geometry of exclusion principles in discrete systems abstract using an n species system of difference equations with very general density dependent growth functions we prove that weak dominance and invariance gives the exclusion of all the n 1 dominated species in the system this result is applied to very specific competition models an example of coexistence in a competition model with no invariance is studied a notion of strong dominance is developed in a general setting and shown to imply exclusion of the n 1 dominated species an example of a competition model illustrating that weak dominance plus invariance does not imply strong dominance is given

partial eigenstructure assignment for the quadratic pencil abstract it is shown in this paper that by the appropriate choice of gain and input influence matrices certain eigenpairs of a vibrating system may be assigned while the other eigenpairs remain unchanged the system under consideration is modelled by a set of second order differential equations and the assignment is carried by multi input state feedback control the solution may be of particular interest in the stabilization and control of flexible structures using smart materials where only a small part of the eigenstructure is to be reassigned and the rest is required to remain unchanged the method presented is illustrated with a numerical example

on the condition of the linear systems associated with discretized bvps of odes the way in which improved conditioning can result when one rewrites an mth order ordinary differential equation as a first order vector system for numerical solution is explained

on the liouville theorem for the stationary navier stokes equations in a critical space abstract in this paper we prove the liouville type theorem for the stationary navier stokes equations on r 3 more specifically if a solution u h 1 r 3 to the stationary navier stokes system satisfies additional conditions characterized by the decays near infinity and by the oscillation then we show that u 0

partial eigenvalue assignment problem of high order control systems using orthogonality relations in this paper we present an explicit solution to the partial eigenvalue assignment problem of high order control system using orthogonality relations between eigenvectors of the matrix polynomial our solution can be implemented with only a partial knowledge of the spectrum and the corresponding left eigenvectors of the matrix polynomial we show that the number of eigenvalues and eigenvectors that need to remain unchanged will not affected by feedback a numerical example is given to illustrate the applicability and the practical usefulness of the proposed method

analyticity of the stokes semigroup in spaces of bounded functions the analyticity of the stokes semigroup with the dirichlet boundary condition is established in spaces of bounded functions when the domain occupied with fluid is bounded or more generally admissible which admits a special estimate for the helmholtz decomposition the proof is based on a blow up argument this is the first proof of the analyticity in spaces of bounded functions which was left open more than thirty years

a remark on liouville type theorems for the stationary navier stokes equations in three space dimensions abstract consider the 3d homogeneous stationary navier stokes equations in the whole space r 3 we deal with solutions vanishing at infinity in the class of the finite dirichlet integral by means of quantities having the same scaling property as the dirichlet integral we establish new a priori estimates as an application we prove the liouville theorem in the marginal case of scaling invariance

pole assignment for a vibrating system with aerodynamic effect this paper deals with a pole assignment problem by single input state feedback control arising from a one dimensional vibrating system with aerodynamic effect on the practical side we derive explicit formulae for the required controlling force terms which can reassign part of the spectrum to the desired values while leaving the remaining spectrum unchanged on the mathematical side unlike the classical sturm liouville problem our eigenvalue problem is associated with a cubic pencil with unbounded operators as coefficients and has many interesting new features one of which is that a new controllability condition appears this condition together with the known controllability condition in the quadratic case are necessary and sufficient this sheds light on the adjustment of the model parameters we also analyze the spectrum of the associated noncompact operator and in particular show that the discrete spectrums of controlled and uncontrolled systems lie outside a closed interval on the negative real axis

quadratic model updating with no spill over and incomplete measured data existence and computation of solution abstract quadratic finite element model updating problem qfemup to be studied in this paper is concerned with updating a symmetric nonsingular quadratic pencil in such a way that a small set of measured eigenvalues and eigenvectors is reproduced by the updated model if in addition the updated model preserves the large number of unupdated eigenpairs of the original model the model is said to be updated with no spill over qfemup is in general a difficult and computationally challenging problem due to the practical constraint that only a very small number of eigenvalues and eigenvectors of the associated quadratic eigenvalue problem are available from computation or measurement additionally for practical effectiveness engineering concerns such as nonorthogonality and incompleteness of the measured eigenvectors must be considered most of the existing methods including those used in industrial settings deal with updating a linear model only ignoring damping only in the last few years a small number of papers been published on the quadratic model updating several of the above issues have been dealt with both from theoretical and computational point of views however mathematical criterion for existence of solution has not been fully developed in this paper we first i prove a set of necessary and sufficient conditions for the existence of a solution of the no spill over qfemup then ii present a parametric representation of the solution assuming a solution exists and finally iii propose an algorithm for qfemup with no spill over and incomplete measured eigenvectors interestingly it is shown that the parametric representation can be constructed with the knowledge of only the few eigenvalues and eigenvectors that are to be updated and the corresponding measured eigenvalues and eigenvectors complete knowledge of eigenvalues and eigenvectors of the original pencil is not needed which makes the solution readily applicable to real life structures

partial eigenvalue assignment with time delay in high order system using the receptance abstract an explicit solution to the partial eigenvalue assignment problem of high order control system is presented by the method of receptance conventional methods e g finite elements are known to contain inaccuracies and assumptions that may hinder the calculations an alternative approach was given by ram and mottershead 1 in the form of receptances typically available from a modal test this paper generalizes the earlier work on partial assignment that is applicable to multi input delayed system without use of the sherman morrison formula the results of our numerical experiments support the validity of our proposed method

partial eigenstructure assignment for undamped vibration systems using acceleration and displacement feedback abstract a new method for partial eigenstructure assignment using acceleration and displacement feedback for undamped vibration systems is presented in this paper firstly a necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged secondly based on this condition an algorithm for determining the required control gain matrices of acceleration and displacement feedback which assign the desired eigenstructure is developed this algorithm is easy to implement and works directly on the second order system model more importantly the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices finally some numerical examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm

an optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures the partial quadratic eigenvalue assignment problem pqevap concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged the problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems the solution of this problem requires computations of a pair of feedback matrices for practical effectiveness these feedback matrices must be computed in such a way that their norms and the condition number of the closed loop eigenvector matrix are as small as possible these considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem mnpqevap and the robust partial quadratic eigenvalue assignment problem rpqevap respectively in this paper we propose new optimization based algorithms for solving these problems the problems are solved directly in a second order setting without resorting to a standard first order formulation so as to avoid the inversion of a possibly ill conditioned matrix and the loss of exploitable structures of the original model the algorithms require the knowledge of only the open loop eigenvalues to be replaced and their corresponding eigenvectors the remaining open loop eigenvalues and their corresponding eigenvectors are kept unchanged the invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result furthermore the gradient formulas needed to solve the problems by using the quasi newton optimization technique employed are computed in terms of the known quantities only above all the proposed methods do not require the reduction of the model order or the order of the controller even when the underlying finite element model has a very large degree of freedom these attractive features coupled with minimal computational requirements such as solutions of small diagonal sylvester equations make the proposed algorithms ideally suited for application to large real life structures numerical results show significant improvement in feedback norms and in the condition number of the closed loop system also the closed loop eigenvalues have acceptable accuracy

minimum norm partial eigenvalue assignment of high order linear system with no spill over abstract in this paper we consider the partial eigenvalue assignment problem peap of high order linear system by state feedback to prevent spill over phenomenon we establish the new orthogonality relations for the eigenvectors of matrix polynomial such that the unwanted eigenvalues are moved to prescribed values and the wanted eigenvalues remain unchanged based on the orthogonality relations the solvability conditions for peap are presented and the parametric expression of feedback matrices is derived in terms of the known quantities only finally an optimization based algorithm is proposed to find the minimum norm solution two numerical examples are given to show the application of the proposed method

asymptotically periodic solutions of second order difference equations abstract in this paper we obtain sufficient conditions for the existence of asymptotically periodic solutions of the second order difference equations of the form r n x n a n f x n b n moreover we give sufficient conditions under which every bounded solution of the above equation is asymptotically periodic our approach allows us to control the degree of approximation

robust partial quadratic eigenvalue assignment with time delay using the receptance and the system matrices abstract in this paper we consider the robust partial quadratic eigenvalue assignment problem in vibration by active feedback control based on the receptance measurements and the system matrices we propose an optimization method for the robust and minimum norm partial quadratic eigenvalue assignment problem we provide a new cost function and the closed loop eigenvalue sensitivity and the feedback norms can be minimized simultaneously our method is also extended to the case of time delay between measurements of state and actuation of control numerical tests demonstrate the effectiveness of our method

pointwise upper bounds for the solution of the stokes equation on lσ ω and applications abstract consider the stokes semigroup t defined on l where r n n 3 denotes an exterior domain with smooth boundary it is shown that t z u 0 for u 0 l and z with 0 2 satisfies pointwise estimates similar to the ones known for g z u 0 where g denotes the gaussian semigroup on r n in particular t extends to a bounded analytic semigroup on l of angle 2 moreover t t allows l c 2 smoothing for every t 0 and the stokes semigroups t p and t q on l p and l q are consistent for all p q 1

liouville theorems in unbounded domains for the time dependent stokes system in this paper we characterize bounded ancient solutions to the time dependent stokes system with zero boundary value in various domains including the half space

linear and numerical linear algebra in control theory some research problems abstract this paper presents an informal survey of theoretical and computational aspects of three linear algebra problems arising in control theory namely the sylvester observer matrix equation the matrix eigenvalue assignment problem and the stability and stabilization of large second order systems difficulties are highlighted recent developments are mentioned some research problems in these areas which should be of interest to both linear algebraists and control theorists are described

controllability and observability criteria for multivariable linear second order models criteria are discussed for the determination of controllability stabilizability observability or detectability of linear second order multivariable models of for example large space structures an initial modal transformation is not required and the criteria are thus applicable to models with arbitrary damping coefficients moreover the criteria are modal in the sense that some or all of the modes may be tested for controllability or observability this aspect has advantages if not all the modes are known or easily computable the criteria are further illustrated for a number of important special cases in a series of corollaries

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

parametric eigenstructure assignment in second order descriptor linear systems this note considers eigenstructure assignment in second order descriptor linear systems via proportional plus derivative feedback it is shown that the problem is closely related with a type of so called second order sylvester matrix equations through establishing two general parametric solutions to this type of matrix equations two complete parametric methods for the proposed eigenstructure assignment problem are presented both methods give simple complete parametric expressions for the feedback gains and the closed loop eigenvector matrices the first one mainly depends on a series of singular value decompositions and is thus numerically simple and reliable the second one utilizes the right factorization of the system and allows the closed loop eigenvalues to be set undetermined and sought via certain optimization procedures an example shows the effect of the proposed approaches

l2 decay for the navier stokes flow in halfspaces on etudie le comportement asymptotique dans l 2 des solutions faibles des equations de navier stokes dans des demi espaces

orthogonal basis selection method for robust partial eigenvalue assignment problem in second order control systems in this paper we study the robust partial eigenvalue assignment problem using state feedback control in second order control systems which means that the feedback control matrices not only assign specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations in the coefficient matrices some measures of robustness of the closed loop system are discussed and a numerical method is proposed such that it aims to minimize one measure of the conditioning of the closed loop system numerical examples show that the method is convergent and often leads to better conditioned closed loop system

projection and deflation method for partial pole assignment in linear state feedback two projection methods are proposed for partial pole placement in linear control systems these methods are of interest when the system is very large and only a few of its poles must be assigned the first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace the second method can be regarded as a variant of the weilandt deflation technique used in eigenvalue methods

least squares solutions of quadratic inverse eigenvalue problem with partially bisymmetric matrices under prescribed submatrix constraints abstract the inverse eigenvalue problems play an important role in broad application areas such as system identification hopfield neural networks control design mass spring system and molecular spectroscopy this paper proposes an algorithm that yields a new method to efficiently and accurately compute the partially bisymmetric solutions m c k under prescribed submatrix constraints of the quadratic inverse eigenvalue problem m x 2 c x k x 0 the algorithm is developed based on the conjugate gradient normal equations residual minimizing cgnr method we discuss the convergence properties of the algorithm finally the performance of the algorithm is tested on two numerical examples and compared to the previous algorithm

active vibration suppression by pole zero placement using measured receptances the paper addresses the problem of pole zero assignment using the receptance method in active vibration control and has applications particularly in vibration absorption and detuning of structures to avoid resonance an output feedback approach is described that makes use of measured receptances there being no requirement at all for the m c k matrices usually obtained by finite elements therefore in the controller design the approximations assumptions and other modelling errors are largely eliminated in addition the method does not require the use of model reduction techniques or the estimation of unmeasured states by an observer an advantage of the output feedback method over state feedback is that collocated actuator sensor arrangements become possible however this is achieved at the expense of creating characteristic equations nonlinear in the control gains numerical examples are provided to illustrate the working of the method this is followed by a series of experimental tests carried out using collocated accelerometers and inertial actuators on a t shaped plate in a series of experiments poles and zeros are assigned separately and simultaneously stability robustness is demonstrated by applying a constraint to the singular values of the matrix return difference

on some inverse eigenvalue problems for hermitian and generalized hamiltonian skew hamiltonian matrices abstract some inverse eigenvalue problems for hermitian and generalized hamiltonian skew hamiltonian matrices are discussed including best approximation problems and eigenvalue updating problems based on the spectral decomposition theory on hermitian and hamiltonian skew hamiltonian matrices simpler parametric expressions of solutions to the general inverse eigenvalue problems are given and then the best approximation problems and eigenvalue updating problems are solved by using these parametric expressions

l q l r estimates for solutions of the nonstationary stokes equations in an exterior domain and the navier stokes initial value problems inl q spaces

partial eigenvalue assignment of high order systems with time delay abstract an explicit solution to the partial eigenvalue assignment problem of high order control systems with time delay is presented the problem is solved by a direct method without turning high order systems into the first order form the solution can be implemented with only a partial knowledge of the eigenvalues and the corresponding eigenvectors of the matrix polynomial necessary and sufficient conditions for our results are proven numerical examples are given to illustrate the effect of the approach

spillover phenomenon in quadratic model updating model updating concerns the modification of an existing but inaccurate model with measured data for models characterized by quadratic pencils the measured data usually involve incomplete knowledge of natural frequencies mode shapes or other spectral information in conducting the updating it is often desirable to match only the part of observed data without tampering with the other part of unmeasured or unknown eigenstructure inherent in the original model such an updating if possible is said to have no spillover this paper studies the spillover phenomenon in the updating of quadratic pencils in particular it is shown that an updating with no spillover is always possible for undamped quadratic pencils whereas spillover for damped quadratic pencils is generally unpreventable

partial pole placement with time delay in structures using the receptance and the system matrices datta et al solved the partial pole placement problem for the symmetric definite quadratic eigenvalue problem where part of the spectrum is relocated to predetermined locations and the rest of the spectrum remains unchanged in this paper the problem is solved by a hybrid combination of this result and the method of receptances this allows for the partial assignment of desired poles with no spillover when there is time delay between the measured or estimated state and actuation of the control

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

exclusion principles for density dependent discrete pioneer climax models abstract the ultimate dynamical result of an undisturbed pioneer climax model is assumed by experimental scientists to be the exclusion of the pioneer species examples that illustrate stable coexistence in a pioneer climax model with no isolated positive equilibria are given sufficient conditions are developed and used to confirm the pioneer exclusion in discrete pioneer climax models other situations are possible in such models in particular a mutual exclusion principle is established as a mathematical theorem

a multi step hybrid method for multi input partial quadratic eigenvalue assignment with time delay natural science foundation of fujian province of china for distinguished young scholars 2010j06002 ncet

arnoldi methods for large sylvester like observer matrix equations and an associated algorithm for partial spectrum assignment abstract we propose an arnoldi based numerical method for solving a sylvester type equation arising in the construction of the luenberger observer given an n n matrix a and an n m matrix g the method simultaneously constructs an m m hessenberg matrix h with a preassigned spectrum and an n m orthonormal matrix x such that ax xh g we consider the case when a is large and sparse so that the standard techniques such as the well known hessenberg schur method for solving a sylvester equation cannot be easily applied as a byproduct we propose an algorithm for the partial pole assignment problem for large matrices

global well posedness of the two dimensional exterior navier stokes equations for non decaying data we prove global well posedness of the two dimensional exterior navier stokes equations for bounded initial data with a finite dirichlet integral subject to the non slip boundary condition as an application we construct global solutions for asymptotically constant initial data and arbitrary large reynolds numbers

space time decay of navier stokes flows invariant under rotations we show that the solutions to the non stationary navier stokes equations in open image in new window d 2 3 which are left invariant under the action of discrete subgroups of the orthogonal group o d decay much faster as open image in new window than in generic case and we compute for each subgroup the precise decay rates in space time of the velocity field

on liouville type theorems for the steady navier stokes equations in r3 abstract in this paper we prove three different liouville type theorems for the steady navier stokes equations in r 3 in the first theorem we improve logarithmically the well known l 9 2 r 3 result in the second theorem we present a sufficient condition for the trivially of the solution v 0 in terms of the head pressure q 1 2 v 2 p the imposed integrability condition here has the same scaling property as the dirichlet integral in the last theorem we present fubini type condition which guarantee v 0

liouville theorems for the navier stokes equations and applications we study bounded ancient solutions of the navier stokes equations these are solutions with bounded velocity defined in rn 1 0 in two space dimensions we prove that such solutions are either constant or of the form u x t b t depending on the exact definition of admissible solutions the general 3 dimensional problem seems to be out of reach of existing techniques but partial results can be obtained in the case of axisymmetric solutions we apply these results to some scenarios of potential singularity formation for axi symmetric solutions and obtain extensions of results in a recent paper by chen strain tsai and yau 4

a solution of the affine quadratic inverse eigenvalue problem abstract the quadratic inverse eigenvalue problem qiep is to find the three matrices m c and k given a set of numbers closed under complex conjugations such that these numbers become the eigenvalues of the quadratic pencil p 2 m c k the affine inverse quadratic eigenvalue problem aqiep is the qiep with an additional constraint that the coefficient matrices belong to an affine family that is these matrices are linear combinations of substructured matrices an affine family of matrices very often arise in vibration engineering modeling and analysis research on qiep and aqiep are still at developing stage in this paper we propose three methods and the associated mathematical theories for solving aqiep a newton method an alternating projections method and a hybrid method combining the two validity of these methods are illustrated with results on numerical experiments on a spring mass problem and comparisons are made with these three methods amongst themselves and with another newton method developed by elhay and ram 2002 12 the results of our experiments show that the hybrid method takes much smaller number of iterations and converges faster than any of these methods

use of indefinite pencils for computing damped natural modes abstract a quadratic eigenvalue problem with symmetric positive definite coefficient matrices may be reduced to linear form while retaining symmetry in the new coefficients but neither of them will be positive definite formally the symmetric lanczos algorithm and subspace iteration may be used to compute some eigenpairs of the linear problem the trouble is that the basis vectors are orthogonal with respect to an indefinite inner product so there is no assurance that they will be linearly independent nevertheless this is an attractive way to solve the original problem and we discuss how to implement it and how it relates to the unsymmetric lanczos procedures we discuss complex origin shifts reorthogonalization and error bounds several methods for solving the reduced problem are mentioned but we have no fully satisfactory technique some dangers are described and examples are given comparing our lanczos program with a modified subspace iteration

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

solutions to a quadratic inverse eigenvalue problem abstract in this paper we consider the quadratic inverse eigenvalue problem qiep of constructing real symmetric matrices m c and k of size n n with m c k 0 so that the quadratic matrix polynomial q 2 m c k has m n m 2 n prescribed eigenpairs it is shown that for almost all prescribed eigenpairs the qiep has a solution with m nonsingular if m m and has only solutions with q 0 otherwise where m n 1 1 8 n 2 we also derive the expression of the general solution of the qiep for both cases furthermore we develop an algorithm for finding a particular solution to the qiep with m positive definite if it exists

liouville theorems for the stokes equations with applications to large time estimates abstract we study liouville theorems for the non stationary stokes equations in exterior domains in r n under decay conditions for spatial variables as applications we prove that the stokes semigroup is a bounded analytic semigroup on l of angle 2 for n 3 we also prove large time estimates for n 2 with zero net force

robust partial eigenvalue assignment problem for the second order system in this paper we study the partial eigenvalue assignment problem for the second order system where only a small part of eigenvalues of the open loop system is to be reassigned and the rest are required to remain unchanged it is desirable that the feedback controller not only assigns specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations we propose a numerical method such that the condition number of the matrix of the eigenvectors of the closed loop system is minimized in the method we only need the knowledge of the eigenvalues to be altered and the corresponding eigenvectors while we do not need the knowledge of the eigenstructures that are required to remain unchanged and are often unknown numerical examples show that the present method often leads to better conditioned closed loop system

symmetry preserving eigenvalue embedding in finite element model updating of vibrating structures the eigenvalue embedding problem addressed in this paper is the one of reassigning a few troublesome eigenvalues of a symmetric finite element model to some suitable chosen ones in such a way that the updated model remains symmetric and the remaining large number of eigenvalues and eigenvectors of the original model is to remain unchanged the problem naturally arises in stabilizing a large scale system or combating dangerous vibrations which can be responsible for undesired phenomena such as resonance in large vibrating structures a new computationally efficient and symmetry preserving method and associated theories are presented in this paper the model is updated using low rank symmetric updates and other computational requirements of the method include only simple operations such as matrix multiplications and solutions of low order algebraic linear systems these features make the method practical for large scale applications the results of numerical experiments on the simulated data obtained from the boeing company and on some benchmark examples are presented to show the accuracy of the method computable error bounds for the updated matrices are also given by means of rigorous mathematical analysis

pole assignment in vibratory systems by multi input control the problem of reassigning some poles of a vibratory system while keeping the other poles unchanged is considered the problem may be solved uniquely by single input state feedback control a family of solutions to the partial pole assignment problem may be obtained by applying multi input control forces an algorithm for determining a multi input control which is small in some sense is presented the non iterative algorithm proposed defines a closed form solution to the partial pole assignment problem in its natural second order form and no first order realization is used the reduction in the control effort achieved by the proposed method is demonstrated by numerical examples