two continuous models for the dynamics of sandpile surfaces we consider a modified bouchaud cates ravi prakash edwards model for pile surface dynamics and show that in the long scale limit this model converges to a quasistationary model of pile growth in the form of an evolutionary variational inequality

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

lagrange multipliers in elastic plastic torsion problem for nonlinear monotone operators abstract the existence of lagrange multipliers as a radon measure is ensured for an elastic plastic torsion problem associated to a nonlinear strictly monotone operator a regularization of this result namely the existence of l p lagrange multipliers is obtained under strong monotonicity assumption on the operator moreover the relationships between elastic plastic torsion problem and the obstacle problem are investigated finally an example of the so called von mises functions is provided namely of solutions of the elastic plastic torsion problem associated to nonlinear monotone operators which are not obtained by means of the obstacle problem in the case f constant

sandpiles and river networks extended systems with nonlocal interactions a proposed continuum model of sandpile growth is able to demonstrate instantaneous long range interactions and sudden collapses typical of real sandpiles the model is shown to be equivalent to an evolutionary quasivariational inequality in the limiting case of zero angle of repose the inequality describes water transport in a river network

directed structure at infinity for infinite dimensional systems in this article the structure at infinity of infinite dimensional linear time invariant systems with finite dimensional input and output spaces is discussed it is shown that a diagonal form describing behaviour near infinity can be found this diagonal form is a generalisation of the smith mcmillan form at infinity for rational matrices it is then used to simplify certain solvability conditions of a regulation problem examples on time delay and distributed parameter systems are given

on impulsive modes of linear singular systems subject to decentralized output feedback some algebraic properties of linear singular systems at infinity under static decentralized output feedback are studied in this note new concepts of algebraic multiplicity and geometric multiplicity of the impulsive decentralized fixed modes and the impulsive decentralized cycle index of the singular system are defined these concepts indicate how much a singular system can be made close to being impulse free by decentralized output feedback and the results are shown to be generic the geometric multiplicity and the impulsive decentralized cycle index are determined in terms of the system matrices explicitly the number of impulsive modes that can be eliminated is given in terms of these indexes the impulsive decentralized cycle index is shown to characterize generic properties on controllability and observability of the closed loop system through an individual channel or an external channel illustrative examples are provided

regular paper model matching for linear systems with delays and 2d systems model matching problem for linear systems with delays is considered via a transfer matrix approach we deal with a general class of neutral delay differential systems which is equivalent to 2d systems from a realizability point of view the solution of the problem is based on the decomposition of the ring of the causal rational functions which is not a principal ideal domain as the intersection of two suitable principal ideal domains

generalized linear systems geometric and structural approaches abstract this paper presents a new way of introducing invariant subspaces for generalized systems this comes from somewhat known geometric algorithms but in most cases with initial conditions different from those usually seen in this context these definitions are shown to be consistent with other ones directly deduced from classical approaches like matrix pencil tools or discrete algebraic formalism the key starting point for their introduction is the extension of structural descriptions for these generalized systems such as have been available for proper systems many results from the proper case can thus be extended for instance the geometric definition for controllability indices and something similar to the famous morse canonical decomposition of the strictly proper case some links with the inversion algorithm are also sketched

brief paper a full characterization of stabilizability of bimodal piecewise linear systems with scalar inputs this paper studies open loop stabilization problem for bimodal systems with continuous vector field it is based on the earlier work of the authors on the controllability problem for the same class of systems a full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions it is also shown that controllability implies stabilizability for these systems in a very similar fashion to the linear case

partial model matching via static feedback the multivariable case the problem of partial model matching is studied for the case of multi input multi output mimo linear time invariant systems using a regular static state feedback law the necessary and sufficient conditions for the problem to have a solution are established the general analytic expressions of the controller matrices are derived for the case of single input single output systems sufficient conditions are derived for the solution of the partial model matching problem with simultaneous stabilizability for the same type of systems the necessary and sufficient conditions for the solution of the partial model matching problem with simultaneous regulation of the free response of the closed loop system are established finally the problem of partial model matching via regular static measurement output feedback is solved for the case of mimo systems

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

regularity conditions via quasi relative interior in convex programming we give some new regularity conditions for fenchel duality in separated locally convex vector spaces written in terms of the notion of quasi interior and quasi relative interior respectively we provide also an example of a convex optimization problem for which the classical generalized interior point conditions given so far in the literature cannot be applied while the one given by us is applicable by using a technique developed by magnanti we derive some duality results for the optimization problem with cone constraints and its lagrange dual problem and we show that a duality result recently given in the literature for this pair of problems has self contradictory assumptions

variational inequalities in critical state problems similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth formation of a network of lakes and rivers magnetization of type ii superconductors and elastoplastic deformations we outline the main steps of such models derivation and try to clarify the origin of this similarity new dual variational formulations analogous to mixed variational inequalities in plasticity are derived for sandpiles and superconductors

quasivariational solutions for first order quasilinear equations with gradient constraint we prove the existence of solutions for a quasi variational inequality of evolution with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself the only required assumption on the nonlinearity of this constraint is its continuity and positivity the method relies on an appropriate parabolic regularization and suitable a priori estimates we also obtain the existence of stationary solutions by studying the asymptotic behaviour in time in the variational case corresponding to a constraint independent of the solution we also give uniqueness results

a polynomial characterization of mathcal a mathcal b invariant and reachability subspaces based on the state space model of p fuhrmann a link is laid between the geometric approach to linear system theory as developed by w m wonham and a s morse and the approach based on polynomial matrices in particular polynomial characterizations of a b invariant and reachability subspaces are given these characterizations are used to prove the equivalence of the disturbance decoupling problem and the exact model matching problem and also to connect the polynomial matrix and the geometric approach to the construction of observers finally constructive procedures and conditions are given for computing the supremal a b invariant subspace and reachability space and for checking the solvability of the exact model matching problem

brief simultaneous model matching and disturbance rejection with stability by state feedback this work deals with the model matching problem and the disturbance rejection problem with stability by state feedback each one of these control problems has separately received a lot of contributions but to our best knowledge we propose here for the first time a complete structural solution for square same number of control inputs and outputs strictly proper systems our structural conditions nicely enhance the role played by the zeros both finite and infinite

duality theory and optimality conditions for generalized complementarity problems abstract in this paper generalized complementarity problems are expressed in terms of suitable optimization problems and some necessary optimality conditions are given the infinite dimensional lagrangean and duality theories play an important role in order to achieve the main results

the infinite dimensional lagrange multiplier rule for convex optimization problems abstract in this paper an infinite dimensional generalized lagrange multipliers rule for convex optimization problems is presented and necessary and sufficient optimality conditions are given in order to guarantee the strong duality furthermore an application is presented in particular the existence of lagrange multipliers associated to the bi obstacle problem is obtained

necessary and sufficient conditions for asymptotic model matching of switching linear systems this paper investigates the problem of designing a feedback controller to force the response of a given plant to match asymptotically that of a prescribed model in case both the plant and the model are switching linear systems matching has to be achieved with stability of the feedback loop for any initial conditions of the plant the model and the controller in case it is dynamic and for any choice of the switching law solvability of the problem is characterized in terms of necessary and sufficient conditions that in part refer to the geometric structure of the difference system which compares the output of the model and of the plant stability is considered both for slow switching and for arbitrary switching proofs of the solvability conditions provide viable procedures for synthesizing the static or dynamic controllers that achieve the matching respectively when the state of the model is measurable and when it is not weaker sufficient conditions that can be practically checked by simple algorithmic procedures are provided both in the general situation and under slightly restrictive hypotheses

stable determination of a crack from boundary measurements we treat the problem of determining a crack inside a conductor when two pairs of current and voltage boundary measurements are given we prove a theorem of continuous dependence from the data

model matching of descriptor systems by proportional state feedback abstract given a regular linear descriptor system e x fx gu y hx with transfer function t s we consider the problem of designing a proportional state feedback u lx mv with m non singular such that the resulting system is regular and its transfer function equals a prespecified rational matrix w s necessary and sufficient conditions are given for the existence of such a feedback as well as for the internal properness and or stability of the resulting system these conditions are interpreted in terms of the zeros of t s and w s a simple design procedure is proposed which consists of finding a constant solution to a polynomial matrix equation

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

fast slow diffusion and collapsing sandpiles we regard the limit as p of the flow governed by the p laplacian as providing a simplistic model for the collapse of an initially unstable sandpile upon rescaling to stretch out the initial layer we obtain some simple dynamics and provide fairly explicit solutions in certain cases involving nonlocal geometric curvature motion in particular we note that such models entail instantaneous mass transfer governed by monge kantorovich theory

a stochastic model for growing sandpiles and its continuum limit we study a stochastic model for the sandpile growth the height of the sandpile above every site of a d dimensional lattice is denoted by an integer the height changes randomly and after a suitable scaling of the time and space we show that the rescaled height converges to a deterministic function the limit is governed by a nonlinear evolution equation

central difference regularization method for the cauchy problem of the laplace s equation abstract in this paper we consider the cauchy problem for the laplace s equation where the cauchy data is given at x 0 and the solution is sought in the interval 0

granular flow in a three dimensional rotating container we considered a flow of a cohesionless granular material in a partially filled three dimensional rotating container a model is suggested to describe a density of the surface flow and the profile of the free surface of the granular material it is shown that when the container has an ellipsoidal shape the obtained system of partial differential equations can be reduced to a set of two ordinary differential equations

model matching and decoupling for continuous and discrete time linear time varying systems solutions to the exact model matching and block decoupling problems for both continuous and discrete time linear time varying systems are presented the parametrisation of the whole class of proper solutions is given for the decoupling the minimal delay problem is also considered in a time varying setting the approach is algebraic and based on the smith macmillan form at infinity of a transfer matrix of a time varying system which has been recently introduced in systems theory this avoids the difficulties related to the inversion of the transfer matrices with entries in non commutative fields over which the determinants of dieudonne or ore type are much more complicated the solutions presented here involve only standard matrix computations excluding direct matrix inversions and are thus easy to implement in practice examples are treated in detail to illustrate the theoretical results and the way in which the computations are done and a physical example is also shown

variational formulation for a general dynamic financial equilibrium problem balance law and liability formula abstract an evolutionary model for a multi sector multi instrument financial equilibrium problem with a general utility function different prices for assets and liabilities and including the expenses for the management of the financial institutions is presented in this general case we give the evolutionary financial equilibrium conditions and prove their equivalence with an evolutionary variational inequality from which existence results of the financial equilibrium follow moreover making use of new nonlinear analysis results we develop a lagrange theory which allows one to study the behaviour of the financial equilibrium by means of the lagrange multipliers as a product of this analysis we prove that for the financial model an equilibrium law together with a liability formula must be fulfilled from which the reorganization of the existing financial disequilibrium depends

a general approach to the eigenstructure assignment for reachability and stabilizability subspaces abstract this paper is concerned with the problem of determining basis matrices for the supremal output nulling reachability and stabilizability subspaces and the simultaneous computation of the associated friends that place the assignable closed loop eigenvalues at desired locations our aim is to show that the moore laub algorithm in moore and laub 1978 for the computation of these subspaces was stated under unnecessary restrictive assumptions we prove the same result under virtually no system theoretic hypotheses this provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust and as general as the standard ones based on the computation of sequences of subspaces

evolution monge kantorovich equation abstract the paper deals with monge kantorovich equation mk for short in an open bounded domain with dirichlet boundary condition we study existence and uniqueness of a solution to the associated evolution problem emk for short and we prove the convergence to a solution of mk when time goes to a solution is a couple u where u is the potential and is the transportation flux we study the problem for a given radon measure source term and we show how to use the numerical method of dumont and igbida 2009 22 to provide numerical approximation of the solution of mk

infinite structure and exact model matching problem a geometric approach we first generalize to a b c d quadruples the geometric characterization of the infinite zero structure we then give a new geometric proof for a solvability condition of the exact model matching problem expressed in terms of this concept and previously established in the polynomial context by morse verghese and pernebo this emphasizes the approach independent character of the infinite zero structure

structure and smith macmillan form of a rational matrix at infinity the use of special row and column operations in the reduction of a rational matrix to its smith macmillan form at infinity is investigated the connections between this reduction procedure and the valuation approach are established a graphical method for finding the smith macmillan form of a rational matrix at infinity from its bode magnitude array and some new results on realization theory for polynomial matrices are presented

fourth order modified method for the cauchy problem for the laplace equation we consider the cauchy problem for the laplace equation in the half plane x 0 y r where the cauchy data is given at x 0 and the solution is sought in the interval 0 x 1 the problem is ill posed the solution if it exists does not depend continuously on the data in order to solve the problem numerically it is necessary to modify the equation so that a bound on the solution is imposed we study a modification of the equation where a fourth order mixed derivative term is added error estimates for this equation are given which show that the solution of the modified equation is an approximation of the solution of the cauchy problem for the laplace equation and it is shown that when the data error tends to zero the error in the approximate solution tends to zero logarithmically numerical implementation is considered and a simple example is given

almost invariance and noninteracting control a frequency domain analysis abstract we solve a number of feedback synthesis problems in the context of noninteracting control or block diagonal decoupling for finite dimensional linear time invariant systems we consider a plant that apart from a control input and a measurement output has a given number of exogenous input vectors and the same number of exogenous output vectors the decoupling problem studied is to find dynamic compensators from the plant measurement output which in this paper will be assumed to be the full plant state to the plant control input in such a way that the following requirements are met 1 the closed loop transfer matrix is block diagonal 2 the remaining diagonal blocks are stable with respect to an a priori given first stability set and 3 the clossed loop system is internaly stable with respect to an a priori given second in general larger stability set in addition we study the almost version of the above problem in the latter the requirement of exact decoupling is replaced by a requirement of approximate decoupling in the sense that the compensators to be designed should yield off diagonal blocks in the closed loop transfer matrix that are arbitrarily small in h norm necessary and sufficient conditions for the existence of such dynamic compensators are formulated in terms of controlled invariant and almost controlled invariant subspaces

a nine fold canonical decomposition for linear systems the zero structure for non minimal proper systems in state space form is investigated the approach is geometric and a complete characterization in geometric terms is given of the invariant decoupling system and transmission zeros as defined by rosenbrock the first main result is a formula for the transmission zeros second a canonical lattice diagram is presented of a decomposition of the state space which can be viewed as the product of the kalman canonical decomposition and the morse canonical decomposition this decomposition gives a straightforward characterization of all zeros just mentioned in terms of spectral properties of subspaces under a certain class of feedback and injection mappings via this diagram a number of equivalent formulae for the transmission zeros are derived the freedom in pole assignment leads to new characterizations for the invariant and system zeros in terms of greatest common divisors of characteristic polynomials finally the relation is demonstrated be

the partial model matching problem with stability the partial model matching problem has been initially introduced in emre and silverman 1980 and amounts to matching the first k 1 markov parameters of the compensated plant with those of the model we give here an algebraic and structural solution to this problem moreover we give an answer to the stability question which has remained open since then as a possibly surprising result we show that if this partial problem is solvable then there always exists a stable solution provided the plant is stabilizable we illustrate on a simple example how this objective can be realized in combination with some h norm attenuation limitations for the existence of static state feedback solutions are also discussed

determining surface temperature and heat flux by a wavelet dual least squares method we apply a wavelet dual least squares method to a general sideways parabolic equation for determining surface temperature and surface heat flux connecting meyer wavelet bases with a special project method dual least squares method we can obtain a regularized solution meanwhile order optimal error estimates between the approximate solution and exact solution are proved

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

computation of the structural invariants of linear multivariable systems with an extended version of the program zeros abstract the structural invariants like finite and infinite zeros play an important role in many problems in the analysis of linear systems in 1 emami naeini and van dooren presented the program zeros for computing the finite zeros of a linear system which in the author s opinion is at present the best commonly available program for this problem such a program does not exist for computing the other structural invariants like the infinite zeros and the kronecker indices this paper presents an extended version of the program zeros which computes the finite zeros as well as the other structural invariants

on the lyapunov equation coinvariant subspaces and some problems related to spectral factorizations a geometric approach to stochastic realization theory and hence to spectral factorization problems has been developed by lindquist and picci 1985 1991 and lindquist et al 1995 most of this work was done abstractly fuhrmann and gombani 1998 adopted an entirely hardy space approach to this set of problems studying the set of rectangular spectral factors of given size for a weakly coercive spectral function the parametrization of spectral factors in terms of factorizations of related inner functions as developed in fuhrmann 1995 had to be generalized this led to a further understanding of the partial order introduced by lindquist and picci in the set of stable spectral factors in the present paper we study the geometry of finite dimensional coinvariant subspaces of a vectorial hardy space h 2 via realization theory emphasizing the role of the lyapunov equation in lifting the hardy space metric to the statespace domain we follow this by deriving state space formulas for rectangular spect

wiener hopf factorization indices and infinite structure of rational matrices the relationship between the infinite structure and the wiener hopf factorization indices of polynomial matrix representations of controllable systems is investigated on the way local wiener hopf factorization indices must be defined in addition the finite and infinite structure of a rational matrix is characterized given its wiener hopf factorization indices

quasi relative interior type constraint qualifications ensuring strong lagrange duality for optimization problems with cone and affine constraints in this article we provide weak sufficient strong duality conditions for a convex optimization problem with cone and affine constraints stated in infinite dimensional spaces and its lagrange dual problem our results are given by using the notions of quasi relative interior and quasi interior for convex sets the main strong duality theorem is accompanied by several stronger yet easier to verify in practice versions of it as exemplification we treat a problem which is inspired from network equilibrium our results come as corrections and improvements to daniele and giuffre 2007 9

a measure type lagrange multiplier for the elastic plastic torsion abstract the existence of lagrange multiplier as a radon measure is ensured for an elastic plastic torsion problem associated to a linear operator the result is obtained by means of strong duality theory

an algebraic theory for design of controllers for linear multivariable systems part i structure matrices and feedforward design in this two part paper a theory is presented in which several control problems can be solved the theory is applicable to a general class of linear multivariable systems where the measured output does not have to be equal to the controlled output or the state the system may be affected by nonmeasurable disturbances only controllers which stabilize the system and have proper transfer functions are allowed i e the controllers have to be physically realizable it is shown that the solutions to control problems of servo type e g problems of model matching decoupling and invertibility are special cases of the solution to a more general problem analogously the solutions to problems of regulator type e g disturbance decoupling output regulation and pole placement are also speclal cases of the solution to a more general problem it is shown that problems of servo type and regulator type can be solved independently of each other in part i generalized polynomials are introduced as a mathematical framework structue matrices which describe how well a system can be controlled are defined finally problems of servo type are solved part ii mainly deals with problems of regulator type

lagrange multipliers and non constant gradient constrained problem abstract the aim of the paper is to study a gradient constrained problem associated with a linear operator two types of problems are investigated the first one is the equivalence between a non constant gradient constrained problem and a suitable obstacle problem where the obstacle solves a hamilton jacobi equation in the viscosity sense the equivalence result is obtained under a condition on the gradient constraint the second problem is the existence of lagrange multipliers we prove that the non constant gradient constrained problem admits a lagrange multiplier which is a radon measure if the free term of the equation f l p p 1 if f is a positive constant we regularize the result namely we prove that the lagrange multipliers belong to l 2

variational and quasivariational inequalities with first order constraints abstract we study the existence of solutions of stationary variational and quasivariational inequalities with curl constraint neumann type boundary condition and a p curl type operator these problems are studied in bounded not necessarily simply connected domains with a special geometry and the functional framework is the space of divergence free functions with curl in l p and null tangential or normal traces the analogous variational or quasivariational inequalities with gradient constraint are also studied considering neumann or dirichlet non homogeneous boundary conditions the existence of a generalized solution for a lagrange multiplier problem with homogeneous dirichlet boundary condition and the equivalence with the variational inequality is proved in the linear case for an arbitrary gradient constraint

simultaneous decoupling and disturbance rejection a structural approach abstract the combined problem of disturbance rejection and decoupling for linear systems is considered new necessary and sufficient conditions are derived for the existence of a state feedback controller that rejects the disturbances and simultaneously decouples the closed loop system these conditions are simple intuitively appealing and are expressed in terms of system structural invariants such as infinite zero orders then we consider the disturbance rejection with simultaneous decoupling problem for structured linear systems necessary and sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

a new necessary and sufficient condition for the strong duality and the infinite dimensional lagrange multiplier rule abstract throughout this paper the authors introduce a new condition defined by assumption s which establishes a necessary and sufficient condition for the validity of the strong duality between a convex optimization problem and its lagrange dual this work will be focused on the context of emptiness of the interior of the ordering cone and convexity of the equality constraints moreover this new condition will be necessary and sufficient for the infinite dimensional lagrange multiplier rule this new principle will find application to the elastic plastic torsion problem to the continuum model of transportation and to a problem with quadratic equality constraint with connected to evolutionary illumination and visibility problems

the model following problem for linear constant a b c d quadruples the aim of this note is to deal with the model following problem mfp for linear constant a b c d quadruples in the first part we tackle the mfp with state feedback and we extend the results previously given by morse 7 for a b c triples the main result of this paper is given in the second part where we give necessary and sufficient conditions under which solutions using regular output feedback may exist such conditions were lacking up until now

all optimal controls for the singular linear quadratic problem without stability a new interpretation of the optimal cost abstract the singular linear quadratic control problem without stability is solved by means of a generalized dual structure algorithm in order to generate all optimal inputs furthermore it is shown that the optimal cost can be interpreted as the smallest nonnegative rank minimizing solution of a certain matrix inequality the so called dissipation inequality

stability and regularization of a discrete approximation to the cauchy problem for laplace s equation the standard five point difference approximation to the cauchy problem for laplace s equation satisfies stability estimates and hence turns out to be a well posed problem when a certain boundedness requirement is fulfilled the estimates are of logarithmic convexity type herewith a regularization method will be proposed and associated error bounds can be derived moreover the error between the given continuous cauchy problem and the difference approximation obtained via a suitable minimization problem can be estimated by a discretization and a regularization term

a new wavelet method for solving an ill posed problem abstract so far there are many papers which deal with the cauchy problem for elliptic equation however most of them are devoted to the case of constant coefficients in this paper we consider a cauchy problem for an elliptic equation with variable coefficients due to ill posedness of this problem we provide a regularization method wavelet dual least squares method to solve the problem via meyer wavelet bases with a special project method dual least squares method we can obtain error estimate between the regularized solution and exact solution

realizations in generalized state space form for polynomial system matrices and the definitions of poles zeros and decoupling zeros at infinity this paper contains three main results firstly a realization procedure is presented that brings a polynomial system matrix of a non proper multivariable system to generalized state space form such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained secondly new definitions are proposed for poles zeros and decoupling zeros at infinity of a general polynomial system matrix as a third result a theorem of rosenbrock 1974 e on the redundancy of lcr multiports is generalized to include the decoupling zeros at infinity

assigning the kronecker invariants of a matrix pencil by row or column completions abstract the challenge consists in describing the relationships between the kronecker invariants of a matrix pencil and one of its subpencils for a given subpencil an algorithm for constructing a matrix pencil with prescribed kronecker invariants should also be proposed

infinite dimensional duality and applications the usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear in this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi relative interior which in all the concrete problems considered is nonempty we apply this theory to solve the until now unsolved problem of finding in the infinite dimensional case the lagrange multipliers associated to optimization problems or to variational inequalities as an example we find the lagrange multiplier associated to a general elastic plastic torsion problem

lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term we are concerned with an infinite dimensional variational inequality which is connected with the dynamic oligopolistic market equilibrium problem we will provide existence theorems and show under minimal assumptions on the data the lipschitz continuity of the solution moreover a general duality theory is provided overcoming the difficulty of the voidness of the interior of the ordering cone which defines the cone constraints