hassett tschinkel correspondence modality and projective hypersurfaces abstract in 1999 b hassett and yu tschinkel introduced a remarkable correspondence between generically transitive actions of the commutative unipotent algebraic group g a n and finite dimensional local algebras in this paper we develop hassett tschinkel correspondence and calculate modality of generically transitive g a n actions on projective spaces classify actions of modality one and characterize generically transitive g a n actions on projective hypersurfaces of given degree in particular actions on degenerate projective quadrics are studied

elastic mode algorithms for mathematical programs with equilibrium constraints global convergence and stationarity properties the elastic mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that for a finite value of the penalty parameter local solutions satisfying first and second order necessary optimality conditions for the original problem are also first and second order points of the elastic mode formulation here we study global convergence properties of methods based on this formulation which involve generating an exact or inexact first or second order point of the formulation for nondecreasing values of the penalty parameter under certain regularity conditions on the active constraints we establish finite or asymptotic convergence to points having a certain stationarity property such as strong stationarity m stationarity or c stationarity numerical experience with these approaches is discussed in particular our analysis and the numerical evidence show that exact complementarity can be achieved finitely even when the elastic mode formulation is solved inexactly

on structure and computation of generalized nash equilibria we consider generalized nash equilibrium problems gnep from a structural and computational point of view in gnep the players feasible sets may depend on the other players strategies moreover the players may share common constraints in particular the latter leads to the stable appearance of nash equilibria which are fritz john fj points but not karush kuhn tucker kkt points basic in our approach is the representation of fj points as zeros of an appropriate underdetermined system of nonsmooth equations here additional nonsmooth variables are taken into account we prove that the set of fj points together with corresponding active lagrange multipliers generically constitutes a lipschitz manifold its dimension is n 1 j 0 where n is the number of players and j 0 is the number of active common constraints in a structural analysis of nash equilibria the number n 1 j 0 plays a crucial role in fact the latter number encodes both the possible degeneracies for the players parametric subproblems and the dimension of the set of nash equilibria in particular in the nondegenerate case the dimension of the set of nash equilibria equals locally n 1 j 0 for the computation of fj points we propose a nonsmooth projection method npm which aims at nding solutions of an underdetermined system of nonsmooth equations npm is shown to be well dened for gnep local convergence of npm is conjectured for gnep under generic assumptions and its proof is challenging however we indicate special cases known from the literature in which convergence holds

on optimality conditions for structured families of nonlinear programming problems optimality conditions for families of nonlinear programming problems inrn are studied from a generic point of view the objective function and some of the constraints are assumed to depend on a parameter while others are held fixed techniques of differential topology are used to show that under suitable conditions certain strong second order conditions are necessary for optimality except possibly for parameter values lying in a negligible set

two sided approximation to periodic solutions of ordinary differential equations a two sided approximation to the periodic orbit of an autonomous ordinary differential equation system is considered first some results about variational equation systems for periodic solutions are obtained in sect 2 then it is proved that if the periodic orbit is convex and stable the explicit difference solution approximates the periodic orbit from the outer part and the implicit one from the inner part respectively finally a numerical example is given to illustrate our result and to point out that the numerical solution no longer has a one sided approximation property if the periodic orbit is not convex

quantum markovian subsystems invariance attractivity and control we characterize the dynamical behavior of continuous time markovian quantum systems with respect to a subsystem of interest markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing subsystem encodings offering a general pathway to faithfully represent quantum information we provide explicit linear algebraic characterizations of the notion of invariant and noiseless subsystem for markovian master equations under different robustness assumptions for model parameter and initial state variations the stronger concept of an attractive quantum subsystem is introduced and sufficient existence conditions are identified based on lyapunov s stability techniques as a main control application we address the potential of output feedback markovian control strategies for quantum pure state stabilization and noiseless subspace generation in particular explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite dimensional markovian systems are obtained

sufficient conditions for conservativity of minimal quantum dynamical semigroups abstract the conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a generalized subharmonic operator bounded from below by the dissipative part of the infinitesimal generator we discuss applications of this criteria in mathematical physics and quantum probability

asymptotic expansion and geometric properties of the spline collocation periodic solution of an ode system the asymptotic expansion of the cubic spline collocation periodic solution of odes is obtained and then some criteria and techniques are developed to prove geometric properties of numerical solutions such as convexity invariance and the one side approximation

degenerate hyperbolic conservation laws with dissipation reduction to and validity of a class of burgers type equations a conservation law is said to be degenerate or critical if the jacobian of the flux vector evaluated on a constant state has a zero eigenvalue in this paper it is proved that a degenerate conservation law with dissipation will generate dynamics on a long time scale that resembles burger s dynamics the case of k fold degeneracy is also treated and it is shown that it leads to a reduction to a quadratically coupled k fold system of burgers type equations validity of the reduction and existence for the reduced system is proved in the class of uniformly local spaces thereby capturing both finite and infinite energy solutions the theory is applied to some examples from stratified shallow water hydrodynamics that model the birth of hydraulic jumps

a note on weakly active constraints in connection with nonconvex quadratic programming abstract in general it is very difficult to determine a true local minimizer in nonconvex quadratic programming the main problems arise if we have so called weakly active constraints we discuss an efficient method for checking the local optimality or determining a direction of descent

review v i arnol d s m gusein zade and a n varchenko singularities of differentiable maps vol 1 the classification of critical sets caustics and wave fronts

on generic one parametric semi infinite optimization we consider differentiable semi infinite optimization problems depending on a real parameter for generic one parametric families we classify the corresponding set of generalized critical points into eight types five of these types also occur in problems with a finite number of inequality constraints whereas the other three types are typical for the semi infinite case we discuss types 7 and 8 in detail while at points of type 6 the singularity is due to the fact that in the associated lower level problem a lagrange multiplier corresponding to an active inequality constraint vanishes at points of type 7 and 8 the gradients of the active constraints in the lower level problem are linearly dependent if the total number of active constraints in the lower level problem does not exceed the lower level dimension the point is of type 7 otherwise it is of type 8 moreover we distinguish between points of type 8a and 8b where a point is of type 8a if the mangasarian fromovitz constraint qualification holds in the lower level problem and of type 8b otherwise at points of type 8a the set of generalized critical points is not smooth but it does not exhibit a turning point the linear and quadratic indices remain constant when passing along a point of type 8a points of type 7 and type 8b are relative boundary points of the set of generalized critical points

the role of the atomic decoherence free subalgebra in the study of quantum markov semigroups we show that for a quantum markov semigroup qms with a faithful normal invariant state atomicity of the decoherence free subalgebra and environmental decoherence are equivalent moreover we prove that the predual of the decoherence free subalgebra is isometrically isomorphic to the subspace of reversible states we also describe in an explicit and constructive way the relationship between the decoherence free subalgebra and the fixed point subalgebra we show that for a quantum markov semigroup qms with a faithful normal invariant state atomicity of the decoherence free subalgebra and environmental decoherence are equivalent moreover we prove that the predual of the decoherence free subalgebra is isometrically isomorphic to the subspace of reversible states we also describe in an explicit and constructive way the relationship between the decoherence free subalgebra and the fixed point subalgebra

classical properties of infinite quantum open systems long time asymptotic properties of a class of environmentally induced dynamical semigroups on arbitrary von neumann algebras are discussed such a semigroup selects observables called effective observables which are immune to the process of decoherence and so evolve in a reversible automorphic way in particular it is shown that effective observables of the quantum system in the thermodynamic limit subjected to a specific interaction with another quantum system obey classical dynamics

critical sets in parametric optimization we deal with one parameter families of optimization problems in finite dimensions the constraints are both of equality and inequality type the concept of a generalized critical point g c point is introduced in particular every local minimum kuhn tucker point and point of fritz john type is a g c point under fairly weak even generic conditions we study the set consisting of all g c points due to the parameter the set is pieced together from one dimensional manifolds the points of can be divided into five characteristic types the subset of nondegenerate critical points first type is open and dense in nondegenerate means strict complementarity nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints a nondegenerate critical point is completely characterized by means of four indices the change of these indices along is presented finally the kuhn tucker subset of is studied in more detail in particular in connection with the failure of the mangasarian fromowitz constraint qualification

numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations the computation of periodic orbits of autonomous ordinary differential equations is considered a new method especially suited for computing limit cycles that bifurcate from stationary solutions is established this novel approach is very easy to implement the method requiring the programming of the right hand side only another topic of this paper is the demonstration of how a direct method should be applied in the computation of hopf bifurcation points these methods solve boundary value problems by means of standard software only the methods are tested on four examples arising in different application areas including chemistry and biology

bifurcations of ordinary differential equations of clairaut type we classify a one parameter family of clairaut type equations in order to pursue the classification we use legendrian singularity theory and the notion of one parameter complete legendrian unfoldings which induces a special class of divergent diagrams of map germs which are called one parameter integral diagrams our normal forms are represented by oneparameter integral diagrams r 2003 elsevier science usa all rights reserved

shape stress trade off design of membrane structures for specified sequence of boundary shapes a new method is presented for parametrically generating optimal shapes and stresses of a membrane structure supported by a frame the problem considered here is a so called trade off design problem where the weighted sum of the deviations of the initial stress and the shape from the desired distribution is to be minimized the membrane is discretized by using the finite element method and optimal shapes are expanded with respect to a parameter defining the shape of the boundary frame an approximate method is presented without exact calculation of the hessian of the stresses with respect to the nodal coordinates the explicit developability conditions derived by the authors are used to guarantee the curved surface to be reduced to a set of plane cutting patterns after removing the pretensioning force in the examples trade off designs are found for an hp type membrane structure and the efficiency of the proposed method is discussed

an inertia theorem for symmetric matrices and its application to nonlinear programming abstract the relationship between the inertia of a symmetric real matrix and the inertia of its projection to a subspace is studied the result is then used to characterize a karush kuhn tucker point of a nonlinear programming problem by the inertia of a hessian of lagrangian with respect to both primal and dual variables a theorem of kojima on the determinant of a matrix in nonlinear programming is also derived as a direct consequence of the result

change of generalized indices of stationary solutions to multiparametric optimization we study the local change of the generalized index which is a modification of the morse index and the stationary index for the multiparametric optimization under the regular value condition the change of the generalized index around a triplet x v t is locally bounded by the dimension of the parameter vector t where x is a variable vector and v a vector of the lagrange multiplier space we also discuss the local change of the generalized index around a pair x t

generalized semi infinite programming a tutorial this tutorial presents an introduction to generalized semi infinite programming gsip which in recent years became a vivid field of active research in mathematical programming a gsip problem is characterized by an infinite number of inequality constraints and the corresponding index set depends additionally on the decision variables there exist a wide range of applications which give rise to gsip models some of them are discussed in the present paper furthermore geometric and topological properties of the feasible set and in particular the difference to the standard semi infinite case are analyzed by using first order approximations of the feasible set corresponding constraint qualifications are developed then necessary and sufficient first and second order optimality conditions are presented where directional differentiability properties of the optimal value function of the so called lower level problem are used finally an overview of numerical methods is given

subharmonic projections for a quantum markov semigroup this article introduces a concept of subharmonic projections for a quantum markov semigroup in view of characterizing the support projection of a stationary state in terms of the semigroup generator these results together with those of our previous article j math phys 42 1296 2001 lead to a method for proving the existence of faithful stationary states this is often crucial in the analysis of ergodic properties of quantum markov semigroups the method is illustrated by applications to physical models

relative eigenvalues of hermitian matrices abstract motivated by the interest in a more thorough understanding of the relationship between the eigenvalues of a hermitian matrix m and those of a matrix of the form a ma we study the relative eigenvalues of a hermitian matrix with respect to a subspace a geometrically meaningful result and some of its useful corollaries are established as a consequence some inertia theorems given in earlier work are also strengthened

decoherence free subspaces of a quantum markov semigroup we give a full characterisation of decoherence free subspaces of a given quantum markov semigroup with generator in a generalised lindbald form which is valid also for infinite dimensional systems our results extending those available in the literature concerning finite dimensional systems are illustrated by some examples