comprehensive analysis of a new fuzzy rule interpolation method the first published result in fuzzy rule interpolation was the spl alpha cut based fuzzy rule interpolation termed as kh fuzzy rule interpolation originally devoted for complexity reduction a modified version of the kh approach has been presented by yam et al 1999 which eliminates the subnormality problem while at the same time intending to maintain the advantageous computational properties of the original method this paper presents a comprehensive analysis of the new method which includes detailed comparison with the original kh fuzzy rule interpolation method concerning the explicit functions of the methods preservation of piecewise linearity and stability the fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques all these comparisons shows that the new method preserves the advantageous properties of the kh method and alleviates its most significant disadvantage the problem of subnormality

imposing dirichlet boundary conditions in the extended finite element method this paper is devoted to the imposition of dirichlet type conditions within the extended finite element method x fem this method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces imposing neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh observed numerically in earlier papers on the contrary much less work has been devoted to dirichlet boundary conditions for the x fem or the limiting case of stiff boundary conditions in this paper we introduce a strategy to impose dirichlet boundary conditions while preserving the optimal rate of convergence the key aspect is the construction of the correct lagrange multiplier space on the boundary as an application we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding rtm process while avoiding remeshing the case of inner conditions is also discussed as well as two important practical cases material interfaces and phase transformation front capturing copyright 2006 john wiley sons ltd

on some techniques for approximating boundary conditions in the finite element method we discuss the stabilization of finite element methods in which essential boundary conditions are approximated by babuska s method of lagrange multipliers and we show that there is a close connection with this technique and a classical method by nitsche

crack tip enrichment in the xfem using a cutoff function we consider a variant of the extended finite element method xfem in which a cutoff function is used to localize the singular enrichment surface the goal of this variant is to obtain numerically an optimal convergence rate while reducing the computational cost of the classical xfem with a fixed enrichment area we give a mathematical result of quasi optimal error estimate one of the key points of this paper is to prove the optimality of the coupling between the singular and the discontinuous enrichments finally we present some numerical computations validating the theoretical result these computations are compared with those of the classical xfem and a non enriched method copyright 2008 john wiley sons ltd

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

the theory of v bezoutians and its applications abstract some propositions of the theory of v bezoutians are presented as an application the following problem is considered to construct an appropriate pontryagin space in which a given matrix boundary value problem containing the eigenvalue parameter in the boundary conditions is self adjoint the solution of this problem is given in three special cases with the help of v bezoutians of matrix polynomials entering the boundary conditions

adaptively weighted numerical integration in the finite cell method abstract with adaptively weighted aw numerical integration for a given set of quadrature nodes order and domain of integration the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense the moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain and then are corrected for the deviation from the original domain using shape sensitivity analysis in this paper we demonstrate the application of aw integration scheme in the context of the finite cell method which must perform numerical integration over arbitrary domains without meshing the standard integration technique employed in fcm is the characteristic function method that converts the continuous integrand over a complex domain into a discontinuous integrand over a simple box domain then well known integrand adaptivity techniques are employed to integrate the resulting discontinuous integrand over the box domain although this method is simple to implement it becomes computationally very expensive for realistic complex 3d domains such as sculptures bones and engines in contrast in aw scheme the quadrature weights directly adapt to the complex geometric domain without the need to making the integrand discontinuous leading to superior computational properties in this paper we demonstrate the computational efficiency of aw over the characteristic function method as it requires fewer subdivisions and less time to achieve a given accuracy in both two and three dimensions in addition aw offers a number of advantages including flexibility in the choice of quadrature points and basis functions

a symmetric method for weakly imposing dirichlet boundary conditions in embedded finite element meshes summary in this paper we propose a way to weakly prescribe dirichlet boundary conditions in embedded finite element meshes the key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation relatively small and can be fixed a priori moreover the formulation is symmetric for symmetric problems an additional element discontinuous stress field is used to enforce the boundary conditions in the poisson problem additional terms are required in order to guarantee stability in the convection diffusion equation and the stokes problem the proposed method is then easily extended to the transient navier stokes equations copyright 2012 john wiley sons ltd

boundary lagrange multipliers in finite element methods error analysis in natural norms a finite element procedure for circumventing the babuska brezzi condition in mixed formulations with lagrange multipliers defined on the boundary is presented residual terms constructed from the euler lagrange equations are added to the classical galerkin formulation in order to attain coercivity in a mesh dependent norm convergence is proven for the primal variable and the multiplier in the natural mesh independent norm of the problem generalizing results of a previous paper

how to count zeroes of polynomials on quadrature domains using the bezout matrix abstract classically the bezout matrix or simply bezoutian of two polynomials is used to locate the roots of the polynomial and in particular test for stability in this paper we develop the theory of bezoutians on real riemann surfaces of dividing type the main result connects the signature of the bezoutian of two real meromorphic functions to the topological data of their quotient which can be seen as the generalization of the classical cauchy index as an application we propose a method to count the number of zeroes of a polynomial in a quadrature domain using the inertia of the bezoutian we provide examples of our method in the case of simply connected quadrature domains

on a class of entire matrix function equations abstract this paper treats a class of linear entire matrix function equations which appear naturally in the study of krei n orthogonal matrix functions necessary and sufficient conditions for solvability are given in terms of root functions of the coefficients

domain integral formulation for stress intensity factor computation along curved three dimensional interface cracks new domain integrals for extracting mixed mode stress intensity factors along curved three dimensional bimaterial interface cracks are derived in the derivation the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are imposed along a curved crack front the general crack tip interaction integral a contour integral surrounding a point on the crack front which is evaluated in the limit as the contour is shrunk onto the crack tip is then expressed in domain form which is more suitable for numerical computation a consequence of imposing the auxiliary fields along a curved crack front is that the auxiliary stress fields do not satisfy equilibrium and the auxiliary strain fields do not satisfy compatibility the terms which arise due to the lack of equilibrium and compatibility are not sufficiently singular to contribute to the crack tip interaction integral or to affect its path independence however these terms become important when domain integral representations are introduced because they involve fields which are not asymptotically close to the crack tip in order to compute the pointwise stress intensity factors along the crack front the domain integrals are evaluated as a post processing step in the finite element method in the numerical results it is demonstrated that it is crucial to incorporate the terms that arise due to lack of equilibrium and compatibility of the auxiliary fields especially in regions where the local crack front curvature is high in the paper we present two numerical examples as a benchmark we first consider the problem of a penny shaped interface crack embedded in a cylinder the results for the complex stress intensity factor and phase angle are found to be in excellent agreement with the analytical solution the problem of an elliptical crack embedded between two dissimilar isotropic materials is also considered and the results are discussed

spectrum separation and inertia for operator polynomials abstract problems on spectrum separation and inertia of operator polynomials are solved using the concept of bezoutian of operator polynomials the main results extend those previously known for matrix polynomials applications of the main results include differential equations with constant coefficients and some problems concerning orthogonal operator polynomials

approximation by pseudo linear operators the approximation operators provided by classical approximation theory use exclusively as underlying algebraic structure the linear structure of the reals also they are all linear operators we address in the present paper the following problems need all the approximation operators be linear is the linear structure the only one which allows us to construct particular approximation operators as an answer to this problem we propose new particular pseudo linear approximation operators which are defined in some ordered semirings we study these approximations from a theoretical point of view and we obtain that these operators have very similar properties to those provided by classical approximation theory in this sense we obtain uniform approximation theorems of weierstrass type and jackson type error estimates in approximation by these operators

stabilizability controllability and observability of linear continuous time systems defined over a commutative banach algebra abstract this paper is concerned with the controllability observability and stabilizability for linear continuous time systems defined over a hermitian commutative banach algebra practical applications of such systems can be found in the joint work of kamen and green it is shown that after gelfand transformation the abovementioned three properties of such systems are reduced to the corresponding ones in finite dimensional linear system theory in the process we basically solve a problem posed by kamen and green

a new face oriented stabilized xfem approach for 2d and 3d incompressible navier stokes equations abstract we develop a new stabilized xfem based fixed grid approach for the transient incompressible navier stokes equations using cut elements our framework is based on a new flexible strategy to handle several degrees of freedom dofs at nodes required for complex shaped embedded meshes as they occur for fixed grid fluid structure interaction problems boundary conditions on embedded boundaries are imposed weakly using a nitsche type approach ghost penalty terms for velocity and pressure are added for stability reasons and to improve the conditioning of the system matrix the idea of ghost penalties previously developed for stokes problems is extended to the incompressible navier stokes equations by using face oriented fluid stabilizations for both viscous and convective dominated flows furthermore the need for additional terms to enforce boundary conditions for non viscous flows is addressed a detailed numerical study of our stabilized fluid formulation including studies of nitsche s parameter and the ghost penalty parameter shows optimal error convergence and a good system conditioning in the viscous and the convective dominated cases compared to other fixed grid fluid formulations our method is much more accurate and less sensitive to the location of the interface regarding the accuracy and the sensitivity with respect to the interface position a clear improvement could be observed for the viscous and pressure fluxes as well as for the imposition of the boundary condition results of a transient two dimensional high reynolds number flow over a cylinder and the flow over a thick plate in 3d confirm the applicability of the proposed method

a new fictitious domain approach inspired by the extended finite element method the purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by moes dolbow and belytschko in internat j numer methods engrg 46 1999 pp 131 150 an optimal method is obtained thanks to an additional stabilization technique some a priori estimates are established and numerical experiments illustrate different aspects of the method the presentation is made on a simple poisson problem with mixed neumann and dirichlet boundary conditions the extension to other problems or boundary conditions is quite straightforward

inertia and controllability in infinite dimensions on demontre des theoremes d inertie pour des operateurs lineaires bornes agissant sun un espace de hilbert complexe

fuzzy systems as universal approximators an additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy an additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input output state space and averaging patches that overlap the fuzzy system computes a conditional expectation e y x if we view the fuzzy sets as random sets each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state space geometry neural or statistical clustering systems can approximate the unknown fuzzy patches from training data these adaptive fuzzy systems approximate a function at two levels at the local level the neural system approximates and tunes the fuzzy rules at the global level the rules or patches approximate the function

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

notes on the approximation rate of fuzzy kh interpolators this paper investigates the approximation behaviour of the koczy hirota kh interpolative fuzzy controllers first in accordance with the remarks in fuzzy sets and systems 125 1 2002 105 it is pointed out that it is a fuzzy generalization of the shepard operator shepard operator has thoroughly studied by approximation theorist since the mid 1970s exploiting the aforementioned relationship we establish analog results on the approximation rate of kh controllers the optimal order and class of approximation saturation problem are determined for certain values of the exponent corresponding results on the modified alpha cut based interpolation method being an improvement of the kh interpolator are also provided the results offer trade off facilities between approximation accuracy and the number of rules as a consequence the necessary and sufficient number of rules can be determined for a prescribed accuracy

the hp d adaptive finite cell method for geometrically nonlinear problems of solid mechanics summary the finite cell method fcm combines the fictitious domain approach with the p version of the finite element method and adaptive integration for problems of linear elasticity it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved this article presents the integration of the fcm into the framework of nonlinear finite element technology however the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map as a consequence of the weak penalization nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries leading to a low algebraic rate of convergence therefore the fcm approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp d method which synergetically uses the h adaptivity of the integration scheme numerical experiments show that the hp d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map the hp d adaptive fcm is thus able to restore high convergence rates for the geometrically nonlinear case while preserving the easy meshing property of the original fcm accuracy and performance of the present scheme are demonstrated by several benchmark problems in one two and three dimensions and the nonlinear simulation of a complex foam sample copyright 2011 john wiley sons ltd

analysis of the fully discrete fat boundary method the fat boundary method is a method of the fictitious domain class which was proposed to solve elliptic problems in complex geometries with non conforming meshes it has been designed to recover optimal convergence at any order despite of the non conformity of the mesh and without any change in the discrete laplace operator on the simple shape domain we propose here a detailed proof of this high order convergence and propose some numerical tests to illustrate the actual behaviour of the method

birkhoff james e orthogonality sets of vectors and vector valued polynomials abstract consider a complex normed linear space x and let x with 0 motivated by recent works on rectangular matrices and on normed linear spaces we study the birkhoff james e orthogonality set of with respect to give an alternative definition for this set and explore its rich structure we also introduce the birkhoff james e orthogonality set of polynomials in one complex variable whose coefficients are members of x and survey and record extensions of results on matrix polynomials to these vector valued polynomials

fictitious domain finite element methods using cut elements i a stabilized lagrange multiplier method we propose a fictitious domain method where the mesh is cut by the boundary the primal solution is computed only up to the boundary the solution itself is defined also by nodes outside the domain

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

imposing dirichlet boundary conditions in hierarchical cartesian meshes by means of stabilized lagrange multipliers this is the pre peer reviewed version of the following article tur m albelda j nadal e and rodenas j j 2014 imposing dirichlet boundary conditions in hierarchical cartesian meshes by means of stabilized lagrange multipliers int j numer meth engng 98 399 417 which has been published in final form at http dx doi org 10 1002 nme 4629 this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

the intersection of the spectra of operator completions abstract let a b h b b k c b k h x b h k and m x a c x b be an operator completion of the partial operator matrix q a c b in this note we consider the intersection of the spectra of mx when x runs over b h k denote by a b c the set of scalar c such that either a c or b c is not right invertible we prove that x b h k m x a b c if dim r c a b c a b c if dim r c where a b c is the set of scalars c such that r a c h r b c k and ind a ind b 0 we also prove that the intersection is empty if and only if a c and b c are controllable

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

some properties of linear systems defined over a commutative banach algebra abstract we consider linear systems defined over a commutative hermitian banach algebra in this case the problem about spectrum displacement posed by kaashoek van der mee and rodman can be solved results related to stability stabilizability and detectability for such systems are obtained which are a natural extension of the corresponding ones in the finite dimensional case

a lagrange multiplier method for the finite element solution of elliptic interface problems using non matching meshes in this paper we propose a lagrange multiplier method for the finite element solution of multi domain elliptic partial differential equations using non matching meshes the interface lagrange multiplier is chosen with the purpose of avoiding the cumbersome integration of products of functions on unrelated meshes e g we will consider global polynomials as multiplier the ideas are illustrated using poisson s equation as a model and the proposed method is shown to be stable and optimally convergent numerical experiments demonstrating the theoretical results are also presented

kernel shapes of fuzzy sets in fuzzy systems for function approximation the shapes of if part fuzzy sets affect the approximating capability of fuzzy systems in this paper the fuzzy systems with the kernel shaped if part fuzzy sets are built directly from the training data it is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single input single output siso case on the basis of these rates the relationships between the approximating capability and the shapes of if part fuzzy sets are developed for the fuzzy systems furthermore the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions the theoretical results are confirmed from the simulation data in addition the estimations of the uniform approximation rates are extended to the multi input single output miso case

xfem based fictitious domain method for linear elasticity model with crack reduction of computational cost of solutions is a key issue for crack identification or crack propagation problems one of the solutions is to avoid remeshing the domain when the crack position changes or when the crack extends to avoid remeshing we propose a new finite element approach for the numerical simulation of discontinuities of displacements generated by cracks inside elastic media the approach is based on a fictitious domain method originally developed for dirichlet conditions for the poisson problem and for the stokes problem which is adapted to the neumann boundary conditions of crack problems the crack is represented by level set functions numerical tests are made with a mixed formulation to emphasize the accuracy of the method as well as its robustness with respect to the geometry enforced by a stabilization technique in particular an inf sup condition is theoretically proven for the latter a realistic simulation with a uniformly pressurized fracture inside a volcano is given for i

optimal convergence analysis for the extended finite element method we establish some optimal a priori error estimate on some variants of the extended finite element method xfem namely the xfem with a cut off function and the standard xfem with a fixed enrichment area the results are established for the lame system homogeneous isotropic elasticity and the laplace problem the convergence of the numerical stress intensity factors is also investigated we show some numerical experiments which corroborate the theoretical results

cutfem discretizing geometry and partial differential equations we discuss recent advances on robust unfitted finite element methods on cut meshes these methods are designed to facilitate computations on complex geometries obtained for example from computer

controllability of linear systems in banach spaces the problem of controllability of linear systems in banach spaces is considered first some properties of dual semigroups with respect to lebesgue measure is presented then based on the properties the criteria for controllability in reflexive banach spaces are extended to general banach spaces and some new criteria for controllability are established an example is presented to show that the scope of controllable systems can be enlarged if the non traditional space of control functions is used

stabilized method of imposing dirichlet boundary conditions using a recovered stress field abstract this paper proposes a new formulation to impose dirichlet boundary conditions on immersed boundary cartesian finite element meshes the method uses a recovered stress field calculated by superconvergent patch recovery to stabilize the lagrange multiplier formulation of the problem the optimal convergence of the method and the convergence of the proposed iterative procedure are demonstrated the proposed method is also suitable for problems with non linear material behavior some numerical examples are included to confirm the theoretical results

a fictitious domain approach for a mixed finite element method solving the two phase stokes problem with surface tension forces abstract in this article we study a mixed finite element formulation for solving the stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor on an interface that splits the domain into two subdomains equality of velocities is assumed at the interface the interface conditions are taken into account with multipliers a suitable lagrangian functional is introduced for deriving a weak formulation of the problem a specificity of this work is the consideration of the interface with a fictitious domain approach the latter is inspired by the xfem approach in the sense that cut off functions are used but it is simpler to implement since no enrichment by singular functions is provided in that context getting convergence for the dual variables defined on the interface is non trivial for that purpose an augmented lagrangian technique stabilizes the convergence of the multipliers which is important because their value would determine the dynamics of the interface in an unsteady framework theoretical analysis is provided where we show that a discrete inf sup condition independent of the mesh size is satisfied for the stabilized formulation this guarantees optimal convergence rates that we observe with numerical tests the capacity of the method is demonstrated with robustness tests and with an unsteady model tested for deformations of the interface that correspond to ellipsoidal shapes in dimension 2

a fictitious domain method for the simulation of thermoelastic deformations in nc milling processes summary this paper presents a higher order finite element approach for the simulation of heat diffusion and thermoelastic deformations in nc milling processes the inherent continuous material removal in the process of the simulation is taken into account via continuous removal dependent refinements of a paraxial hexahedron base mesh covering a given workpiece these refinements rely on isotropic bisections of these hexahedrons along with subdivisions of the latter into tetrahedrons and pyramids in correspondence to a milling surface triangulation obtained from the application of the marching cubes algorithm the resulting mesh is employed for an element wise defined characteristic function for the milling dependent workpiece within that paraxial hexahedron base mesh using this characteristic function a higher order fictitious domain method is used to compute the heat diffusion and thermoelastic deformations where the corresponding ansatz spaces are defined for some hexahedron based refinement of the base mesh numerical experiments compared to real physical experiments exhibit the applicability of the proposed approach to predict deviations of the milled workpiece from its designed shape due to thermoelastic deformations in the process this article is protected by copyright all rights reserved

bezoutians of rational matrix functions matrix equations and factorizations abstract the notion of bezoutian for a quadruple of rational matrix functions introduced by the authors in previous works is shown to be an adequate connecting link between certain factorization problems for rational matrix functions and quadratic and linear matrix equations particular attention is given to various types of coprime factorizations a characterization of bezoutians as angle operators between certain pairs of subspaces is also given

bezout equation vandermonde operators and common multiples for operator polynomials soit h un espace de hilbert complexe on considere des polynomes d operateurs de type p j 0 m i p j ou p j sont des operateurs agissant dans h et est un parametre complexe on considere des p pour lequel le spectre p est un ensemble compact

calculation of fracture mechanics parameters for an arbitrary three dimensional crack by the equivalent domain integral method summary in this paper an equivalent domain integral edi method and the attendant numerical algorithms arc presented for the computation of a near crack tip field parameter the vector je integral and its variation along the front of an arbitrary three dimensional crack in a structural component account is taken of possible non elastic strains present in the structure in this case the near tip je values may be significantly different from the far field values jf especially under non proportional loading

resultant operators and the bezout equation for analytic matrix functions i this paper is a continuation of 4 it contains our results on resultant operators for a family of matrix functions that are analytic in a finitely connected domain the proofs are based on the results about the bezout equation obtained in 4 it is assumed that the reader is familiar with the concepts and results from 4 let f denote a cauchy contour in the complex plane consisting of several non intersecting simple smooth closed contours which form the positively oriented boundary of a finitely connected bounded domain a throughout this chapter we assume for convenience that 0 e a the general case can be obtained by a shift in the complex plane let a a be regular n x n matrix functions which are analytic in a and continuous in a u r and assume that c a n r 3 the paper consists of two sections in section 1 we show that the role of the resultant operator of the matrix functions a a is played by the operator r l t l 1 p co defined by

on strong controllability of infinite dimensional linear systems abstract if an infinite dimensional linear system is strongly controllable i e every state can be reached from any state in finite time then it is strongly controllable in uniform finite time

bezout and hankel matrices associated with row reduced matrix polynomials barnett type formulas abstract based on the approach introduced by b d o anderson and e i jury in 1976 the definition of finite hankel and bezout matrices corresponding to matrix polynomials is extended to the case where the denominator of the corresponding rational matrix function is not necessarily monic but is row reduced the matrices introduced keep most of the well known properties that hold in the monic case in particular we derive extensions of formulas giving a connection with polynomials in the companion matrix usually called barnett formulas of the inversion theorem and of formulas concerning alternating products of hankel and bezout matrices

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

generalized bezoutian and matrix equations abstract a natural generalization of the classical bezout matrix of two polynomials is introduced for a family of several matrix polynomials the main aim of the paper is to show that this generalized bezoutian serves as an adequate connecting link between the class of equations in matrix polynomials m y z l r and the class of linear matrix equations ax xb c each equation in one of these classes is coupled with a certain equation in the other class so that for each couple the generalized bezoutian corresponding to a solution y z of the equation in matrix polynomials is a solution of the matrix equation and conversely any solution x of the matrix equation is a generalized bezoutian corresponding to a certain solution of the equation in matrix polynomials in particular either both equations are solvable or both have no solutions explicit formulas connecting the solutions of the two equations are given also various representation formulas for the generalized bezoutian are derived and its relation to the resultant matrix and the greatest common divisor of several matrix polynomials is discussed

common eigenvalues divisors and multiples of matrix polynomials a review abstract the main objective of this paper is to review some results obtained in the last decade using methods of spectral theory and concerning common multiples common divisors and common eigenvalues for matrix polynomials this includes discussion of resultant and bezoutian matrices for matrix polynomials and descriptions of their kernels in terms of spectral data some extensions to operator polynomials whose coefficients are bounded linear operators on a hilbert space are also included

stability of interpolative fuzzy kh controllers the classical approaches in fuzzy control zadeh and mamdani deal with dense rule bases when this is not the case i e in sparse rule bases one has to choose another method fuzzy rule interpolation proposed first by koczy and hirota internat j approx reason 9 1993 197 225 offers a possibility to construct fuzzy controllers kh controllers under such conditions the main result of this paper shows that the kh interpolation method is stable it also contributes to the application oriented use of balazs shepard interpolation operators investigated extensively by researchers in approximation theory the numerical analysis aspect of the result contributes to the well known problem of finding a stable interpolation method in the following sense we would like to approximate a function that is only known at distinct points e g where it can be measured since measurement errors cannot be eliminated in practice it is a natural requirement that the interpolation method should be stable independently from the selection of measurement points the classical interpolation methods generally do not fulfil this condition only with certain strong restrictions concerning the measurement points if we neglect the classical form of the approximating function polynomial and trigonometrical we can produce better behaving approximation the kh controller approximating function being a simple fractional function fulfils the stability condition this can also be interpreted as kh controllers are universal approximators in the space of continuous functions with respect to e g the supremum norm

high order extended finite element method for cracked domains the aim of the paper is to study the capabilities of the extended finite element method xfem to achieve accurate computations in non smooth situations such as crack problems although the xfem method ensures a weaker error than classical nite element methods the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity the di culty can be overcome by modifying the enrichment of the nite element basis with the asymptotic crack tip displacement solutions as well as with the heaviside function numerical simulations show that the modi ed xfem method achieves an optimal rate of convergence i e like in a standard nite element method for a smooth problem

matrix representations of bezoutians abstract an approach is presented to get matrix representations for classical and more general r bezoutians with entries from a noncommutative ring formulas due to ammar and gader barnett gohberg and semencul gohberg and heinig kravitsky and russakovskii lerer and tismentsky ptak and wimmer as well as some generalizations and modifications are obtained in a unified way

a comparative study on sufficient conditions for takagi sugeno fuzzy systems as universal approximators universal approximation is the basis of theoretical research and practical applications of fuzzy systems studies on the universal approximation capability of fuzzy systems have achieved great progress in recent years in this paper linear takagi sugeno ts fuzzy systems that use linear functions of input variables as rule consequent and their special case named simplified fuzzy systems that use fuzzy singletons as rule consequent are investigated on condition that overlapped fuzzy sets are employed new sufficient conditions for simplified fuzzy systems and linear ts fuzzy systems as universal approximators are given respectively then a comparative study on existing sufficient conditions is carried out with numeric examples

stability and inertia abstract the purpose of this paper is to present a brief overview of matrix stability and inertia theory a few applications of inertia and stability theorems and a nonspectral implicit matrix equation method for determining stability and inertia of a nonhermitian matrix are also presented inter relationships between different theorems are explicitly stated whenever appropriate the paper concludes with some problems for future research in this area

fuzzy systems and approximation abstract the basic motivation of using fuzzy rule based systems especially for control purposes is to deduce simple and fast approximations of the unknown or too complicated models fuzzy rule based systems have become very popuar because of their transparency and easiness of tuning and modification recently some results concerning the explicit functions implemented by realistic fuzzy controllers presented the class of functions that could be implemented in this way some parallel results on the other hand attempted to prove that the main advantage of using fuzzy systems was the suitability for approximation with arbitrary accuracy in their universality the explicit formulas and some very recent theoretical results made it clear however that fuzzy systems were not really good approximators as realistic fuzzy controllers could generate only very rough approximations of given transference functions in connection with approximation the question can be asked whether there is an optimal fineness roughness of a fuzzy rule base that controls a certain action with roughness gives minimal time complexity as an example a target tracking problem was chosen cat and mouse or hawk and sparrow problem where the antagonistic criteria of minimizing inference time by the given rule base and minimizing action time search for the target with given uncertainty provided by the rule model were examined under certain assumptions the solution of this optimization problem leads to nontrivial rule base sizes these results have also practical applicability since if a fine enough model of the system is known it is always possible to generate a rougher version of the same by applying the model transformation technique offered by rule interpolation with levels

bezoutian and schur cohn problem for operator polynomials abstract a generalized bezout operator bezoutian for a pair of operator polynomials is introduced and its kernel is described in terms of common spectral data of the underlying polynomials the location of the spectrum of an operator polynomial with compact spectrum with respect to the unit circle infinite dimensional version of the schur cohn problem is expressed via the inertia of a suitable bezoutian an application to the geometric dichotomy problem for difference equations with operator coefficients is given as well

a stabilized lagrange multiplier method for the finite element approximation of contact problems in elastostatics in this work we consider a stabilized lagrange or kuhn tucker multiplier method in order to approximate the unilateral contact model in linear elastostatics the particularity of the method is that no discrete inf sup condition is needed in the convergence analysis we propose three approximations of the contact conditions well adapted to this method and we study the convergence of the discrete solutions several numerical examples in two and three space dimensions illustrate the theoretical results and show the capabilities of the method

a stable lagrange multiplier space for stiff interface conditions within the extended finite element method this paper introduces a new algorithm to define a stable lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method in contrast to earlier approaches we do not work with an interior penalty formulation as e g for nitsche techniques but impose the constraints weakly in terms of lagrange multipliers roughly speaking a stable and optimal discrete lagrange multiplier space has to satisfy two criteria a best approximation property and a uniform inf sup condition owing to the fact that the interface does not match the edges of the mesh the choice of a good discrete lagrange multiplier space is not trivial here we propose a new algorithm for the local construction of the lagrange multiplier space and show that a uniform inf sup condition is satisfied a counterexample is also presented i e the inf sup constant depends on the mesh size and degenerates as it tends to zero numerical results in two dimensional confirm the theoretical ones copyright

an immersed finite element method based on a locally anisotropic remeshing for the incompressible stokes problem abstract in the present paper we study a finite element method for the incompressible stokes problem with a boundary immersed in the domain on which essential constraints are imposed such type of methods may be useful to tackle problems with complex geometries interfaces such as multiphase flow and fluid structure interaction the method we study herein consists in locally refining elements crossed by the immersed boundary such that newly added elements called subelements fit the immersed boundary in this sense this approach is of a fitted type but with an original mesh given independently of the location of the immersed boundary we use such a subdivision technique to build a new finite element basis which enables us to represent accurately the immersed boundary and to impose strongly dirichlet boundary conditions on it however the subdivision process may imply the generation of anisotropic elements which for the incompressible stokes problem may result in the loss of inf sup stability even for well known stable element schemes we therefore use a finite element approximation which appears stable also on anisotropic elements we perform numerical tests to check stability of the chosen finite elements several numerical experiments are finally presented to illustrate the capabilities of the method the method is presented for two dimensional problems

ordering distance and closeness of fuzzy sets abstract in dense rule bases where the observation usually overlaps with several antecedents in the rule base various algorithms are used for approximate reasoning and control if the antecedents are located sparsely and the observation does not overlap as a rule with any of the antecedents function approximation techniques combined with the resolution principle lead to applicable conclusions this kind of approximation is possible only if a new concept of ordering and distance i e a metric in the state space and a partial ordering among convex and normal fuzzy sets cnf sets is introduced so the fuzzy distance of two cnf sets can be defined and by this distance closeness and similarity of cnf sets as well

the generalized finite element method an example of its implementation and illustration of its performance the generalized finite element method gfem was introduced in reference 1 as a combination of the standard fem and the partition of unity method the standard mapped polynomial finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data the geometry of the domain the loads and the boundary conditions the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and are pasted to the existing finite element basis to construct a conforming approximation the essential boundary conditions can be imposed exactly as in the standard fem adaptive numerical quadrature is used to ensure that the errors in integration do not affect the accuracy of the approximation this paper gives an example of how the gfem can be developed for the laplacian in domains with multiple elliptical voids and illustrates implementation issues and the superior accuracy of the gfem versus the standard fem copyright 2000 john wiley sons ltd

fuzzy spline interpolation with optimal property in parametric form in this paper we propose a new fuzzy interpolation procedure that uses cubic splines with an optimal property obtained in parametric form this fuzzy interpolation operator is also a linear operator of uniform approximation that preserves the monotonicity moreover by integrating this fuzzy cubic spline we obtain the trapezoidal quadrature rule for fuzzy henstock integrable functions

inertia theorems for operator lyapunov inequalities we study operator lyapunov inequalities and equations for which the in1nitesimal generator is not necessarily stable but it satis1es the spectrum decomposition assumption and it has at most 1nitely many unstable eigenvalues moreover the input or output operators are not necessarily bounded but are admissible we prove an inertia result under mild conditions we show that the number ofunstable eigenvalues ofthe generator is less than or equal to the number ofnegative eigenvalues ofthe self adjoint solution ofthe operator lyapunov inequality c 2001 elsevier science b v all rights reserved

a study on unfitted 1d finite element methods in the present paper we consider a 1d poisson model characterized by the presence of an interface where a transmission condition arises due to jumps of the coefficients we aim at studying finite element methods with meshes not fitting such an interface it is well known that when the mesh does not fit the material discontinuities the resulting scheme provides in general lower order accurate solutions we focus on so called embedded approaches frequently adopted to treat fluid structure interaction problems with the aim of recovering higher order of approximation also in presence of non fitting meshes we implement several methods inspired by the immersed boundary method the fictitious domain method and the extended finite element method in particular we present four formulations in a comprehensive and unified format proposing several numerical tests and discussing their performance moreover we point out issues that may be encountered in the generalization to higher dimensions and we comment on possible solutions

a stabilized lagrange multiplier method for the enriched finite element approximation of tresca contact problems of cracked elastic bodies abstract in this paper we propose a local projection stabilized lagrange multiplier method in order to approximate the two dimensional linear elastostatics unilateral contact problem with tresca friction in the framework of the extended finite element method x fem this last method allows to perform finite element computations on cracked domains by using meshes of the non cracked domain the advantage of the used stabilization technique is to affect only the equation on multipliers and thus to be equation independent we study the existence uniqueness and a priori error estimate of three hybrid discrete formulations

on relative primeness of operator polynomials abstract given operator polynomials a and b one of which is monic conditions are given for the existence of operator polynomials c and d such that a c b d i for every c a special case will give a characterization of controlla bility of an infinite dimensional linear control system