analysis of multiple scattering iterations for high frequency scattering problems i the two dimensional case we present an analysis of a recently proposed integral equation method for the solution of high frequency electromagnetic and acoustic scattering problems that delivers error controllable solutions in frequency independent computational times within single scattering configurations the method is based on the use of an appropriate ansatz for the unknown surface densities and on suitable extensions of the method of stationary phase the extension to multiple scattering configurations in turn is attained through consideration of an iterative neumann series that successively accounts for further geometrical wave reflections as we show for a collection of two dimensional cylindrical convex obstacles this series can be rearranged into a sum of periodic orbits of increasing period each corresponding to contributions arising from waves that reflect off a fixed subset of scatterers when these are transversed sequentially in a periodic manner here we analyze the properties of these periodic orbits in the high frequency regime by deriving precise asymptotic expansions for the currents i e the normal derivative of the fields that they induce on the surface of the obstacles as we demonstrate these expansions can be used to provide accurate estimates of the rate at which their magnitude decreases with increasing number of reflections which defines the overall rate of convergence of the multiple scattering series moreover we show that the detailed asymptotic knowledge of these currents can be used to accelerate this convergence and thus to reduce the number of iterations necessary to attain a prescribed accuracy

existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

on the large time galerkin approximation of the navier stokes equations in this article we are interested in the difficult problem of relating the large time behaviour of the navier stokes equations to the large time behaviour of their galerkin approximation we restrict ourselves to the simplest situation dealing with stationary solutions and the question is the following one if the computed approximation of the time dependent equations seems to converge to some limit as t to infty is the same true for the exact problem and are the limits related we give here some sufficient conditions reasonably easy to verify which guarantee a positive answer to this question

a stable runge kutta methods for semilinear evolution equations we consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of hilbert spaces in this setting we prove the existence of solutions which are temporally smooth in the norm of the lowest rung of the scale for an open set of initial data on the highest rung of the scale under the same assumptions we prove that a class of implicit a stable runge kutta semidiscretizations in time of such equations are smooth as maps from open subsets of the highest rung into the lowest rung of the scale under the additional assumption that the linear part of the evolution equation is normal or sectorial we prove full order convergence of the semidiscretization in time for initial data on open sets our results apply in particular to the semilinear wave equation and to the nonlinear schrodinger equation 2012 elsevier inc

theory and method for updating least squares finite element model of symmetric generalized centro symmetric matrices let x f be a displacement matrix and load matrix respectively c obtained by calculations or measurements is an estimate matrix of the analytical model a method is presented for correction of the model c based on the theory of inverse problem of matrices the corrected model is symmetric generalized centro symmetric with specified displacements and loads satisfying the mechanics characters of finite element model the application of the method is illustrated it is more important that a perturbation analysis is given which is not given in the earlier papers numerical results show that the method is feasible and effective

inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation in this paper we first give the solvability condition for the following inverse eigenproblem iep given a set of vectors xi i 1m in cn and a set of complex numbers i i 1m find a centrosymmetric or centroskew matrix c in rn n such that xi i 1m and i i 1m are the eigenvectors and eigenvalues of c respectively we then consider the best approximation problem for the ieps that are solvable more precisely given an arbitrary matrix b in rn n we find the matrix c which is the solution to the iep and is closest to b in the frobenius norm we show that the best approximation is unique and derive an expression for it

on bounded pseudodifferential operators in wiener spaces we aim at extending the definition of the weyl calculus to an infinite dimensional setting by replacing the phase space r2n by b2 where i h b is an abstract wiener space a first approach is to generalize the integral definition using the wigner function the symbol is then a function defined on b2 and belonging to a l1 space for a gaussian measure the weyl operator is defined as a quadratic form on a dense subspace of l2 b for example the symbol can be the stochastic extension on b2 in the sense of l gross of a function f which is continuous and bounded on h2 in the second approach this function f defined on h2 satisfies differentiability conditions analogous to the finite dimensional ones one needs to introduce hybrid operators acting as weyl operators on the variables of finite dimensional subset of h and as anti wick operators on the rest of the variables the final weyl operator is then defined as a limit and it is continuous on a l2 space under rather weak conditions it is an extension of the operator defined by the first approach we give examples of monomial symbols linking this construction to the classical pseudodifferential operators theory and other examples related to other fields or previous works on this subject

a recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices as the efficient calculation of eigenpairs of a matrix especially a general real matrix is significant in engineering and neural networks run asynchronously and can achieve high performance in calculation this paper introduces a recurrent neural network rnn to extract some eigenpair the rnn whose connection weights are dependent upon the matrix can be transformed into a complex differential system whose variable z t is a complex vector by the analytic expression of z t 2 the convergence properties of the rnn are analyzed in detail with general nonzero initial complex vector the rnn obtains the largest imaginary part of all eigenvalues by a rearrangement of connection matrix the largest real part is obtained a practice of a 7x7 matrix indicates the validity of this method two matrices whose dimensionalities are 50 and 100 respectively are employed to test the efficiency of this approach when dimension number becomes large the results imply that the iteration number at which the network enters into equilibrium state is not sensitive with dimensionality this rnn can be used to estimate the largest modulus of eigenvalues etc compared with other neural networks designed for the similar aims this rnn is applicable to general real matrices

proof of a mckean conjecture on the rate of convergence of boltzmann equation solutions the present work provides a definitive answer to the problem of quantifying relaxation to equilibrium of the solution to the spatially homogeneous boltzmann equation for maxwellian molecules under really mild conditions on the initial datum and a weak physically consistent angular cutoff hypothesis our main result theorem 1 contains the first precise statement that the total variation distance between the solution and the limiting maxwellian distribution admits an upper bound of the form c e varlambda b t varlambda b being the least negative eigenvalue of the linearized collision operator and c a constant depending only on the initial datum the validity of this quantification was conjectured about fifty years ago by henry p mckean as to the proof of our results we have taken as point of reference an analogy between the problem of convergence to equilibrium and the central limit theorem of probability theory highlighted by mckean

existence and stability results for 3 d regular flows of viscoelastic fluids of white metzner type abstract this paper is concerned with regular flows of incompressible viscoelastic fluids which obey a differential constitutive law of white metzner type we study the existence and uniqueness of local solutions in 3 d domain as well as the global existence for small data by a classical stability argument we deduce the existence and stability of small periodic and stationary solutions we also generalize the 2 d results more precisely we prove that the results obtained by hakim j math anal appl 185 1994 675 remain true without any restriction on the smallness of the retardation parameter which is the linking coefficient between the equation of velocity navier stokes equation and the transport equation verified by the extra stress tensor the hypothesis of boundedness on the relaxation function is also dropped

semilinear pseudodifferential equations in spaces of tempered ultradistributions abstract we study a class of semilinear elliptic equations on spaces of tempered ultradistributions of beurling and roumieu type assuming that the linear part of the equation is a pseudodifferential operator of infinite order satisfying a suitable ellipticity condition we prove a regularity result in the functional setting above for weak sobolev type solutions

a constructive approach to regularity of lagrangian trajectories for incompressible euler flow in a bounded domain the 3d incompressible euler equations are an important research topic in the mathematical study of fluid dynamics not only is the global regularity for smooth initial data an open issue but the behaviour may also depend on the presence or absence of boundaries for a good understanding it is crucial to carry out besides mathematical studies high accuracy and well resolved numerical exploration such studies can be very demanding in computational resources but recently it has been shown that very substantial gains can be achieved first by using cauchy s lagrangian formulation of the euler equations and second by taking advantage of analyticity results of the lagrangian trajectories for flows whose initial vorticity is holder continuous the latter has been known for about 20 years serfati in j math pures appl 74 95 104 1995 but the combination of the two which makes use of recursion relations among time taylor coefficients to obtain constructively the time taylor series of the lagrangian map has been achieved only recently frisch and zheligovsky in commun math phys 326 499 505 2014 podvigina et al in j comput phys 306 320 342 2016 and references therein here we extend this methodology to incompressible euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity non constructive regularity results for these cases have already been obtained by glass et al ann sci ec norm sup 45 1 51 2012 using the invariance of the boundary under the lagrangian flow we establish novel recursion relations that include contributions from the boundary this leads to a constructive proof of time analyticity of the lagrangian trajectories with analytic boundaries which can then be used subsequently for the design of a very high order cauchy lagrangian method

off spectral analysis of bergman kernels the asymptotic analysis of bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention such interfaces typically occur when the associated limiting bergman density function vanishes on a portion of the plane the off spectral region this type of behavior is observed when the metric is negatively curved somewhere or when we study partial bergman kernels in the context of positively curved metrics in this work we cover these two situations in a unified way for exponentially varying weights on the complex plane we obtain a uniform asymptotic expansion of the coherent state of depthn rooted at an off spectral point which we also refer to as the root function at the point in question the expansion is valid in the entire off spectral component containing the root point and protrudes into the spectrum as well this allows us to obtain error function transition behavior of the density of states along the smooth interface previous work on asymptotic expansions of bergman kernels is typically local and valid only in the bulk region of the spectrum which contrasts with our non local expansions

least square solutions for inverse problems of centrosymmetric matrices let csrnxn a aij rnxn aij an 1 j i j 1 2 n in this paper we mainly discuss solving the following problems problem io given x b rnxm find a csrn n such that ax b problem i given x b rn m find a csrn n such that ax b min problem ii given a rn n find a se such that where is the frobenius norm and se is the solution set of problem i or i0 the expressions of the general solution of problems i and 10 have been derived the sufficient and necessary conditions for the solvability of problem i0 have been provided the numerical algorithm to find the optimal approximate solution and some numerical experiments have been given

initial value problems for creeping flow of maxwell fluids abstract we consider the flow of nonlinear maxwell fluids in the unsteady quasistatic case where the effect of inertia is neglected we study the well posedness of the resulting pde initial boundary value problem locally in time this well posedness depends on the unique solvability of an elliptic boundary value problem we first present results for the 3d case with sufficiently small initial data and for a simple shear flow problem with arbitrary initial data after that we extend our results to some 3d flow problems with large initial data we solve our problem using an iteration between linear subproblems the limit of the iteration provides the solution of our original problem

partial linearization for planar nonautonomous differential equations abstract we prove a partial linearization theorem for planar nonautonomous differential equations with one center like direction and one hyperbolic direction gap conditions are formulated in terms of the dichotomy spectral intervals the result is applied to the duffing van der pol oscillator under a nonautonomous parametric perturbation

the solvability conditions for the inverse problems of symmetric ortho symmetric matrices this paper studies the following two problems problem igiven x email protected r n x m find email protected sr n p such that ax b wheresr n p email protected sr n x n email protected sr n x n email protected or n x nsatisfyingp t p problem iigiven email protected email protected r n x n find a s e such email protected email protected a inf a s email protected email protected email protected where email protected is the frobenius norm and s e is the solution set of problem i necessary and sufficient conditions for the solvability of problem i and the general form of the solution of problem i are given for problem ii the expression of the solution is provided furthermore it is pointed that some results of math numer sin 1 2000 29 are special cases of this paper

solutions blowing up on any given compact set for the energy subcritical wave equation abstract we consider the focusing energy subcritical nonlinear wave equation t t u u u p 1 u in r n n 1 given any compact set k r n we construct finite energy solutions which blow up at t 0 exactly on k the construction is based on an appropriate ansatz the initial ansatz is simply u 0 t x t a x 2 p 1 where a 0 vanishes exactly on k which is a solution of the ode h h p we refine this first ansatz inductively using only ode techniques and taking advantage of the fact that for suitably chosen a space derivatives are negligible with respect to time derivatives we complete the proof by an energy argument and a compactness method

lp theory for a generalized nonlinear viscoelastic fluid model of differential type in various domains abstract this paper studies a coupled system of hyperbolic and parabolic equations governing the motion of viscoelastic incompressible fluids on various domains the model under consideration covers a wide range of nonlinear fluids including generalized newtonian fluids generalized oldroyd b fluids or peterlin approximations existence and uniqueness of strong l p solutions for large times are proved for small data for arbitrarily large data local well posedness is shown

the solvability conditions for the inverse eigenproblems of symmetric and generalized centro symmetric matrices and their approximations let be the frobenius norm of matrices we consider i the set se of symmetric and generalized centro symmetric real n n matrices rn with some given eigenpairs j qj j 1 2 m and ii the element r in se which minimizes r r for a given real matrix r necessary and sufficient conditions for se to be nonempty are presented a general form of elements in se is given and an explicit expression of the minimizer r is derived finally a numerical example is reported

asymptotic expansion of the dulac map and time for unfoldings of hyperbolic saddles local setting abstract in this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle we give a structure theorem for the asymptotic expansion of the local dulac time as well as the local dulac map with the remainder uniformly flat with respect to the unfolding parameters here local means close enough to the saddle in order that the normalizing coordinates provided by a suitable normal form can be used the principal part of the asymptotic expansion is given in a monomial scale containing a deformation of the logarithm the so called roussarie ecalle compensator especial attention is paid to the remainder s properties concerning the derivation with respect to the unfolding parameters

exterior powers of the adjoint representation and the weyl ring of e8 abstract i derive explicitly all polynomial relations in the character ring of e 8 of the form k e 8 p k 1 8 0 where k e 8 is an arbitrary exterior power of the adjoint representation and i is the ith fundamental character this has simultaneous implications for the theory of relativistic integrable systems seiberg witten theory quantum topology orbifold gromov witten theory and the arithmetic of elliptic curves the solution is obtained by reducing the problem to a large but finite dimensional linear problem which is amenable to an efficient solution via distributed computation

regularity of the geodesic flow of the incompressible euler equations on a manifold in this paper we investigate the regularity in time of the volume preserving geodesic flow which is associated with the incompressible euler equations on a compact d dimensional riemannian manifold with boundary our result which completes the local in time well posedness theory of ebin and marsden ann math 92 102 163 1970 states roughly that the time smoothness of geodesic curves is only limited by the smoothness of the manifold such regularity is measured in a broad class of ultradifferentiable functions which includes the real analytic and gevrey classes a by product of this simple and constructive proof is new ideas to design high order semi lagrangian methods for integrating the incompressible euler equations on a manifold

a perturbation method for optimizing matrix stability we present the first practical perturbation method for optimizing matrix stability using spectral abscissa minimization using perturbation theory for a matrix with simple eigenvalues and coupling this with linear programming we successively reduce the spectral abscissa of a matrix until it reaches a local minimum optimality conditions for a local minimizer of the spectral abscissa are provided and proved for both the affine matrix problem and the output feedback control problem experiments show that this novel perturbation method is efficient especially for a matrix with the majority of whose eigenvalues are already located in the left half of the complex plane moreover unlike most available methods the method does not require the introduction of lyapunov variables the method is illustrated for a small size matrix from an affine matrix problem and is then applied to large matrices actually arising from more sophisticated control problems used in the design of the boeing 767 jet and a nuclear powered turbo generator

sobolev regularity of the equation on the hartogs triangle the regularity of the overline partial problem on the domain left z 1 right left z 2 right 1 in mathbb c 2 is studied using l 2 methods estimates are obtained for the canonical solution in weighted l 2 sobolev spaces with a weight that is singular at the point 0 0 in particular the singularity of the bergman projection for the hartogs triangle is contained at the singular point and it does not propagate

an iterative algorithm for solving a finite dimensional linear operator equation t x f with applications abstract this paper proposes an iterative algorithm for solving a general finite dimensional linear operator equation t x f and demonstrates that it will get the exact solution within a finite number of iteration steps this algorithm unifies all the iterative methods in huang 2008 3 peng 2005 7 and peng and peng 2006 8 and provides an iterative method for solving an inverse problem related to hermitian generalized hamiltonian matrices 2 12

smooth invariant manifolds in banach spaces with nonuniform exponential dichotomy we establish the existence of smooth stable manifolds for semiflows defined by ordinary differential equations v a t v f t v in banach spaces assuming that the linear equation v a t v admits a nonuniform exponential dichotomy our proof of the ck smoothness of the manifolds uses a single fixed point problem in the unit ball of the space of ck functions with holder continuous kth derivative this is a closed subset of the space of continuous functions with the supremum norm by an apparently not so well known lemma of henry see proposition 3 the estimates showing that the functions maintain the original bounds when transformed under the fixed point operator are obtained through a careful application of the faa di bruno formula for the higher derivatives of the compositions see 31 and 35 as a consequence we obtain in a direct manner not only the exponential decay of solutions along the stable manifolds but also of their derivatives up to order k when the vector field is of class ck

ultradistributional boundary values of harmonic functions on the sphere abstract we present a theory of ultradistributional boundary values for harmonic functions defined on the euclidean unit ball we also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions to this end we obtain explicit estimates for partial derivatives of spherical harmonics which are of independent interest and refine earlier estimates by calderon and zygmund we apply our results to characterize the support of ultradistributions on the sphere via abel summability of their spherical harmonic expansions

smooth center manifolds for nonuniformly partially hyperbolic trajectories abstract we establish the existence of unique smooth center manifolds for ordinary differential equations v a t v f t v in banach spaces assuming that v a t v admits a nonuniform exponential trichotomy this allows us to show the existence of unique smooth center manifolds for the nonuniformly partially hyperbolic trajectories in addition we prove that the center manifolds are as regular as the vector field our proof of the c k smoothness of the manifolds uses a single fixed point problem in an appropriate complete metric space to the best of our knowledge we establish in this paper the first smooth center manifold theorem in the nonuniform setting

nonlinear stability of flows of jeffreys fluids at low weissenberg numbers we consider the stability of steady flows of viscoelastic fluids of jeffreys type for sufficiently small weissenberg numbers but arbitrary reynolds numbers it is proved that the flow is stable to small disturbances if the spectrum of the linearized operator is in the left half plane

concavity of the mutual information rate for input restricted memoryless channels at high snr we consider a memoryless channel with an input markov process supported on a mixing finite type constraint we continue the development of asymptotics for the entropy rate of the output hidden markov chain and deduce that at high signal to noise ratio the mutual information rate of such a channel is concave with respect to almost all input markov chains of a given order

approximate solutions and micro regularity in the denjoy carleman classes abstract we begin with a sequence m of positive real numbers and we consider the denjoy carleman class c m we show how to construct m approximate solutions for complex vector fields with c m coefficients we then use our construction to study micro local properties of boundary values of approximate solutions in general m involutive structures of codimension one where the approximate solution is defined in a wedge whose edge where the boundary value exists is a maximally real submanifold we also obtain a c m version of the edge of the wedge theorem

comparison of fast boundary element methods on parametric surfaces we compare fast black box boundary element methods on parametric surfaces in r3 these are the adaptive cross approximation the multipole method based on interpolation and the wavelet galerkin scheme the surface representation by a piecewise smooth parameterization is in contrast to the common approximation of surfaces by panels nonetheless parametric surface representations are easily accessible from computer aided design cad and are recently topic of the studies in isogeometric analysis especially we can apply two dimensional interpolation in the multipole method a main feature of this approach is that the cluster bases and the respective moment matrices are independent of the geometry this results in a superior compression of the far field compared to other cluster methods

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

a new algorithm for computing the multivariate faa di bruno s formula abstract a new algorithm for computing the multivariate faa di bruno s formula is provided we use a symbolic approach based on the classical umbral calculus that turns the computation of the multivariate faa di bruno s formula into a suitable multinomial expansion we propose a maple procedure whose computational times are faster compared with the ones existing in the literature some illustrative applications are also provided

divided differences of implicit functions under general conditions the equation g x y 0 implic itly denes y locally as a function of x in this article we express divided dierences of y in terms of bivariate divided dierences of g generalizing a recent result on divided dierences of inverse functions

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

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

linear parameterized inverse eigenvalue problem of bisymmetric matrices abstract in this paper we consider the linear parameterized inverse eigenvalue problem of bisymmetric matrices which is described as follows problem i given real bisymmetric matrices b 0 b 1 b 2 b n and real numbers 1 2 n find values of c c 1 c 2 c n t such that the eigenvalues of the matrix b c b 0 c 1 b 1 c 2 b 2 c n b n are precisely 1 2 n we first establish the structure of bisymmetric matrices based on the newton type iterative method we then turn problem i into the inverse eigenvalue problems of symmetric matrices with small sizes and solve these problems finally we present numerical examples to illustrate our results

the hermitian reflexive solutions to the matrix inverse problem ax b in this paper the necessary and sufficient conditions for the solvability of the matrix inverse problem ax b in hermitian reflexive matrix set hj n x n are given and the solution expression of this matrix inverse problem is also presented moreover an optimal approximation to any matrix in the above solution set in frobenius norm is provided

linear restriction problem of hermitian reflexive matrices and its approximation in this paper we consider a linear restriction problem of hermitian reflexive matrices and its approximation by using the properties and structure of hermitian reflexive matrices and the special properties of reflexive vectors and anti reflexive vectors we convert the linear restriction problem to an equivalence problem trickily which is a special feature of this paper and is a different method from other articles then we solve this problem completely and also obtain its optimal approximate solution moreover an algorithm provided for it and the numerical examples show that the algorithm is feasible

derivatives of entropy rate in special families of hidden markov chains consider a hidden markov chain obtained as the observation process of an ordinary markov chain corrupted by noise recently zuk et al showed how in principle one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise namely they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time we generalize this result to a natural class of hidden markov chains called black holes we also discuss in depth special cases of binary markov chains observed in binary symmetric noise and give an abstract formula for the first derivative in terms of a measure on the simplex due to blackwell

approximate cayley transform methods for inverse eigenvalue problems and convergence analysis abstract based on an approximation to cayley transform we propose an approximate cayley transform method and its inexact version for solving inverse eigenvalue problems which has the advantage over other known methods in the sense that it avoids solving systems in obtaining the approximate eigenvectors under the nonsingular condition used in d sun and j sun 29 we show that the proposed methods converge at least superlinearly moreover numerical experiments are given which illustrate that comparing with the cayley transform methods our methods need much less inner iterations and cpu time

approaches to robust pole assignment abstract robust pole assignment is a non linear optimization problem in many variables we describe numerical methods for determining robust or well conditioned so lutions to the problem of pole assignment by state feedback the solutions are chosen to minimize various objective functions based on the condition number of the eigenvector matrix careful choice of parametrization and objective function avoids singularities and artificial variable constraints explicit formulae for the gradient and hessian permit rigorous stopping criteria and rapid local convergence several computational examples are included

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

a numerical method of structure preserving model updating problem and its perturbation theory a method is presented to update a special finite element fe analytical model based on matrix approximation theory with spectral constraint at first the model updating problem is treated as a matrix approximation problem dependent on the spectrum data from vibration test and modal parameter identification the optimal approximation is the first modified solution of fe model an algorithm is given to preserve the sparsity of the model by multiple correction the convergence of the algorithm is investigated and perturbation of the modified solution is analyzed finally a numerical example is provided to confirm the convergence of the algorithm and perturbation theory

asymptotic expansion of multivariate conservative linear operators in this paper we study the asymptotic expansion of the partial derivatives of a sequence of linear conservative operators we find sufficient conditions on the sequence that guarantee that such an expansion can be derived from the asymptotic formula for the nondifferentiated sequence our results are valid even if the operators of the sequence present difficult conservative properties different form the classical preservation of the usual convexities we use our theorems to obtain the complete asymptotic expansions and voronovskaja formulae for the partial derivatives of multivariate versions of the meyer konig and zeller operators and the bleimann butzer and hahn operators

existence of slow steady flows of viscoelastic fluids of white metzner type abstract this work is concerned with the study of steady flows of viscoelastic fluids for which the extra stress is given by a differential constitutive equation of white metzner type

solving inverse eigenvalue problems via householder and rank one matrices abstract a brief and practical algorithm is introduced to solve symmetric inverse eigenvalue problems which we call hrou algorithm the algorithm is based on householder transformations and rank one updating we give some basic properties and the computational amount and develop sensitivity analysis of hrou algorithm furthermore we develop hrou algorithm into a multi level and adaptive one named mlahrou to solve symmetric nonnegative inverse eigenvalue problems new sufficient conditions to ensure symmetric nonnegative matrices and symmetric m matrices are given many numerical examples are given to verify our theory compare with existing results and show the efficiency of our algorithms

a matrix inverse eigenvalue problem and its application the problem of generating a matrix a with specified eigenvalues which maps a given set of vectors of another given set is presented an existence theorem is given and proved a stable algorithm for producing the matrix a is discussed the relation between this problem and the pole assignment problem in control theory is investigated the application of this problem in the design of neural networks is discussed

hyperbolicity and change of type in the flow of viscoelastic fluids the equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators propagation of singularities is discussed and conditions for a change of type are investigated the vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied this leads to a partitioning of the field of flow into subcritical and supercritical regions as in the problem of transonic flow

analysis of the domain mapping method for elliptic diffusion problems on random domains in this article we provide a rigorous analysis of the solution to elliptic diffusion problems on random domains in particular based on the decay of the karhunen loeve expansion of the domain perturbation field we establish decay rates for the derivatives of the random solution that are independent of the stochastic dimension for the implementation of a related approximation scheme like quasi monte carlo quadrature stochastic collocation etc we propose parametric finite elements to compute the solution of the diffusion problem on each individual realization of the domain generated by the perturbation field this simplifies the implementation and yields a non intrusive approach having this machinery at hand we can easily transfer it to stochastic interface problems the theoretical findings are complemented by numerical examples for both stochastic interface problems and boundary value problems on random domains

a multivariate faa di bruno formula with applications a multivariate faa di bruno formula for computing arbitrary partial derivatives of a function composition is presented it is shown by way of a general identity how such derivatives can also be expressed in the form of an infinite series applications to stochastic processes and multivariate cumulants are then delineated

fundamental study a concise functional neural network computing the largest modulus eigenvalues and their corresponding eigenvectors of a real skew matrix quick extraction of the largest modulus eigenvalues of a real antisymmetric matrix is important for some engineering applications as neural network runs in concurrent and asynchronous manner in essence using it to complete this calculation can achieve high speed this paper introduces a concise functional neural network fnn which can be equivalently transformed into a complex differential equation to do this work after obtaining the analytic solution of the equation the convergence behaviors of this fnn are discussed simulation result indicates that with general initial complex values the network will converge to the complex eigenvector which corresponds to the eigenvalue whose imaginary part is positive and modulus is the largest of all eigenvalues comparing with other neural networks designed for the like aim this network is applicable to real skew matrices

a kam theorem for finitely differentiable hamiltonian systems abstract given l 2 2 d 4 we prove the persistence of a cantor family of kam tori of measure o e 1 2 l for any non degenerate nearly integrable hamiltonian system of class c l d t d where 1 is the diophantine power of the frequencies of the persistent kam tori and d r d is a bounded domain provided that the size e of the perturbation is sufficiently small this extends a result by d salamon in 25 according to which we do have the persistence of a single kam torus in the same framework moreover as for the persistence of a single torus the regularity assumption is essentially optimal

the fbi transforms and their use in microlocal analysis abstract using a more general class of fbi transforms introduced by s berhanu and j hounie in 12 we completely characterize regularity and microregularity in denjoy carleman non quasi analytic classes which includes the gevrey classes and m christ version of the fbi transform defined in 22 as examples we also exhibit a result on microlocal regularity for solutions of first order partial differential equations in these classes that do not seem possible to prove using the classical fbi transform

least squares solution for inverse eigenpair problem of nonnegative definite matrices suppose we know some eigenvalues i and eigenvectors xi associated with i i 1 2 m for a positive semidefinite may be unsymmetric matrix let x x1 x2 xm diag 1 2 m in this paper we mainly discuss solving the following two problems problem i given x rn m diag 1 m find matrices a such that ax x min where a is a positive semidefinite may be unsymmetric matrix problem ii given a rn n find a se such that a a mina se a a where is frobenius norm and se denotes the solution set of problem i an existence theorem of solution for problems i and ii has been given and proved and the general solutions of problem i have been derived sufficient conditions that prove an explicit solution have been provided

mathematical analysis of viscoelastic fluids of white metzner type abstract this work is concerned with the study of the flow of an incompressible viscoelastic fluid of white metzner type because of the dependence of the viscosity and relaxation functions on the second invariant of the rate of deformation tensor this model leads to a nonlinear not quasilinear partial differential equations system we establish several results on the existence uniqueness and stability of solutions of the 2 d initial boundary value problem

center manifolds for infinite delay we obtain a c1 center manifold theorem for perturbations of delay difference equations in banach spaces with infinite delay our results extend in several directions the existing center manifold theorems besides considering infinite delay equations we consider perturbations of nonuniform exponential trichotomies and generalized trichotomies that may exhibit stable unstable and central behaviors with respect to arbitrary asymptotic rates ec n for some diverging sequence n this includes as a very special case the usual exponential behavior with n n