homotopical stable ranks for banach algebras abstract the connected stable rank and the general stable rank are homotopy invariants for banach algebras whereas the bass stable rank and the topological stable rank should be thought of as dimensional invariants this paper studies the two homotopical stable ranks viz their general properties as well as specific examples and computations the picture that emerges is that of a strong affinity between the homotopical stable ranks and a marked contrast with the dimensional ones

representations p adiques et equations differentielles in this paper we associate to every p adic representation v a p adic differential equation d rig v that is to say a module with a connection over the robba ring we do this via the theory of fontaine s k modules this construction enables us to relate the theory of k modules to p adic hodge theory we explain how to construct dcris v and dst v from d rig v which allows us to recognize semi stable or crystalline representations the connection is then unipotent or trivial on d rig v 1 t in general the connection has an infinite number of regular singularities but v is de rham if and only if those are apparent singularities a structure theorem for modules over the robba ring allows us to get rid of all singularities at once and to obtain a classical differential equation with a frobenius structure using this we construct a functor from the category of de rham representations to that of classical p adic differential equations with frobenius structure a recent theorem of y andre gives a complete description of the structure of the latter object this allows us to prove fontaine s p adic monodromy conjecture every de rham representation is potentially semi stable as an application we can extend to the case of arbitrary perfect residue fields some results of hyodo h1g h1st of perrin riou the semi stability of ordinary representations of colmez absolutely crystalline representations are of finite height and of bloch and kato if the weights of v are 2 then bloch kato s exponential expv is an isomorphism

on stabilization for discrete linear time varying systems abstract in this paper we consider the stabilization problem for discrete linear time varying systems in an operator theoretic framework by using the complete finiteness of a certain discrete nest algebra we show that a system is stabilizable if and only if it has one kind of strong representation and we also give a parametrization for all the stabilizing controllers in terms of this strong representation this result extends the youla parametrization theorem by only requiring a strong left or a strong right representation but not both the strong stabilization problem is also discussed

a low complexity interior point algorithm for linear programming this paper describes an interior point algorithm for linear programming that is almost as simple as the affine scaling method and yet achieves the currently best complexity of o sqrt n t iterations to attain precision t the basic algorithm needs neither dual estimates nor lower bounds although its analysis is based on ye s results for the primal dual potential function some computationally preferable variants are also presented

on stabilization and the existence of coprime factorizations shows that any transfer function matrix whose elements belong to the quotient field of h sub infinity and which is stabilizable has a matrix fraction representation over h sub infinity which is coprime in the sense that a matrix bezout identity can be satisfied

the stable rank of topological algebras and a problem of r g swan abstract various notions of stable ranks are studied for topological algebras some partial answers to r g swan s problem have two banach or good frechet algebras as in the density theorem in k theory the same stable rank are obtained for example a frechet dense subalgebra a of a c algebra b closed under c functional calculus of self adjoint elements has the same bass stable rank as b

bicoprime factor stability criteria for linear time varying systems in the nest algebra this paper presents a bicoprime factorisation approach to deal with various stability problems for linear discrete time varying systems within the framework of nest algebra first we show that a s

chaotic behavior of the affine scaling algorithm for linear programming the affine scaling algorithm for linear programming involves a step size parameter t that must be chosen in the interval 0 1 it is known that the algorithm converges to an optimal solution for values of t le 2 3 in this paper we examine the behavior of the algorithm for values of t 2 3 we show that for certain values of t in this range the algorithm can exhibit chaotic behavior

connectedness of the invertibles in certain nest algebras of order type ω we solve the connectedness problem for a class of nests of order type with finite dimensional atoms

boundary behavior of interior point algorithms in linear programming this paper studies the boundary behavior of some interior point algorithms for linear programming the algorithms considered are karmarkar s projective rescaling algorithm the linear rescaling algorithm which was proposed as a variation on karmarkar s algorithm and the logarithmic barrier technique the study includes both the continuous trajectories of the vector fields induced by these algorithms and also the discrete orbits it is shown that although the algorithms are defined on the interior of the feasible polyhedron they actually determine differentiable vector fields on the closed polyhedron conditions are given under which a vector field gives rise to trajectories that each visit the neighborhoods of all the vertices of the klee minty cube the linear rescaling algorithm satisfies these conditions thus limits of such trajectories obtained when a starting point is pushed to the boundary may have an exponential number of breakpoints it is shown that limits of projective rescaling trajectories may have a linear number of such breakpoints however projective rescaling trajectories may visit the neighborhoods of linearly many vertices the behavior of the linear rescaling algorithm near vertices is analyzed it is proved that all the trajectories have a unique asymptotic direction of convergence to the optimum

stable ranks of split extensions of banach algebras in this paper we estimate the stable ranks of a banach algebra in terms of the stable ranks of its quotient algebra and ideal under the assumption that the quotient map splits as an application several results about the bass and the connected stable ranks of nest algebras are obtained

simultaneous controller design for time varying linear systems abstract in this paper we establish the parametrization of all simultaneously stabilizing controllers for two time varying linear systems a new approach to the simultaneous stabilization of three time varying linear systems is also provided

overholonomicity of overconvergent f isocrystals over smooth varieties we prove the overholonomicity of overconvergent f isocrystals over smooth varieties this implies that the notions of overholonomicity and devissability in overconvergent f isocrystals are equivalent then the overholonomicity is stable under tensor products so the overholonomicity gives a p adic cohomology stable under grothendieck s cohomological operations

on a general structure of the stabilizing controllers based on stable range in this paper we prove that some stabilizing controllers of a plant which admits a left right coprime factorization have a special form where their stable and unstable parts are separated the dimension of the unstable part depends on the algebraic concept of stable range of the ring a of siso stable plants moreover we prove that if the stable range of a is equal to 1 then every plant defined by a transfer matrix with entries in the quotient field of a and admitting a left right coprime factorization can be stabilized by a stable controller strong stabilization in particular using a result of treil proving that the stable range of h infty mathbb d is equal to 1 we show that every stabilizable plant defined by a transfer matrix with entries in the quotient field of h infty mathbb d or h infty mathbb c is strongly stabilizable and equivalently every couple of stabilizable plants can be simultaneously stabilized by a controller simultaneous stabilization finally using the fact that the topological stable range of h infty mathbb d is equal to 2 a result due to suarez we show that every unstabilizable siso plant defined by a transfer function with entries in the quotient field of h infty mathbb d is as close as we want to a stabilizable plant in the product topology

superlinear convergence of the affine scaling algorithm in this paper we show that a variant of the long step affine scaling algorithm with variable stepsizes is two step superlinearly convergent when applied to general linear programming lp problems superlinear convergence of the sequence of dual estimates is also established for homogeneous lp problems having the origin as the unique optimal solution we also show that 2 3 is a sharp upper bound on the fixed stepsize that provably guarantees that the sequence of primal iterates converge to the optimal solution along a unique direction of approach since the point to which the sequence of dual estimates converge depend on the direction of approach of the sequence of primal iterates this result gives a plausible but not accurate theoretical explanation for why 2 3 is a sharp upper bound on the fixed stepsize that guarantees the convergence of the dual estimates

stability analysis for time varying systems via quadratic constraints abstract in this paper we introduce the concept of quadratic constraint qc to deal with various stability problems for infinite dimensional linear discrete time varying ltv systems first we derive a necessary and sufficient condition for the close loop stability based on quadratic constraints qcs an equivalent condition of this stability criterion presents the relationship between the stabilization of each finite dimensional truncation system and that of the whole system moreover applying this stability criterion and the complete finiteness of the nest algebra we show that the plant is stabilizable if and only if it has a single strong representation finally we use qcs to give a necessary and sufficient condition for the robust stabilization of connected uncertainty set defined by gap metric

an implementation of karmarkar s algorithm for linear programming this paper describes the implementation of power series dual affine scaling variants of karmarkar s algorithm for linear programming based on a continuous version of karmarkar s algorithm two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested linear programs are expressed in an inequality form which allows for the inexact computation of the algorithm s direction of improvement resulting in a significant computational advantage implementation issues particular to this family of algorithms such as treatment of dense columns are discussed the code is tested on several standard linear programming problems and compares favorably with the simplex codeminos 4 0

on the sundberg approximation theorem abstract let h be the banach algebra of bounded holomorphic functions on the open unit disk d c we extend sundberg s theorem on uniform approximation of functions in bmoa by h functions to other classes of holomorphic functions on d in our proofs we use a new characterization of meromorphic functions on d that extend to continuous maps of the maximal ideal space of h to the riemann sphere

global convergence of a long step affine scaling algorithm for degenerate linear programming problems in this paper we present new global convergence results on a long step affine scaling algorithm obtained by means of the local karmarkar potential functions this development was triggered by dikin s interesting result on the convergence of the dual estimates associated with a long step afflne scaling algorithm for homogeneous lp problems with unique optimal solutions without requiring any assumption on degeneracy we show that moving a fixed proportion lambda up to two thirds of the way to the boundary at each iteration ensures convergence of the iterates to an interior point of the optimal face as well as the dual estimates to the analytic center of the dual optimal face where the asymptotic reduction rate of the value of the objective function is 1 lambda we also give an example showing that this result is tight to obtain convergence of the dual estimates to the analytic center of the dual optimal face

topological stable rank of nest algebras we establish a general result about extending a right invertible row over a banach algebra to an invertible matrix this is applied to the computation of right topological stable rank of a split exact sequence we also introduce a quantitative measure of stable rank these results are applied to compute the right left topological stable rank for all nest algebras this value is either 2 or infinity and rtsr t n 2 occurs only when n is of ordinal type less than 2 and the dimensions of the atoms grows sufficiently quickly we introduce general results on partial matrix algebras over a banach algebra this is used to obtain an inequality akin to rieffel s formula for matrix algebras over a banach algebra this is used to give further insight into the nest case

l2 and bibo stability of systems with variable delays this paper considers l 2 and bibo stability and stabilization issues for systems with time varying delays which can be of retarded or neutral type an important role is played by a nominal system with fixed delays which are close to the time varying ones under stability or stabilizability conditions of this nominal system sufficient conditions are given in order to ensure similar properties for the system with time varying delays

analogue p adique du theoreme de turrittin et le theoreme de la monodromie p adique 1 rappel de quelques resultats sur la structure p adique d un point singulier d une equation differentielle 322 2 cas d une pente entiere 327 3 cas d une pente fractionnaire premiere a p 333 4 cas d un rang premier a p 335 5 cas general 339 6 l exemple mx 1 3 343 7 la theorie des modules et l implication dr pst 346

stabilizability and existence of system representations for discrete time time varying systems in this paper right and left representations as an alternate but equivalent framework to coprime factorizations of operators are developed the main theorem of the paper establishes that a linear time varying discrete time plant is stabilizable if and only if its graph can be represented as the range respectively kernel of a causal bounded operator which is left respectively right invertible the proof relies on certain factorization theorems of arveson for nest algebras the paper extends the youla parametrization of all stabilizing compensators to this framework also it is proven that a time invariant plant that is not stabilizable by a time invariant compensator is not stabilizable with a time varying compensator an example of a time varying plant of feintuch is considered and shown to be not stabilizable finally the continuous time case is examined and the problems encountered in extending the proof are discussed however it is shown that a stabilizable plant must have a closed graph

filtrations de type hasse arf et monodromie p adique one proves the crew tsuzuki p adic local monodromy conjecture for local fields of characteristic p 0

global convergence property of the affine scaling methods for primal degenerate linear programming problems in this paper we investigate the global convergence property of the affine scaling method under the assumption of dual nondegeneracy the behavior of the method near degenerate vertices is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous lp problems and karmarkar s method it is shown that the step size 1 8 where the displacement vector is normalized with respect to the distance in the scaled space is sufficient to guarantee the global convergence for dual nondegenerate lp problems the result can be regarded as a counterpart to dikin s global convergence result on the affine scaling method assuming primal nondegeneracy

topology of the maximal ideal space of h revisited abstract let m h be the maximal ideal space of the banach algebra h of bounded holomorphic functions on the unit disk d c we prove that m h is homeomorphic to the freudenthal compactification m a of the set m a of all non trivial analytic disks gleason parts of m h also we give alternative proofs of important results of suarez asserting that the set m s of trivial one pointed gleason parts of m h is totally disconnected and that the cech cohomology group h 2 m h z 0

the stable rank of the algebra h equals 1 abstract it is proved that if the functions f g h f 1 g 1 satisfy the carleson corona condition z inf f z g z def o then there exists a function g h such that the fucntion f gg is invertible in h and moreover g c 1 c where the constant c depends only on

rank one solvable p adic differential equations and finite abelian characters via lubin tate groups we introduce a new class of exponentials of artin hasse type called exponentials these exponentials depend on the choice of a generator of the tate module of a lubin tate group mathfrak g over mathbb z p they arise naturally as solutions of solvable differential modules over the robba ring if mathfrak g is isomorphic to widehat mathbb g m over mathbb z p we develop methods to test their over convergence and get in this way a stronger version of the frobenius structure theorem for differential equations we define a natural transformation of the artin schreier complex into the kummer complex this provides an explicit generator of the kummer unramified extension of epsilon dagger k infty whose residue field is a given artin schreier extension of k t where k is the residue field of k we then compute explicitly the group under tensor product of isomorphism classes of rank one solvable differential equations moreover we get a canonical way to compute the rank one module over epsilon dagger k infty attached to a rank one representation of mathrm gal k t mathrm sep k t defined by an artin schreier character

a p adic local monodromy theorem we produce a canonical filtration for locally free sheaves on an open p adic annulus equipped with a frobenius structure using this filtration we deduce a conjecture of crew on p adic differential equations analogous to grothendieck s local monodromy theorem also a consequence of results of andre and of mebkhout namely given a finite locally free sheaf on an open p adic annulus with a connection and a compatible frobenius structure the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix

image directe superieure et unipotence let x be a proper smooth curve over a perfect field of characteristic p 0 and u an open dense subscheme of x we prove that convergent f isocrystals on u are overconvergent under the condition that they are overconvergent at each point in x nu using this criterion we show that the higher direct images rfcrys ov by a proper smooth morphism of schemes f v u are overconvergent introduction soient u k une courbe a ne et lisse sur un corps parfait de caracteristique p 0 x k une compactification lisse de u et f v u un morphisme propre et lisse en utilisant un critere de surconvergence dont l idee initiale revient a de jong cf 9 et gr ce aux resultats locaux de kedlaya 13 nous montrons que les images directes superieures rf ov sont surconvergentes repondant ainsi dans le cas d une courbe a ne et lisse a une conjecture de 3 en particulier leurs groupes de cohomologie sont de dimension finie et verifient la dualite de poincare enfin nous montrons que le theoreme de monodromie p adique local de 1 14 et 17 permet de deduire que tout f isocristal surconvergent sur u provient apres une eventuelle extension finie etale d un f log isocristal nous remercions kiran kedlaya pour nous avoir indique comment obtenir des resultats de descente de modules via ses lemmes de factorisations de matrices a notations soit k un corps parfait de caracteristique p on note w l anneau des vecteurs de witt de k ok une extension finie de w et k0 respectivement k le corps des fractions de w resp ok on suppose le corps k muni d un frobenius s relevant le frobenius canonique de k0 pour une indeterminee t on notera s 1 4 ok 1 21 2t nok k a 1 4 py i1 40 ait i ai a k jaijr i 0 i y pour tout 0 r 1 h 1 4 a 1 4 p y i1 40 ait i ai a k jaij 0 i y hy 1 4 a a h jaijr 0 i y pour un certain 0 r 1

on the topological stable rank of non selfadjoint operator algebras we provide a negative solution to a question of m rieffel who asked if the right and left topological stable ranks of a banach algebra must always agree our example is found amongst a class of nest algebras we show that for many other nest algebras both the left and right topological stable ranks are infinite we extend this latter result to popescu s non commutative disc algebras and to free semigroup algebras as well

dimension and stable rank in the k theory of c algebras in topological k theory which can be viewed as the algebraic side of the theory of vector bundles some of the interesting properties which one investigates are for example the conditions under which bundles must possess trivial direct summands or the extent to which the cancellation property for direct whitney sums of bundles holds such properties turn out to be controlled in part by the dimension of the base space and results describing the nature of this control are among what are frequently called stability results 17 during the past few years there has been a sudden flowering of a theory for c algebras see surveys 35 36 37 since c algebras are profitably thought of as non commutative locally compact spaces with the finitely generated projective modules being the appropriate generalization of vector bundles according to swan s theorem 40 it would be natural to look for stability results for c algebras but until now the theory has been focussed on the c groups of c algebras and there has been little discussion of stability properties presumably in part for lack of an appropriate concept of dimension for c algebras one of the main objectives of this paper is to introduce a concept of dimension for c algebras which directly generalizes the classical concept of dimension for compact spaces 16 20 22 and to develop some techniques for calculating it notably for c algebras which are obtained as crossed product algebras for an action of the group of integers in algebraic k theory which is the generalization of topological c theory to rings a substantial number of stability properties have been discovered 2 39 42 48 within that theory the concept which has played a role most analogous to that of dimension is the bass stable rank but despite its many successes the bass stable rank has often been difficult to calculate even for relatively uncomplicated rings another main objective of the present paper is to make accessible for application to c algebras some of the stability results from algebraic c theory this comes about from the fact that the concept of dimension which we introduce dominates the bass stable rank i was led to seek stability results for c algebras by my desire to determine whether the cancellation property for projective modules holds for the irrational rotation c algebras discussed in 30 which as elliott 11 has suggested can appropriately be called 2 dimensional non commutative tori in more concrete terms the question is whether two projections in such an algebra which have the same trace must be unitarily equivalent the present paper provides the general theory which is needed for the affirmative answer which i obtained in a subsequent paper i will derive the

limiting behavior of the affine scaling continuous trajectories for linear programming problems we consider the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form by characterizing these trajectories as solutions of certain parametrized logarithmic barrier families of problems we show that these trajectories tend to an optimal solution which in general depends on the starting point by considering the trajectories that arise from the lagrangian multipliers of the above mentioned logarithmic barrier families of problems we show that the trajectories of the dual estimates associated with the affine scaling trajectories converge to the so called centered optimal solution of the dual problem we also present results related to asymptotic direction of the affine scaling trajectories we briefly discuss how to apply our results to linear programs formulated in formats different from the standard form finally we extend the results to the primal dual amne scaling algorithm

the transitivity in simultaneous stabilization this paper deals with the transmission problem in simultaneous stabilization of time varying linear systems we establish two criteria for the transitivity in simultaneous stabilization in particular we give a necessary and sufficient condition for certain linear systems to satisfy a strengthened version of transitivity

global convergence of the affine scaling algorithm for convex quadratic programming in this paper we give a global convergence proof of the second order affine scaling algorithm for convex quadratic programming problems where the new iterate is the point which minimizes the objective function over the intersection of the feasible region with the ellipsoid centered at the current point and whose radius is a fixed fraction beta in 0 1 of the radius of the largest scaled ellipsoid inscribed in the nonnegative orthant the analysis is based on the local karmarkar potential function introduced by tsuchiya for any beta in 0 1 and without assuming any nondegeneracy assumption on the problem it is shown that the sequences of primal iterates and dual estimates converge to optimal solutions of the quadratic program and its dual respectively

suboptimal solutions to the time varying model matching problem abstract two approaches to the characterization of suboptimal solutions are given the first via parrot s theorem gives all solutions the second uses j spectral factorizations and gives a particularly simple parametrization of all solutions unlike the time invariant case however j spectral factorizations do not always exist

on a generalization of the youla kucera parametrization part i the fractional ideal approach to siso systems abstract in this paper we show how to use the theory of fractional ideals in order to study the fractional representation approach to analysis and synthesis problems for siso systems within this mathematical framework we give necessary and sufficient conditions so that a plant is internally strongly bistably stabilizable or admits a weak coprime factorization moreover we show how to generalize the youla kucera parametrization of the stabilizing controllers to any stabilizable plant which does not necessarily admit a coprime factorization this parametrization is generally affine in two free parameters

sensitivity reduction by stable controllers for mimo infinite dimensional systems via the tangential nevanlinna pick interpolation we study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an mimo infinite dimensional system the systems we consider have finitely many simple transmission zeros in c but they are allowed to possess infinitely many poles in c we compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential nevanlinna pick interpolation we also obtain stable controllers attaining such an upper bound to illustrate the results we discuss a repetitive control system as an application of the proposed method

on the convergence of the affine scaling algorithm the affine scaling algorithm first proposed by dikin is presently enjoying great popularity as a potentially effective means of solving linear programs an outstanding question about this algorithm concerns its convergence in the presence of degeneracy in this paper we give new convergence results for this algorithm that do not require any non degeneracy assumption on the problem in particular we show that if the stepsize choice of either dikin or barnes or vanderbei et al is used then the algorithm generates iterates that converge at least linearly with a convergence ratio of 1 beta sqrt n wheren is the number of variables and 0 1 is a certain stepsize ratio for one particular stepsize choice which is an extension of that of barnes we show that the cost of the limit point is within o 1 of the optimal cost and for sufficiently small roughly proportional to how close the cost of the nonoptimal vertices are to the optimal cost is exactly optimal we prove the latter result by using an unusual proof technique that of analyzing the ergodic convergence of the corresponding dual vectors for the special case of network flow problems with integer data we show that it suffices to take 1 6mc wherem is the number of constraints andc is the sum of the cost coefficients to attain exact optimality

on strong stabilization for linear continuous time time varying systems this paper deals with the strong stabilization problem for linear time varying continuous time systems the main result is that for such systems internally stabilizable systems may not be strongly stabilizable this follows from the fact that the algebra of stable systems has infinite bass stable rank

stable controller design for mixed sensitivity reduction of infinite dimensional systems abstract in this paper we study the design of stable controllers for mixed sensitivity reduction for systems that have input output delays and infinitely many unstable zeros the proposed method is based on interpolation with a unit in h which gives a necessary and sufficient condition for stabilization by stable controllers using the youla parameterization we introduce a two block problem for the stable h controller design the two block problem is then transformed to a one block problem solvable by the skew toeplitz approach

sensitivity reduction by strongly stabilizing controllers for mimo distributed parameter systems this note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time invariant multi input multioutput distributed parameter system the plant we consider has finitely many unstable zeros which are simple and blocking but can possess infinitely many unstable poles we obtain a necessary condition and a sufficient condition for the solvability of the problem using the matrix nevanlinna pick interpolation with boundary conditions we also develop a necessary and sufficient condition for the solvability of the interpolation problem and show an algorithm to obtain the solutions our method to solve the interpolation problem is based on the schur nevanlinna algorithm

the stabilization problem for discrete time varying linear systems in this paper we consider the strong stabilization problem for a time varying linear system which admits a coprime factorization we also study the simultaneous and robust stabilization problems for this class of systems

h and bibo stabilization of delay systems of neutral type frequency domain tests for the h and bibo stability of large classes of delay systems of neutral type are derived the results are applied to discuss the stabilizability of such systems by finite dimensional controllers

quadratic convergence in a primal dual method we show that the mizuno todd ye o nl iteration predictor corrector primal dual interior point algorithm for linear programming is quadratically convergent our proof does not assume that the problems be nondegenerate we do not assume that the iterate generated by the algorithm be convergent an assumption common to all previous asymptotic convergence analysis

overconvergent modular forms and the fontaine mazur conjecture we prove a conjecture of fontaine and mazur on modularity of representations of g which are potentially semi stable at p for representations coming from finite slope overconvergent eigenforms we also give an application of our technique to a question of gouvea on overconvergence of certain modular forms if is a suitable representation of g s on a two dimensional vector space over a finite field product of m and the s a finite set of primes we construct a rigid analytic subspace of the universal deformation space of which is defined by a purely representation theoretic condition and contains the eigencurve of coleman mazur conjecturally it is equal to this curve

finite local monodromy of overconvergent unit root f isocrystals on a curve we prove that the category of p adic continuous representations of a fundamental group of a curve over a perfect field of a positive characteristic p with finite local monodromy is equivalent to that of overconvergent unit root f isocrystals on the curve to show the equivalence of categories we study the local theory and apply it to the global case

on strong stabilizability of mimo infinite dimensional systems abstract the strong stabilization problem i e the problem of designing a real stable stabilizing controller is considered for multi input multi output infinite dimensional real linear systems the considered systems may have infinitely many poles and zeros in the open right half plane as well as on the imaginary axis it is shown that the well known parity interlacing property pip for real rational systems is also a necessary condition in the most general case as long as the plant has coprime factorizations over h which is a necessary condition for stabilizability furthermore it is shown that pip is also sufficient under some additional mild assumptions

global convergence of the affine scaling methods for degenerate linear programming problems in this paper we show the global convergence of the affine scaling methods without assuming any condition on degeneracy the behavior of the method near degenerate faces is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous lp problems and karmarkar s method it is shown that the step size 1 8 where the displacement vector is normalized with respect to the distance in the scaled space is sufficient to guarantee the global convergence of the affine scaling methods

trivial gleason parts and the topological stable rank of h we show that the subset of the maximal ideal space of h formed by the trivial gleason parts is totally disconnected a pair g h h is called a corona pair if inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i 0 where inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i is the open unit disc we prove that the set u 2 h of corona pairs is dense in h h

theory of weights in p adic cohomology let k be a finite field of characteristic p 0 we construct a theory of weights for overholonomic complexes of arithmetic d modules with frobenius structure on varieties over k the notion of weight behave like deligne s one in the adic framework first the six operations preserve weights and secondly the intermediate extension of an immersion preserves pure complexes and weights this is joint work with tomoyuki abe

transitivity in simultaneous stabilization for a family of time varying systems abstract this paper develops necessary and sufficient conditions for the so called transitivity and strong transitivity precise definitions later for a family of discrete time varying linear systems which when satisfied lead to characterizations for simultaneous stabilizability and simultaneously stabilizing feedback controllers some criteria for the strong transitivity are established in terms of single coprime factorizations of only one plant and one controller the resulting characterization involves coprime factorizations of fewer systems compared to previous work

bounded functions in mobius invariant dirichlet spaces abstract for p 0 1 let q p q p 0 be the space of analytic functions f on the unit disk with sup w f w d p w 1 f w d p 0 where d p means the weighted dirichlet norm and w is the mobius map of onto itself with w 0 w in this paper we prove the corona theorem for the algebra q p h q p 0 h then we provide a fefferman stein type decomposition for q p q p 0 and finally we describe the interpolating sequences for q p h q p 0 h

coprime factorization and dynamic stabilization of transfer functions it is known that a matrix valued transfer function p has a stabilizing dynamic controller q i e begin smallmatrix i q p i end smallmatrix 1 in rm h infty iff p has a right or left coprime factorization we show that the same result is true in the operator valued case thus the standard youla bongiorno parameterization applies to every dynamically stabilizable function we then derive further equivalent conditions one of them being that p has a stabilizing controller with internal loop this and some others are new even in the scalar valued case we also establish certain related results for example we extend the classical results on coprime factorization and partial feedback measurement feedback stabilization to nonrational transfer functions all our results apply in both discrete and continuous time settings except that in the latter it is not clear whether the controller q can always be chosen so that it is continuous time proper holomorphic and bounded on a right half plane unless e g p z rightarrow0 as operatorname re z rightarrow infty

a variation on karmarkar s algorithm for solving linear programming problems the algorithm described here is a variation on karmarkar s algorithm for linear programming it has several advantages over karmarkar s original algorithm in the first place it applies to the standard form of a linear programming problem and produces a monotone decreasing sequence of values of the objective function the minimum value of the objective function does not have to be known in advance secondly in the absence of degeneracy the algorithm converges to an optimal basic feasible solution with the nonbasic variables converging monotonically to zero this makes it possible to identify an optimal basis before the algorithm converges

the bass stable rank for the real banach algebra a k sym we compute the bass stable rank of the algebra a k sym of real symmetric functions that are continuous on symmetric compact planar sets k and holomorphic in the interior k of k this answers a problem posed by rupp and sasane 2010 24 we also give a characterization of the reducible pairs in c k c k sym and a k sym

convergence analysis of the projective scaling algorithm based on a long step homogeneous affine scaling algorithm in this paper we give a new convergence analysis of a projective scaling algorithm we consider a long step affine scaling algorithm applied to a homogeneous linear programming problem obtained from the original linear programming problem this algorithm takes a fixed fraction 2 3 of the way towards the boundary of the nonnegative orthant at each iteration the iteration sequence for the original problem is obtained by pulling back the homogeneous iterates onto the original feasible region with a conical projection which generates the same search direction as the original projective scaling algorithm at each iterate the recent convergence results for the long step affine scaling algorithm by the authors are applied to this algorithm to obtain some convergence results on the projective scaling algorithm specifically we will show i polynomiality of the algorithm with complexities of o nl and o n2l iterations for 2 3 and 2 3 respectively ii global covnergence of the algorithm when the optimal face is unbounded iii convergence of the primal iterates to a relative interior point of the optimal face iv convergence of the dual estimates to the analytic center of the dual optimal face and v convergence of the reduction rate of the objective function value to 1

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part ii internal stabilization in this second part of the paper a quadrat siam j control optim 40 2003 pp 266 299 we show how to reformulate the fractional representation approach to synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions for internal stabilizability moreover we characterize all the integral domains a of siso stable plants such that every mimo plant defined by means of a transfer matrix whose entries belong to the quotient field k q a of a is internally stabilizable finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 s shankar and v r sule siam j control optim 30 1992 pp 11 30 v r sule siam j control optim 32 1994 pp 1675 1695 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

on the rationality and continuity of logarithmic growth filtration of solutions of p adic differential equations we study the asymptotic behavior of solutions of frobenius equations defined over the ring of overconvergent series as an application we prove chiarellotto tsuzuki s conjecture on the rationality and right continuity of dwork s logarithmic growth filtrations associated to ordinary linear p adic differential equations with frobenius structures

infinitesimal deformation of p adic differential equations on berkovich curves we show that if a differential equation mathscr f over a quasi smooth berkovich curve x has a certain compatibility condition with respect to an automorphism sigma of x then mathscr f acquires a semi linear action of sigma i e lifting that on x the compatibility condition forces the automorphism sigma to be close to the identity of x so the above construction applies to a certain class of automorphisms called infinitesimal this generalizes andre and di vizio asterisque 1 296 55 111 2004 and pulita compos math 144 4 867 919 2008 we also obtain an application to morita s p adic gamma function and to related values of p adic l functions

the convergence newton polygon of a p adic differential equation i affinoid domains of the berkovich affine line we prove that the radii of convergence of the solutions of a p adic differential equation fancyscript f over an affinoid domain x of the berkovich affine line are continuous functions on x that factorize through the retraction of x to gamma of x onto a finite graph gamma subseteq x we also prove their super harmonicity properties this finiteness result means that the behavior of the radii as functions on x is controlled by a finite family of data

time varying optimal disturbance minimization in presence of plant uncertainty the optimal robust disturbance rejection problem plays an important role in feedback control theory here its time varying version is solved explicitly in terms of duality and operator theory in particular the optimum is shown to satisfy a time varying allpass property moreover optimal performance is given in terms of the norm of a bilinear form the latter depends on a lower triangular projection and a multiplication operator defined on special versions of spaces of compact operators

on strong stabilization for linear time varying systems abstract this paper deals with the strong stabilization problem for linear time varying systems and gives a sufficient condition in terms of the coprime factors for the existence of strong stabilizers for such a system

stable controllers for robust stabilization of systems with infinitely many unstable poles abstract this paper studies the problem of robust stabilization by a stable controller for a linear time invariant single input single output infinite dimensional system we consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles first we show that the problem can be reduced to an interpolation minimization by a unit element next by the modified nevanlinna pick interpolation we obtain both lower and upper bounds on the multiplicative perturbation under which the plant can be stabilized by a stable controller in addition we find stable controllers to provide robust stability we also present a numerical example to illustrate the results and apply the proposed method to a repetitive control system

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

actions infinitesimales dans la correspondance de langlands locale p adique let v be a two dimensional absolutely irreducible overline mathbb qp representation of rm gal overline mathbb qp mathbb qp and let prod v be the rm gl 2 mathbb qp banach representation associated by colmez s p adic langlands correspondence we establish a link between the action of the lie algebra of rm gl 2 mathbb qp on the locally analytic vectors prod v rm an of prod v the connection nabla on the varphi gamma module associated to v and the sen polynomial of v this answers a question of harris concerning the infinitesimal character of prod v rm an using this result we give a new proof of a theorem of colmez stating that prod v has nonzero locally algebraic vectors if and only if v is potentially semi stable with distinct hodge tate weights

on the strong stabilization of slowly time varying linear systems abstract this paper considers the strong stabilization problem given a linear time varying system which is stabilizable by dynamic feedback when can the stabilizer be chosen to be itself stable we consider here the case of the algebra of discrete time time varying systems which are slowly time varying

parameterization of stabilizing controllers with either right or left coprime factorization a parameterization method of stabilizing controllers that requires only one of right left coprime factorizations is presented as an illustrative model we will consider the multidimensional system with structural stability for which it is not yet known in general whether or not a doubly coprime factorization always exists a parameterization of stabilizing controllers for the model is presented