical examples the validity of the suggested methods is illustrated particularly we compare the newly proposed method with an existing method to show that the new method finds the correct bound of the maximum singular value with no exception

additivity for unital qubit channels additivity of the holevo capacity is proved for product channels under the condition that one of the channels is a unital qubit channel with the other completely arbitrary as a byproduct this proves that the holevo bound is the classical information capacity of such qubit channels and provides an explicit formula for this classical capacity additivity of minimal entropy and multiplicativity of p norms are also proved under the same assumptions the proof relies on a new bound for the p norm of an output state from the half noisy phase damping channel

time dependent lagrangian systems a geometric approach to the theory of systems with constraints a geometric approach to the theory of time dependent regular lagrangian systems with constraints is presented using the framework of the exact contact manifold tq r l the main subject of the article concerns the properties of the time dependent nonholonomic constraints and the geometric approach to the method of the lagrange multipliers it is shown that every constraint determines a contact one form a vertical vector field and a nonvertical vector field the explicit form of the vector field representing the constrained dynamics is obtained and finally the properties of all these one forms and vector fields are discussed

counter example to a recent result on the stability of interval matrices by s bialas abstract in bialas 1983 a condition is given which is supposedly necessary and sufficient for the stability of interval matrices we demonstrate via a counter example that the condition given is in fact not sufficient

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

comments on a necessary and sufficient condition for the positive definiteness of interval symmetric matrices shi and gao 1986 gave a necessary and sufficient condition for the positive definiteness of interval symmetric matrices we point out that their result is not new and the assumptions can be less restrictive

on the geometry of non holonomic lagrangian systems we present a geometric framework for non holonomic lagrangian systems in terms of distributions on the configuration manifold if the constrained system is regular an almost product structure on the phase space of velocities is constructed such that the constrained dynamics is obtained by projecting the free dynamics if the constrained system is singular we develop a constraint algorithm which is very similar to that developed by dirac and bergmann and later globalized by gotay and nester special attention to the case of constrained systems given by connections is paid in particular we extend the results of koiller for caplygin systems an application to the so called non holonomic geometry is given

simplified sufficient conditions for the asymptotic stability of interval matrices it will be shown that the sufficient conditions for the asymptotic stability of interval matrices proved in mansour 1988 can be further simplified by considering only a part of the extreme matrices

minimax guaranteed cost control for linear continuous time systems with large parameter uncertainty abstract this paper presents a method for designing a robust controller for linear systems with structured time varying uncertainty the proposed robustness design method results in a simple linear output feedback control law which not only guarantees the asymptotic stability of the closed loop system but also minimizes the maximal performance bound over all possible parameter perturbations the problem is solved by employing a constrained optimization method using analytical gradients a comparative study of an example shows the improvements and advantages of the proposed method over previous ones

sufficient conditions for stability of interval matrices extremely simple sufficient conditions are presented for the stability of interval matrices these complement the necessary and sufficient conditions developed by bialas 1983 which become unwieldy for large matrices 4 4 and above

the minimum entropy output of a quantum channel is locally additive we show that the minimum von neumann entropy output of a quantum channel is locally additive hastings counterexample for the additivity conjecture makes this result quite surprising in particular it indicates that the nonadditivity of the minimum entropy output is a global effect of quantum channels

robust stability and robust pole assignment of linear systems with structured uncertainty sufficient conditions for the robust stability of linear time varying systems are presented the stability criteria are extended to the problem of the robust pole assignment of linear time invariant systems to a specified region these criteria both for robust stability and robust pole assignment improve some results in the literature examples are given to demonstrate the new criteria

necessary and sufficient conditions for stability of a matrix polytope with normal vertex matrices abstract it is shown that the eigenvalue set of a matrix polytope with normal vertex matrices is a subset of the convex hull of eigenvalues of the vertex matrices

comments on sufficient condition for the asymptotic stability of interval matrices abstract recently jiang 1987 has shown that a set of interval matrices is stable if the symmetric part of the vertex matrices are stable this result of jiang 1987 is shown to be only applicable to matrices with all the diagonal elements negative

sufficient conditions for the stability of interval matrices the stability of interval dynamical systems is studied sufficient conditions for the polytope of interval matrices are examined and some of the proofs are greatly simplified more generally sufficient conditions are obtained and the approach taken in the new proofs has the potential for further generalizations of the result obtained in this paper

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

geometric theory of the equivalence of lagrangians for constrained systems the lagrangian description of a system is analysed from a geometric viewpoint in order to find a concept for equivalence of singular lagrangians generalising that of the regular case geometric and gauge equivalence of singular lagrangians are studied and the authors also give some conditions in which second order differential equations exist satisfying the dynamical equation on the final constraint submanifold

on the extreme points of quantum channels abstract let l m n denote the convex set of completely positive trace preserving operators from c m m to c n n i e quantum channels we give a necessary condition for l l m n to be an extreme point we show that generically this condition is also sufficient we characterize completely the extreme points of l 2 2 and l 3 2 i e quantum channels from qubits to qubits and from qutrits to qubits

stability of interval parameter matrices the stability of interval matrices has been studied by many authors in this paper the stability of interval parameter matrices is introduced and some criteria for this stability are given our results are effective for testing the stability of interval matrices and are more general than previous results furthermore criteria for the stability of time varying matrices are obtained

geometric lagrangian approach to first order systems and applications the geometric theory of presymplectic systems is developed to study both the lagrangian and hamiltonian formulations of a system described by a lagrangian linear in the velocities the results are used to study some related problems for second order differential equations and regular lagrangians

comments on the presymplectic formalism and the theory of regular lagrangians with constraints the lagrangian formalism for systems with constraints is developed using a singular lagrangian defined in the extended tangent bundle t q r the dynamics defined by the new extended lagrangian that incorporates the constraints is studied using the formalism of the presymplectic geometry a comparative study with other geometric approaches is presented

smooth manifold structure for extreme channels a quantum channel from a system a of dimension da to a system b of dimension db is a completely positive trace preserving map from complex da da to db db matrices and the set of all such maps with kraus rank r has the structure of a smooth manifold we describe this set in two ways first as a quotient space of a subset of the rdb da dimensional stiefel manifold second as the set of all choi states of a fixed rank r these two descriptions are topologically equivalent this allows us to show that the set of all choi states corresponding to extreme channels from system a to system b of a fixed kraus rank r is a smooth submanifold of dimension 2rdadb da2 r2 of the set of all choi states of rank r as an application we derive a lower bound on the number of parameters required for a quantum circuit topology to be able to approximate all extreme channels from a to b arbitrarily well

comments on a necessary and sufficient condition for the positive detiniteness of interval symmetric matrices the main results obtained recently by shi and gao are already known and can be strengthened

an interval kalman filtering with minimal conservatism abstract the interval kalman filtering ikf can handle parametric interval uncertainties of the system matrices and it computes the lower and upper boundaries of the estimated states in this paper we propose an alternative form of interval kalman filtering to reduce the conservatism inherent to the existing interval kalman filtering first we address why the existing interval kalman filtering scheme induces conservatism in the boundary estimation then to remove the conservatism we derive noise covariance matrices taking into account of interval uncertainties as well as process and measurement noises following the typical derivation process of the standard kalman filtering a new recursive form of interval kalman filtering is derived through numerical simulations the superiority of the new algorithm over existing ikf is illustrated

a geometric approach to the gibbs appell equations in lagrangian mechanics we present a geometrical derivation of the gibbs appell equations in constrained lagrangian mechanics using the affine structures existing in the spaces of velocities and accelerations the theoretical basis is the gauss principle of least constraint and the necessary conditions for the minimum expressed in terms of the gibbs function give rise to the gibbs appell equations we give a second order formulation of the constraint equation and using the concept of moore penrose inverse we provide an explicit intrinsic construction of the projector on the space of the effective or non ideal forces the gibbs appell equations are expressed in an intrinsic way in terms of the fibre derivative of the gibbs function and the effective part of the applied force

a constraint algorithm for singular lagrangians subjected to nonholonomic constraints we construct a constraint algorithm for singular lagrangian systems subjected to nonholonomic constraints which generalizes that of dirac for constrained hamiltonian systems

reduction of some classical non holonomic systems with symmetry two types of nonholonomic systems with symmetry are treated i the configuration space is a total space of a g principal bundle and the constraints are given by a connection ii the configuration space is g itself and the constraints are given by left invariant forms the proofs are based on the method of quasicoordinates in passing a derivation of the maurer cartan equations for lie groups is obtained simple examples are given to illustrate the algorithmical character of the main results

comments on a necessary and sufficient condition for the stability of interval matrices in a recent paper by bialas a new proof of a known result concerning interval polynomials was given this result is summarized here and a much stronger result is mentioned bialas main theorem on the stability of interval matrices is shown to be false

necessary and sufficient conditions for stability of time varying discrete interval matrices sufficient conditions for the stability of time varying discrete interval systems are presented the spectral radius of the maximum absolute matrix of all interval matrices is employed as opposed to utilizing the matrix norm or lyapunov theorem for special cases our result becomes a necessary and sufficient condition for stability furthermore the proposed conditions are inclusive of the previous results of stability of time invariant interval systems

sufficient condition for the asymptotic stability of interval matrices the stability of interval matrices has been studied by bialas 1983 but bialas s main theorem on the stability of interval matrices has been shown to be false by barmish 1984 a new sufficient condition for the asymptotic stability of interval matrices is given in the present paper

the geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems the vakonomic bracket a vakonomic mechanical system can be alternatively described by an extended lagrangian using the lagrange multipliers as new variables since this extended lagrangian is singular the constraint algorithm can be applied and a dirac bracket giving the evolution of the observables can be constructed

non holonomic lagrangian systems in jet manifolds a geometrical setting in terms of jet manifolds is developed for time dependent non holonomic lagrangian systems an almost product structure on the evolution space is constructed in such a way that the constrained dynamics is obtained by projection of the free dynamics a constrained poincare cartan 2 form is defined if the non holonomic system is singular a constraint algorithm is constructed special attention is devoted to caplygin systems and a reduction theorem is proved

lyapunov stability robust analysis and robustness design for linear continuous time systems the linear continuous time systems to be discussed are described by state space models with structured time varying uncertainties first the explicit maximal perturbation bound for maintaining quadratic lyapunov stability of the closed loop systems is presented then a robust design method is proposed given an open loop nominal system with information of the uncertainty structure the proposed robust design method produces a linear constant output feedback control law which maximizes the perturbation bound for maintaining quadratic lyapunov stability both the optimal results for robust analysis and robustness design can be obtained by using an efficient numerical algorithm e g minimax of matlab with analytic gradients given in this paper examples are investigated in some detail to show the improvements and advantages of the proposed methods over previous ones