canonical forms for linear differential algebraic equations with variable coefficients abstract we give a new set of local characterizing quantities for the treatment of linear differential algebraic equations with variable coefficients this leads to new global invariances under which we can find a generalization of the global or differentiation index and get a new existence and uniqueness theorem

fuzzy matrices of permanent one abstract we study the n n fuzzy matrices of permanent one hall matrices which are generalizations of the reflexive fuzzy matrices we give some necessary and sufficient conditions for a hall matrix to have a generalized inverse in the semigroup hn of n n hall matrices as applications we also study the fuzzy linear maps and the principal left ideals of hn

characteristic spaces and rigidity for analytic hilbert modules abstract it is well known that a polynomial in one variable is completely determined by its zeros counting multiplicities we generalize this result to an ideal of polynomials in several variables by introducing the characteristic spaces of the ideal one finds that the ideal is completely determined by its characteristic spaces on a characteristic set in particular a primary ideal is completely determined by its characteristic space at any zero point some straightforward applications of the above results yield the algebraic reduction theorem for analytic hilbert modules in several variables also we obtain some general rigidity results for analytic hilbert modules by using the techniques of af envelopes of analytic hilbert modules

derivative and proportional state feedback for linear descriptor systems with variable coefficients abstract we study linear descriptor systems with rectangular variable coefficient matrices using local and global equivalence transformations we introduce normal and condensed forms and get sets of characteristic quantities these quantities allow us to decide whether a linear descriptor system with variable coefficients is regularizable by derivative and or proportional state feedback or not regularizable by feedback means for us that there exists a feedback which makes the closed loop system uniquely solvable for every consistent initial vector

numerical solution of hybrid systems of differential algebraic equations abstract we present a mathematical framework for general over and under determined hybrid switched systems of differential algebraic equations hdaes we give a systematic formulation of hdaes and discuss existence and uniqueness of solutions the treatment of the switch points and how to perform consistent initialization at switch points we show how numerical solution methods for daes can be adapted for hdaes and present a numerical results for these methods for the real world example of simulating an automatic gearbox

determinant theory for fuzzy matrices abstract we study determinant theory for fuzzy square matrices including some boolean matrices and consider the cayley hamilton theorem for these matrices we prove that det a adj a det a det adj a a where adj a denotes the adjoint matrix of a fuzzy matrix a

on the dirichlet space for finitely connected regions this paper is devoted to the study of the dirichlet space dir g for finitely connected regions g we are particularly interested in the algebra of bounded multiplication operators on this space results in different directions are obtained one direction deals with the structure of closed subspaces invariant under all bounded multiplication operators in particular we show that each such subspace contains a bounded function for regions with circular boundaries we prove that a finite codimensional closed subspace invariant under multiplication by z must be invariant under all bounded multiplication operators and furthermore it is of the form p dir g where p is a polynomial with all its roots lying in g another direction is to study cyclic and noncyclic vectors for the algebra of all bounded multiplication operators typical results are if f e dir g and f is bounded away from zero then f is cyclic on the other hand if the zero set of the radial limit function of f on the boundary has positive logarithmic capacity then f is not cyclic also some other sufficient conditions for a function to be cyclic are given lastly we study transitive operator algebras containing all bounded multiplication operators we prove that they are dense in the algebra of all bounded operators in the strong operator topology

determinant theory for d 01 lattice matrices abstract we study determinant theory for d01 lattice matrices and consider the cayley hamilton theorem for these matrices a distributive lattice l is said to be d01 lattice if 0 1 l and 0 x 1 for all x l we prove that det ab det a det b det aadj a det a det adj a a where adj a denotes the adjoint matrix of a d01 lattice matrice a

regular solutions of nonlinear differential algebraic equations and their numerical determination for a general class of nonlinear possibly higher index differential algebraic equations we show existence and uniqueness of solutions these solutions are regular in the sense that newton s method will converge locally and quadratically on the basis of the presented theoretical results numerical methods for the determination of consistent initial values and for the computation of regular solutions are developed several numerical examples are included

analytic hilbert spaces over the complex plane in this paper we study the structure of quasi invariant subspaces of analytic hilbert spaces over the complex plane we especially investigate when two quasi invariant subspaces are similar or unitarily equivalent for an analytic hilbert space over the complex plane

invariant subspaces quasi invariant subspaces and hankel operators abstract in this paper using the theory of hilbert modules we study invariant subspaces of the bergman spaces on bounded symmetric domains and quasi invariant subspaces of the segal bargmann spaces we completely characterize small hankel operators with finite rank on these spaces

one step and extrapolation methods for differential algebraic systems the paper analyzes one step methods for differential algebraic equations dae in terms of convergence order in view of extrapolation methods certain perturbed asymptotic expansions are shown to hold for the special dae extrapolation solver based on the semi implicit euler discretization the perturbed order pattern of the extrapolation tableau is derived in detail the theoretical results lead to modifications of the known code the efficiency of the modifications is illustrated by numerical comparisons over critical examples mainly from chemical combustion

resolution of the cartesian product of fuzzy sets abstract the problem given a in v n b in v m and b in v m find all a in v n such that a a b b where denotes max min composition x denotes cartesian product and v n denotes the set of all fuzzy vectors with n members is investigated the condition for the existence of a solution is shown and an analytical solution is given

classical and generalized solutions of time dependent linear differential algebraic equations abstract a coordinate free reduction procedure is developed for linear time dependent differential algebraic equations that transforms their solutions into solutions of smaller systems of ordinary differential equations the procedure applies to classical as well as distribution solutions in the case of analytic coefficients the hypotheses required for the reduction not only are necessary for the validity of the existence and uniqueness results but even allow for the presence of singularities straightforward extensions including undetermined systems and systems with nonanalytic coefficients are also discussed

automatic integration of euler lagrange equations with constraints abstract numerical difficulties in the integration of euler lagrange and similar equations are discussed a technique for reducing their index from three to two is introduced and it is shown that variable order variable step bdf methods converge for these index two problems the practical application of this reduction in a numerical setting is examined

stabilization of planar switched systems this paper considers the problem of stabilization of single input planar switched systems we assume the switching law is observable a formula is presented which provides a necessary and sufficient condition for the system to be quadratically stabilizable a set of linear inequalities are given to describe the set of all quadratic lyapunov functions the solvability and the control design technique are clearly described in a straightforward computation algorithm

finite codimensional invariant subspaces of bergman spaces abstract for a large class of bounded domains in c we describe thosefinite codimensional subspaces of the bergman space that are invariant undermultiplication by z using different techniques for certain domains in cn wedescribe those finite codimensional subspaces of the bergman space that areinvariant under multiplication by all the coordinate functions fix a positive integer n and let v denote lebesgue volume measure on cn sothat if n 1 then v is just area measure let q c c be a domain which asusual means that 0 is a nonempty open connected subset of c for an analyticfunction from 0 to c and 1 p oo the norm n p is defined by wfh r jn f pdv the bergman space l q is defined to be the set of analytic functions from fi toc such that n p oo our goal in this paper is to describe the closed finite codimensional subspaces oflpa 0 that are invariant under multiplication by the coordinate functions zi

invariant subspaces with finite codimension in bergman spaces let omega be a domain in the complex plane denote by l p roman a omega 1 le p infty the bergman space over omega the author presents a description of finite codimensional space e subset l p roman a omega such that ze subset e under some conditions on omega an analogous result is due to n s axler en and n p bourdon en same journal bf306 1988 no 2 805 817 mr0933319 89f 46051 for an arbitrary bounded domain in c there are described those finite codimensional subspaces of the bergman space that are invariant under multiplication by z

a behavioral approach to time varying linear systems part 2 descriptor systems in the sequel to a ilchmann and v mehrmann em siam j control optim 44 2005 pp 1725 1747 we discuss a behavioral approach for linear time varying differential algebraic descriptor systems with real analytic coefficients the analysis is almost global in the sense that the analysis is not restricted to an interval i subset r but is allowed for the time axis r setminus t where t is a discrete set of critical points at which the solution may exhibit a finite escape time controllable observable and autonomous behavior for linear time varying descriptor systems is characterized

a new class of discretization methods for the solution of linear differential algebraic equations with variable coefficients we discuss new discretization methods for linear differential algebraic equations daes with variable coefficients we introduce numerical methods to compute the local invariants of such daes that were introduced by the authors in a previous paper p kunkel and v mehrmann j comput appl math 56 1994 pp 225 251 using these quantities we are able to determine numerically global invariances like the strangeness index which generalizes the differentiation index for daes that in particular include undetermined solution components based on these methods we then obtain regularization schemes which allow us to employ general solution methods the new methods are tested on a number of numerical examples

a new look at pencils of matrix valued functions abstract matrix pencils depending on a parameter and their canonical forms under equivalence are discussed the study of matrix pencils or generalized eigenvalue problems is often motivated by applications from linear differential algebraic equations daes based on the weierstrass kronecker canonical form of the underlying matrix pencil one gets existence and uniqueness results for linear constant coefficients daes in order to study the solution behavior of linear daes with variable coefficients one has to look at new types of equivalence transformations this then leads to new canonical forms and new invariances for pencils of matrix valued functions we give a survey of recent results for square pencils and extend these results to nonsquare pencils furthermore we partially extend the results for canonical forms of hermitian pencils and give new canonicalforms there too based on these results we obtain new existence and uniqueness theorems for differential algebraic systems which generalize the classical results of weierstrass and kronecker

regularization of linear descriptor systems with variable coefficients we study linear descriptor control systems with rectangular variable coefficient matrices we introduce condensed forms for such systems under equivalence transformations and use these forms to detect whether the system can be transformed to a uniquely solvable closed loop system via state or derivative feedback we show that under some mild assumptions every such system consists of an underlying square subsystem that behaves essentially like a standard state space system plus some solution components that are constrained to be zero

a behavioral approach to time varying linear systems part 1 general theory we develop a behavioral approach to linear time varying differential algebraic systems the analysis is almost everywhere in the sense that the statements hold on mathbb r setminus mathbb t where mathbb t is a discrete set controllability observability and autonomy are introduced and related to the behavior of the system classical results on the behavior of time invariant systems are studied in the context of time varying systems

discontinuous solutions of semilinear differential algebraic equations ii p consistency abstract part 1 of this paper presented a theory of distribution solutions of semilinear differential algebraic equations dae s in particular it was shown that uniqueness of solutions of initial value problems breaks down completely in the class of discontinuous solutions here a mathematical procedure is introduced for selecting physically acceptable solutions which satisfy some new consistency condition relative to admissible perturbations of the original dae several nonlinear circuit examples are given to support the theory an

discontinuous solutions of semilinear differential algebraic equations i distribution solutions abstract there is strong physical evidence that a full treatment of differential algebraic equations should be incorporate solutions with jump discontinuities it is shown here that for semilinear problems the setting of distributions allows for the development of a theory where indeed such discontinuities may occur this approach also settles the problem of inconsistent initial conditions in a very simple way on the other hand new issues arise as not only uniqueness but even countability of the number of solutions of initial value problems may now be lost a physically motivated but purely mathematical selection procedure to overcome this difficulty is discussed in part 2 of this paper an

a new software package for linear differential algebraic equations we describe the new software package gelda for the numerical solution of linear differential algebraic equations with variable coefficients the implementation is based on the new discretization scheme introduced in p kunkel and v mehrmann siam j numer anal 33 1996 pp 1941 1961 it can deal with systems of arbitrary index and with systems that do not have unique solutions or inconsistencies in the initial values or the inhomogeneity the package includes a computation of all the local invariants of the system a regularization procedure and an index reduction scheme and it can be combined with every solution method for standard index 1 systems nonuniqueness and inconsistencies are treated in a least square sense we give a brief survey of the theoretical analysis of linear differential algebraic equations with variable coefficients and discuss the algorithms used in gelda furthermore we include a series of numerical examples as well as comparisons with results from other codes as far as this is possible

an inequality for the critical value of nonlinear eigenvalue problems soit un domaine borne de r n de classe c 2 pour 0 1 soit l un operateur differentiel d ordre 2 fortement uniformement elliptique on considere le probleme aux valeurs propres non lineaire lu pf u dans u 0 ou est un poids positif et f c 2 positive croissante et convexe on demontre une inegalite sur la valeur propre critique

the determinant of a fuzzy matrix with respect to t and co t norms abstract we study determinants of square matrices over the interval 0 1 when ordinary multiplication is replaced by a triangular norm and ordinary addition is replaced by a triangular conorm

the index of general nonlinear daes in the last few years there has been considerable research on differential algebraic equations daes f t y y 0 where f y is identically singular much of the mathematical effort has focused on computing a solution that is assumed to exist more recently there has been some discussion of solvability of daes there has historically been some imprecision in the use of the two key concepts of solvability and index for daes the index is also important in control and systems theory but with different terminology the consideration of increasingly complex nonlinear daes makes a clear and correct development necessary this paper will try to clarify several points concerning the index after establishing some new and more precise terminology that we need some inaccuracies in the literature will be corrected the two types of indices most frequently used the differentiation index and the perturbation index are defined with respect to solutions of unperturbed problems examples are given to show that these indices can be very different for the same problem we define new maximum indices which are the maxima of earlier indices in a neighborhood of the solution over a set of perturbations and show that these indices are simply related to each other these indices are also related to an index defined in terms of jacobians