perturbation analysis of orthogonal canonical forms abstract we present a complete perturbation analysis of orthogonal canonical forms ocfs of linear multivariable systems both local linear and nonlocal nonlinear perturbation bounds are derived in particular the conditioning of ocfs is determined

a computational algorithm for pole assignment of linear single input systems an efficient computational algorithm for pole assignment of linear multiinput systems is proposed a preliminary stage of the algorithm is a reduction of the system matrices into orthogonal canonical form the gain matrix elements are then found by orthogonal transformation of the closed loop system matrix into upper quasi triangular form whose diagonal blocks correspond to the desired poles the algorithm is numerically stable the computed gain matrix being exact for a system with slightly perturbed matrices it works equally well with real and complex distinct and multiple poles and is applicable to ill conditioned and high order problems

refined similarity hypothesis using three dimensional local averages the refined similarity hypotheses of kolmogorov regarded as an important ingredient of intermittent turbulence has been tested in the past using one dimensional data and plausible surrogates of energy dissipation we employ data from direct numerical simulations at the microscale reynolds number r 650 on a periodic box of 4096 3 grid points to test the hypotheses using three dimensional averages in particular we study the small scale properties of the stochastic variable v u r re r 1 3 where u r is the longitudinal velocity increment and e r is the dissipation rate averaged over a three dimensional volume of linear size r we show that v is universal in the inertial subrange in the dissipation range the statistics of v are shown to depend solely on a local reynolds number

on the application of orthogonal transformation for the design and analysis of feedforward networks orthogonal transformation which can lead to compaction of information has been used in two ways to optimize on the size of feedforward networks 1 through the selection of optimum set of time domain inputs and the optimum set of links and nodes within a neural network nn and 2 through the orthogonalization of the data to be used in nn s in case of processes with periodicity the proposed methods are efficient and are also extremely robust numerically the singular value decomposition svd and qr with column pivoting factorization qrcp are the transformations used svd mainly serves as the null space detector qrcp coupled with svd is used for subset selection which is one of the main operations on which the design of the optimal network is based svd has also been used to devise a new approach for the assessment of the convergence of the nn s which is an alternative to the conventional output error analysis

on the universality of the kolmogorov constant in numerical simulations of turbulence motivated by a recent survey of experimental data k r sreenivasan phys fluids 2778 1995 we examine data on the kolmogorov spectrum constant in numerical simulations of isotropic turbulence using results both from previous studies and from new direct numerical simulations over a range of reynolds numbers up to 240 on the taylor scale at grid resolutions up to 5123 it is noted that in addition to k 5 3 scaling identification of a true inertial range requires spectral isotropy in the same wavenumber range we found that a plateau in the compensated three dimensional energy spectrum at k eta 0 1 0 2 commonly used to infer the kolmogorov constant from the compensated three dimensional energy spectrum actually does not represent proper inertial range behavior rather a proper if still approximate inertial range emerges at k eta 0 02 0 05 when r sub sub sub sub sub sub sub sub 0 53 for c 1 62 in excellent agreement with experiments however the one and three dimensional estimates are not fully consistent because of departures due to numerical and statistical limitations from isotropy of the computed spectra at low wavenumbers the inertial scaling of structure functions in physical space is briefly addressed since dns is still restricted to moderate reynolds numbers an accurate evaluation of the kolmogorov constant is very difficult we focus on providing new insights on the interpretation of kolmogorov 1941 similarity in the dns literature and do not consider issues pertaining to the refined similarity hypotheses of kolmogorov

parallel and large scale matrix computations in control some ideas abstract the design and analysis of time invariant linear control systems give rise to a variety of interesting linear algebra problems numerically effective methods now exist for several of these problems however algorithms for large scale computations and efficient parallel algorithms for these problems are virtually nonexistent in this paper we propose several efficient general purpose parallel algorithms for single input and multiinput eigenvalue assignment problems a desirable feature of these algorithms is that they are composed of simple linear algebraic operations such as matrix vector multiplication solution of a linear system and computations of the eigensystem and singular values of a symmetric matrix for which efficient parallel algorithms have already been developed and parallel software libraries are being built based on these algorithms the proposed algorithms thus have potential for implementations on some existing and future parallel processors we also propose a numerical method for the sylvester matrix equation arising in the construction of a luenberger observer the method does not need reduction to condensed forms and is thus suitable for large and sparse matrices the method also exhibits a certain parallelism

an algorithm for pole assignment in high order multivariable systems an efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions a given multiinput system is first transformed to an upper block hessenberg form by means of orthogonal state coordinate transformations the state feedback problem is then reformulated in terms of the sylvester equation the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively a distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast computational aspects of the algorithm are discussed and numerical examples are provided

fiber dynamics in turbulent flows general modeling framework the paper at hand deals with the modeling of turbulence effects on the dynamics of a long slender elastic fiber independent of the choice of the drag model a general aerodynamic force concept is derived on the basis of the velocity field for the randomly fluctuating component of the flow its construction as a centered differentiable gaussian field complies thereby with the requirements of the stochastic k epsilon turbulence model and kolmogorov s universal equilibrium theory on local isotropy

computational methods for linear matrix equations given the square matrices a b d e and the matrix c of conforming dimensions we consider the linear matrix equation a mathbf x e d mathbf x b c in the unknown matrix mathbf x our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing

improved epsilon expansion for three dimensional turbulence two loop renormalization near two dimensions an improved epsilon expansion in the d dimensional d 2 stochastic theory of turbulence is constructed at two loop order which incorporates the effect of pole singularities at d 2 in coefficients of the epsilon expansion of universal quantities for a proper account of the effect of these singularities two different approaches to the renormalization of the powerlike correlation function of the random force are analyzed near two dimensions by direct calculation it is shown that the approach based on the mere renormalization of the nonlocal correlation function leads to contradictions at two loop order on the other hand a two loop calculation in the renormalization scheme with the addition to the force correlation function of a local term to be renormalized instead of the nonlocal one yields consistent results in accordance with the ultraviolet uv renormalization theory the latter renormalization prescription is used for the two loop renormalization group analysis amended with partial resummation of the pole singularities near two dimensions leading to a significant improvement of the agreement with experimental results for the kolmogorov constant

feedback design for regularizing descriptor systems this paper surveys numerical techniques for the regularization of descriptor generalized state space systems by proportional and derivative feedback we review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the weierstras canonical form three condensed forms display the controllability and observability properties of a descriptor system the condensed forms are obtained through orthogonal equivalence transformations and rank decisions so they may be computed by numerically stable algorithms in addition the condensed forms display whether a descriptor system is regularizable i e when the system pencil can be made to be regular by derivative and or proportional output feedback and if so what index can be achieved also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback

detection filter design spectral theory and algorithms a new formulation of the detection filter problem is generated by assignment of the closed loop eigenstructure under certain constraints detection filters which are actually a specific class of observers fix the output error direction of the system so that it can be associated with a particular failure mode and its known design failure direction the derivation of detection filters from an eigensystem assignment approach permits a very transparent theory the detection filter gains and closed loop eigenvectors are obtained from a set of simultaneous equations necessary and sufficient conditions for the solution of these algebraic equations are determined which produce a complete theory for detection filters

inviscid limit for damped and driven incompressible navier stokes equations in mathbb r 2 we consider the zero viscosity limit of long time averages of solutions of damped and driven navier stokes equations in mathbb r 2 we prove that the rate of dissipation of enstrophy vanishes stationary statistical solutions of the damped and driven navier stokes equations converge to renormalized stationary statistical solutions of the damped and driven euler equations these solutions obey the enstrophy balance

principal pivot transforms properties and applications the principal pivot transform ppt is a transformation of the matrix of a linear system tantamount to exchanging unknowns with the corresponding entries of the right hand side of the system the notion of the ppt is encountered in mathematical programming statistics and numerical analysis among other areas the purpose of this paper is to draw attention to the main properties and uses of ppts make some new observations and motivate further applications of ppts in matrix theory special consideration is given to ppts of matrices whose principal minors are positive 2000 elsevier science inc all rights reserved

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

nonperturbative renormalization group study of the stochastic navier stokes equation we study the renormalization group flow of the average action of the stochastic navier stokes equation with power law forcing using galilean invariance we introduce a nonperturbative approximation adapted to the zero frequency sector of the theory in the parametric range of the holder exponent 4 2e of the forcing where real space local interactions are relevant in any spatial dimension d we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis kolmogorov s 5 3 law is thus recovered for e 2 as also predicted by perturbative renormalization at variance with the perturbative prediction the 5 3 law emerges in the presence of a saturation in the e dependence of the scaling dimension of the eddy diffusivity at e 3 2 when according to perturbative renormalization the velocity field becomes infrared relevant

matrix bidiagonal form the matrix bidiagonal form is analysed and some applications to linear system theory are shown in the first part it is shown that the reduction of a given matrix a to the mbf is immediate in the very common situation in which a vector b such that a b is controllable is known in the second part some applications are presented such as the evaluation of a function of a matrix and the solution of the lyapunov equation

a gametheoretic approach for non uniform pole shifting and pole homothety this paper investigates the problems of non uniform pole shifting or pole homothety in multivariable linear systems by using a gametheoretic approach and more specifically a particular nash strategy with an open loop information structure for a game including a time preference rate in the quadratic criteria such a result is possible due to properties of non symmetric algebraic riccati equations associated with an open loop nash strategy numerical examples allow to illustrate the efficiency of the proposed approach

conditional mode elimination and scale invariant dissipation in isotropic turbulence abstract we show that a conditional average based on a limit in which the fourier modes of the turbulent velocity field with wavenumber k k c where k c is an arbitrary cutoff wavenumber are held constant can be used to separate the nonlinear coupling to high k modes into coherent and random parts with the latter rigorously determining the net energy transfer in addition we show that three symmetry breaking terms which are generated by the conditional average of the navier stokes equation do not contribute to the equation for the energy dissipation two of these terms vanish identically under unconditional averaging and wavenumber integration respectively and the remaining one vanishes in the limit of asymptotic freedom when calculated by a quasi stochastic estimate from the high k momentum equation if the cutoff k c is chosen to be large enough then the conditionally averaged high k equation can be solved perturbatively in terms of the local reynolds number which is less than unity on this basis an expression for the renormalized dissipation rate is obtained as an expansion in a parameter which is equal to the square of the local reynolds number a recursive calculation is made of the renormalized dissipation rate in which the expansion parameter reaches a maximum value of 0 16 at the fixed point it is also shown that a previous markovian approximation can be replaced by an exact summation to consistent order in perturbation theory

explicit small scale velocity simulation for high re turbulent flows a new approach two level simulation tls is developed based on the explicit reconstruction of the small scale velocity by solving the small scale governing equations on the domain with reduced dimension representing a collection of one dimensional lines embedded in the three dimensional flow domain a coupled system of equations that is not based on an eddy viscosity hypothesis is derived based on the decomposition of flow variables into the large scale and the small scale components without introducing the concept of filtering simplified treatment of the small scale equations is proposed based on neglecting the small scale advective and dissipative terms in the line orthogonal directions fully coupled simulation of the forced isotropic turbulence at re l 65 114 demonstrates potential benefits and challenges of the tls approach for high re turbulent flows using coarse grids

two loop calculation of the turbulent prandtl number the turbulent prandtl number has been calculated in the two loop approximation of the epsilon expansion of the stochastic theory of turbulence the strikingly small value obtained for the two loop correction explains the good agreement of the earlier one loop result with the experiment this situation is drastically different from other available nontrivial two loop results which exhibit corrections of the magnitude of the one loop term the reason is traced to the mutual cancellation of additional divergences appearing in two dimensions which have had a major effect on the results of previous calculations of other quantities

a formal derivation of the local energy transfer let theory of homogeneous turbulence a statistical closure of the navier stokes hierarchy which leads to equations for the two point two time covariance of the velocity field for stationary homogeneous isotropic turbulence is presented it is a generalisation of the self consistent field method due to edwards 1964 for the stationary single time velocity covariance the probability distribution functional p u t is obtained in the form of a series from the liouville equation by means of a perturbation expansion about a gaussian distribution which is chosen to give the exact two point two time covariance the triple moment is calculated in terms of an ensemble averaged infinitesimal velocity field propagator and shown to yield the edwards result as a special case the use of a gaussian zero order distribution has been found to justify the introduction of a fluctuation response relation which is in accord with modern dynamical theories in a sense this work completes the analogy drawn by edwards between turbulence and brownian motion originally edwards had shown that the noise input was determined by the correlation of the velocity field with the externally applied stirring forces but was unable to determine the system response now we find that the system response is determined by the correlation of the velocity field with internal quasi entropic forces this analysis is valid to all orders of perturbation theory and allows the recovery of the local energy transfer let theory which had previously been derived by more heuristical methods the let theory is known to be in good agreement with experimental results it is also unique among two point statistical closures in displaying an acceptable i e non markovian relationship between the transfer spectrum and the system response in accordance with experimental results as a result of the latter property it is compatible with the kolmogorov k41 spectral phenomenology

orthogonal canonical forms for second order systems it is shown that a linear second order system with arbitrary damping cannot be reduced to hessenberg triangular form by means of orthogonal transformations however it is also shown that such an orthogonal reduction is always possible for the modal damping commonly assumed for models of flexible structures it is shown that modally damped models can be orthogonally reduced to a new triangular second order schur form

an algorithm for the assignment of system zeros abstract this paper presents an algorithm for assigning the locations and number of zeros to a linear system through synthesis of the system input and output space couplings the approach imposes no restrictions on the state space model can assign both real and complex zeros using only real arithmetic and is computationally efficient numerical properties of the algorithm are discussed and examples are given to illustrate its performance

a schur decomposition for hamiltonian matrices abstract a schur type decomposition for hamiltonian matrices is given that relies on unitary symplectic similarity transformations these transformations preserve the hamiltonian structure and are numerically stable making them ideal for analysis and computation using this decomposition and a special singular value decomposition for unitary symplectic matrices a canonical reduction of the algebraic riccati equation is obtained which sheds light on the sensitivity of the nonnegative definite solution after presenting some real decompositions for real hamiltonian matrices we look into the possibility of an orthogonal symplectic version of the qr algorithm suitable for hamiltonian matrices a finite step initial reduction to a hessenberg type canonical form is presented however no extension of the francis implicit shift technique was found and reasons for the difficulty are given

multicomponent turbulence the spherical limit and non kolmogorov spectra a set of models for homogeneous isotropic turbulence is considered in which the navier stokes equations for incompressible fluid flow are generalized to a set of n coupled equations in n velocity fields it is argued that in order to be useful these models must embody a new group of symmetries and a general formalism is laid out for their construction the work is motivated by similar techniques that have had extraordinary success in improving the theoretical understanding of equilibrium phase transitions in condensed matter systems we consider two classes of models a simpler class model i which does not contain an exact galilean symmetry and a more complicated extended class model ii which does the key result is that these models simplify when n is large the so called spherical limit n ensuremath rightarrow ensuremath infty can be solved exactly yielding closed sets of nonlinear integral equations for the response and correlation functions for model i these equations known as kraichnan s direct interaction approximation equations are solved fully in the scale invariant turbulent regime for model ii these equations are more complicated and their full solution is left for future work implications of these results for real turbulence n 1 are discussed in particular it is argued that previously applied renormalization group techniques based on an expansion in the exponent y that characterizes the driving spectrum are incorrect and that the kolmogorov exponent ensuremath zeta has a nontrivial dependence on n with ensuremath zeta n ensuremath rightarrow ensuremath infty 3 2 for both sets of models this value is close to the experimental result ensuremath zeta ensuremath simeq 5 3 which must therefore result from higher order corrections in powers of 1 n prospects for calculating these corrections are briefly discussed though daunting such calculations might provide a controlled perturbation expansion for the kolmogorov and other exponents our techniques may also be applied to other nonequilibrium dynamical problems such as the kardar parisi zhang equation for interface growth and perhaps to turbulence in nonlinear wave systems

fully developed isotropic turbulence nonperturbative renormalization group formalism and fixed point solution we investigate the regime of fully developed homogeneous and isotropic turbulence of the navier stokes ns equation in the presence of a stochastic forcing using the nonperturbative functional renormalization group nprg within a simple approximation based on symmetries we obtain the fixed point solution of the nprg flow equations that corresponds to fully developed turbulence both in d 2 and 3 dimensions deviations to the dimensional scalings kolmogorov in d 3 or kraichnan batchelor in d 2 are found for the two point functions to further analyze these deviations we derive exact flow equations in the large wave number limit and show that the fixed point does not entail the usual scale invariance thereby identifying the mechanism for the emergence of intermittency within the nprg framework the purpose of this work is to provide a detailed basis for nprg studies of ns turbulence the determination of the ensuing intermittency exponents is left for future work

computing the radius of controllability for state space systems abstract in this paper we discuss the problem of computing the nearest uncontrollable system to a given control system represented by a matrix pair a b in order to do so we construct a sequence of structured matrices from given system matrices a and b controllability of the pair a b is equivalent to a condition on the null space dimension of an appropriate matrix in this sequence we show that the dimension of the reachability space is also related to the above condition further it is shown that the nearest structured low rank approximation slra of this structured matrix corresponds to a nearest uncontrollable system to the pair a b

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

elimination of turbulence modes using a conditional average with asymptotic freedom the part of the nonlinear term in the navier stokes equation which represents coupling to the small scale modes may be averaged out by introducing a weak conditional average with asymptotic freedom in wavenumber a residual deterministic part while important for individual realizations makes a negligible contribution to the renormalization of the dissipation rate this is because the full ensemble average needed to establish the energy balance relaxes the constraint on the conditional average

energy transfer and dissipation in forced isotropic turbulence a model for the reynolds number dependence of the dimensionless dissipation rate ce was derived from the dimensionless karman howarth equation resulting in ce ce c rl o 1 rl where rl is the integral scale reynolds number the coefficients c and ce arise from asymptotic expansions of the dimensionless second and third order structure functions this theoretical work was supplemented by direct numerical simulations dns of forced isotropic turbulence for integral scale reynolds numbers up to rl 5875 r 435 which were used to establish that the decay of dimensionless dissipation with increasing reynolds number took the form of a power law rln with exponent value n 1 000 0 009 and that this decay of ce was actually due to the increase in the taylor surrogate u3 l the model equation was fitted to data from the dns which resulted in the value c 18 9 1 3 and in an asymptotic value for ce in the infinite reynolds number limit of ce 0 468 0 006

a large eddy simulation method for dgsem using non linearly optimized relaxation filters abstract in this paper we apply a specifically designed dissipative spatial filter as sub grid scale model within the increasingly popular discontinuous galerkin methods and the closely related flux reconstruction high order methods for large eddy simulation the parameters of the filter kernel are optimized with data obtained from direct numerical simulation that is filtered and used as a ground truth to fit the overall kinetic energy and dissipation rate over time the optimization is carried out for polynomial degree 3 to 10 the optimal kernels are rigorously tested in the limit of infinite reynolds number flows hit and taylor green vortex flow additionally a brief extension to plane turbulent channel flow is given

on hamiltonian and symplectic hessenberg forms abstract characterizations are given for the hamiltonian matrices that can be reduced to hamiltonian hessenberg form and the symplectic matrices that can be reduced to symplectic hessenberg form by orthogonal symplectic similarity transformations the reduction to these special hessenberg forms is the missing link in the solution of the open problem of constructing a stable structure preserving qr like method of complexity o n 3 for the computation of invariant subspaces of hamiltonian and symplectic matrices our considerations lead us to propose an approach to the computation of lagrangian invariant subspaces of a hamiltonian or symplectic matrix

a new parameter estimate in singular perturbations abstract a new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system general time invariant systems with a single small parameter are considered the paper employs a riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics an application of the brouwer fixed point theorem to the riccati equation and of liapunov s direct method to the fast and slow subsystems results in the desired upper bound computation of the estimate requires only the solution of two liapunov matrix equations

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

on the computation of sensitivity functions of linear time invariant systems responses via diagonalization this note presents a method for computing the sensitivity functions of parametrized linear time invariant systems for the case where the system matrix a is diagonalizable the method is based on a formula derived in the note for the sensitivity of an exponential of a diagonalizable matrix

bias reduction in parameter estimation abstract the upper bound of the bias in the estimated parameters is derived in terms of the spectral norm it is then established that the bias is related to the condition of the problem as well as the noise existing in the data conventional methods such as the generalized least squares gls the instrumental variables iv and the extended matrix em method seek to minimize bias by reducing the level of noise correlation in the data the method presented in this paper approaches the bias reduction problem via the condition number which acts as a multiply factor on the bias due to noise correlation by improving the condition of the problem it can be shown that bias in the estimated parameters is significantly reduced

comment on the paper on the scaling of three dimentsional homogeneous and isotropic turbulence by benzi et al abstract benzi et al presented experimental data and an analysis to the effect that the well known 2 3 kolmogorov obukhov exponent in the inertial range of local structure in turbulence should be corrected by a small but definitely nonzero amount we reexamine the very same data and show that this conclusion is unjustified the data are in fact consistent with incomplete similarity in the inertial range and with an exponent that depends on the reynolds number and tends to 2 3 in the limit of vanishing viscosity

spatiotemporal velocity velocity correlation function in fully developed turbulence turbulence is a ubiquitous phenomenon in natural and industrial flows since the celebrated work of kolmogorov in 1941 understanding the statistical properties of fully developed turbulence has remained a major quest in particular deriving the properties of turbulent flows from a mesoscopic description that is from the navier stokes equation has eluded most theoretical attempts here we provide a theoretical prediction for the functional space and time dependence of the velocity velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to the navier stokes equation with stochastic forcing this prediction which goes beyond kolmogorov theory is the analytical fixed point solution of nonperturbative renormalization group flow equations which are exact in the limit of large wave numbers this solution is compared to two point two times correlation functions computed in direct numerical simulations we obtain a remarkable agreement both in the inertial and in the dissipative ranges

functional renormalization group approach to the kraichnan model we study the anomalous scaling of the structure functions of a scalar field advected by a random gaussian velocity field the kraichnan model by means of functional renormalization group techniques we analyze the symmetries of the model and derive the leading correction to the structure functions considering the renormalization of composite operators and applying the operator product expansion

generalized schur methods with condition estimators for solving the generalized sylvester equation stable algorithms are presented for solving the generalized sylvester equation they are based on orthogonal equivalence transformations of the original problem perturbation theory and rounding error analysis are included condition estimators dif sup 1 estimators are developed which when substituted into derived error bounds give accuracy estimates of a computed solution results from numerical experiments on well conditioned and ill conditioned problems are reported

deformation retracts of stein spaces let x be an n dimensional stein space it was proved in 4 5 3 that x has the homotopy type of a cw complex of dimension5n in the algebraic case this was proved in 8 with the additional conclusion that the cw complex is nite it is therefore natural to ask if there exists a subset q of x with the same topological properties as x for instance q is a strong deformation retract of x and q is a cw complex of dimension5 n the main result of the paper is

improved epsilon expansion for three dimensional turbulence summation of nearest dimensional singularities an improved epsilon expansion in the d dimensional d 2 stochastic theory of turbulence is constructed by taking into account pole singularities at d 2 in coefficients of the epsilon expansion of universal quantities effectiveness of the method is illustrated by a two loop calculation of the kolmogorov constant in three dimensions

decomposition and stability for multiparameter singular perturbation problems time scale separation and stability of linear time varying and time invariant multiparameter singular perturbation problems are analyzed the first problem considered in the paper is that of deriving upper bounds on the small parasitic parameters ensuring the existence of an invertible bounded transformation exactly separating fast and slow dynamics this problem is most interesting for the time varying case the analysis of this problem in the time varying case requires the two time scale setting introduced by h k khalil and p v kokotovic 16 this entails that the mutual ratios of the small parameters are bounded by known positive constants the second problem considered is to derive parameter bounds ensuring that the system in question is uniformly asymptotically stable the results on decomposition are used to facilitate the derivation of these latter bounds fortunately the analysis of decomposition and stability questions for time invariant multiparameter singular perturbation problems requires no restriction on the relative magnitudes of the small parameters a concept of strong d stability is introduced and shown to greatly simplify the stability analysis of time invariant multiparameter problems

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

some specific features of the e expansion in the theory of turbulence and the possibility of its improvement specific problems arising in the use of the method of renormalization group and e expansion in the theory of developed turbulence are discussed the necessity to take into account the dependence of the model parameters on the expansion parameter e and the large magnitude of the physical value of the expansion parameter it is shown that quantities independent of the amplitude of the correlation function of the random force possess a uniquely defined e expansion on the example of the two loop calculation of the kolmogorov constant and the turbulent prandtl number effectiveness of the improved expansion is demonstrated which uses an approximate summation of the high order terms of the e expansion

numerical linear algebra aspects of control design computations the interplay between recent results and methodologies in numerical linear algebra and mathematical software and their application to problems arising in systems control and estimation theory is discussed the impact of finite precision finite range arithmetic including the implications of the proposed ieee floating point standard s on control design computations is illustrated with numerous examples as are pertinent remarks concerning numerical stability and conditioning basic tools from numerical linear algebra such as linear equations linear least squares eigenproblems generalized eigenproblems and singular value decomposition are then outlined a selected list of applications of the basic tools then follows including algorithms for solution of problems such as matrix exponentials frequency response system balancing and matrix riccati equations the implementation of such algorithms as robust mathematical software is then discussed a number of issues are addressed including characteristics of reliable mathematical software availability and evaluation language implications fortran ada etc and the overall role of mathematical software as a component of computer aided control system design

on the center problem for ordinary differential equations we study the center problem for equations v i 1 a i x v i 1 this problem is closely connected to the classical poincare center focus problem about the characterization of planar polynomial vector fields whose integral trajectories are closed curves with interiors containing a fixed point a center

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

oka properties of ball complements let n 1 be an integer we prove that holomorphic maps from stein manifolds x of dimension n to the complement mathbb c n setminus l of a compact convex set l subset mathbb c n satisfy the basic oka property with approximation and interpolation if l is polynomially convex then the same holds when 2 dim x le n we also construct proper holomorphic maps immersions and embeddings x rightarrow mathbb c n with additional control of the range thereby extending classical results of remmert bishop and narasimhan

two loop renormalization group analysis of the burgers kardar parisi zhang equation a systematic analysis of the burgers kardar parisi zhang equation in d 1 dimensions by dynamic renormalization group theory is described the fixed points and exponents are calculated to two loop order we use the dimensional regularization scheme carefully keeping the full d dependence originating from the angular parts of the loop integrals for dimensions less than mathit d mathit c 2 we find a strong coupling fixed point which diverges at d 2 indicating that there is nonperturbative strong coupling behavior for all d ensuremath ge 2 at d 1 our method yields the identical fixed point as in the one loop approximation and the two loop contributions to the scaling functions are nonsingular for dg2 dimensions there is no finite strong coupling fixed point in the framework of a 2 ensuremath epsilon expansion we find the dynamic exponent corresponding to the unstable fixed point which described the nonequilibrium roughening transition to be z 2 o mathrm ensuremath epsilon 3 in agreement with a recent scaling argument by doty and kosterlitz phys rev lett 69 1979 1992 similarly our result for the correlation length exponent at the transition is 1 ensuremath nu ensuremath epsilon o mathrm ensuremath epsilon 3 for the smooth phase some aspects of the crossover from gaussian to critical behavior are discussed

renormalization group operator product expansion and anomalous scaling in a model of advected passive scalar field theoretical renormalization group methods are applied to the obukhov kraichnan model of a passive scalar advected by the gaussian velocity field with the covariance mathbf v t mathbf x mathbf v t ensuremath mathbf x ensuremath mathbf v t mathbf x mathbf v t ensuremath mathbf x ensuremath ensuremath propto ensuremath delta t ensuremath t ensuremath mathbf x ensuremath mathbf x ensuremath ensuremath varepsilon inertial range anomalous scaling for the structure functions and various pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain essential or dangerous composite operators powers of the local dissipation rate whose negative critical dimensions determine anomalous exponents the main technical result is the calculation of the anomalous exponents in the order ensuremath varepsilon 2 of the ensuremath varepsilon expansion generalization of the results obtained to the case of a slow velocity field is also presented

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

a non perturbative approach to critical dynamics this paper is devoted to a non perturbative renormalization group nprg analysis of model a which stands as a paradigm for the study of critical dynamics the nprg formalism has appeared as a valuable theoretical tool to investigate non equilibrium critical phenomena yet the simplest and nontrivial models for critical dynamics have never been studied using nprg techniques in this paper we focus on model a taking this opportunity to provide a pedagogical introduction to nprg methods for dynamical problems in statistical physics the dynamical exponent z is computed in d 3 and d 2 and is found to be in close agreement with results from other methods