flexible skew symmetric shape model for shape representation classification and sampling skewness of shape data often arises in applications e g medical image analysis and is usually overlooked in statistical shape models in such cases a gaussian assumption is unrealistic and a formulation of a general shape model which accounts for skewness is in order in this paper we present a novel statistical method for shape modeling which we refer to as the flexible skew symmetric shape model fssm the model is sufficiently flexible to accommodate a departure from gaussianity of the data and is fairly general to learn a mean shape template with a potential for classification and random generation of new realizations of a given shape robustness to skewness results from deriving the fssm from an extended class of flexible skew symmetric distributions in addition we demonstrate that the model allows us to extract principal curves in a point cloud the idea is to view a shape as a realization of a spatial random process and to subsequently learn a shape distribution which captures the inherent variability of realizations provided they remain with high probability within a certain neighborhood range around a mean specifically given shape realizations fssm is formulated as a joint bimodal distribution of angle and distance from the centroid of an aggregate of random points mean shape is recovered from the modes of the distribution while the maximum likelihood criterion is employed for classification

numerical presentation of eigenvalue curve veering and mode localization in coupled pendulums to be 0 01 0 01 0 01 0 0 and 0 01 0 the e rst variations and the eigenvalues obtained by the classic method and the improved calculation are given in table 1 the relative errors of the variations are shown in fig 2 the result of the improved calculation is in the very good agreementwith the exact one apartfromthe third mode the e rst variations given by the improved calculation are even better than those with the second variations by the classic method a large modie cation of the truss is considered by multiplying a and b with a factor from 1 through 10 the relative errors of the e rst variations are shown in fig 3 the errors in the e rst mode increase from 0 0827 to 0 8410 whereas those of the classic method change from 0 4159 to 4 1834 the fourth mode shows the biggest difference as the largest error of the improved calculation is 0 0023 but 9 9982 for the classic method conclusions an improved calculation of eigenvalue variations has been presented the eigenvalue approximation from the e rst variation is a rayleigh quotient the variations are different from those in the classic method when there is a variation of b which is the inertiarelated matrix in a structural dynamics although there are more terms in the variations of eigenvalues no extra matrix operation is required thegivenexamplecone rmsthattheaccuracyoftheeigenvalue variations is much better than that obtained with the classic method

fisher information for inverse problems and trace class operators this paper provides a mathematical framework for fisher information analysis for inverse problems based on gaussian noise on infinite dimensional hilbert space the covariance operator for the gaussian noise is assumed to be trace class and the jacobian of the forward operator hilbert schmidt we show that the appropriate space for defining the fisher information is given by the cameron martin space this is mainly because the range space of the covariance operator always is strictly smaller than the hilbert space for the fisher information to be well defined it is furthermore required that the range space of the jacobian is contained in the cameron martin space in order for this condition to hold and for the fisher information to be trace class a sufficient condition is formulated based on the singular values of the jacobian as well as of the eigenvalues of the covariance operator together with some regularity assumptions regarding their relative rate of convergence an explicit example is given regarding an electromagnetic inverse source problem with external spherically isotropic noise as well as internal additive uncorrelated noise

asymptotic global confidence regions for 3 d parametric shape estimation in inverse problems this paper derives fundamental performance bounds for statistical estimation of parametric surfaces embedded in ropf3 unlike conventional pixel based image reconstruction approaches our problem is reconstruction of the shape of binary or homogeneous objects the fundamental uncertainty of such estimation problems can be represented by global confidence regions which facilitate geometric inference and optimization of the imaging system compared to our previous work on global confidence region analysis for curves two dimensional 2 d shapes computation of the probability that the entire surface estimate lies within the confidence region is more challenging because a surface estimate is an inhomogeneous random field continuously indexed by a 2 d variable we derive an asymptotic lower bound to this probability by relating it to the exceedence probability of a higher dimensional gaussian random field which can in turn be evaluated using the tube formula due to sun simulation results demonstrate the tightness of the resulting bound and the usefulness of the three dimensional global confidence region approach

particularities of newton s method in space frame force determination utilising eigenpair functions abstract redundant space frame dynamics are modelled through the structural eigenproblem which is formulated to account for the geometric stiffness due to self equilibrating membrane forces the resulting mathematical eigenvalues and eigenvectors respectively indicative of natural frequencies and modes of oscillation are then assumed to be continuous functions of a scalar factor upon a normalised set of forces in equilibrium newton s method or sensitivity analysis provides a means for minimising the difference between mathematical and physically observed eigenvalues whereupon the axial forces are inferred from the model issues of convergence and root uniqueness are anticipated eigenvalue coalescence in which eigenvalues transitorily coalesce to permute their arbitrarily numerical ordering is seen to define non smooth eigenvalue functions and hence encumber newton s method mode tracing strategies to overcome this are discussed the existence of various degrees of eigenvalue degeneracy owing to frame cyclic symmetry or otherwise is anticipated in terms of the influence upon newton s method if the degree of frame static redundancy is greater than one and there exist a number of linearly independent force distributions then the required force determination is a multidimensional newton method problems encountered in these manifold dimensions including those arising from frame spatial periodicity and the adversity of newton s method are overcome emphasis is placed upon minimising the dimensionality of newton s method through enforcement of equilibrium constraints illustrative numerical simulations are given and some applications of the method are proposed

behavior of derivatives of eigenvalues and eigenvectors in curve veering and mode localization and their relation to close eigenvalues the problem to measure the phenomena of eigenvalue curve veering and mode localization is addressed in this paper the second derivative of an eigenvalue and the first derivative of an eigenvector are taken as the measures numerically showing curve veering and mode localization based on the measurement close eigenvalues as a key factor for the occurrence of the phenomena are defined two eigenvalues are considered to be close if their difference is small enough to cause the occurrence of the phenomena the curve veering and mode localization can be noted by comparison of the derivatives with a critical value and hence the associated eigenvalues are close weakly coupled springs are given as an example

periodic solution to nonlinear differential equation at resonance abstract in this paper a class of nonlinear sturm liouville problems at resonance is discussed an extended form of a non variational version of a max min principle is applied to show that the equation possesses unique 2 periodic solution under a less restrictive condition this result extends what we have already known

reconstruction from projections based on detection and estimation of objects parts i and ii performance analysis and robustness analysis the problem of reconstructing a multidimensional field from noisy limited projection measurements is approached using an object based stochastic field model objects within a cross section are characterized by a finite dimensional set of parameters which are estimated directly from limited noisy projection measurements using maximum likelihood estimation in part i the computational structure and performance of the ml estimation procedure are investigated for the problem of locating a single object in a deterministic background simulations are also presented in part ii the issue of robustness to modeling errors is addressed

modal analysis of a nonlinear periodic structure with cyclic symmetry this paper carries out modal analysis of a nonlinear periodic structure with cyclic symme try the nonlinear normal mode nnm theory is brie y described and a computational algorithm for the nnm computation is presented the results obtained on a simpli ed model of a bladed assembly show that this system possesses a very complicated struc ture of nnms including similar and nonsimilar nnms nonlocalized and localized nnms bifurcating and internally resonant nnms modal interactions that occur without neces sarily having commensurate natural frequencies in the underlying linear system are also discussed

on the existence and uniqueness for higher order periodic boundary value problems abstract this paper discusses the existence and uniqueness for the n th order periodic boundary value problem l n u t f t u t 0 t 2 u i 0 u i 2 i 0 1 n 1 where l n u t u n t i 0 n 1 a i u i t is an n th order linear differential operator n 2 and f 0 2 r r is continuous in the case that l n has an even order derivative we present some new spectral conditions for the nonlinearity f t u to guarantee the existence and uniqueness these spectral conditions allow f t u to be a superlinear growth and are the extension for the spectral separation condition presented recently in y li existence and uniqueness for higher order periodic boundary value problems under spectral separation conditions j math anal appl 322 2 2006 530 539

mode localization phenomena in large space structures the possibility of localization or confinement of vibratory modes in large space structures is investigated theoretically and numerically these structures belong to a class of periodic structures that have recently been shown to be sensitive to periodicity b reaking disorder or imperfections when localization occurs the modal amplitude of a global mode becomes confined to a local region of the structure with serious implications for the control problem the results of this study indicate that mode localization is most likely to occur in structures consisting of a large number of weakly coupled substructures certain large space structures with high modal densities fall in this category and it is therefore important to include the effect of structural imperfections and disorder when designing control systems for shape or directional control of such structures k kh kw ku k k m m m n n p qi qt t u v w uf 8fj e 6

wavelet descriptors for multiresolution recognition of handprinted characters we present a novel set of shape descriptors that represents a digitized pattern in a concise way and that is particularly well suited for the recognition of handprinted characters the descriptor set is derived from the wavelet transform of a pattern s contour the approach is closely related to feature extraction methods by fourier series expansion the motivation to use an orthonormal wavelet basis rather than the fourier basis is that wavelet coefficients provide localized frequency information and that wavelets allow us to decompose a function into a multiresolution hierarchy of localized frequency bands we describe a character recognition system that relies upon wavelet descriptors to simultaneously analyze character shape at multiple levels of resolution the system was trained and tested on a large database of more than 6000 samples of handprinted alphanumeric characters the results show that wavelet descriptors are an efficient representation that can provide for reliable recognition in problems with large input variability

joint estimation and correction of geometric distortions for epi functional mri using harmonic retrieval magnetic resonance imaging mri uses applied spatial variations in the magnetic field to encode spatial position therefore nonuniformities in the main magnetic field can cause image distortions in order to correct the image distortions it is desirable to simultaneously acquire data with a field map in registration we propose a joint estimation je framework with a fast noniterative approach using harmonic retrieval hr methods combined with a multi echo echo planar imaging epi acquisition the connection with hr establishes an elegant framework to solve the je problem through a sequence of 1 d hr problems in which efficient solutions are available we also derive the condition on the smoothness of the field map in order for hr techniques to recover the image with high signal to noise ratio compared to other dynamic field mapping methods this method is not constrained by the absolute level of the field inhomogeneity over the slice but relies on a generous pixel to pixel smoothness moreover this method can recover image field map and t2 map simultaneously

frequency coalescence and mode localization phenomena a geometric theory physical systems the natural frequencies of which depend parametrically on certain quantities may exhibit the phenomenon of frequency coalescence when two or more natural frequencies become equal or the phenomenon of avoided crossings when two or more frequencies approach rapidly and then avoid crossing each other in the process the natural modes undergo significant variations it is shown that both phenomena can be described in a unified manner from the singularities of the mapping from the complex parameter plane into the complex frequency plane in particular the formation of a saddle point in the frequency plane and a branch point in the parameter space is the basis for explaining the properties associated with these phenomena the question of sensitivity of the system response near such singularities is subsequently examined it is shown that the development of a branch point singularity in the complex parameter plane can cause large or even infinite sensitivity of the system about this point depending on the distance of the branch point from the real axis in the parameter space it is further shown that mode localization is also associated with the appearance of a branch point near the real axis of the complex parameter plane which causes the large sensitivity that characterizes the phenomenon the theory is applied to examples of conservative and dissipative systems undergoing free vibrations

on nonlinear frequency veering and mode localization of a beam with geometric imperfection resting on elastic foundation this work presents an investigation on the effect of an initial geometric imperfection wavelength amplitude and degree of localization on the in plane nonlinear natural frequencies veering and mode localization of an elastic euler bernoulli beam resting on a winkler elastic foundation the beam is assumed to be pinned pinned with a linear torsional spring at one end the effect of the axial force induced by mid plane stretching is accounted for in the derivation of the mathematical model due to its known importance and significant effect on the nonlinear dynamic behavior of the beam as it was proved and presented in earlier investigations the governing partial differential equation is discretized using the assumed mode method and the resulting nonlinear temporal equation was solved using the harmonic balance method to obtain results for the nonlinear natural frequencies and mode shapes the results are presented in the form of characteristic curves which show the variations of the nonlinear natural frequencies of the first three modes of vibration for a selected range of physical parameters like torsional spring constant elastic foundation stiffness and amplitude and wavelength of a localized and non localized initial slack

beyond the limitations of perturbation methods for real random eigenvalue problems using exceptional points and analytic continuation a numerical method is proposed to approximate the solution of parametric eigenvalue problem when the variability of the parameters exceed the radius of convergence of low order perturbation methods the radius of convergence of eigenvalue perturbation methods based on taylor series is known to decrease when eigenvalues are getting closer to each other this phenomenon knwon as veering in structural dynamics is a direct consequence of the existence of branch point singularity in the complex plane of the varying parameters where some eigenvalues are defective when this degeneracy referred to as exceptional point ep is close to the real axis the veering becomes stronger the main idea of the proposed approach is to combined a pair of eigenvalues to remove this singularity to do so two analytic auxiliary functions are introduced and are computed through high order derivatives of the eigenvalue pair with respect to the parameter this yields a new robust eigenvalue reconstruction scheme which is compared to taylor and puiseux series in all cases theoretical bounds are established and all approximations are compared numerically on a three degrees of freedom toy model this system illustrate the ability of the method to handle the vibrations of a structure with a randomly varying parameter computationally efficient the proposed algorithm could also be relevant for actual numerical models of large size arising from other applications involving parametric eigenvalue problems e g waveguides rotating machinery or instability problems such as squeal or flutter

forced response statistics of mistuned bladed disks a stochastic reduced basis approach this paper presents a stochastic reduced basis approach for predicting the forced response statistics of mistuned bladed disk assemblies in this approach the system response in the frequency domain is represented using a linear combination of complex stochastic basis vectors with undermined coefficients the terms of the preconditioned stochastic krylov subspace are used here as basis vectors two variants of the stochastic bubnov galerkin scheme are employed for computing the undetermined terms in the reduced basis representation which arise from how the condition for orthogonality between two random vectors is interpreted explicit expressions for the response quantities can then be derived in terms of the random system parameters which allow for the possibility of efficiently computing the response statistics in the post processing stage numerical studies are presented for mistuned cyclic assemblies of mono coupled single mode components it is demonstrated that the accuracy of the response statistical moments computed using stochastic reduced basis methods can be orders of magnitude better than classical perturbation methods

the vibration and stability of a friction guided translating string abstract eyelets capstans and cylindrical surfaces are often used in thread fiber and paper handling machinery to guide the axially moving element in addition to providing positional control these guides introduce dry friction forces that alter the vibration and stability characteristics of the system this paper examines the lateral response of a string that slides through an elastically supported dry friction guide exact expressions are derived for the linear response under free and forced conditions solutions for the eigenvalue spectrum exhibit unusual features including multiple divergence instabilities regions of flutter instability and regions of curve veering associated with mode localization a second order perturbation solution is derived to examine the behavior of the eigenvalue spectrum in regions of flutter instability and curve veering the analysis highlights the common features of these two phenomena and suggests ways to minimize vibration by adjusting various design variables the analysis also demonstrates that the eigenvalue loci in regions of flutter instability and curve veering are naturally described by a local hyperbolic approximation

multi parameter perturbation methods for the eigensolution sensitivity analysis of nearly resonant non defective multi degree of freedom systems the dynamic behavior of structural systems may be strongly characterized by the occurrence of multiple internal resonances for particular combinations of the mechanical parameters the linear models governing these resonant or nearly resonant systems tend to exhibit high sensitivity of the eigenvalues and eigenvectors to small parameter modifications this pathological condition is recognized as a source of relevant phenomena such as frequency veering and mode localization or hybridization the paper presents the generalization of uniformly valid perturbation methods to perform eigensolution sensitivity analyses in multi degree of freedom hamiltonian systems with a generic number of close eigenvalues the leading idea is to treat systematically nearly resonant systems as multi parameter perturbations of a perfectly resonant non defective though a priori unknown reference system given a single nearly resonant system a multi parameter perturbation method is presented to achieve a two fold objective first identify a close resonant system suited to serve as a starting point for sensitivity analyses inverse problem second to approximate asymptotically the eigensolution of all the nearly resonant systems which may arise from its generic perturbation direct problem the conditions of existence and uniqueness of the inverse problem solution are discussed the direct problem solution is analyzed with a focus on the eigensolution sensitivity to parameter perturbations with different physical meanings such as a slight geometric disorder or weak elastic coupling in periodic structures finally the procedure is verified on a prototypical structural system describing the section dynamics of a suspended bridge

cramer rao bounds for 2 d target shape estimation in nonlinear inverse scattering problems with application to passive radar we present new methods for computing fundamental performance limits for two dimensional 2 d parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging we evaluate cramer rao lower bounds crb on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory the crb provides an unbeatable performance limit for any unbiased estimator and under fairly mild regularity conditions is asymptotically achieved by the maximum likelihood estimator mle the resultant crbs are used to define an asymptotic global confidence region centered around the true boundary in which the boundary estimate lies with a prescribed probability these global confidence regions conveniently display the uncertainty in various geometric parameters such as shape size orientation and position of the estimated target and facilitate geometric inferences numerical simulations are performed using the layer approach and the nystrom method for computation of domain derivatives and using fourier descriptors for target shape parameterization this analysis demonstrates the accuracy and generality of the proposed methods

localization of vibrations by structural irregularity an investigation of the localization phenomenon is presented for disrodered structural systems consisting of weakly coupled component systems emphasis is placed on the development of a perturbation method that allows one to obtain the localized modes of vibration of the disordered system from the modes of the individual subsystems the principal feature of this perturbation method is that it not only considers the variations of the parameters as perturbations but it also treats the small coupling between subsystems as a perturbation such a perturbation analysis is cost effective as compared to a global eigenvalue analysis of the entire system and proves to be very accurate moreover it provides physical insight into the localization phenomenon and allows one to formulate a criterion that predicts the occurrence of strongly localized modes results are obtained for a chain of single degree of freedom coupled oscillators but these can be readilt generalized to deal with chains of multi degree of freedom component systems

vibration isolation from irregularity in a nearly periodic structure theory and measurements this article describes the theory and a simple experiment carried out to demonstrate the phenomenon of anderson localization in an acoustical context this is an effect whereby the propagation of vibration in a structure which is not entirely regular is impeded by the irregularities giving rise on the average to an exponential decay of vibration level away from the driving point even in the absence of any dissipation the structure used in the experiment was a stretched string with masses attached to it this string was studied with regular spacings of the masses and after the masses had been moved in a controlled way to provide a small degree of irregularity in both cases the transmission of energy from end to end of the string was measured as a function of frequency and also the mode shapes in the second and fourth passbands were measured so as to demonstrate the underlying physics of the localization phenomenon in which the individual modes making up each passband change from being extended throughout the structure in the regular case to being localized in specific areas of the structure in the presence of irregularity all measurements yielded satisfactory agreement with the theoretical predictions

odd periodic solutions for 2nth order ordinary differential equations this paper deals with the existence of periodic solutions for the 2nth order ordinary differential equation u 2n t f t u t u t u 2n 2 t where the nonlinear term f r rn r is a continuous odd function and f t x0 x1 xn 1 is 2 periodic in t some existence results for odd 2 periodic solutions are obtained under the condition that f satisfies some linear superlinear or sublinear growth conditions on x0 x1 xn 1

on periodic solutions for even order differential equations abstract a class of sufficient conditions are obtained for the existence of a unique 2 periodic solution of even order differential equations employing an initial value problem

perfect reconstruction formulas and bounds on aliasing error in sub nyquist nonuniform sampling of multiband signals we examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples this sampling scheme which has been studied previously has an interesting optimality property that uniform sampling lacks one can sample and reconstruct the class spl bscr spl fscr of multiband signals with spectral support spl fscr at rates arbitrarily close to the landau 1969 minimum rate equal to the lebesgue measure of spl fscr even when spl fscr does not tile r under translation using the conditions for exact reconstruction we derive an explicit reconstruction formula we compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band limited to the span of spl fscr the smallest interval containing spl fscr which is a bigger class than the valid signals spl bscr spl fscr band limited to spl fscr we also examine the performance of the reconstruction system when the input contains additive sample noise

minimax emission computed tomography using high resolution anatomical side information and b spline models in this paper a minimax methodology is presented for combining information from two imaging modalities having different intrinsic spatial resolutions the focus application is emission computed tomography ect a low resolution modality for reconstruction of radionuclide tracer density when supplemented by high resolution anatomical boundary information extracted from a magnetic resonance image mri of the same imaging volume the mri boundary within the two dimensional 2 d slice of interest is parameterized by a closed planar curve the cramer rao cr lower bound is used to analyze estimation errors for different boundary shapes under a spatially inhomogeneous gibbs field model for the tracer density a representation for the minimax mri enhanced tracer density estimator is obtained it is shown that the estimator is asymptotically equivalent to a penalized maximum likelihood pml estimator with resolution selective gibbs penalty quantitative comparisons are presented using the iterative space alternating generalized expectation maximization sage fm algorithm to implement the pml estimator with and without minimax weight averaging

periodic solutions for 2kth boundary value problem with resonance abstract in this paper a non variational version of a max min principle is extended and some unique existence results for the periodic boundary value problem of the higher order nonconservative systems with resonance u 2 k t j 1 k a j u 2 j 1 t 1 k 1 g u t e t are obtained

effects of mode localization on input output directional properties of structures abstract the singular value decomposition svd is employed to study the effects of localization phenomena on input output relationships and power and energy transmission ratios of structures for weakly and strongly coupled systems existence of strong localization of singular vectors and abrupt veering of singular value loci are shown occurrence of strong localization causes abrupt changes in input output directional properties in contrast to eigenvalues singular values do not veer away by introducing a disorder in weakly coupled systems in particular the use of singular values and vectors is computationally advantageous in considering multiple load cases while eigenvalue based analyses give information about the resonance frequencies and vibration modes of a structure singular values of the structure are related to the forced response characteristics and give the dynamic behavior in the frequency domain representative examples in structural dynamics are presented

an invariant subspace based approach to the random eigenvalue problem of systems with clustered spectrum the repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix which makes capturing the behavior of these eigenpairs very difficult similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean in addition the methods to solve the random eigenvalue problem often differ in characterizing the problem which leads to different interpretations of the solution thus the solutions obtained from different methods become mathematically incomparable these two issues the difficulty of solving and the non unique characterization are addressed here a different approach is used where instead of tracking a few individual eigenpairs the corresponding invariant subspace is tracked the spectral stochastic finite element method is used for analysis where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors however the main concept of tracking the invariant subspace remains mostly independent of any such representation the approach is successfully implemented in response prediction of a system with repeated natural frequencies it is found that tracking only an invariant subspace could be sufficient to build a modal based reduced order model of the system copyright c 2012 john wiley sons ltd

on the periodic solution to the newtonian equation of motion on considere l equation du mouvement newtonienne d un systeme mecanique soumis a des forces internes conservatives et a des forces externes periodiques u t grad g u t p t ou p r r 11 est continue et de periode 2 et g a des derivees partielles d ordre 2 continues

mode localization in a class of multidegree of freedom nonlinear systems with cyclic symmetry the free oscillations of n degree of freedom dof nonlinear systems with cyclic symmetry and weak coupling between substructures are examined an asymptotic methodology is used to detect localized nonsimilar normal modes i e free periodic motions spatially confined to only a limited number of substructures of the cyclic system it is shown that nonlinear mode localization occurs in the perfectly symmetric weakly coupled structure in contrast to linear mode localization which exists only in the presence of substructure mistuning in addition to the localized modes nonlocalized modes are also found in the weakly coupled system the stability of the identified modes is investigated by means of an approximate two timing averaging methodology and the general theory is applied to the case of a cyclic system with three dof the theoretical results are then verified by direct numerical integrations of the equations of motion

mode localization by structural imperfections in one dimensional continuous systems longitudinal free oscillations of a beam with small axial rigidity continuously restrained by imperfect elastic springs are analyzed it is shown that small imperfections can localize the first modes of vibration in a restricted region of the beam systems with single localized defects are first considered these provide physical insights and make clear that the phenomenon is governed by a turning point mathematical problem analogies with similar problems in quantum mechanics are emphasized periodic or nearly periodic imperfections are then analyzed by applying the floquet theory and finally non periodic imperfections are numerically treated it is shown that when the exponential decay of the solution is strong the modes localize in the neighbourhood of each defect so it is possible to limit oneself to a local analysis the problem of a beam of infinite length with a single imperfection is then solved by applying the asymptotic wkb method an application relative to a parabolic imperfection is analytically developed

eigenvalue curve veering in stressed structures an experimental study there have been extensive research works on the veering phenomenon in dynamic systems as eigenvalues change under parametric variation converging loci are commonly seen to veer away suddenly in a small region of the graph such that the modes swap trajectories all of the modal properties are swapped in the process leading to some curious behaviour in the transition zone theoretical studies of this behaviour have been reported for half a century but despite this heritage explicit references to experimental results are scarce in this paper detailed experimental and numerical investigations on veering are reported the parameter varied is the internal pre load of a redundant frame an fe model is presented and stress stiffening approximations are employed to obtain a tangent stiffness for a nonlinear static solution which is then used in a linear dynamic analysis experimental results are given and the behaviour is found to correspond well with the analytical results in particular the mode shape variation is found to be consistent and the implications of this finding with regard to modal correlation and model validation are noted analyses of the mode shapes in terms of eigenvector rotations are presented and are found to form a valuable tool for the interpretation of experimental results

worst case cramer rao bounds for parametric estimation of superimposed signals with applications the problem of parameter estimation of superimposed signals in white gaussian noise is considered the effect of the correlation structure of the signals on the cramer rao bounds is studied for both the single and multiple experiment cases the best and worst conditions are found using various criteria the results are applied to the example of parameter estimation of superimposed sinusoids or plane wave direction finding in white gaussian noise and best and worst conditions on the correlation structure and relative phase of the sinusoids are found this provides useful information on the limits of the resolvability of sinusoid signals in time series analysis or of plane waves in array processing the conditions are also useful for designing worst case simulation studies of estimation algorithms and for the design of minimax signal acquisition and estimation procedures as demonstrated by an example

diffeomorphisms with banach space domains so f is a local diffeomorphism at every point by the inverse function theorem the aim of this paper is to find a sufficient condition for f to be injective and so a global diffeomorphism x f x theorem 2 l and a sufficient condition for f to be bijective and so a global diffeomorphism onto y theorem 3 1 this last condition is also necessary in the particular case x y r in these theorems the key role is played by nonnegative auxiliary scalar coercive functions that is continuous mappings k x r with k x a as llxll a as far as we know the use of such auxiliary functions in these questions is new first we find some corollaries to the aforementioned theorems the author hopes that suitable auxiliary functions adapted to particular problems may lead to new consequences in order to briefly discuss the results and some of their relations with the literature let us consider the case where x is a hilbert space with scalar product and k e c this simplifies the formulas a little however our results will be formulated and proved for banach spaces where we will ask for k to be locally lipschitz continuous and to have the right directional derivatives only these last assumptions are not made to quibble about this matter but are related to the nondifferentiability of the map x y ix in general banach spaces in this paper we use the hypothesis that the operator norm 11 f i x 11 is bounded on bounded sets i e sup iif ii vr o r w 1 2 il4 5 r

a non variational version of a max min principle f u w 4 2 milwl12 1 then there exists a unique uo e h such that vf ug 0 furthermoref uo min f u in 1975 ueh lazer landesman meyer l l m 3 extended these results to the following situation let x and y be two closed subspaces of h such that h x y x is finite dimensional and x and y are not necessarily orthogonal let t vf then t h h and is a c mapping its frechet derivative at u e his given by t rc d f u let ml and ml be two positive constants such that vu e h vx e x and vy e y we have

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

mode localization and eigenvalue loci veering phenomena in disordered structures an investigation of the effects of disorder on the modes of vibration of nearly periodic structures is presented it is shown that in structures with close eigenvalues small structural irregularities result in both strong localization of the mode shapes and abrupt veering away or mutual repulsion of the loci of the eigenvalues when these are plotted against a parameter representing the disorder in the system perturbation methods for the eigenvalue problem are applied to predict the occurrence of strong localization and eigenvalue loci veering which are shown to be two manifestations of the same phenomenon also perturbation methods that handle the dramatic effects of small disorder are developed to analyze eigenvalue loci veering and strong localization two representative disordered nearly periodic structures are studied a mistuned assembly of coupled oscillators and a multi span beam with irregular spacing of the supports

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

comments on curve veering in eigenvalue problems abstract the dependence of eigenvalues on a system parameter is frequently illustrated by a family of loci when two loci approach each other they often cross or abruptly diverge the latter case called curve veering has been observed in approximate solutions associated with discretized models the influence of discretization in producing curve veering has raised doubt on the validity of many approximate solutions the existence of curve veering in continuous models is illustrated by presenting the exact solution of an elementary eigenvalue problem veering is then examined in a general eigenvalue problem criteria are established to distinguish veerings from crossings in both continuous and discretized models the application of the criteria is illustrated by examples

an application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations abstract in this paper a class of systems of nonlinear differential equations at resonance is considered with the use of a global inversion theorem which is an extended form of a non variational version of a max min principle we prove that this class of equations possesses a unique 2 periodic solution under a rather weaker condition for existence and uniqueness than those given in papers j chen w li periodic solution for 2 k th boundary value problem with resonance j math anal appl 314 2006 661 671 f cong periodic solutions for 2 k th order ordinary differential equations with nonresonance nonlinear anal 32 1998 787 793 f cong periodic solutions for second order differential equations appl math lett 18 2005 957 961 w li periodic solutions for 2 k th order ordinary differential equations with resonance j math anal appl 259 2001 157 167 w li h li a min max theorem and its applications to nonconservative systems int j math math sci 17 2003 1101 1110 w li z shen a constructive proof of existence and uniqueness of 2 periodic solution to duffing equation nonlinear anal 42 2000 1209 1220 this result extends the results known so far

maximum likelihood estimation of object location in diffraction tomography the problem is formulated within the context of diffraction tomography where the complex phase of the diffracted wavefield is modeled using the rytov approximation and the measurements consist of noisy renditions of this complex phase at a single frequency the log likelihood function is computed for the case of additive zero mean gaussian white noise and shown to be expressible in the form of the filtered backpropagation algorithm of diffraction tomography in this form however the filter function is no longer the rho filter appropriate to least square reconstruction but is now the generalized projection propagation of the object centered at the origin onto the line s parallel to the measurement line s but passing through the origin this result allows the estimation problem to be solved via a diffraction tomographic imaging procedure where the noisy data is filtered and backpropagated in a first step and the point of maximum value of the resulting image is then the maximum likelihood ml estimate of the object s location the authors include a calculation of the cramer rao bound for the estimation error and a computer simulation study illustrating the estimation procedure

asymptotic analysis of wave propagation along weakly non uniform repetitive systems we consider monochromatic wave propagation along a long finite one dimensional slightly non uniform waveguide whose ends are connected to uniform semi infinite waveguides the non uniformity in the system parameters which is assumed slowly varying and deterministic can be tuned to produce a desired scattered wave field or reflection transmission properties for a broad range of incident wave fields with this objective in mind we obtain an analytic solution for wave propagation along repetitive systems asymptotic in the slowness of the variation of the system parameters we consider systems governed by a second order finite difference equation and apply the wkb method allowing the index variable to be complex this allows complex turning points to be considered the coefficients of the difference equation are represented by their discrete fourier modes for complex turning points we obtain exponentially small reflection a new result in the context of difference equations the asymptotic solution besides revealing how the non uniformity in the parameters affects wave propagation furnishes an analytic expression for the system scattering matrix as a function of the system parameters it also sheds light on the mechanism of localization phenomena for this class of repetitive systems we also compare the asymptotic results with numerical experiments for large finite one dimensional non uniform chains of coupled pendula

asymptotic global confidence regions in parametric shape estimation problems we introduce confidence region techniques for analyzing and visualizing the performance of two dimensional parametric shape estimators assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary cramer rao bounds are used to define an asymptotic confidence region centered around the true boundary computation of the probability that an entire boundary estimate lies within the confidence region is a challenging problem because the estimate is a two dimensional nonstationary random process we derive lower bounds on this probability using level crossing statistics the same bounds also apply to asymptotic confidence regions formed around the estimated boundaries lower bounding the probability that the entire true boundary lies within the confidence region the results make it possible to generate asymptotic confidence regions for arbitrary prescribed probabilities these asymptotic global confidence regions conveniently display the uncertainty in various geometric parameters such as shape size orientation and position of the estimated object and facilitate geometric inferences numerical simulations suggest that the new bounds are quite tight

asymptotic governing equation for wave propagation along weakly non uniform euler bernoulli beams abstract non uniformity in beams arises either from manufacturing imperfections or by design and can have a singular impact on the qualitative properties of the vibratory response of the beam to describe the mechanism causing such large changes on the dynamics of the beam we derived asymptotically a simpler equation in the form ss q s s 0 the coefficient function q s is given by equation 52 herein in terms of the beam flexural rigidity the mass per unit length and the tensile force applied to the beam the equation is asymptotic to the non uniformity of the beam but under certain restrictions namely of having constant tension and a constant product of the beam mass per unit length and flexural rigidity it is an exact governing equation for wave propagation along bernoulli euler beams and it has a helmholtz like form the behavior of the equation is systematically explored and illustrated through numerical results

cramer rao bounds for parametric shape estimation in inverse problems we address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems when the boundaries are parameterized by a finite number of unknown variables our model applies to multiple unknown objects each with its own unknown gray level or color and boundary parameterization on an arbitrary known background while such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the cramer rao lower bounds very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation we provide a general formula for computing cramer rao lower bounds in inverse problems where the observations are related to the object by a general linear transform followed by a possibly nonlinear and noisy measurement system as an illustration we derive explicit formulas for computed tomography fourier imaging and deconvolution problems the bounds reveal that highly accurate parametric reconstructions are possible in these examples using severely limited and noisy data