the transient amplitude of the viscoelastic travelling string an integral constitutive law abstract the problem considered is an initially stressed viscoelastic string subjected to steady state and harmonic variation of axial motion the string material is assumed to be constituted by the hereditary integral type the partial differential integral equation of motion is derived first then by applying galerkin s method the governing equation is reduced to a set of second order non linear differential integral equations which are solved by finite difference numerical integration procedures the viscoelastic string with a linear spring dashpot model is considered as the voigt element in series with a spring three parameter model the qualitative aspect of parametric excitation due to the non uniform travelling velocity of a viscoelastic string is investigated finally the results are compared with those obtained by a constitutive law of a differential type method the effects of elastic and viscoelastic parameters constant and non constant transport speeds the wave propagation speed ratio and the non linear term on the transient amplitudes are also investigated

suppression of vibration in the axially moving kirchhoff string by boundary control the lyapunov technique has been used to prove that the non linear axially moving kirchhoff string can be stabilized by the linear boundary control the boundary control is the negative feedback of the transversal velocity of the string at one end

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

stochastic excitation of suspended cables involving three simultaneous internal resonances using monte carlo simulation abstract in the neighborhood of three simultaneous internal resonance conditions among four normal modes the response behavior of a suspended cable to random gaussian excitation is studied using computational simulations the study includes the interaction between the first two in plane and the first two out of plane modes when the first in plane mode is externally excited its response can act as a parametric excitation to the other three modes through nonlinear coupling the governed modal equations of motion are numerically simulated using a double precision initial value problem solver adam moulton algorithm the random excitation is generated numerically from a normal distribution using an inverse cumulative distribution function cdf technique the numerical results are processed to estimate response statistics such as mean squares power spectra probability density functions and autocorrelation functions the modes which are indirectly excited exhibit the well known phenomenon on off intermittency in the neighborhood of stochastic bifurcation furthermore in the neighborhood of internal resonances the directly excited mode is found to transfer energy to other modes under gaussian excitation the response coordinates of the four modes are essentially non gaussian narrow band random processes with a central frequency close to each mode natural frequency

2 d shape classification using hidden markov model the authors present a planar shape recognition approach based on the hidden markov model and autoregressive parameters this approach segments closed shapes to make classifications at a finer level the algorithm can tolerate a lot of shape contour perturbation and a moderate amount of occlusion an orientation scheme is described to make the overall classification insensitive to shape orientation excellent recognition results have been reported a distinct advantage of the approach is that the classifier does not have to be trained again when a new class of shapes is added

non linear vibrations of viscoelastic moving belts part i free vibration analysis abstract the non linear free vibration of viscoelastic moving belts is studied based on the linear viscoelastic differential constitutive law the generalized equation of motion is derived for a moving belt with geometric non linearities the method of multiple scales is applied directly to the governing equation which is in the form of continuous autonomous gyroscopic systems with weak non linearity this direct treatment does not involve a prior assumption regarding the spatial solutions the non linear natural frequencies and free response amplitude for autonomous systems are predicted by the perturbation method the results obtained with the quasi static assumption and those without this assumption are compared the effects of elastic and viscoelastic parameters axial moving speed and the geometric non linearity on natural frequencies and amplitudes of the free response are investigated from numerical examples

responses of strongly non linear oscillator parametrically excited by random narrow band noise the principal response of a strongly van der pol duffing oscillator subjected to parametric random narrow band excitation is investigated the technique of modified lindstedt poincare mlp method is used to transform the strongly non linear system to a weak one by introducing a new expansion parameter and then the multiple scales method is applied to determine the modulation equations for amplitude and phase of the response of the system the effect of damping detuning and bandwidth on the dynamic behaviors such as stability bifurcation are examined by computing the maximum lyapunov exponent analytically also the numerical simulation is carried out to verify the analytical results and random jump phenomenon may be observed in the region of the parameters of the system the excellent agreement between theoretical results and numerical ones can be found immediately and so the present method in this paper is applicable to solve strongly non linear problems

non linear non planar and non periodic vibrations of a string abstract we study the vibrations of a string subject to planar harmonic excitation both experimentally and theoretically we observe multiple periodic motions planar and non planar whirling as well as quasi periodic whirling and irregularly precessing oscillations when the forcing frequency is near that of a transverse normal mode a two degree of freedom model is derived and it is shown that these motions can be partially understood in terms of the completely integrable hamiltonian system obtained when damping and forcing tend to zero in that model

transverse vibrations of the elastically connected rectangular double membrane compound system abstract the free and forced vibrations of a system of two rectangular membranes attached together by a winkler elastic layer are studied analytically the motion of the system is described by two non homogeneous partial differential equations the solutions of the free vibrations are obtained by the bernoulli fourier method solving the boundary value problem the natural frequencies and the mode shape functions are found the initial value problem is also solved the free vibrations of the double membrane system are realised by synchronous and asynchronous deflections the forced vibrations of membranes subjected to arbitrarily distributed continuous loads are determined by using the classical method of the expansion in a series of the normal modes of vibrations discussing the vibrations caused by the harmonic exciting forces it is shown that the dynamic absorption phenomenon appears therefore the double membrane system can be used as a dynamic vibration absorber as a numerical example the vibrations of the system consisting of two identical membranes subjected to harmonic uniform distributed load are treated in detail

an investigation of multiple solutions yielded by the equivalent linearization method abstract the equivalent linearization method is a standard technique for the approximate solution of non linear random vibration problems it is known that in some cases the method can yield multiple stable solutions for the mean value and the standard deviation of the system response the validity and accuracy of this type of solution is investigated here by considering a single degree of freedom system for which the multiple solutions which are obtained may be compared with the exact response statistics it is found that the multiple solutions correspond to distinguishable states which occur in the response of the system a state is defined here as a form of response which persists for some time and whose local temporal statistics differ from the ensemble statistics of the complete response the accuracy of the equivalent linearization method is found to be variable

experiments on the application of iohmms to model financial returns series input output hidden markov models iohmm are conditional hidden markov models in which the emission and possibly the transition probabilities can be conditioned on an input sequence for example these conditional distributions can be linear logistic or nonlinear using for example multilayer neural networks we compare the generalization performance of several models which are special cases of input output hidden markov models on financial time series prediction tasks an unconditional gaussian a conditional linear gaussian a mixture of gaussians a mixture of conditional linear gaussians a hidden markov model and various iohmms the experiments compare these models on predicting the conditional density of returns of market and sector indices note that the unconditional gaussian estimates the first moment with the historical average the results show that although for the first moment the historical average gives the best results for the higher moments the iohmms yielded significantly better performance as estimated by the out of sample likelihood

harmonic frequency spectra of vibrating stepped strings the frequency spectrum of a vibrating string with a step in density is investigated for proportions of length and 1 having different constant densities in corresponding ratio r if the quantity r r 1 is a rational number then the vibrations of the string with fixed ends exhibit harmonic and or odd harmonic frequency sub spectra expressible in simple analytical form if r 1 then the entire frequency spectrum is a pure harmonic series indistinguishable from that of a homogeneous string consideration of the string vibrating in the free fixed configuration serves to remove this coincidence the free free configuration is also dealt with in a similar approach

non linear string random vibration abstract an investigation is described of the concave shape generation mechanism in the displacement and its first derivative vibration velocity amplitude probability density functions of the narrow band random vibration of a non linear string three types of strings are studied in detail characterized as follows 1 constant damping factor and non linear stiffness 2 the damping factor an even function with respect to the displacement and its first derivative and non linear stiffness 3 the damping factor an even function of the displacement and its first derivative and linear stiffness it is verified by numerical calculation that for a response sample of relatively long duration of the order of eight representative periods of the oscillation the generation of the concave shape depends mainly upon 1 the saturation of the amplitude and the growth of higher harmonic oscillation due to the non linear stiffness or the even function damping and 2 a jump phenomenon in the input output relation

induction theorems for finite groups including a common generalization of two classical theorems abstract roquette proved results involving induction about rings related to the character rings of finite groups and consisting of functions that vanish outside a p section kletzing did something similar for q characters this paper gives new generalizations of these results involving k characters for any field k of characteristic 0 as well as corresponding theorems for a set of primes that these facts are useful is illustrated by showing that they imply a common generalization of the witt berman and artin induction theorems as well as results of chen fan hu robinson and sin

a study on reduced support vector machines recently the reduced support vector machine rsvm was proposed as an alternate of the standard svm motivated by resolving the difficulty on handling large data sets using svm with nonlinear kernels it preselects a subset of data as support vectors and solves a smaller optimization problem however several issues of its practical use have not been fully discussed yet for example we do not know if it possesses comparable generalization ability as the standard svm in addition we would like to see for how large problems rsvm outperforms svm on training time in this paper we show that the rsvm formulation is already in a form of linear svm and discuss four rsvm implementations experiments indicate that in general the test accuracy of rsvm are a little lower than that of the standard svm in addition for problems with up to tens of thousands of data if the percentage of support vectors is not high existing implementations for svm is quite competitive on the training time thus from this empirical study rsvm will be mainly useful for either larger problems or those with many support vectors experiments in this paper also serve as comparisons of 1 different implementations for linear svm and 2 standard svm using linear and quadratic cost functions

properties of the maximum a posteriori path estimator in hidden markov models a hidden markov model hmm consists of a nonobservable markov chain x x0 x1 and a measured process y y 0 y1 whose distribution is determined by x to estimate the hidden path of x up to time n x0 x1 xn by the observations y 0 y1 yn usually the maximum a posteriori probability path estimator map path estimator is applied an effective means for calculating this estimator is the viterbi algorithm which is widely employed in the fields of coding theory correction of intersymbol interference and text recognition here properties of the map estimator are derived under a certain condition c it is shown that the limiting process u u0 u1 is a regenerative process particularly this means that u has an asymptotic distribution satisfies the central limit theorem and possesses a mean error furthermore condition c is satisfied for a broad class of hmms including the most important case for applications the hmm with additive white gaussian noise

multiple time scaling of the response of a duffing oscillator to narrow band random excitation the response of a duffing oscillator to narrow band random excitation is considered two approaches multiple time scaling and stochastic averaging are used both lead to the same set of three state equations for the slowly varying local mean square response or envelope and two other variables the stationary solution of these equations is similar to results previously obtained by using statistical linearization the stationary and nonstationary from the three state equations results compare favourably with digital simulations random jumps are shown to occur if the excitation bandwidth is sufficiently small

reduced complexity estimation for large scale hidden markov models in this paper we address the problem of reduced complexity estimation of general large scale hidden markov models hmms with underlying nearly completely decomposable discrete time markov chains and finite state outputs an algorithm is presented that computes o spl epsi where spl epsi is the related weak coupling parameter approximations to the aggregate and full order filtered estimates with substantial computational savings these savings are shown to be quite large when the chains have blocks with small individual dimensions some simulation studies are presented to demonstrate the performance of the algorithm

beam beam interaction models under narrow band random excitation abstract the aim of this paper is to continue our previous investigations on beam beam interaction models in particle accelerators by considering these models under narrow band random excitation in this investigation the multiple scale and the moment methods are used the equations of modulation of the amplitude and the phase are derived and perturbation techniques are used to seek approximate steady state solutions two special cases are considered to illustrate this study and excellent agreement is found between analytical and numerical results other cases can be similarly studied the effects of noise and detuning parameters are examined numerically and theoretically and we find that the system demonstrates a diffused limit cycle as the intensity of noise increases the numerical results show that the multiple scale method is effective for these stochastic systems

boundary stabilization of nonlinear vibrations of a flexible structure in a bounded domain in rn abstract we study a problem of boundary stabilization of the vibrations of elastic structure governed by the nonlinear integro differential equation u a 2 b u 2 d x u f in a bounded domain in r n with a smooth boundary under mixed boundary conditions to stabilize this system we apply a velocity feedback control only on a part of the boundary we prove that the solution of such system is stable subject to some restriction on the uncertain disturbing force f we also estimate the total energy of the system over any time interval 0 t with a tolerance level of the disturbances finally we establish the uniform decay of solution by a direct method with an explicit form of exponential energy decay estimate when this disturbing force f is insignificant

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

pairwise markov chains we propose a model called a pairwise markov chain pmc which generalizes the classical hidden markov chain hmc model the generalization which allows one to model more complex situations in particular implies that in pmc the hidden process is not necessarily a markov process however pmc allows one to use the classical bayesian restoration methods like maximum a posteriori map or maximal posterior mode mpm so akin to hmc pmc allows one to restore hidden stochastic processes with numerous applications to signal and image processing such as speech recognition image segmentation and symbol detection or classification among others furthermore we propose an original method of parameter estimation which generalizes the classical iterative conditional estimation ice valid for a classical hidden markov chain model and whose extension to possibly non gaussian and correlated noise is briefly treated some preliminary experiments validate the interest of the new model

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

nonlinear interactions and chaotic dynamics of suspended cables with three to one internal resonances abstract nonlinear planar oscillations of suspended cables subjected to external excitations with three to one internal resonances are investigated at first the galerkin method is used to discretize the governing nonlinear integral partial differential equation then the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance the equilibrium solutions the periodic solutions and chaotic solutions of the modulation equations are also investigated the newton raphson method and the pseudo arclength path following algorithm are used to obtain the frequency force response curves the supercritical hopf bifurcations are found in these curves choosing these bifurcations as the initial points and applying the shooting method and the pseudo arclength path following algorithm the periodic solution branches are obtained at the same time the floquet theory is used to determine the stability of the periodic solutions numerical simulations are used to illustrate the cascades of period doubling bifurcations leading to chaos at last the nonlinear responses of the two degree of freedom model are investigated

wave synthesis in a non linear stretched string with time varying length or tension abstract this paper is concerned with the numerical tone synthesis of a non linear stretched string the length or tension of which varies with time 1 at a constant rate 2 at a cosine function rate and 3 at a rate determined by a handwritten input function listening to the results for the analytical waveforms transformed by a digital to analog converter indicates that the case of the constant rate time varying length corresponds closely to a guitar string positive or negative feedback compensation for the analytically obtained frequency brings the analytical waveforms close to the numerically calculated waveforms a simple method is proposed with lower order polynomials for smoothly connecting two discontinuous waveforms into continuous waveforms a fourier series synthesizer procedure is described to aid rapid real time synthesis of tones of desired timbre

bounded input bounded output stability of a damped nonlinear string in this paper we prove that the displacement of a damped nonlinear string under bounded distributed forces is bounded the proof is achieved by showing that an energy like lyapunov function corresponding to the string is bounded

a truly 2 d hidden markov model for off line handwritten character recognition abstract in recent years there have been several attempts to extend one dimensional hidden markov model hmm to two dimension unfortunately the previous efforts have not yet achieved a truly two dimensional 2 d hmm because of both the difficulty in establishing a suitable 2 d model and its computational complexity this paper presents a new framework for the recognition of handwritten characters using a truly 2 d model hidden markov mesh random field hmmrf the hmmrf model is an extension of a 1 d hmm to 2 d that can provide a better description of the 2 d nature of characters the application of hmmrf model to character recognition necessitates two phases the training phase and the decoding phase our optimization criterion for training and decoding is based on the maximum marginal a posteriori probability we also develop a new formulation of parameter estimation for character recognition computational concerns in 2 d however necessitate certain simplifying assumptions on the model and approximations on the implementation of the estimation algorithm in particular the image is represented by a third order mmrf and the proposed estimation algorithm is applied over the look ahead observations rather than over the entire image thus the formulation is derived from the extension of the look ahead technique devised for a real time decoding experimental results confirm that the proposed approach offers a great potential for solving difficult handwritten character recognition problems under reasonable modeling assumptions

technical communique boundary control of the axially moving kirchhoff string in this note the axially moving kirchhoff string is considered it is proved that this non linear string can be stabilized by the linear boundary control which is the negative feedback of the transversal velocity of the string at one end furthermore it is concluded that the axially moving kirchhoff string is stable without an active control when one of its ends is free to move transversally

free vibration of a membrane stretched by inextensible strings at opposite edges abstract an analysis of presented for the free vibration of a membrane stretched by inextensible strings along two opposite edges the membrane is transformed into a square membrane of unit length by a certain transformation of variables the transverse deflection of the membrane is expressed in a series of the products of the deflection functions of strings strips of membrane parallel to the edges of the square membrane and the frequency equation is derived by the ritz method the natural frequencies and the mode shapes are calculated numerically up to higher modes for membranes symmetrical with respect to the centre lines by the application of the present method

analysis of time series subject to changes in regime abstract this paper introduces an em algorithm for obtaining maximum likelihood estimates of parameters for processes subject to discrete shifts in autoregressive parameters with the shifts themselves modeled as the outcome of a discrete valued markov process the simplicity of the em algorithm permits potential application of the approach to large vector systems

recognition of degraded characters using dynamic bayesian networks in this paper we investigate the application of dynamic bayesian networks dbns to the recognition of degraded characters dbns are an extension of one dimensional hidden markov models hmms which can handle several observation and state sequences in our study characters are represented by the coupling of two hmm architectures into a single dbn model the interacting hmms are a vertical hmm and a horizontal hmm whose observable outputs are the image columns and image rows respectively various couplings are proposed where interactions are achieved through the causal influence between state variables we compare non coupled and coupled models on two tasks the recognition of artificially degraded handwritten digits and the recognition of real degraded old printed characters our models show that coupled architectures perform more accurately on degraded characters than basic hmms the linear combination of independent hmm scores as well as discriminative methods such as support vector machines svms

signal and image segmentation using pairwise markov chains the aim of this paper is to apply the recent pairwise markov chain model which generalizes the hidden markov chain one to the unsupervised restoration of hidden data the main novelty is an original parameter estimation method that is valid in a general setting where the form of the possibly correlated noise is not known several experimental results are presented in both gaussian and generalized mixture contexts they show the advantages of the pairwise markov chain model with respect to the classical hidden markov chain one for supervised and unsupervised restorations

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

chaos in a noisy mechanical system with stress relaxation the influence of periodic and random external excitation on the chaotic behaviour of a self excited system is considered the lyapunov exponents of the noisy system have been defined as random variables the properties of their distribution which allow one to quantify chaos have been determined

free transverse vibrations of elastically connected simply supported double beam complex system abstract in this paper the free vibration analysis of two parallel simply supported beams continuously joined by a winkler elastic layer is presented the motion of the system is described by a homogeneous set of two partial differential equations which is solved by using the classical bernoulli fourier method the natural frequencies of the system are determined the initial value problem is considered to find the final form of the free vibrations the free vibrations of an elastically connected double beam complex system are realized by synchronous and asynchronous deflections the presented theoretical analysis is illustrated by a numerical example in which the effect of physical parameters characterizing the vibrating system on the natural frequencies is investigated

maximum confidence hidden markov modeling for face recognition this paper presents a hybrid framework of feature extraction and hidden markov modeling hmm for two dimensional pattern recognition importantly we explore a new discriminative training criterion to assure model compactness and discriminability this criterion is derived from the hypothesis test theory via maximizing the confidence of accepting the hypothesis that observations are from target hmm states rather than competing hmm states accordingly we develop the maximum confidence hidden markov modeling mc hmm for face recognition under this framework we merge a transformation matrix to extract discriminative facial features the closed form solutions to continuous density hmm parameters are formulated attractively the hybrid mc hmm parameters are estimated under the same criterion and converged through the expectation maximization procedure from the experiments on the feret database and gtfd we find that the proposed method obtains robust segmentation in the presence of different facial expressions orientations and so forth in comparison with the maximum likelihood and minimum classification error hmms the proposed mc hmm achieves higher recognition accuracies with lower feature dimensions

vibration and stability analysis of a multi guided rotating string abstract the small displacement vibrations of a rotating circular string restrained by point and distributed springs are studied in the present paper the model used includes the translating string as a special case the governing equations and boundary conditions are derived using hamilton s principle analytical solutions are obtained for free vibrations and some specific cases are discussed in addition approximate solutions with trigonometric shape functions are constructed by the rayleigh ritz method numerical results are given showing the effectiveness of the rayleigh ritz formulation constructed and some features of the string vibration and stability are discussed

signature verification using a modified bayesian network abstract in this paper a novel bayesian network representation is proposed for signature verification it is different from the traditional bayesian network in that its nodes are divided into two classes common hypotheses and alternative hypotheses to ensure the constructed network is a tree structure the network not only captures the conditional probability associated with each node but also the topological relations among components associated with the network nodes so that the uncertainty in structure description and the dependencies among components are encoded results based on eight persons signatures indicate that the method offers a considerable improvement in performance over some other popular techniques for signature verification since the uncertainty and interaction of pattern components are common phenomena in pattern representation and matching the approach may also be enlightening for other pattern classification problems

the response of a non uniformly tensioned circular string to a moving load abstract a non uniformly tensioned circular string on a damped elastic foundation is acted upon by a moving concentrated load this configuration can be viewed as a very simplified representation of a spinning rectangularly orthotropic disk acted upon by a spatially fixed force or of a stationary orthotropic disk subjected to a circumferentially moving load the natural frequencies and normal modes of vibration of the string on elastic foundation are determined for a range of values of the tension inhomogeneity the response of the string to a moving load is then determined the results indicate that there are many speeds below the critical speed of the uniformly tensioned string for which the forced response is large it is anticipated that the response of this simple model to a moving load can provide insight into the behavior of the mathematically more complicated rectangularly orthotropic circular disk

on the connected components of the spectrums of the character rings of a finite group abstract the numbers of connected components of the spectrums of three kinds of rings of characters of a finite group are determined in terms of the numbers of special kinds of conjugacy classes of the group

exponential energy decay estimates for the solutions of n dimensional kirchhoff type wave equation here we study uniform exponential stabilization of the vibrations of kirchhoff type wave equation in a bounded domain in rn with a smooth boundary under mixed boundary conditions to stabilize the system we incorporate separately the passive viscous damping and the internal material damping of kelvin voigt type in the model explicit forms of exponential energy decay rates are obtained by a direct method for the solution of such boundary value problems

transverse vibration of an axially accelerating string abstract the transverse vibration of an axially accelerating string is investigated the equation of motion is developed using hamilton s principle the resulting partial differential equations are discretized using galerkin s method assuming the axial velocity to be periodic a stability analysis is performed using floquet theory one two three four six and eight term series approximations are considered in the galerkin s method the one term approximation leads to a mathieu equation the solution of which is well known the numerical results for one term are compared with the analytical solution for the mathieu equation and they are in full agreement the two term approximation leads to gyroscopically coupled equations and the solutions differ significantly from that of the one term approximation whereas the three term approximation solutions look similar to the one term approximation solutions the analysis is carried out for higher order even approximations and the solutions are in qualitative agreement the two and four term approximation solutions are compared with the analytical results from hsu s method and are in reasonable agreement the results show that instabilities occur at much higher amplitudes and frequencies of the periodic axial velocity than that of typical devices such as tape machines and band saws

on the connected components of the spectrum of the extended character ring of a finite group abstract let r g be the character ring of a finite group g for any subring s of the complex field let be the set of such rational primes whose inverse do not lie in s and consider the prime spectrum of the coefficient extended character ring s r g by means of a generalized version of brauer s induction theorem we show that the number of the connected components of the prime spectrum of s r g equals the number of the regular conjugacy classes of g

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

random superharmonic and subharmonic response multiple time scaling of a duffing oscillator narrowband random third order superharmonic and one third order subharmonic response of a duffing oscillator is discussed a multiple time scale approach is used the work is a more rigorous approach than that already published on random superharmonic response by the authors and the results obtained corroborate the previous ones in particular random jumps in amplitude can occur but are less likely to occur as the bandwidth of the excitation is increased the results are further corroborated by comparison with digital simulation in addition new results on random subharmonic response are also presented obtained by using the same approach

a generalized treatment of the energetics of translating continua part i strings and second order tensioned pipes the energetics of translating one dimensional uniform strings and highly tensioned pipes with vanishing bending stiffness and flowing fluid are analyzed for fixed free and damped boundary conditions the interaction between the translating continua and the boundary supports causes energy transfer at a fixed boundary the transverse component of tension does work and the coriolis forces at a free end cause energy flux into the second order continuum under a symmetric boundary configuration the total energy of free oscillation varies periodically at the fundamental natural frequency asymmetric boundary supports in the pipe fluid system lead to damped or self excited motions at a viscously damped boundary the condition for maximal energy dissipation the destabilizing effect of dissipation and the stabilizing effect of negative damping are examined analytically using travelling wave solutions the energies transferred at the different boundary supports are quantified by energy reflection coefficients which are determined completely by the boundary conditions numerical simulations verify the analytically predicted energy variations

response of a duffing oscillator to combined deterministic harmonic and random excitation the response of duffing oscillator to combined deterministic harmonic and random excitation is investigated the method of harmonic balance and the method of stochastic averaging are used to determine the response of the system theoretical analyses and numerical simulations show that when the intensity of the random excitation increases the non trivial steady state solution may change from a limit cycle to a diffused limit cycle under some conditions the system may have two steady state solutions and jumps may exist

the stability of modes at rest in a chaotic system abstract the stability of modes at rest in non linear mechanical systems which have one active mode undergoing chaotic oscillations is considered a general formulation is developed for these systems results from the theory of almost sure stability infante 1 for stochastic systems are briefly reviewed in order to determine the minimal statistical measures of the chaos which are required to determine the stability of the inactive modes a specific non linear two degree of freedom system is then considered for which these measures can be explicitly estimated by using a method developed by brunsden et al 2 3 analytical results for the almost sure stability of the inactive mode are obtained and compared with simulation results

phase plane for narrow band random excitation of a duffing oscillator abstract the response of a duffing oscillator to narrow band random excitation is consedered it is shown that multiple values of the response can occur at some frequencies for very narrow excitation bandwidths but these reduce to a single value as the bandwidth is increased time histories of quantities such as mean square displacement are obtained from the time dependent fokker planck equation smoothed time histories of mean square velocity and displacement are plotted on a phase plane the phase plane can show either one sink or two sinks and a saddle point as in the sinusoidal case but again excitation bandwith determines whether or not multiple sinks occur

stochastic response and stability of the duffing oscillator under narrowband excitation the duffing equation under narrowband gaussian excitation is studied almost sure asymptotic stability analysis is used to discuss the realizability of multivalued steady states the theoretical predictions are supported by numerical simulation results

discriminant waveletfaces and nearest feature classifiers for face recognition feature extraction discriminant analysis and classification rules are three crucial issues for face recognition we present hybrid approaches to handle three issues together for feature extraction we apply the multiresolution wavelet transform to extract the waveletface we also perform the linear discriminant analysis on waveletfaces to reinforce discriminant power during classification the nearest feature plane nfp and nearest feature space nfs classifiers are explored for robust decisions in presence of wide facial variations their relationships to conventional nearest neighbor and nearest feature line classifiers are demonstrated in the experiments the discriminant waveletface incorporated with the nfs classifier achieves the best face recognition performance

face recognition using nearest feature space embedding face recognition algorithms often have to solve problems such as facial pose illumination and expression pie to reduce the impacts many researchers have been trying to find the best discriminant transformation in eigenspaces either linear or nonlinear to obtain better recognition results various researchers have also designed novel matching algorithms to reduce the pie effects in this study a nearest feature space embedding called nfs embedding algorithm is proposed for face recognition the distance between a point and the nearest feature line nfl or the nfs is embedded in the transformation through the discriminant analysis three factors including class separability neighborhood structure preservation and nfs measurement were considered to find the most effective and discriminating transformation in eigenspaces the proposed method was evaluated by several benchmark databases and compared with several state of the art algorithms according to the compared results the proposed method outperformed the other algorithms

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

stabilization of quasi linear vibrations of an inhomogeneous beam in this note we study the stabilization of a vibrating inhomogeneous beam under distributed disturbing force we prove that the amplitude of such vibration is bounded subject to some restriction on the uncertain disturbing force we also estimate the total energy of the system over time interval 0 t for any time t 0 together with a tolerance level of the disturbance finally we establish the uniform decay of solution with an explicit form of exponential energy decay estimate when the uncertain disturbances are insignificant

an analytic solution for estimating two dimensional hidden markov models two dimensional hidden markov model 2 d hmm is an extension of 1 d hmm to 2 d it provides a reasonable statistical method to model matrix data this paper presents some new strict definitions of 2 d hmm and proves the equivalence between them and gives a study of the three basic problems for 2 d hmm namely probability evaluation optimal state matrix and parameter estimation by using the ideal that the sequences of states on columns or rows of a 2 d hmm can be seen as states of a 1 d hmm several new formulae solving these problems are theoretically derived and further demonstrated by computer simulations

response of a strongly non linear oscillator to narrowband random excitations abstract the principal resonance of a van der pol duffing oscillator subject to narrowband random excitations has been studied by introducing a new expansion parameter e e e u 0 the method of multiple scales is adapted for the strongly non linear system the behavior of steady state responses together with their stability and the effects of system damping and the detuning and magnitude of the random excitation on steady state responses are analyzed in detail theoretical analyses are verified by some numerical results it is found that when the random noise intensity increases the steady state solution may change form a limit cycle to a diffused limit cycle and the system may have two different stable steady state solutions for the same excitation under certain conditions the results obtained for the strongly non linear oscillator complement previous results in the literature for weakly non linear systems

the cartan ring of a finite group abstract we determine the structure of the cartan ring of a finite group g defined as the grothendieck ring of g modulo its ideal generated by projective modules and we identify the ideal of the cartan ring arising from all relatively q projective modules for a p subgroup q of g

parametric oscillations of a non linear string abstract a study of the nature of periodic oscillations bifurcation of vibrations and growth of chaos is presented with the negative stiffness parametric oscillations of a non linear stretched string used as a model the influences of the variables on the behavior of the oscillations are analyzed the variables studied are the damping factor the frequency ratio the non linear term the parametric driving amplitudeqand the linear stiffness p the oscillations of this system were approximated and calculated by computer these results were analyzed in several ways trajectories poincare maps probability density functions of displacement and velocity root mean square responses and lyapunov exponents these pictorial representations were in good agreement with the independently calculated map of chaotic periodic regions over p q it was found that the magnitudes of the linear stiffness and the parametric driving amplitude are the most important determinants of the presence of chaos additionally the damping factor was found to influence the appearance of chaos varying the non linear term was found to have only a minimal effect on the appearance of chaos similarly the frequency ratio was found not to effect the occurrence of chaos

robust sequential data modeling using an outlier tolerant hidden markov model hidden markov chain models using finite gaussian mixture models as their hidden state distributions have been successfully applied in sequential data modeling and classification applications nevertheless gaussian mixture models are well known to be highly intolerant to the presence of untypical data within the fitting data sets used for their estimation finite student s t mixture models have recently emerged as a heavier tailed robust alternative to gaussian mixture models overcoming these hurdles to exploit these merits of student s t mixture models in the context of a sequential data modeling setting we introduce in this paper a novel hidden markov model where the hidden state distributions are considered to be finite mixtures of multivariate student s t densities we derive an algorithm for the model parameters estimation under a maximum likelihood framework assuming full diagonal and factor analyzed covariance matrices the advantages of the proposed model over conventional approaches are experimentally demonstrated through a series of sequential data modeling applications

a parametrically driven harmonic analysis of a non linear stretched string with time varying length abstract this paper is concerned with the first second and third harmonic lateral vibrations of a string having a forced periodic small length variation account is taken of the non linear term arising from the correction to the tension of the string due to local elongation it is found that increasing the amplitude of the length variation of the string results in a narrowing of the frequency response range of each of the harmonic oscillation components both numerical and analytical calculations of the harmonic frequency responses have been carried out the relationships for initial values between the original differential equation and the approximate differential equations for the harmonic responses are discussed in detail

off line recognition of large set handwritten characters with multiple hidden markov models there are many uncertainties in handwritten character recognition stochastic modeling is a flexible and general method for modeling such problems and entails the use of probabilistic models to deal with uncertain or incomplete information this paper presents an efficient scheme for off line recognition of large set handwritten characters in the framework of stochastic models the first order hidden markov models hmms to facilitate the processing of unconnected patterns and patterns with isolated noises four types of feature vectors based on the regional projection contour transformation rpct are employed the recognition system consists of two phases for each character in the training phase multiple hmms corresponding to different feature types of rpct are built in the classification phase the results of individual classifiers to produce the final recognition result for an input character are integrated where each individual hmm classifier produces one score that is the probability of generating the test observation sequence for each character model in this paper several methods for integrating the results of different classifiers are considered so that a better result could be obtained in order to verify the effectiveness of the proposed scheme the most frequently used 520 types of hangul characters in korea have been considered in the experiments experimental results indicate that the proposed scheme is very promising for the recognition of large set handwritten characters with numerous variations

dynamic stability of a three dimensional string subjected to both magnetic and tensioned excitations this paper presents the dynamic stability of an axially moving string subjected to both actions of an alternating uniform transverse magnetic field and a periodic tension force owing to time varying actions terms with time dependent coefficients appear in the equations of motion which resutls in the existence of parametric instability

face recognition using the embedded hmm with second order block specific observations the paper is concerned with face recognition using the embedded hidden markov model ehmm with second order block specific observations the proposed method partitions a face image into a 2 d lattice type composed of many blocks each block is represented by the second order block specific observation that consists of a combination of first and second order feature vectors the first order or second order feature vector is obtained by projecting the original or residual block image onto the first or second basis vector that is obtained block specifically by applying the pca to a set of original or residual block images a sequence of feature vectors obtained from the top to bottom and the left to right scanned blocks are used as an observation sequence to train ehmm the ehmm models the face image in a hierarchical manner as follows several super states are used to model the vertical facial features such as the forehead eyes nose mouth and chin and several states in the super state are used to model the localized features in a vertical face feature recognition is performed by identifying the person of the model that provides the highest value of observation probability experimental results show that the proposed recognition method outperforms many existing methods such as the second order eigenface method the ehmm with dct observations and the second order eigenface method using a confidence factor in terms of average of the normalized modified retrieval rank and false identification rate

non linear resonance in strings under narrow band random excitation part i planar response and stability non linear planar response of a string to planar narrow band random excitation is investigated in this paper a response equation for the mean square deflection 2 is obtained under a single mode approximation by using the equivalent linearization technique it is shown that the response is triple valued as in the case of harmonic excitation if the centre frequency of excitation lies in a certain specified range the triple valued response occurs only if the excitation bandwidth is smaller than a critical value crit which is a monotonically increasing function of the intensity of excitation an approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the 2 plane have been charted it is shown that planar response can become unstable either due to an unbounded growth of the in plane component of motion or due to a spontaneous appearance of an out of plane component