transverse vibrations of tensioned pipes conveying fluid with time dependent velocity abstract in this study the transverse vibrations of highly tensioned pipes with vanishing flexural stiffness and conveying fluid with time dependent velocity are investigated two different cases the pipes with fixed fixed end and fixed sliding end conditions are considered the time dependent velocity is assumed to be a harmonic function about a mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is derived using hamilton s principle and solved analytically by direct application of the method of multiple scales a perturbation technique the natural frequencies are found increasing the ratio of fluid mass to the total mass per unit length increases the natural frequencies the principal parametric resonance cases are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system when the velocity fluctuation frequency is close to zero no instabilities are detected up to the first order of perturbation numerical results are presented for the first two modes

stabilization of an axially moving web via regulation of axial velocity in this paper a novel control algorithm for suppression of the transverse vibration of an axially moving web system is presented the principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving beam so as to track a profile according to which the vibration energy decays most quickly the optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method the galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations odes for control design purposes these odes are rewritten into state space equations the vibration energy of the axially moving beam is represented by the quadratic form of the state variables in the optimal control problem the cost function modified from the vibration energy function is subjected to the constraints on the state variables and the axial transport velocity is considered as a control input numerical simulations are performed to confirm the effectiveness of the proposed control algorithm

nonlinear transverse free vibrations of piles the nonlinear partial differential equation governing the nonlinear transverse vibration of pile was derived under the assumption of that both the materials of pile and soil obey nonlinear elastic and linear viscoelastic constitutive relations the approximate expressions of the nth order main frequency and the response of the nonlinear vibration of pile with ends hinged have been obtained by the complex mode method and multiple time scales method results point out that the main frequency of the nonlinear system is related to not only the natural frequency of linear vibration system but also the amplitude damping and nonlinearity of materials there are high order harmonic waves with twice the main frequency and the main frequency of three times as well as the sum and or difference of 2 or 3 main frequencies besides the harmonic wave with the main frequency in the response of the nonlinear system numerical examples were given and the effect of parameters was considered in detail

fast full search equivalent encoding algorithms for image compression using vector quantization three fast search routines to be used in the encoding phase of vector quantization vq image compression systems are presented these routines which are based on geometric considerations provide the same results as an exhaustive or full search examples show that the proposed algorithms need only 3 20 of the number of mathematical operations required by a full search and fewer than 50 of the operations required by recently proposed alternatives

a comparison of several vector quantization codebook generation approaches a review and a performance comparison of several often used vector quantization vq codebook generation algorithms are presented the codebook generation algorithms discussed include the linde buzo gray lbg binary splitting algorithm the pairwise nearest neighbor algorithm the simulated annealing algorithm and the fuzzy c means clustering analysis algorithm a new directed search binary splitting method which reduces the complexity of the lbg algorithm is presented also a new initial codebook selection method which can obtain a good initial codebook is presented by using this initial codebook selection algorithm the overall lbg codebook generation time can be reduced by a factor of 1 5 2

image compression using address vector quantization a novel vector quantization scheme called the address vector quantizer a vq is proposed it is based on exploiting the interblock correlation by encoding a group of blocks together using an address codebook the address codebook consists of a set of address codevectors where each codevector represents a combination of addresses indexes each element of this codevector is an address of an entry in the lbg codebook representing a vector quantized block the address codebook consists of two regions one is the active addressable region and the other is the inactive nonaddressable region during the encoding process the codevectors in the address codebook are reordered adaptively in order to bring the most probable address codevectors into the active region when encoding an address codevector the active region of the address codebook is checked and if such an address combination exist its index is transmitted to the receiver otherwise the address of each block is transmitted individually the quality snr value of the images encoded by the proposed a vq method is the same as that of a memoryless vector quantizer but the bit rate would be reduced by a factor of approximately two when compared to a memoryless vector quantizer

on the transversal vibrations of a conveyor belt with a low and time varying velocity part ii the beam like case in this paper initial boundary value problems for a linear wave string equation are considered these problems can be used as simple models to describe the vertical vibrations of a conveyor belt for which the velocity is small with respect to the wave speed and is assumed to move with a time varying speed formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt it will also be shown that the truncation method cannot be applied to this problem in order to obtain approximations valid on long time scales

vibrations and stability of axially traveling laminated beams abstract in this paper vibrations and stability of an axially traveling laminated composite beam are investigated analytically via the method of multiple scales based on classical laminated beam theory the governing equations of motion for a time variant axial speed are obtained using newton s second law of motion and constitutive relations the method of multiple scales an approximate analytical method is applied directly to the gyroscopic governing equations of motion and complex eigenfunctions and natural frequencies of the system are obtained the stability boundaries of the system near resonance are determined via the routh hurwitz criterion finally a parametric study is conducted which considers the effects of laminate type and configuration as well as the mean speed and amplitude of speed fluctuations on the vibration response natural frequencies and stability boundaries of the system

two fast nearest neighbor searching algorithms for image vector quantization in this paper two efficient codebook searching algorithms for vector quantization vq are presented the first fast search algorithm utilizes the compactness property of signal energy on transform domain and the geometrical relations between the input vector and every codevector to eliminate those codevectors that have no chance to be the closest codeword of the input vector it achieves a full search equivalent performance as compared with other fast methods of the same kind this algorithm requires the fewest multiplications and the least total times of distortion measurements then a suboptimal searching method which sacrifices the reconstructed signal quality to speed up the search of nearest neighbor is presented this algorithm performs the search process on predefined small subcodebooks instead of the whole codebook for the closest codevector experimental results show that this method not only needs less cpu time to encode an image but also encounters less loss of reconstructed signal quality than tree structured vq does

on variable length induced vibrations of a vertical string abstract the purpose of this paper is to study the free lateral responses of vertically translating media with variable length velocity and tension subject to general initial conditions the translating media are modeled as taut strings with fixed boundaries the problem can be used as a simple model to describe the lateral vibrations of an elevator cable for which the length changes linearly in time or for which the length changes harmonically about a constant mean length in this paper an initial boundary value problem for a linear axially moving string equation is formulated in the given model a rigid body is attached to the lower end of the string and the suspension of this rigid body against the guide rails is assumed to be rigid for linearly length variations it is assumed that the axial velocity of the string is small compared to nominal wave velocity and the string mass is small compared to car mass and for the harmonically length variations small oscillation amplitudes are assumed and it is also assumed that the string mass is small compared to the total mass of the string and the car a multiple timescales perturbation method is used to construct formal asymptotic approximations of the solutions to show the complicated dynamical behavior of the string for the linearly varying length analytic approximations of the exact solution are compared with numerical solution for the harmonically varying length it will be shown that galerkin s truncation method cannot be applied in all cases to obtain approximations valid on long timescales

fuzzy declustering based vector quantization vector quantization is a useful approach for multi dimensional data compression and pattern classification one of the most popular techniques for vector quantization design is the lbg linde buzo gray algorithm to address the problem of producing poor estimate of vector centroids which are subjected to biased data in vector quantization we propose a fuzzy declustering strategy for the lbg algorithm the proposed technique calculates appropriate declustering weights to adjust the global data distribution using the result of fuzzy declustering based vector quantization design we incorporate the notion of fuzzy partition entropy into the distortion measures that can be useful for classification of spectral features experimental results obtained from simulated and real data sets demonstrate the effective performance of the proposed approach

dynamic response of clamped axially moving beams integral transform solution the generalized integral transform technique gitt is employed to obtain a hybrid analytical numerical solution for dynamic response of clamped axially moving beams the use of the gitt approach in the analysis of the transverse vibration equation leads to a coupled system of second order differential equations in the dimensionless temporal variable the resulting transformed ode system is then solved numerically with automatic global accuracy control by using the subroutine divpag from imsl library excellent convergence behavior is shown by comparing the vibration displacement of different points along the beam length numerical results are presented for different values of axial translation velocity and flexural stiffness a set of reference results for the transverse vibration displacement of axially moving beam is provided for future co validation purposes

nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide abstract in this paper transversal nonlinear vibration of an axially moving viscoelastic string supported by a partial viscoelastic guide is analytically investigated the string is traveling under time variant velocity which includes a mean velocity along with small harmonic fluctuations the model of the viscoelastic guide is also a parallel combination of springs and viscous dampers the governing partial differential equation is derived from hamilton s principle and geometrical relations the method of multiple scales is applied to the governing partial differential equation to obtain solvability conditions for both non resonance and principal parametric resonance cases additionally in the case of principal parametric resonance the stability and bifurcation of trivial and non trivial steady state responses are analyzed through the routh hurwitz criterion eventually numerical simulations are presented to highlight the effects of mean velocity guide length stiffness and damping coefficient of the guide and viscosity coefficient of the string on the natural frequencies stability frequency response curves and bifurcation points of the system

rough clustering using generalized fuzzy clustering algorithm in this paper we present a rough k means clustering algorithm based on minimizing the dissimilarity which is defined in terms of the squared euclidean distances between data points and their closest cluster centers this approach is referred to as generalized rough fuzzy k means grfkm algorithm the proposed method solves the divergence problem of available approaches where the cluster centers may not be converged to their final positions and reduces the number of user defined parameters the presented method is shown to be converged experimentally compared to available rough k means clustering algorithms the proposed method provides less computing time unlike available approaches the convergence of the proposed method is independent of the used threshold value moreover it yields better clustering results than rfkm for the handwritten digits data set landsat satellite data set and synthetic data set in terms of validity indices compared to mrkm and rfkm grfkm can reduce the value of xie beni index using the handwritten digits data set where a lower xie beni index value implies the better clustering quality the proposed method can be applied to handle real life situations needing reasoning with uncertainty

predictive classified vector quantization a vector quantization scheme based on the classified vector quantization cvq concept called predictive classified vector quantization pcvq is presented unlike cvq where the classification information has to be transmitted pcvq predicts it thus saving valuable bit rate two classifiers one operating in the hadamard domain and the other in the spatial domain were designed and tested the classification information was predicted in the spatial domain the pcvq schemes achieved bit rate reductions over the cvq ranging from 20 to 32 for two commonly used color test images while maintaining the same acceptable image quality bit rates of 0 70 0 93 bits per pixel bpp were obtained depending on the image and pcvq scheme used

vibrations of an axially accelerating beam with small flexural stiffness transverse vibrations of an axially moving beam are considered the axial velocity is harmonically varying about a mean velocity the equation of motion is expressed in terms of dimensionless quantities the beam effects are assumed to be small since in this case the fourth order spatial derivative multiplies a small parameter the mathematical model becomes a boundary layer type of problem approximate solutions are searched using the method of multiple scales and the method of matched asymptotic expansions results of both methods are contrasted with the outer solution

spectral analysis for the transverse vibration of an axially moving timoshenko beam the use of frequency dependent spectral element matrix or exact dynamic stiffness matrix in structural dynamics is known to provide very accurate solutions while reducing the number of degrees of freedom to resolve the computational and cost problems thus in the present paper the spectral element model is formulated for the axially moving timoshenko beam under a uniform axial tension the high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions the effects of the axial velocity and axial tension on the vibration characteristics the dispersion relation and the stability of a moving timoshenko beam are analytically and numerically investigated

non linear parametric vibration and stability of axially moving visco elastic rayleigh beams abstract an axially moving visco elastic rayleigh beam with cubic non linearity is considered and the governing partial differential equation of motion for large amplitude vibration is derived through geometrical constitutive and dynamical relations by directly applying the method of multiple scales to the governing equations of motion and considering the solvability condition the linear and non linear frequencies and mode shapes of the system are analytically formulated in the presence of damping terms it can be seen that the amplitude is exponentially time dependent and as a result the non linear natural frequencies of the system will be time dependent for the resonance case through considering the solvability condition and routh hurwitz criterion the stability conditions are developed analytically eventually the effects of system parameters on the vibrational behavior stability and bifurcation points of the system are investigated through parametric studies

a fast vq codebook generation algorithm using codeword displacement in this paper we present a fast codebook generation algorithm called cgaucd codebook generation algorithm using codeword displacement by making use of the codeword displacement between successive partition processes by implementing a fast search algorithm named mfaupi modified fast algorithm using projection and inequality for vq encoding in the partition step of cgaucd the codebook generation time can be further reduced significantly using mfaupi the computing time of cgaucd can be reduced by a factor of 4 7 7 6 compared to generalized lloyd algorithm gla our proposed method can reduce the codebook generation time by a factor of 35 9 121 2 compared to the best codebook generation algorithm to our knowledge our approach can further reduce the corresponding computing time by 26 0 32 8 it is noted that our proposed algorithm can generate the same codebook as that produced by the gla the superiority of our method is more remarkable when a larger codebook is generated

coupled longitudinal transverse dynamics of an axially accelerating beam abstract the coupled longitudinal transverse nonlinear dynamics of an axially accelerating beam is numerically investigated this problem is classified as a parametrically excited gyroscopic system the axial speed is assumed to be comprised of a constant mean value along with harmonic fluctuations hamilton s principle is employed to derive the equations of motion of the system which are in the form of two coupled partial differential equations the equations are discretized using the galerkin method which yields a set of coupled second order nonlinear ordinary differential equations with time dependent coefficients the sub critical dynamics of the system is examined via the pseudo arclength continuation technique while the global dynamics is investigated using direct time integration the mean axial speed and the amplitude of the speed variations are varied so as to construct the bifurcation diagrams of poincare maps the vibration specifications of the system are investigated more detailed via plotting time histories phase plane portraits and fast fourier transforms ffts

on resonances and the applicability of galerkin s truncation method for an axially moving string with time varying velocity abstract in this paper an initial boundary value problem for a linear homogeneous equation describing an axially moving string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity with a small fluctuation amplitude the two timescales perturbation method and the laplace transform method have been employed to the equation of motion in search of infinite mode approximate solutions all resonance cases are investigated in detail it will be shown that galerkin s truncation method cannot be applied to this problem in all cases to obtain approximations valid on long timescales

on the influence of lateral vibrations of supports for an axially moving string in this paper the transverse oscillations in travelling strings due to arbitrary lateral vibrations of the supports will be studied using the method of laplace transforms exact solutions will be constructed for the initial boundary value problems which describe these transverse oscillations

stability in parametric resonance of axially moving viscoelastic beams with time dependent speed stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated the governing equation is derived from newton s second law the kelvin constitution relation and the geometrical relation when the axial speed is a constant mean speed with small harmonic variations the governing equation can be regarded as a continuous gyroscopic system under small periodically parametric excitations and a damping term the method of multiple scales is applied directly to the governing equation without discretization the stability conditions are obtained for combination and principal parametric resonance numerical examples are presented for beams with simple supports and fixed supports respectively to demonstrate the effect of viscoelasticity on the stability boundaries in both cases

remarks on the hyers ulam stability of some systems of functional equations abstract in this paper we present a method that allows to study the hyers ulam stability of some systems of functional equations connected with the cauchy jensen and quadratic equations in particular we generalize and extend some already known results

steady state response of axially moving viscoelastic beams with pulsating speed comparison of two nonlinear models abstract principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed a nonlinear partial differential equation governing the transverse vibration is derived from the dynamical constitutive and geometrical relations under certain assumption the partial differential reduces to an integro partial differential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams the method of multiple scales is applied to two equations to calculate the steady state response closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms the stability of straight equilibrium and nontrivial steady state response are analyzed by use of the lyapunov linearized stability theory numerical examples are presented to highlight the effects of speed pulsation viscoelascity and nonlinearity and to compare results obtained from two equations

lossless compression of vq index with search order coding in memoryless vector quantization vq for images each block is quantized independently and its corresponding index is sent to the decoder this paper presents a new lossless algorithm that exploits the interblock correlation in the index domain we compare the current index with previous indices in a predefined search path and then send the corresponding search order to the decoder the new algorithm achieves significant reduction of bit rates without introducing extra coding distortion when compared to memoryless vq it is very simple and computationally efficient

a fast exact gla based on code vector activity detection this paper introduces a new method for reducing the number of distance calculations in the generalized lloyd algorithm gla which is a widely used method to construct a codebook in vector quantization reduced comparison search detects the activity of the code vectors and utilizes it on the classification of the training vectors for training vectors whose current code vector has not been modified we calculate distances only to the active code vectors a large proportion of the distance calculations can be omitted without sacrificing the optimality of the partition the new method is included in several fast gla variants reducing their running times over 50 on average

infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations abstract the transverse vibrations of simply supported axially moving euler bernoulli beams are investigated the beam has a time varying axial velocity with viscous damping traveling beam eigenfunctions with infinite number of modes are considered approximate analytical solutions are sought using the method of multiple scales a perturbation technique a detailed analysis of the resonances in which upto four modes of vibration involved are performed stability analysis is treated for each type of resonance approximate stability borders are given for the resonances involving only two modes for higher number of modes involved in a resonance sample numerical examples are presented for stabilities

nonlinear vibrations of axially moving timoshenko beams under weak and strong external excitations in this paper nonlinear vibrations under weak and strong external excitations of axially moving beams are analyzed based on the timoshenko model the governing nonlinear partial differential equation of motion is derived from newton s second law accounting for the geometric nonlinearity caused by finite stretching of the beams the complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation the method of multiple scales is employed to investigate primary resonances nonsyntonic excitations superharmonic resonances and subharmonic resonances some numerical examples are presented to demonstrate the effects of a varying parameter such as axial speed external excitation amplitudes and nonlinearity on the response amplitudes for the first and second modes when other parameters are fixed the stability of the response amplitudes is investigated and the boundary of instability is located

a complexity reduction technique for image vector quantization a technique for reducing the complexity of spatial domain image vector quantization vq is proposed the conventional spatial domain distortion measure is replaced by a transform domain subspace distortion measure due to the energy compaction properties of image transforms the dimensionality of the subspace distortion measure can be reduced drastically without significantly affecting the performance of the new quantizer a modified lbg algorithm incorporating the new distortion measure is proposed unlike conventional transform domain vq the codevector dimension is not reduced and a better image quality is guaranteed the performance and design considerations of a real time image encoder using the techniques are investigated compared with spatial domain a speed up in both codebook design time and search time is obtained for mean residual vq and the size of fast ram is reduced by a factor of four degradation of image quality is less than 0 4 db in psnr

a fast k means clustering algorithm using cluster center displacement in this paper we present a fast k means clustering algorithm fkmcucd using the displacements of cluster centers to reject unlikely candidates for a data point the computing time of our proposed algorithm increases linearly with the data dimension d whereas the computational complexity of major available kd tree based algorithms increases exponentially with the value of d theoretical analysis shows that our method can reduce the computational complexity of full search by a factor of sf and sf is independent of vector dimension the experimental results show that compared to full search our proposed method can reduce computational complexity by a factor of 1 37 4 39 using the data set from six real images compared with the filtering algorithm which is among the available best algorithms of k means clustering our algorithm can effectively reduce the computing time it is noted that our proposed algorithm can generate the same clusters as that produced by hard k means clustering the superiority of our method is more remarkable when a larger data set with higher dimension is used

image restoration of compressed image using classified vector quantization abstract to reduce communication bandwidth or storage space image compression is needed however the subjective quality of compressed images may be unacceptable and the improvement of quality for compressed images may be desirable this paper extends and modifies classified vector quantization cvq to improve the quality of compressed images the process consists of two phases the encoding phase and the decoding phase the encoding procedure needs a codebook for the encoder which transforms a compressed image to a set of codeword indices the decoding phase also requires a different codebook for the decoder which enhances a compressed image from a set of codeword indices using cvq to improve a compressed image s quality is different from the existing algorithm which cannot reconstruct the high frequency components for compressed images the experimental results show that the image quality is improved dramatically for images in the training set the improvement of psnr is about 3 db for images which are outside the training set the improvement of psnr is about 0 57 db which is comparable to the existing method

inverse error diffusion using classified vector quantization this correspondence extends and modifies classified vector quantization cvq to solve the problem of inverse halftoning the proposed process consists of two phases the encoding phase and decoding phase the encoding procedure needs a codebook for the encoder which transforms a halftoned image to a set of codeword indices the decoding process also requires a different codebook for the decoder which reconstructs a gray scale image from a set of codeword indices using cvq the reconstructed gray scale image is stored in compressed form and no further compression may be required this is different from the existing algorithms which reconstructed a halftoned image in an uncompressed form the bit rate of encoding a reconstructed image is about 0 51 b pixel

divergence and flutter instabilities of nanobeams in moving state accounting for surface and shear effects abstract transverse vibrations of elastically rested moving beam like nanostructures accounting for surface effect are of high concern the role of nonlocality on the free dynamic response of moving nanobeams has been revealed in recent years nevertheless the influence of the surface energy on the mechanical behavior of such elements has not been explained yet in this paper equations of motion of rested nanoscaled beams in the moving state are derived carefully via surface energetic shear deformable beam models subsequently the transverse vibrations of the nanostructure are evaluated using galerkin based assumed mode method the explicit expressions of divergence velocities are obtained analytically and these are successfully verified with the results of a numerical approach the roles of crucial parameters on the first divergence velocity are addressed in some detail additionally the stable and unstable regions are determined systematically and the influence of both surface energy and shear energy on the stability of moving nanostructure is discussed

a fixed point approach to the stability of isometries in this paper we apply a fixed point theorem to the proof of hyers ulam rassias stability property for isometries from a normed space into a banach space in which the parallelogram law holds

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

nonlinear dynamics of axially moving plates abstract the nonlinear dynamics for forced motions of an axially moving plate is numerically investigated using von karman plate theory and retaining in plane displacements and inertia the equations of motion are obtained via an energy method based on lagrange equations this yields a set of second order nonlinear ordinary differential equations with coupled terms the equations are transformed into a set of first order nonlinear ordinary differential equations and are solved via the pseudo arclength continuation technique the near resonance nonlinear dynamics is examined via plotting the frequency response curves of the system results are shown through frequency response curves time histories and phase plane diagrams the effect of system parameters such as the axial speed and the pretension on the resonant responses is also highlighted

galerkin methods for natural frequencies of high speed axially moving beams in this paper natural frequencies of planar vibration of axially moving beams are numerically investigated in the supercritical ranges in the supercritical transport speed regime the straight equilibrium configuration becomes unstable and bifurcate in multiple equilibrium positions the governing equations of coupled planar is reduced to two nonlinear models of transverse vibration for motion about each bifurcated solution those nonlinear equations are cast in the standard form of continuous gyroscopic systems by introducing a coordinate transform the natural frequencies are investigated for the beams via the galerkin method to truncate the corresponding governing equations without nonlinear parts into an infinite set of ordinary differential equations under the simple support boundary numerical results indicate that the nonlinear coefficient has little effects on the natural frequency and the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters and the integro partial differential equation yields results quantitatively closer to those of the coupled equations

computing the dynamic response of an axially moving continuum the aim of this study was to apply an approximate galerkin finite element method to solve the initial boundary value problem of a viscously damped axially moving pre tensioned beam including arbitrary support excitations in order to validate the galerkin finite element method the results were compared with exact solutions when available and with solutions obtained using the finite difference and galerkin methods the energy dissipation of the system was considered in the form of an equivalent viscous damping model it was also shown that for certain values of the parameters especially at high velocities the galerkin method using stationary string eigenfunctions can give a poor prediction of the dynamic response

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

asymptotic stability analysis with numerical confirmation of an axially accelerating beam constituted by the standard linear solid model stability of an axially accelerating viscoelastic beam constituted by the standard linear solid model is investigated the material time derivative is used in the viscoelastic constitutive relation the instability condition is determined for combination and principal parametric resonances via the asymptotic analysis the differential quadrature scheme is developed to solve numerically the partial differential equation governing transverse motion of axially accelerating viscoelastic beams the stability boundaries are numerically located in the excitation amplitude and the excitation frequency plane numerical simulation demonstrates the effects of the stiffness the viscosity and constant mean speed of beam the numerical calculations validate the analytical results in the principal parametric resonance

transition behaviour from string to beam for an axially accelerating material an approximate analytical expression for the natural frequency is given for the problem for velocity profiles harmonically varying about a mean velocity stability borders are determined analytically for fluctuation frequency versus amplitudes beam effects cause the stability boundaries to shift to higher frequency values

hybrid lms mmse inverse halftoning technique the objective of this work is to reconstruct high quality gray level images from bilevel halftone images we develop optimal inverse halftoning methods for several commonly used halftone techniques which include dispersed dot ordered dither clustered dot ordered dither and error diffusion at first the least mean square lms adaptive filtering algorithm is applied in the training of inverse halftone filters the resultant optimal mask shapes are significantly different for various halftone techniques and these mask shapes are also quite different from the square shape that was frequently used in the literature in the next step we further reduce the computational complexity by using lookup tables designed by the minimum mean square error mmse method the optimal masks obtained from the lms method are used as the default filter masks finally we propose the hybrid lms mmse inverse halftone algorithm it normally uses the mmse table lookup method for its fast speed when an empty cell is referred the lms method is used to reconstruct the gray level value consequently the hybrid method has the advantages of both excellent reconstructed quality and fast speed in the experiments the error diffusion yields the best reconstruction quality among all three halftone techniques

a functional equation having monomials as solutions for each n 1 2 3 we obtain the general solution and the stability of the functional equation f 2x y f 2x y 2 n 2 f x y f x y 6f x and we obtain the general solution and the stability of the functional equation f 2x y f 2x y 6f y 4 f x y f x y 6f x using the fixed point method we prove the generalized hyers ulam stability of these functional equations

vibrations of an axially moving beam with time dependent velocity the dynamic response of an axially accelerating elastic tensioned beam is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is solved by using perturbation analysis principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for different flexural stiffness values and for the first two modes

an efficient encoding algorithm for vector quantization based on subvector technique in this paper a new and fast encoding algorithm for vector quantization is presented this algorithm makes full use of two characteristics of a vector the sum and the variance a vector is separated into two subvectors one is composed of the first half of vector components and the other consists of the remaining vector components three inequalities based on the sums and variances of a vector and its two subvectors components are introduced to reject those codewords that are impossible to be the nearest codeword thereby saving a great deal of computational time while introducing no extra distortion compared to the conventional full search algorithm the simulation results show that the proposed algorithm is faster than the equal average nearest neighbor search enns the improved enns the equal average equal variance nearest neighbor search eenns and the improved eenns algorithms comparing with the improved eenns algorithm the proposed algorithm reduces the computational time and the number of distortion calculations by 2 4 to 6 and 20 5 to 26 8 respectively the average improvements of the computational time and the number of distortion calculations are 4 and 24 6 for the codebook sizes of 128 to 1024 respectively

side match and overlap match vector quantizers for images a class of vector quantizers with memory that are known as finite state vector quantizers fsvqs in the image coding framework is investigated two fsvq designs namely side match vector quantizers smvqs and overlap match vector quantizers omvqs are introduced these designs take advantage of the 2 d spatial contiguity of pixel vectors as well as the high spatial correlation of pixels in typical gray level images smvq and omvq try to minimize the granular noise that causes visible pixel block boundaries in ordinary vq for 512 by 512 gray level images smvq and omvq can achieve communication quality reproduction at an average of 1 2 b pixel per image frame and acceptable quality reproduction because block boundaries are less visible the perceived improvement in quality over ordinary vq is even greater owing to the structure of smvq and omvq simple variable length noiseless codes can achieve as much as 60 bit rate reduction over fixed length noiseless codes

principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law the steady state transverse responses and the stability of an axially accelerating viscoelastic string are investigated the governing equation is derived from the eulerian equation of motion of a continuum which leads to the mote model for transverse motion the kirchhoff model is derived from the mote model by replacing the tension with the averaged tension over the string the method of multiple scales is applied to the two models in the case of principal parametric resonance closed form expressions of the amplitudes and the existence conditions of steady state periodical responses are presented the lyapunov linearized stability theory is employed to demonstrate that the first second non trivial steady state response is always stable unstable numerical calculations show that the two models are qualitatively the same but quantitatively different numerical results are also presented to highlight the effects of the mean axial speed the axial speed fluctuation amplitude and the viscoelastic parameters

nonlinear free transverse vibration of an axially moving beam comparison of two models nonlinear free transverse vibration of an axially moving beam is investigated a partial differential equation governing the transverse vibration is derived from the newton s second law under the assumption that the tension of beam can be replaced by the averaged tension over the beam the partial differential reduces to a widely used integro partial differential equation for nonlinear free transverse vibration the method of multiple scales is applied directly to two equations to evaluate nonlinear natural frequencies numerical examples are presented to demonstrate the analytical results and to highlight the difference between two models two models yield the essentially same results for the weak nonlinearity the small axial speed and the low mode while the difference between two models increases with the nonlinear term the axial speed and the order of mode

solvability condition in multi scale analysis of gyroscopic continua abstract the solvability condition is investigated for the method of multiple scales applied to gyroscopic continua the general framework of the multi scale analysis is proposed for a linear gyroscopic continuous system under small nonlinear time dependent disturbances the solvability condition is derived from the properties of the systems the condition holds only for appropriate boundary conditions the appropriateness of the boundary conditions can be examined for unperturbed linear systems an example is presented to highlight the requirements on the boundary conditions

on the transversal vibrations of an axially moving continuum with a time varying velocity transient from string to beam behavior in this paper an initial boundary value problem for a linear equation describing an axially moving stretched beam will be considered the velocity of the beam is assumed to be time varying since the order of magnitude of the bending stiffness terms depends on the vibration modes and the frequencies involved a combination of two simplified models that is a string equation for the lower frequencies and a beam with string effect equation for the higher frequencies will be used to describe the transversal vibrations of the system accurately based on the calculations of the natural frequencies the regions of applicability of these sub models will be determined a two time scales perturbation method will be used to construct formal asymptotic approximations of the solutions non resonant and some resonant cases will be studied for four different values of the relative errors an important implication of the earlier results in the literature is that for these types of axially moving continua problems the use of only string like models is not appropriate to describe the dynamics of these types of axially moving continua problems correctly one has to include small bending stiffness in the model in this paper it is explicitly shown how to work with a combined model that is a string model at the low frequencies and a tensioned beam model at the higher frequencies

dynamic stability in parametric resonance of axially accelerating viscoelastic timoshenko beams abstract this paper investigates dynamic stability of an axially accelerating viscoelastic beam undergoing parametric resonance the effects of shear deformation and rotary inertia are taken into account by the timoshenko thick beam theory the beam material obeys the kelvin model in which the material time derivative is used the axial speed is characterized as a simple harmonic variation about the constant mean speed the governing partial differential equations are derived from newton s second law euler s angular momentum principle and the constitutive relation the method of multiple scales is applied to the equations to establish the solvability conditions in summation and principal parametric resonances the sufficient and necessary condition of the stability is derived from the routh hurvitz criterion some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries

fast global k means clustering using cluster membership and inequality in this paper we present a fast global k means clustering algorithm by making use of the cluster membership and geometrical information of a data point this algorithm is referred to as mfgkm the algorithm uses a set of inequalities developed in this paper to determine a starting point for the jth cluster center of global k means clustering adopting multiple cluster center selection mcs for mfgkm we also develop another clustering algorithm called mfgkm mcs mcs determines more than one starting point for each step of cluster split while the available fast and modified global k means clustering algorithms select one starting point for each cluster split our proposed method mfgkm can obtain the least distortion while mfgkm mcs may give the least computing time compared to the modified global k means clustering algorithm our method mfgkm can reduce the computing time and number of distance calculations by a factor of 3 78 5 55 and 21 13 31 41 respectively with the average distortion reduction of 5 487 for the statlog data set compared to the fast global k means clustering algorithm our method mfgkm mcs can reduce the computing time by a factor of 5 78 8 70 with the average reduction of distortion of 30 564 using the same data set the performances of our proposed methods are more remarkable when a data set with higher dimension is divided into more clusters

fast searching algorithm for vector quantization using projection and triangular inequality in this paper a new and fast searching algorithm for vector quantization is presented two inequalities one used for terminating the searching process and the other used to delete impossible codewords are presented to reduce the distortion computations our algorithm makes use of a vector s features mean value edge strength and texture strength to reject many unlikely codewords that cannot be rejected by other available approaches experimental results show that our algorithm is superior to other algorithms in terms of computing time and the number of distortion calculations compared with available approaches our method can reduce the computing time and the number of distortion computations significantly compared with the best method of reducing distortion computation our algorithm can further reduce the number of distortion calculations by 29 to 58 4 compared with the best encoding algorithm for vector quantization our approach also further reduces the computing time by 8 to 47 7

on the boundary conditions for axially moving beams axially moving beam typed structures are of technical importance and present in a wide class of engineering problem as the axial speed of a beam may significantly affect the dynamic characteristics of the structure even at a low velocity it is important to accurately predict the dynamic characteristics and stability of such structures in most previous studies the net energy flux through the left end and right end boundaries of the finite beam over two simple supports has been implicitly assumed to be zero by completely ignoring the effects of its left incoming and right outgoing semi infinite beam parts or by applying fixed boundary conditions for its longitudinal vibration which seems to be very non realistic from the physical point of view thus this paper investigates the effects of the continuously incoming and outgoing semi infinite beam parts on the dynamic characteristics and stability of an axially moving beam by using the spectral element method the spectral element model is formulated from the equations of motion derived by using the hamilton s principle extended for the systems of changing mass it is numerically shown that the effects of the continuously incoming and outgoing semi infinite beam parts should be taken into account for further accurate prediction of the dynamic characteristics and stability for such axially moving beams

stability in parametric resonance of axially accelerating beams constituted by boltzmann s superposition principle stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated the governing equation is derived from newton s second law boltzmann s superposition principle and the geometrical relation when the axial speed is a constant mean speed with small harmonic variations the governing equation can be treated as a continuous gyroscopic system with small periodically parametric excitations and a damping term the method of multiple scales is applied directly to the governing equation without discretization the stability conditions are obtained for combination and principal parametric resonance numerical examples demonstrate that the increase of the viscosity coefficient causes the lager instability threshold of speed fluctuation amplitude for given detuning parameter and smaller instability range of the detuning parameter for given speed fluctuation amplitude the instability region is much bigger in lower order principal resonance than that in the higher order

a new vector quantization clustering algorithm the pairwise nearest neighbor pnn algorithm is presented as an alternative to the linde buzo gray 1980 lbg generalized lloyd 1982 algorithm for vector quantization clustering the pnn algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required without sacrificing performance in addition the time needed to generate a codebook grows only o n log n in training set size and is independent of the number of code words desired using this method one can either minimize the number of code words needed subject to a maximum rate the pnn algorithm can be used with squared error and weighted squared error distortion measure simulations on a variety of images encoded at 1 2 b pixel indicate that pnn codebooks can be developed in roughly 5 of the time required by the lbg algorithm

the generalized hyers ulam rassias stability of a cubic functional equation abstract in this paper we obtain the general solution and the generalized hyers ulam stability for a cubic functional equation f 2x y f 2x y 2f x y 2f x y 12f x

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

transient vibration of gyroscopic systems with unsteady superposed motion abstract the equation of motion for a gyroscopic system with unsteady superposed motion is derived for the prototypical problem in which motion of an oscillating particle is measured relative to a non inertial frame the resulting coefficient matrices are time dependent and skew symmetric acceleration terms are present both as coriolis acceleration and as a component of net stiffness such mathematical structure is also demonstrated in the context of other unsteady gyroscopic systems including flexible media that translate with time dependent speed following the asymptotic approach of krylov bogoliubov and mitropolsky a perturbation method is developed for the case in which the superposed motion varies slowly when viewed on the time scale of the system s natural periods of oscillation first order approximations for the modal amplitude and phase are obtained in closed form the method is illustrated through two examples of technical interest a two degree of freedom model of a rotating shaft and a distributed parameter model of a moving tape or web