introduction to matrix analytic methods in stochastic modeling preface part i quasi birth and death processes 1 examples part ii the method of phases 2 ph distributions 3 markovian point processes part iii the matrix geometric distribution 4 birth and death processes 5 processes under a taboo 6 homogeneous qbds 7 stability condition part iv algorithms 8 algorithms for the rate matrix 9 spectral analysis 10 finite qbds 11 first passage times part v beyond simple qbds 12 nonhomogeneous qbds 13 processes skip free in one direction 14 tree processes 15 product form networks 16 nondenumerable states bibliography index

an exact finite rotation shell theory its mixed variational formulation and its finite element implementation a non linear shell theory including transverse shear strains with exact description of the kinematical fields is developed the strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor thus in plane rotations also called drilling degrees of freedom are included in a natural way various alternatives of the theory are derived for a special version of the theory with altogether six kinematical fields different mixed variational principles are given a hybrid finite element formulation which does not exhibit locking phenomena is developed numerical examples of shell deformation at finite rotations with excellent element performance are presented comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation

a general beam finite element with deformable cross section a general beam finite element is proposed in the paper the formulation of the element relies on the assumption that the beam type structural response can be described by using the usual beam and 3d continuum theories the beam behaviour is represented through the beam degrees of freedom of the global nodes on reference axis and local effects are taken into account through the relative displacements of the cross sectional nodes defining the in plane and out of plane deformations of the cross section consistent derivations for small and large displacements within incremental analysis are presented the cross section is modeled by segments cross sectional elements and can be of arbitrary shape including thick and thin walled types the element is formulated as a superelement consisting of the isoparametric subelements 3d shell beam with the relative displacements as the internal degrees of freedom of the element group which is considered as a substructure the relative displacements can be translations and rotations depending on the type of the subelements continuity of the relative displacements is ensured within the element group and connection of the beam elements with other finite element fe groups is realized through global beam degrees of freedom incompatible generalized displacements are implemented to subelements to improve their behavior external loading of the element can correspond to global and cross sectional nodes the proposed beam superelement bs is easy for application within fe general purpose package as our program pak in the preparation of input and in the postprocessing a number of typical examples illustrate accuracy of results obtained by use of the beam superelement in linear and geometrically nonlinear analysis

an assumed covariant strain based 9 node shell element a new shell element which is free from serious locking problems and which does not possess hourglass modes is proposed solutions obtained with this element exhibit good convergence and are satisfactorily insensitive to mesh distortion the element also exhibits good convergence for plates with variable thickness this element is based on the use of assumed covariant strains which are obtained from the covariant strain field defined with respect to the element natural co ordinate system only the linear version for thin shell cases is considered the element performance is tested by application to several standard plate and shell problems a problem involving variable thickness is also presented

analysis of locking and stress oscillations in a general curved beam element the exactly integrated general quadratic curved beam element has both membrane and shear locking and significant quadratic oscillations in the axial force and cubic oscillations in the shear force the functional re constitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations the orthogonally correct field consistent interpolations are determined for the optimal form of the element and it is shown that the popular two point gaussian integrated13 version of the element is non orthogonal and has a cubic13 oscillation in the shear force that curiously vanishes at the barlow points

rich families and projectional skeletons in asplund wcg spaces abstract we show a way of constructing projectional skeletons using the concept of rich families in banach spaces which admit a projectional generator our next result is that a banach space x is asplund and weakly compactly generated if and only if there exists a commutative 1 projectional skeleton q on x such that q is a commutative 1 projectional skeleton on x we consider both real and also complex banach spaces

a nine node assumed strain finite element for large deformation analysis of laminated shells an application of the element based lagrangian formulation is described for large deformation analysis of both single layered and laminated shells natural co ordinate based stresses strains and constitutive equations are used throughout the formulation of the present shell element which offers significant implementation advantages compared with the traditional lagrangian formulation in order to avoid locking phenomena an assumed strain method has been employed with judicious selection of the sampling points three strictly successive finite rotations are used to represent the current orientation of the shell normal the equivalent natural constitutive equation is derived using an explicit transformation scheme to consider the multi layer effect of laminated structures the arc length control method is used to trace complex load displacement paths several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element 1998 john wiley sons ltd

higher order shell elements based on a cosserat model and their use in the topology design of structures for the purpose of carrying out topology optimization of shell structures we show that it is advantageous to use shell elements based on a classical shell theory such as the cosserat theory rather than elements based on the degenerated solid approach since the shell thickness appears explicitly in the formulation thereby greatly simplifying the sensitivity analysis one of the well known shell elements based on the cosserat shell theory is the four node element presented by simo et al comput methods appl mech engrg 72 1989 267 73 1989 53 although one could use this element the use of lower order elements often results in instabilities such as the checkerboard instability in the resulting topologies this provides the motivation for developing higher order shell elements based on a classical shell theory in this work we present the formulation and implementation details for six node and seven node triangular and nine node quadrilateral shell elements which are based on the variational formulation of simo et al and show that good accuracy is obtained even with coarse meshes in fairly demanding problems we also present the topology optimization formulation and some examples of optimal topologies that are obtained using this formulation

a new eight node quadrilateral shear bending plate finite element a new reissner mindlin plate finite element for the very thin and thick plates without locking and spurious zero energy modes is presented the element has very good convergence characteristics both for thin and thick plates is hardly insensitive to mesh distortions and passes the patch tests the formulation of the element is derived from a displacement variational principle and some general criteria to compute inconsistent transverse shear strains these criteria have been applied with success to four and eight node quadrilateral plate finite elements and could be applied to construct triangular elements

natural examples of valdivia compact spaces abstract we collect examples of valdivia compact spaces their continuous images and associated classes of banach spaces which appear naturally in various branches of mathematics we focus on topological constructions generating valdivia compact spaces linearly ordered compact spaces compact groups l 1 spaces banach lattices and noncommutative l 1 spaces

simultaneous projectional skeletons abstract we prove the existence of a simultaneous projectional skeleton for certain subspaces of c k spaces this generalizes a result on simultaneous projectional resolutions of identity proved by m valdivia we collect some consequences of this result in particular we give a new characterization of asplund spaces using the notion of projectional skeleton

model reduction by moment matching for linear and nonlinear systems the model reduction problem for single input single output linear and nonlinear systems is addressed using the notion of moment a re visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment this in turn is used to pose and solve the model reduction problem by moment matching for nonlinear systems to develop a notion of frequency response for nonlinear systems and to solve model reduction problems in the presence of constraints on the reduced model connections between the proposed results projection methods the covariance extension problem and interpolation theory are presented finally the theory is illustrated by means of simple worked out examples and case studies

a state space calculus for rational probability density functions and applications to non gaussian filtering we propose what we believe to be a novel approach to performing calculations for rational density functions using state space representations of the densities by standard results from realization theory a rational probability density function is considered to be the transfer function of a linear system with generally complex entries the stable part of this system is positive real which we call the density summand the existence of moments is investigated using the markov parameters of the density summand moreover explicit formulae are given for the existing moments in terms of these markov parameters some of the main contributions of the paper are explicit state space descriptions for products and convolutions of rational densities as an application which is of interest in its own right the filtering problem is investigated for a linear time varying system whose noise inputs have rational probability density functions in particular state space formulations are derived for the calculation of the prediction and update equations the case of cauchy noise is treated as an illustrative example

phenomenological invariants and their application to geometrically nonlinear formulation of triangular finite elements of shear deformable shells abstract a phenomenological definition of classical invariants of strain and stress tensors is considered based on this definition the strain and stress invariants of a shell obeying the assumptions of the reissner mindlin plate theory are determined using only three normal components of the corresponding tensors associated with three independent directions at the shell middle surface the relations obtained for the invariants are employed to formulate a 15 dof curved triangular finite element for geometrically nonlinear analysis of thin and moderately thick elastic transversely isotropic shells undergoing arbitrarily large displacements and rotations the question of improving nonlinear capabilities of the finite element without increasing the number of degrees of freedom is solved by assuming that the element sides are extensible planar nearly circular arcs the shear locking is eliminated by approximating the curvature changes and transverse shear strains based on the solution of the timoshenko beam equations the performance of the finite element is studied using geometrically linear and nonlinear benchmark problems of plates and shells

a stabilization procedure for the quadrilateral plate element with one point quadrature a stabilization procedure is developed for controlling the kinematic modes of the four node bilinear quadrilateral element when single point quadrature is used these kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness in this stabilization procedure additional generalized strains are defined which are activated by the kinematic modes these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral by using a scaling law developed in an earlier paper the stabilization parameters are defined so they do not adversely affect the element s performance several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems

a hybrid strain finite element for plates and shells this paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells the formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields to facilitate extension to materially non linear analysis the variational principle is used in rate form and the plane stress assumption is not imposed a priori in the formulation when desired the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions the element geometry is based on a nine noded quadrilateral with biquadratic interpolation of the displacement field the strain field is based on a bilinear interpolation with additional non linear terms chosen on the basis of eigenvalue analysis the element passes the required patch tests does not display either membrane or shear locking effects and is free of communicable spurious modes numerical results are presented for elastic analyses of several standard plate and shell test problems

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

extension of mitc to higher order beam models and shear locking analysis for compact thin walled and composite structures summary a class of mixed interpolated beam elements is introduced in this paper under the framework of the carrera unified formulation cuf to eliminate the detrimental effects due to shear locking the mixed interpolation of tensorial components mitc method is adopted to generate locking free displacement based beam models using general 1d finite elements an assumed distribution of the transverse shear strains is employed for the derivation of the virtual work and the full gauss legendre quadrature is used for the numerical computation of all the components of the stiffness matrix linear quadratic and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact laminated and thin walled structures a comprehensive study of how shear locking affects general beam elements when different classical integration schemes are employed is presented evidencing the outstanding capabilities of the mitc method to overcome this numerical issue refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of lagrange and legendre polynomials over the cross sectional domain allowing one to capture complex states of stress with a 3d like accuracy the numerical examples are compared to analytic numerical solutions from the literature and commercial software solutions whenever it is possible the efficiency and robustness of the proposed method is demonstrated throughout all the assessments illustrating that mitc elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations this article is protected by copyright all rights reserved

convergence of curved shell elements based on assumed covariant strain interpolations a c0 9 node shell element based on assumed interpolations of covariant strain components defined with respect to the element natural co ordinate system has recently been proposed in this formulation the covariant strains are obtained directly from the cartesian strains by tensor transformation without any need to compute laminar co ordinate based strains in the present work the interpolated covariant strains used in this element are analysed to determine their satisfaction of the basic requirements for successful strain interpolation these basic requirements are stated as invariance to rigid body motions and ability to represent constant and linear strain states in the finite element formulation the weak form of momentum balance is expressed in terms of covariant strains and contravariant stresses the corresponding elasticity tensor is a function of the components of the metric tensor associated with the element natural co ordinate system the invariance properties of the metric tensor in the context of the finite element approximation are also discussed

a finite element formulation with stabilization matrix for geometrically non linear shells an assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non linear problems of isotropic and laminated composite shells the present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement the assumed independent strain field is divided into a lower order part and a higher order part subsequently the lower order part is set equal to the displacement dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix the strains and the determinant of the jacobian matrix are assumed to vary linearly in the thickness direction this assumption allows analytical integration through thickness independent of the number of plies a nine node element with a judiciously chosen set of higher order assumed strain field is developed numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation

two higher order shell finite elements with stabilization matrix a 32 node three dimensional solid element and a 16 node degenerate solid element that are applicable to analysis of thin shell structural problems are presented in this paper both elements are formulated by using the hellinger reissner principle with independent strain the assumed independent strain field is divided into higherand lower order polynomial terms the element stiffness matrix associated with the higher order assumed strain plays the role of the stabilization matrix various types of the higher order assumed strain are tested for the present elements the resulting finite element models require much less time to compute the element stiffness matrix than the corresponding conventional mixed models or assumed displacement models with a full gaussian quadrature rule numerical results demonstrate that with a properly chosen set of higher order assumed strain the present elements produce reliable and very accurate solutions even for very thin plates and thin shells with deeply curved geometry

higher order mitc general shell elements two mixed interpolated general shell finite elements for non linear analysis a 9 node element and a 16 node element are presented the elements are based on the mixed interpolation of tensorial components mitc approach in which the covariant strain component fields for the in plane and shear actions are interpolated and tied to the also interpolated displacement field both the 9 node element referred to as the mitc9 element and the 16 node element referred to as the mitc16 element are tested numerically and found to have high predictive capabilities

efficient linear and nonlinear heat conduction with a quadrilateral element a method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one point quadrature the stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter it is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values in fact the values 3 2 and 1 for the normalized stabilization parameter lead to the 5 point finite difference 9 point finite difference and fully integrated finite element operators respectively for rectangular meshes numerical experiments reported here show that the three have identical rates of convergence in the l2 norm eigenvalues of the element matrices which are needed for stability limits are also given numerical applications are used to show that the method yields accurate solutions with large increases in efficiency particularly in nonlinear problems

asplund spaces characterized by rich families and separable reduction of frechet subdifferentiability abstract asplund property of a banach space x is characterized by the existence of a rich family in the product x x consisting of some carefully chosen separable subspaces this structural result is then used to add a lot of precision and simplicity to the known separable reductions of frechet subdifferentials

exploratory projection pursuit abstract a new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods a number of practical issues concerning its application are addressed a connection to multivariate density estimation is established and its properties are investigated through simulation studies and application to real data the goal of exploratory projection pursuit is to use the data to find low one two or three dimensional projections that provide the most revealing views of the full dimensional data with these views the human gift for pattern recognition can be applied to help discover effects that may not have been anticipated in advance since linear effects are directly captured by the covariance structure of the variable pairs which are straightforward to estimate the emphasis here is on the discovery of nonlinear effects such as clustering or other general nonlinear associations among the variables although arbitrary

phase type distributions and representations some results and open problems for system theory in this paper we consider phase type distributions these distributions correspond to the random hitting time of an absorbing markov chain they are used for modelling various random times in particular those which appear in manufacturing systems as processing times times to failure repair times etc the markovian nature of these distributions allows the use of very efficient matrix based computer methods for performance evaluation in this paper we give a system theory oriented introduction to phase type distributions we concentrate mainly on the representation problem which consists of finding a markov chain associated with some phase type distribution this is a realization problem in the sense of system theory with a lot of links with the classical linear system theory but also with a number of constraints which make the problem harder but more interesting indeed this problem has strong connections with the positive realization problem in control theory the paper recalls known results gives s

decompositions of preduals of jbw and jbw algebras abstract we prove that the predual of any jbw algebra is a complex 1 plichko space and the predual of any jbw algebra is a real 1 plichko space i e any such space has a countably 1 norming markushevich basis or equivalently a commutative 1 projectional skeleton this extends recent results of the authors who proved the same for preduals of von neumann algebras and their self adjoint parts however the more general setting of jordan algebras turned to be much more complicated we use in the proof a set theoretical method of elementary submodels as a byproduct we obtain a result on amalgamation of projectional skeletons

model reduction of neutral linear and nonlinear time invariant time delay systems with discrete and distributed delays the problem of model reduction by moment matching for linear and nonlinear differential time delay systems is studied the class of models considered includes neutral differential time delay systems with discrete delays and distributed delays the description of moment is revisited by means of a sylvester like equation for linear time delay systems and by means of the center manifold theory for nonlinear time delay systems in addition the moments at infinity are characterized for both linear and nonlinear time delay systems parameterized families of models achieving moment matching are given the parameters can be exploited to derive delay free reduced order models or time delay reduced order models with additional properties e g interpolation at an arbitrary large number of points finally the problem of obtaining a reduced order model of an unstable system is discussed and solved

moments of random variables a systems theoretic interpretation moments of continuous random variables admitting a probability density function are studied we show that under certain assumptions the moments of a random variable can be characterized in terms of a sylvester equation and of the steady state output response of a specific interconnected system this allows to interpret well known notions and results of probability theory and statistics in the language of systems theory including the sum of independent random variables the notion of mixture distribution and results from renewal theory the theory developed is based on tools from center manifold theory the theory of the steady state response of nonlinear systems and the theory of output regulation our formalism is illustrated by means of several examples and can be easily adapted to the case of discrete and multivariate random variables

if cp x is strongly dominated by a second countable space then x is countable abstract we establish that a tychonoff space x is countable if and only if c p x is strongly dominated by a second countable space the same is true for a compact space k such that c p k 0 1 is strongly dominated by a second countable space we also prove that strong domination by a second countable space of the complement of the diagonal of a tychonoff space x implies that x is an 0 space our results solve several published open questions

monotone retractability and retractional skeletons abstract we prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton in particular a compact space is monotonically retractable if and only if it is corson this gives an answer to a question of r rojas hernandez and v v tkachuk further we apply this result to characterize retractional skeleton using a topology on the space of continuous functions answering thus a question of the first author and a related question of w kubi

a monotone version of the sokolov property and monotone retractability in function spaces abstract we introduce the monotone sokolov property and show that it is dual to monotone retractability in the sense that x is monotonically retractable if and only if c p x is monotonically sokolov besides a space x is monotonically sokolov if and only if c p x is monotonically retractable monotone retractability and monotone sokolov property are shown to be preserved by r quotient images and f subspaces furthermore every monotonically retractable space is sokolov so it is collectionwise normal and has countable extent we also establish that if x and c p x are lindelof spaces then they are both monotonically retractable and have the monotone sokolov property an example is given of a space x such that c p x has the lindelof property but neither x nor c p x is monotonically retractable we also establish that every lindelof space with a unique non isolated point is monotonically retractable on the other hand each lindelof space with a unique non isolated point is monotonically sokolov

c0 finite element discretization of kirchhoff s equations of thin plate bending an alternative formulation of kirchhoff s equations is given which is amenable to a standard c 0 finite element discretization in this formulation the potential energy of the plate is formulated entirely in terms of rotations whereas the deflections are the outcome of a subsidiary problem the nature of the resulting equations is such that c 0 interpolation can be used on both rotations and deflections in particular general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method unlike other finite element methods which are based on three dimensional or mindlin formulations the present approach deals directly with kirchhoff s equations of thin plate bending excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns

model reduction by matching the steady state response of explicit signal generators model reduction by moment matching for interpolation signals which do not have an implicit model i e they do not satisfy a differential equation is considered particular attention is devoted to discontinuous possibly periodic signals the notion of moment is reformulated using an integral matrix equation it is shown that under specific conditions the new definition and the one based on the sylvester equation are equivalent new parameterized families of models achieving moment matching are given the results are illustrated by means of a numerical example

locking free curved beam element based on curvature the formulation of a curved beam element with 3 nodes for curvature to eliminate the shear membrane locking phenomenon is presented the element is based on curvature so that it may represent the bending energy fully and the shear membrane strain energy is incorporated into the formulation by the equilibrium equations to deal with general boundary conditions a transformation matrix between nodal curvature and nodal displacement vector is introduced several examples are presented in order to verify the element formulation and its analytical capability the solutions obtained reveal that the element describes the curved beam behaviour quite correctly and efficiently showing no locking phenomena and that it is also applicable to the analysis of both thin and thick curved beams

families of continuous retractions and function spaces in this paper we mainly study certain families of continuous retractions r skeletons having some rich properties it is shown that if the space x has a full r skeleton then its alexandroff duplicate also has a full r skeleton in a very similar way it is proved that the alexandroff duplicate of a monotonically retractable space is monotonically retractable by using monotonically retractable spaces we solve a question posed by r z buzyakova in 7 concerning the alexandroff duplicate of a space the notion of q skeleton is introduced and it is shown that every compact subspace of cp x is corson when x has a full q skeleton the notion of strong r skeleton is also introduced to answer a question suggested by f casarrubias segura and the second author in 8 certainly it is established that a space x is monotonically sokolov if and only if it is monotonically monolithic and has a strong r skeleton the techniques used here allow us to give a topological proof of a result of i bandlow 5 who used elementary submodels and uniform spaces

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

explicit algorithms for the nonlinear dynamics of shells abstract a finite element formulation and algorithm for the nonlinear analysis of the large deflection materially nonlinear response of impulsively loaded shells is presented a unique feature of this algorithm is the use of a bilinear four node quadrilateral element with single point quadrature and a simple hourglass control which is orthogonal to rigid body modes on an element level and does not compromise the consistency of the equations the geometric nonlinearities are treated by using a corotational description wherein a coordinate system that rotates with the material is embedded at the integration point thus the algorithm is directly applicable to anisotropic materials without any corrections for frame invariance of material property tensors this algorithm can treat about 200 element time steps per cpu second on a cyber 170 730 computer in the explicit time integration mode numerous results are presented for both elastic and elastic plastic problems with large strains that show that the method in most cases is comparable in accuracy with an earlier version of this algorithm employing a cubic triangular plate shell element but substantially faster

a faddeev sequence method for solving lyapunov and sylvester equations lyapunov and sylvester equations play an important role in linear systems theory this paper deals with a method of solving such equations of the form ap pb k and p apb k with a rm m b rn n and p k rm n by exploiting the matrix algebra structure of the problem no use is made of kronecker products and the largest matrices occurring in the algorithms are of sizes m m n n and m n the faddeev method for matrix inversion lies at the very heart of the algorithms presented it occurs on several levels of the problem for the matrices a and b and for the lyapunov and sylvester operators the resulting algorithms are capable of solving the equations in a finite number of recursion steps they are very much apt for symbolic calculation it is shown how a solution can be quickly obtained for an equation with an arbitrary right hand side k provided a solution is known for a right hand side xyt of rank 1 where a x and bt y are reachable pairs the concept of a faddeev reachability matrix introduced here turns out to be very useful it establishes a close connection between the controller canonical companion form of a reachable pair a b and the faddeev sequence of a if a is already on controller form then its faddeev sequence takes on an especially simple form also in the symmetric case where a bt many important simplifications arise for this case alternative algorithms that require less iterations are developed the paper concludes with some examples concerning the symbolic solution of the lyapunov equation ap pat bbt with a b on controller form showing the potential of the algorithms

characterizing corson and valdivia compact spaces abstract we give a new characterization of valdivia compact spaces a compact space is valdivia if and only if it has a dense commutatively monotonically retractable subspace this result solves problem 5 12 from 6 besides we introduce the notion of full c skeleton and prove that a compact space is corson if and only if it has a full c skeleton

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

on using degenerated solid shell elements in adaptive refinement analysis three different degenerated shell elements are studied in an adaptive refinement procedure for the solution of shell problems the stress recovery procedure expressed in a convective patch co ordinate system is used for the construction of continuous smoothed stress fields for the a posteriori error estimation the performance of the stress recovery procedure the error estimator and the adaptive refinement strategy are tested by solving three benchmark shell problems it is found that when adaptive refinement is used the adverse effects of boundary layers and stress singularities are eliminated and all the elements tested are able to achieve their optimal convergence rates it is also found that the accuracy of the shell elements increases with the number of polynomial terms included in the stress and strain approximations in addition if complete lagrangian polynomial terms are used the element will be less sensitive to shape distortion than the one in which only complete polynomial terms are employed copyright 1999 john wiley sons ltd

a consistent control of spurious singular modes in the 9 node lagrange element for the laplace and mindlin plate equations abstract when 2 2 quadrature is used with the 9 node lagrange element which is essential in c 0 plate elements to avoid locking spurious singular modes appear on the element level which can lead to singularity or near singularity of the global equations here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired hence the procedure passes the patch test applications to the diffusion and mindlin plate equations are presented results show that h 3 convergence in the l 2 norm is almost retained

overlapping block balanced canonical forms for various classes of linear systems abstract through the use of balanced realizations it has been possible to derive parametrizations and canonical forms for various classes of minimal linear systems of given dimension a possible problem of these parametrizations is that they are not overlapping this could be a drawback for the application of balanced parametrizations in such areas as system identification model reduction and optimization it is the topic of this paper to derive overlapping parametrizations which are closely related to the existing balanced parametrizations we first introduce input normal canonical forms which are defined through a novel way of choosing nice selections of columns of the reachability matrix these canonical forms provide overlapping parametrizations in the sense that they form a real analytic atlas of the manifold of systems which are considered then we introduce so called block balanced input normal forms which use the previously constructed input normal forms as building blocks the classes of systems for which such parametrizations are given are the stable minimal systems positive real minimal systems bounded real minimal systems and the class of all minimal systems of given mcmillan degree the results include both the single input single output and the multivariable case in the single input single output case however the issue of choosing nice selections of columns does not occur therefore in this case the derivation and presentation of the results is considerably simplified

control of spurious modes in the nine node quadrilateral element the nine node quadrilateral is much more accurate than its eight node relative if elements are non rectangular however the nine node element may display spurious low energy modes under 2 2 gauss quadrature these modes can be controlled by using the 3 3 quadrature rule but at added cost this paper investigates two inexpensive control devices that can be used with 2 2 gauss quadrature

direct evaluation of the worst imperfection shape in shell buckling abstract for the evaluation of the imperfection sensitivity of elastic and elastic plastic shells a fully nonlinear finite element method has been developed that directly gives the worst imperfection shape connected to the ultimate limit load the approach uses no approximations such as asymptotical theories or computations in the deep postcritical range the key point of the method is the description of imperfections as nodal degrees of freedom at the element level these unknown quantities are implemented by isoparametric shape functions in a finite shell element including finite rotations and thickness stretch the ultimate buckling load and the corresponding worst imperfection shape is defined by two different criteria and numerically determined by an extended system of nonlinear equations in the computation of the structurally stable collapse the deflections the imperfection shape the eigenvector and the lowest possible load level are obtained the method is illustrated by several numerical examples

banach spaces with projectional skeletons a projectional skeleton in a banach space is a directed family of projections onto separable subspaces covering the entire space the class of banach spaces with projectional skeletons is strictly larger than the class of plichko spaces i e banach spaces with a countably norming markushevich basis we show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to spaces we characterize the existence of a projectional skeleton in terms of elementary substructures providing simple proofs of known results concerning weakly compactly generated spaces and plichko spaces we prove a preservation result for plichko banach spaces involving transfinite sequences of projections as a corollary we show that a banach space is plichko if and only if it has a commutative projectional skeleton

a geometrically non linear tensorial formulation of a skewed quadrilateral thin shell finite element a 48 degree of freedom d o f skewed quadrilateral thin shell finite element including the effect of geometrical non linearity is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates the directions of the curvilinear co ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element in the present case of a skewed quadrilateral with non orthogonal curvilinear coordinates the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish such as in the case of orthogonal co ordinates the tensor form is used in the setup of the shape functions geometric derivatives stiffness matrix and computer code this allows for the treatment of shells with irregular shapes and variable curvatures to evaluate the efficiency and accuracy of this formulation a systematic list of examples is chosen i linear and non linear static analysis of square and rhombic plates cylindrical and spherical shells ii linear vibrations of trapezoidal flat and curved plates iii large amplitude vibrations of a rhombic plate for the square plate and cylindrical and spherical shell shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element all results are compared with alternative available solutions including those obtained using regular rectangular meshes pinched thin cylindrical and spherical shells are studied using different skewed meshes and various gauss integration meshes and no membrane locking phenomenon is observed

state space calculations for discrete probability densities abstract state space methods have proved to be powerful theoretical and computational tools in a number of areas of applications in particular filtering and control theory in this paper we advocate the use of state space methods for the study of discrete probability densities on the set 0 1 2 the fundamental approach is to consider the class d of all discrete probability densities that can be represented as the impulse response convolution kernel of a finite dimensional discrete time state space system we show that all standard operations such as the calculation of moments convolution scaling translation product etc can be carried out using system representations