analysis of dynamic algorithms in knuth s model abstract this paper analyzes the average behaviour of algorithms that operate on dynamically varying data structures subject to insertions i deletions d positive resp negative queries q resp q under the following assumptions if the size of the data structure is k k n then the number of possibilities for the operations d and q is a linear function of k whereas the number of possibilities for the ith insertion or negative query is equal to i this statistical model was introduced by francon 6 7 and knuth 12 and differs from the model used in previous analyses 2 7 integrated costs for these dynamic structures are defined as averages of costs taken over the set of all their possible histories i e evolutions considered up to order isomorphism of length n we show that the costs can be calculated for the data structures serving as implementations of linear lists priority queues and dictionaries the problem of finding the limiting distributions is also considered and the linear list case is treated in detail the method uses continued fractions and orthogonal polynomials but in a paper in preparation we show that the same results can be recovered with the help of a probabilistic model

non similar normal oscillations in a strongly non linear discrete system abstract the free oscillations of a strongly non linear discrete oscillator are examined by computing its non similar non linear normal modes these are motions represented by curves in the configuration space of the system and they are not encountered in classical linear vibration theory or in existing non linear perturbation techniques the mikhlin manevich asymptotic methodology is used for solving the singular functional equation describing the non similar modes and approximate analytical expressions are derived for an oscillator with weak coupling stiffness and mistuning both localized and non localized modes are detected occurring in small neighborhoods of degenerate and global similar modes of the tuned system when strong coupling is considered only non localized modes were found to exist an interesting result of this work is the detection of mode localization in the tuned periodic system a result with no counterpart in existing theories on linear mode localization as a check of the analytical results numerical integrations of the equations of motion were carried out and the existence of the theoretically predicted non similar modes was verified

fuzzy approach to solve the recognition problem of handwritten chinese characters abstract a method based on the concept of fuzzy set for handwritten chinese character hcc recognition is proposed in this paper chinese characters can be viewed as a collection of line segments called strokes since the strokes under consideration here are fuzzy in nature the concept of fuzzy set is utilized in the similarity measure two membership functions are defined for the location measure and type measure between two strokes and a function of fuzzy entropy is used in information measure although the recognition problem can be reduced to the assignment problem some modifications are still necessary all the similarities between the corresponding strokes can be chosen by solving the assignment problem using the cost function of fuzzy entropy and then are averaged to derive the score of similarity between two chinese characters 881 classes of chinese characters in etl 8 160 variations class are used as the test patterns and the recognition rate is about 96 in addition experiments about the effects of the membership function based on the class separability are also discussed in this paper

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

improving dynamic programming to solve image registration a new method of dynamic programming dp is presented a picture is paired with a reference map in order to arrive at picture registration an ordered sequence of primitive patterns is formed from the map an attempt is made to locate a similar sequence from the picture using classical picture processing methods this yields a distorted and unordered sequence marked by noise dp is then used to search for a common match to the two sequences both the initial and final registration states are however unknown moreover the continuity of the path is frequently interrupted due to shortcomings in detection or perhaps occlusions thus classical dp algorithms appear to give only poor results under practical conditions when well adapted to treat signals issued from a first order markovian process they can be used as this method shows to treat kth order processes the concept of the virtual state kept in memory suspends broken paths until they can be reconnected thus bridging the existing gaps between the different parts of the path the proposed algorithm has been applied to satellite images with their contours sectioned by clouds the result leads to the guarantee of very good registration in spite of image contours badly hampered by noise and or clouds

passive spatial confinement of impulsive responses in coupled nonlinear beams a system of weakly coupled geometrically nonlinear beams is examined a galerkin procedure is used to express the motions of the two beams in terms of their linearized flexural modes transient impulsive excitations are considered and the response of the system is analytically and numerically computed for small values of a coupling nonlinear parameter the vibrational energy injected into the system is proved to localize mainly at the directly forced beam and only a small portion of this energy leaks to the unforced one this passive transient motion confinement is solely due to nonlinear localized modes of the unforced system and it becomes more profound for stronger impulse excitations and as the nonlinearity increases and or the coupling stiffness connecting the two beams decreases

stability of an axially accelerating string subjected to frictional guiding forces abstract the dynamic response of an axially translating continuum subjected to the combined effects of a pair of spring supported frictional guides and axial acceleration is investigated such systems are both non conservative and gyroscopic the continuum is modeled as a tensioned string translating between two rigid supports with a time dependent velocity profile the equations of motion are derived with the extended hamilton s principle and discretized in the space domain with the finite element method the stability of the system is analyzed with the floquet theory for cases where the transport velocity is a periodic function of time direct time integration using an adaptive step runge kutta algorithm is used to verify the results of the floquet theory this approach can also be employed in the general case of arbitrary time varying velocity results are given in the form of time history diagrams and instability point grids for different sets of parameters such as the location of the stationary load the stiffness of the elastic support and the values of initial tension this work showed that presence of friction adversely affects stability but using non zero spring stiffness on the guiding force has a stabilizing effect this work also showed that the use of the finite element method and floquet theory is an effective combination to analyze stability in gyroscopic systems with stationary friction loads

free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints abstract an analytical method is derived for determining the vibrations of two plates which are generally supported along the boundary edges and elastically coupled together at an arbitrary angle the interactions of all four wave groups bending waves out of plane shearing waves in plane longitudinal waves and in plane shearing waves have been taken into account at the junction via four types of coupling springs of arbitrary stiffnesses each of the transverse and in plane displacement functions is expressed as the superposition of a two dimensional 2 d fourier cosine series and several supplementary functions which are introduced to ensure and improve the convergence of the series representation by removing the discontinuities that the original displacement and its derivatives will potentially exhibit at the edges when they are periodically expanded onto the entire x y plane as mathematically implied by a 2 d fourier series the unknown expansions coefficients are calculated using the rayleigh ritz procedure which is actually equivalent to solving the governing equation and the boundary and coupling conditions directly when the assumed solutions are sufficiently smooth over the solution domains numerical examples are presented for several different coupling configurations a good comparison is observed between the current results and the fea models although this study is specifically focused on the coupling of two plates the proposed method can be directly extended to structures consisting of any number of plates

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

the analysis of simple list structures abstract we present an analysis of simple lists either sorted or unsorted under the set of all their possible histories i e evolutions considered up to order isomorphism of length n using the theory of continued fractions and orthogonal polynomials flajolet francon and vuillemin have determined average costs of sequences of operations for many data structures of the dictionary or priority queue type we show here that for the simplest structures variance estimates can also be obtained the method uses continued fractions and properties of nonclassical q generalizations of hermite and laguerre polynomials

transverse vibrations of elastically connected double string complex system part i free vibrations this paper analyzes the forced transverse vibrations of an elastically connected double string complex continuous system the general solutions of forced vibrations of strings subjected to arbitrarily distributed continuous loads are found by using the method of expansion in a series of the mode shape functions different cases of exciting loadings are analyzed the action of stationary harmonic loads and moving concentrated forces is considered vibrations caused by the harmonic exciting forces are discussed and conditions of resonance and dynamic vibration absorption are formulated thus the string type dynamic absorber can be used to suppress the excessive vibrations of corresponding string systems the dynamic string type damper is a new concept of a continuous dynamic vibration absorber cdva it is shown that a corresponding two degree of freedom discrete system is an analogue of an elastically connected double string complex system theoretical analysis is illustrated by a numerical example

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

statistical distribution of frequency response in disordered periodic structures a structure designed to be spatially periodic cannot be exactly periodic the departure from exact periodicity is known as disorder and it causes localization of normal modes and additional attenuation of wave motions in the structure not related to damping the present investigation is directed at a possible adverse effect of disorder namely higher structural response near the point at which a dynamic excitation is applied than would occur in a perfectly periodic structure thereby reducing structure safety and reliability a systematic procedure is developed herein for the analysis of such an effect for a generic disordered periodic structure in particular the probability distribution of structural response is obtained by analysis and by monte carlo simulation which is needed both for fundamental understanding of the effect and for predicting the reliability of a system it is shown also that given probability distributions of the disordered parameters of a structure the mean and standard deviation of structural response can be obtained exactly for a damped randomly disordered periodic structure if the number of disordered cell units is not large and approximately if the number is large application of the procedure is illustrated by an example and the results are compared with monte carlo simulations

on line recognition of cursive korean characters using dp matching and fuzzy concept abstract this paper proposes an on line recognition method of cursive korean characters based on dynamic programming dp matching and fuzzy concept the proposed algorithm invariant to rotation and size reduces greatly the computational requirement of dp matching by matching phonemes rather than character patterns where the angle difference and the ratio of lengths between input and reference patterns are adopted as matching features correct matching of poorly written cursive characters becomes possible by introducing the fuzzy concept in representing phoneme features and the positional relationships between adjacent phonemes computer simulation results show the effectiveness of the proposed algorithm

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

statistical characteristics of frequency response localization in nearly periodic systems premature failures or malfunctions often occur in a mechanical system that has periodically repeated subcomponents due to slight irregularities among subcomponents of the periodic system maximal frequency responses of a few subcomponents become often significantly larger than those of other subcomponents these phenomena called frequency response localization need to be analyzed elaborately for reliable designs of the periodic systems in the present study the strength of frequency response localization for the periodic system is defined and the effects of some parameters on the strength of frequency response localization are investigated statistically

on moving continua with contacts and sliding friction modeling general properties and examples abstract many technical applications feature contacts between moving continua where the contact zone is more or less spatially fixed this contribution describes the modeling of such systems by means of weak formulations derived from hamilton s principle in a material as well as a spatial formulation furthermore linearizations about a stationary solution are carried out the arising differential operators are stated and discussed with respect to symmetry particular attention is paid to the structure and physical interpretation of the contributions arising from the contacts as well as those due to the transport motion the article closes with several examples

random walks gaussian processes and list structures abstract an asymptotic analysis of list structure properties leads to limiting gaussian markovian processes several costs functions are shown to have asymptotic normal distributions

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

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

vibration mode localization in two dimensional systems the method of regular perturbation is applied to study vibration mode localization in randomly disordered weakly coupled two dimensional cantilever spring arrays localization factors which characterize the average exponential rates of decay or growth of the amplitudes of vibration are defined in terms of the angles of orientation first order approximate results of the localization factor are obtained using a combined analytical numerical approach the localization factors are symmetric about the cantilever and the horizontal and vertical axes passing through the cantilever at which vibration is originated for the systems under consideration the direction in which vibration is originated corresponds to the smallest localization factor whereas the diagonal directions correspond to the largest rate of decay or growth of the amplitudes of vibration when plotted in the logarithmic scale the vibration modes are of hill shape with the amplitudes of vibration decaying linearly away from the cantilever at which vibration is originated

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

modal analysis of a continuous gyroscopic second order system with nonlinear constraints abstract a method for the modal analysis of continuous gyroscopic systems with nonlinear constraints is developed this method assumes that the nonlinear constraint can be expressed as a piecewise linear force deflection profile located at an arbitrary position within the domain using this assumption the mode shapes and natural frequencies are first found for each state then a mapping method based on the inner product of the mode shapes is developed to map the displacement of the system between the in contact and out of contact states to illustrate this method a model for the vibration of a traveling string in contact with a piecewise linear constraint is developed as an analog of the interaction between magnetic tape and a guide in data storage systems five design parameters of the guide are considered flange clearance flange stiffness symmetry of the force deflection profile in terms of flange stiffness and offset and the guide s position along the length of the string there are critical bifurcation thresholds below which the system exhibits no chaotic behavior and is dominated by period one symmetric behavior and above which the system contains asymmetric higher periodic motion with windows of chaotic behavior these bifurcation thresholds are particularly pronounced for the transport speed flange clearance symmetry of the force deflection profile and guide position the stability of the system is sensitive to the system s velocity and compared to stationary systems more mode shapes are needed to accurately model the dynamics of the system

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

the dynamics of large scale arrays of coupled resonators abstract this work describes an analytical framework suitable for the analysis of large scale arrays of coupled resonators including those which feature amplitude and phase dynamics inherent element level parameter variation nonlinearity and or noise in particular this analysis allows for the consideration of coupled systems in which the number of individual resonators is large extending as far as the continuum limit corresponding to an infinite number of resonators moreover this framework permits analytical predictions for the amplitude and phase dynamics of such systems the utility of this analytical methodology is explored through the analysis of a system of n non identical resonators with global coupling including both reactive and dissipative components physically motivated by an electromagnetically transduced microresonator array in addition to the amplitude and phase dynamics the behavior of the system as the number of resonators varies is investigated and the convergence of the discrete system to the infinite n limit is characterized

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

probabilistic vibration analysis of nearly periodic structures a disordered structure with weakly coupled subsystems has localized modes with the vibratory energy concentrated in one part of the mode shape the localization of modes may significantly affect the forced vibration response increasing the maximum vibration amplitude dramatically in some cases it is the scope of this paper to study the forced vibration of nearly periodic systems consisting of almost identical substructures and to analyze their free and forced dynamic responses probabilistically it is shown that the sensitivity of the forced response to the degree of localization depends on a combination of the symmetry of the mode which is excited and the phase difference between the forces acting on each substructure these results might explain the range of contrasting conclusions of earlier publications on the effects of forced response on mistuned structures a probabilistic analysis of the free and forced responses of a nearly periodic structure is shown to be useful in the design of structures that are sensitive to the degree of localization the results of the probabilistic analysis are verified using monte carlo simulation

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

waveform correlation by tree matching a waveform correlation scheme is presented the scheme consists of four parts 1 the representation of waveforms by trees 2 the definition of basic operations on tree nodes and tree distance 3 a tree matching algorithm and 4 a backtracking procedure to find the best node to node correlation this correlation scheme has been implemented results show that the scheme has the capability of handling distortions that result from stretching or shrinking of intervals or from missing intervals