a normalized schur cohn stability test for the delta operator based polynomials the author previously 1997 proposed two delta operator based stability tests or more generally zero location tests those tests establish two families of such tests each spanning from the discrete time to the continuous time with the delta operator providing smooth transitions between the two domains in this paper a third family is proposed specifically the normalized schur cohn test in the discrete time domain is transformed into the delta operator domain resulting in a new delta operator test the limit of this new test as the sampling interval vanishes is shown to be the pham le breton test 1991 in the continuous time domain its relationships with the well known routh test and others are studied a numerical example shows the advantage of the new test for fast sampling

some exact solutions for the bending of beams with spatially stochastic stiffness to the best of the knowledge of the authors there are no exact solutions available for the bending of beams with spatially stochastic stiffness investigators are therefore utilizing various approximate techniques in the present study a new method is developed to obtain exact solutions for first and second moments of displacements for statically determinate beams that have spatially random stiffness the method is based on the full probabilistic characterization of the random stiffness so that the solutions are valid for any value of the coefficient of variation of the stiffness the deterministic governing equations and boundary conditions derived for both first and second moments allow apparently for the first time in the literature the exact solutions for the mean and covariance functions of the displacements to be determined two governing equations are uncoupled from each other and can be solved separately several exact solutions for the mean and covariance functions are obtained to illustrate the application of the method it is hoped that the exact solutions determined will serve as benchmark solutions to enable the researchers to check the accuracy of various approximate analytical and numerical techniques on the test solutions presented in this study

a levinson type algorithm for modeling fast sampled data the standard discrete time autoregressive model is poorly suited for modeling series obtained by sampling continuous time processes at fairly rapid rates large computational errors can occur when the levinson algorithm is used to estimate the parameters of this model because the toeplitz covariance matrix is ill suited for inversion an alternative model is developed based on an incremental difference operator rather than the shift operator it is shown that as the sampling period goes to zero unlike the standard autoregressive parameters the coefficients of this model converge to certain parameters that depend directly on the statistics of the continuous time process a levinson type algorithm for efficiently estimating the parameters of this model is derived numerical examples are given to show that when the sampling interval is small this algorithm is considerably less sensitivity to arithmetic roundoff errors than the levinson algorithm

periodic homogenization for hypoelliptic diffusions we study the long time behavior of an ornstein uhlenbeck process under the influence of a periodic drift we prove that under the standard diffusive rescaling the law of the particle position converges weakly to the law of a brownian motion whose covariance can be expressed in terms of the solution of a poisson equation we also derive upper bounds on the convergence rate in several metrics

upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation abstract for a smooth bounded domain r n n 3 and e a real parameter consider the hyperbolic equation eu tt u t u u g in with dirichlet boundary conditions under certain conditions on this equation has a compact attractor a e in h 0 1 l 2 for e 0 the parabolic equation also has a compact attractor which can be naturally embedded into a compact set a 0 in h 0 1 l 2 it is shown that for any neighborhood u of a 0 the set a e u for e small

on the influence of sampling and observation times on estimation of the bandwidth parameter of a gauss markov process the statistical problem of estimating the bandwidth parameter of a gauss markov gm process from a realization of fixed and finite duration t at selectable sampling interval spl delta is addressed in this paper as the observation time t is fixed and finite the variance of estimated autocorrelation and continuous time parameter does not vanish as spl delta approaches 0 this necessitates a second order taylor expansion in deriving the parameter estimator bias and variance the second order taylor expansion produces better bias and variance results than a first order one does the distribution of the estimator is also discussed according to the gradient change of the variance a key result is that three sample size regions which are termed finite large and very large corresponding to substantial gradual and very slight decrease in the variance of the parameter estimator respectively are quantified in terms of analysis bw the three regions are 23 35 35 55 and 55 spl infin db the characterization of the tradeoff between the variance decrease and sampling rate results in a practical guideline for choosing sampling rate these results are applied to the prediction problems of a time invariant gm process to show their value

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

the singular limit dynamics of semilinear damped wave equations on considere la dynamique qualitative d une equation d onde amortie semi lineaire a une dimension dans la limite singuliere correspondant a l annulation du coefficient de la derivee d ordre 2 en temps

least squares parameter estimation of continuous time arx models from discrete time data when modeling a system from discrete time data a continuous time parameterization is desirable in some situations in a direct estimation approach the derivatives are approximated by appropriate differences for an arx model this lead to a linear regression the well known least squares method would then be very desirable since it can have good numerical properties and low computational burden in particular for fast or nonuniform sampling it is examined under what conditions a least squares fit for this linear regression will give adequate results for an arx model the choice of derivative approximation is crucial for this approach to be useful standard approximations like euler backward or euler forward cannot be used directly the precise conditions on the derivative approximation are derived and analyzed it is shown that if the highest order derivative is selected with care a least squares estimate will be accurate the theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation

on asymptotic properties of maximum likelihood estimators for parabolic stochastic pde s we investigate asymptotic properties of the maximum likelihood estimators for parameters occurring in parabolic spdes of the form du t x a 0 theta a 1 u t x dt dw t x wherea 0 anda 1 are partial differential operators andw is a cylindrical brownian motion we introduce a spectral method for computing mles based on finite dimensional approximations to solutions of such systems and establish criteria for consistency asymptotic normality and asymptotic efficiency as the dimension of the approximation goes to infinity we derive the asymptotic properties of the mle from a condition on the order of the operators in particular the mle is consistent if and only if ord a 1 1 2 ord a 0 a 1 d

the stochastic wave equation in two spatial dimensions keywords stochastic wave equation gaussian noise process solution reference prob article 1998 001view record in web of science record created on 2008 12 01 modified on 2017 05 12

delta operator formulated discrete time approximations of continuous time systems given a continuous time system a technique to directly obtain an approximate delta operator formulated discrete time system spl delta system is presented for this purpose the analog of the well known boxer thaler integrators q forms applicable to shift operator formulated discrete time systems q systems are derived for spl delta systems next using these spl delta forms a method to obtain an approximate spl delta system of a given continuous time system is derived this algorithm is easily implementable in a computer with little computational burden it is shown that as sampling time decreases the spl delta system thus obtained yields the given continuous time system further verifying the close equivalence between this formulation and continuous time systems two examples illustrating advantages that may be gained by utilizing these spl delta forms in digitizing analog systems are also included

an efficient order recursive algorithm with a lattice structure for estimating continuous time ar process parameters abstract an order recursive algorithm is proposed to solve the normal equation in estimating continuous time ar process parameters the new algorithm requires o m 2 computations where m is the order of the ar process and therefore is computationally efficient this is similar to the levinson type algorithm of pham and le breton however the proposed algorithm has a new associated lattice structure and as a consequence a new stability test for continuous time systems not just ar processes by checking the reflection coefficients of the lattice this can be viewed as a continuous time analogy that is recursive in order of the well known discrete time version its discrete time approximation when sampled data are given and connections with other algorithms are also discussed

improved finite word length characteristics in digital control using delta operators this paper examines some of the consequences of finite word lengths in digital control it is shown that in many cases of practical importance the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach this latter approach is shown to give better coefficient representation and less roundoff noise in many cases we thus argue that the shift operator and its associated z transform can be replaced by delta operators and their associated transform which we designate a transform an added advantage of this approach is that discrete designs and transforms converge to their continuous time counterparts as the sampling rate is increased

delta levinson and schur type rls algorithms for adaptive signal processing in this paper we develop delta operator based levinson and schur type on line rls algorithms such algorithms have the potential of improved numerical behavior for ill conditioned input data these new algorithms are obtained by a unified transformation on the existing q operator based ones we first show that the conventional lattice structure can be naturally derived when the backward delta operator is used with this operator levinson and schur algorithms for the stationary stochastic model in q domain can easily be transformed into the delta domain then same transformation will be applied to the q domain on line levinson and schur type rls algorithms to obtain the delta domain counterparts their normalized versions as well as a systolic array architecture implementing the new delta schur rls algorithm are proposed extension to the equal length multichannel case is also given computer simulations show the expected numerical advantages of the delta based algorithms for fast sampled data in real time over the q domain ones under finite precision implementation

on convergent rate of the attractor for a singularly perturbed wave equation abstract by applying the pullback property of attractor the paper obtains the continuity and the convergent rate p 1 2 of the attractor for a singularly perturbed wave equation without help of the hyperbolic property of stationary points

a delta mywe algorithm for parameter estimation of noisy ar processes we develop a delta operator based modified yule walker equation algorithm mywe for parameter estimation of a noisy autoregressive ar process the methodology in developing this new algorithm is similar to the previous works on pure ar processes computer simulation results are given to show the improvement of performance in estimating ar parameters in white noise over the q operator mywe algorithm

a delta least squares lattice algorithm for fast sampling most shift operator based adaptive algorithms exhibit poor numerical behavior when the input discrete time process is obtained from a continuous time process by fast sampling this includes the shift operator based least squares lattice algorithm we develop a delta least squares lattice algorithm this algorithm has a low computational complexity compared with the delta levinson rls algorithm and shows better numerical properties compared with the shift least squares lattice algorithm under fast sampling computer simulations show that the new algorithm also outperforms an existing delta least squares lattice algorithm

on the smoluchowski kramers approximation for a system with an infinite number of degrees of freedom according to the smolukowski kramers approximation we show that the solution of the semi linear stochastic damped wave equations utt t x u t x ut t x b x u t x qopen image in new window t u 0 u0 ut 0 v0 endowed with dirichlet boundary conditions converges as goes to zero to the solution of the semi linear stochastic heat equation ut t x u t x b x u t x qopen image in new window t u 0 u0 endowed with dirichlet boundary conditions moreover we consider relations between asymptotics for the heat and for the wave equation more precisely we show that in the gradient case the invariant measure of the heat equation coincides with the stationary distributions of the wave equation for any 0

unified type non stationary lyapunov matrix equation simultaneous eigenvalue bounds abstract simultaneous eigenvalue bounds for the solution of the unified non stationary lyapunov matrix equation are presented when the solution becomes stationary the results reduce to bounds of the unified type algebraic lyapunov equation in the limiting cases the results reduce to bounds for the solution of the differential and difference lyapunov equations the bounds given in this paper are a generalization of some existing bounds obtained separately for the continuous and discrete type stationary and non stationary lyapunov equations

a qr type algorithm for fitting the delta ar model to autocorrelation windowed data a qr algorithm is developed to fit the delta autoregressive dar model of vijayan et al see ieee trans automat cont vol 36 p 314 1991 to autocorrelation windowed sampled data to obtain the dar model parameters one must solve a linear system in the matrix called q sub n unfortunately there is presently no way to obtain good estimates of q sub n the proposed qr type algorithm overcomes this problem by computing the dar model parameters without the need for estimating q sub n directly the qr algorithm proposed is a simple modification of the classical qr algorithm for the conventional ar model due to c p rialan and l l scharf 1986

on properties of information matrices of delta operator based adaptive signal processing algorithms in this paper we study the properties of information matrices of the difference operator or the so called delta spl delta operator based algorithms for adaptive signal processing we show that the conditioning of a transformed information matrix in the spl delta domain is always better than that of the original information matrix in the conventional q domain for ill conditioned problems the results obtained in this paper give an explanation of the advantages of using delta operator algorithms for adaptive signal processing that have been developed the analysis in this paper also helps to clarify the problem about the effect of spl delta in the delta operator algorithms and justify the use of sampling interval as spl delta in most cases when the ill conditioning is caused by fast sampling of continuous time systems

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

limiting dynamics for stochastic wave equations abstract in this paper relations between the asymptotic behavior for a stochastic wave equation and a heat equation are considered by introducing almost surely d contracting property for random dynamical systems we obtain a global random attractor of the stochastic wave equation u t t u t u f u w endowed with dirichlet boundary condition for any 0 1 the upper semicontinuity of this global random attractor and the global attractor of the heat equation z t z f z 0 with dirichlet boundary condition as goes to zero is investigated furthermore we show the stationary solutions of the stochastic wave equation converge in probability to some stationary solution of the heat equation

higher order weighted integral stochastic finite element method and simplified first order application it is well known that expansion based stochastic methods are approximate schemes as they are based on a first or at most second order series expansion on the basic variable e g displacement therefore expansion based stochastic analysis schemes are bound to show small response variability when compared with monte carlo simulation mcs results and application of these schemes is limited to stochastic problems with relatively small variability in order to overcome these general drawbacks of the expansion methods we suggest a higher order stochastic field function that can be employed in the expansion based stochastic analysis scheme of the weighted integral method we then propose a new weighted integral formulation using the higher order stochastic field function the new formulation is not only applicable to stochastic problems with a high degree of uncertainty but also can reproduce the phenomenon of accelerated increase in the response variability when the coefficient of variation of the stochastic field increases as observed in the mcs in order to show the validity of the proposed formulation we provide two numerical examples and the results are discussed in detail

a berry esseen bound in the smoluchowski kramers approximation in this paper we use the kolmogorov distance to investigate the smoluchowski kramers approximation for stochastic differential equations we obtain an explicit berry esseen error bound for the rate of convergence our main tools are the techniques of malliavin calculus

unified polynomial expansion for interval and random response analysis of uncertain structure acoustic system with arbitrary probability distribution abstract for structure acousticsystem with uncertainties the interval model the random model and the hybrid uncertain model have been introduced in the interval model and the random model the uncertain parameters are described as either the random variable with well defined probability density function pdf or the interval variable without any probability information whereas in the hybrid uncertain model both interval variable and random variable exist simultaneously for response analysis of these three uncertain models of structure acoustic problem involving arbitrary pdfs a unified polynomial expansion method named as the interval and random arbitrary polynomial chaos method irapcm is proposed in irapcm the response of the structure acoustic system is approximated by apc expansion in a unified form particularly only the weight function of polynomial basis is required to be changed to construct the apc expansion for the response of different uncertain models through the unified apc expansion the uncertain properties of the response of three uncertain models can be efficiently obtained as the apc expansion can provide a free choice of the polynomial basis the optimal polynomial basis for the random variable with arbitrary pdfs can be obtained by using the proposed irapcm the irapcm has been employed to solve a mathematical problem and a structure acoustic problem and the effectiveness of the unified irapcm for response analysis of three uncertain models is demonstrated by fully comparing it with the hybrid first order perturbation method and several existing polynomial chaos methods

from ballistic to diffusive behavior in periodic potentials the long time large scale small friction asymptotic for the one dimensional langevin equation with a periodic potential is studied in this paper it is shown that the freidlin wentzell and central limit theorem homogenization limits commute we prove that in the combined small friction long time large scale limit the particle position converges weakly to a brownian motion with a singular diffusion coefficient which we compute explicitly we show that the same result is valid for a whole one parameter family of space time rescalings the proofs of our main results are based on some novel estimates on the resolvent of a hypoelliptic operator

some remarks on the smoluchowski kramers approximation according to the smoluchowski kramers approximation solution qt of the equation mu ddot q t mu b q t mu dot q t mu sigma q t mu dot w t q 0 q dot q p where dot w t is the white noise converges to the solution of equation dot q t b q t sigma q t dot w t q 0 q as 0 many asymptotic problems for the last equation were studied in recent years we consider relations between asymptotics for the first order equation and the original second order equation homogenization large deviations and stochastic resonance approximation of brownian motion wt by a smooth stochastic process stationary distributions are considered

nonlinear stochastic wave and heat equations we study nonlinear wave and heat equations on d driven by a spatially homogeneous wiener process for the wave equation we consider the cases of d 1 2 3 the heat equation is considered on an arbitrary d space we give necessary and sufficient conditions for the existence of a function valued solution in terms of the covariance kernel of the noise

existence of strong solutions for ito s stochastic equations via approximations given strong uniqueness for an ito s stochastic equation with discontinuous coefficients we prove that its solution can be constructed on any probability space by using for example euler s polygonal approximations stochastic equations in d and in domains in d are considered

the rate of convergence for the smoluchowski kramers approximation for stochastic differential equations with fbm in this paper we study the rate in the smoluchowski kramers approximation for the solution of the equation x t x b t h int 0 t b x s ds where b t h t in 0 t is a fractional brownian motion with hurst parameter h in big frac 1 2 1 big based on the techniques of malliavin calculus we provide an explicit bound on total variation distance for the rate of convergence

on delta operator schur cohn zero location tests for fast sampling a stability test or more generally a zero location test algorithm similar to the well known schur cohn test is proposed when a complex polynomial formulated in the delta operator is given the real polynomial case falls out naturally as a special case the method used is a simple linear transformation based on the schur cohn test and the proposed algorithm is computationally efficient furthermore it is shown that as the sampling interval vanishes the new algorithm converges to a new continuous time test therefore providing a smooth transition from the shift operator based discrete time algorithm to the continuous time one furthermore a sensitivity analysis shows that the sensitivity of the new test in the delta operator remains finite with respect to parameter perturbation and converges to that of the continuous time one whereas that of the shift operator grows without bound as the sampling interval vanishes examples are given to show the clear numerical advantages over the traditional shift operator based schur cohn test in the case of fast sampling

stochastic second order perturbation approach to the stress based finite element method abstract the paper is devoted to the application of the second order perturbation second probabilistic moment method to the stress based finite element method fem the approach is introduced for the linear elastic heterogeneous medium up to the second order variational equations of the complementary energy principle are presented together with an additional stochastic finite element discretization based on airy and prandtl stress functions the numerical examples shown in this paper illustrate the probabilistic stress and strain tensors in the cantilever beam under shear loading and torsioned square beam with randomly defined material and geometrical parameters the results obtained in the tests can be applied in probabilistic analyses of the boundary value problems having any closed form mathematical solutions as well as in the stress based stochastic fem analysis of solids and structures

comparative study of projection schemes for stochastic finite element analysis we present a comparison of subspace projection schemes for stochastic finite element analysis in terms of accuracy and computational efficiency more specifically we compare the polynomial chaos projection scheme with reduced basis projection schemes based on the preconditioned stochastic krylov subspace numerical studies are presented for two problems 1 static analysis of a plate with random young s modulus and 2 settlement of a foundation supported on a randomly heterogeneous soil monte carlo simulation results based on exact structural analysis are used to generate benchmark results against which the projection schemes are compared we show that stochastic reduced basis methods require significantly less computer memory and execution time compared to the polynomial chaos approach particularly for large scale problems with many random variables for the class of problems considered we find that stochastic reduced basis methods can be up to orders of magnitude faster while providing results of comparable or better accuracy

singular root distribution problem for delta operator based real polynomials efficient zero location tests for the delta operator based polynomials have been a recent topic of interest these tests not only provide the needed efficient tests for the delta operator formulated systems control and signal processing problems which are numerically better behaved than the traditional shift operator based tests for fast sampling they also provide missing links between classical tests in the z domain and the s domain such as the schur cohn test sct and the routh test rt these will also be accomplished in this paper but for the singular cases specifically the recently developed singular case i schur cohn test by pal and kailath 1994 is modified and transformed into the delta domain as the sampling interval vanishes this new algorithm converges to an s domain singular case i test associated with the recently developed s domain sct singular case ii is also considered and the difference between the traditional approaches in the z domain and the s domain reconciled numerical examples are given to illustrate better numerical properties of the new test over pal kailath recursion for fast sampling

a stochastic wave equation in two space dimension smoothness of the law we prove the existence and uniqueness for any time of a real valued process solving a nonlinear stochastic wave equation driven by a gaussian noise white in time and correlated in the two dimensional space variable we prove that the solution is regular in the sense of the malliavin calculus we also give a decay condition on the covariance function of the noise under which the solution has holder continuous trajectories a d show that under an additional ellipticity assumption the law of the solution at any strictly positive time has a smooth density

random perturbations of reaction diffusion equations the quasi deterministic approximation on considere des champs aleatoires u e t x u 1 e t x u n e t x definis comme les solutions d un systeme d equations aux derivees partielles u k e t l k u k e f k x u 1 e u n e e k t x les l k sont des operateurs elliptiques lineaires d ordre 2 k sont des champs gaussiens bruit blanc

on the convergence of stationary solutions in the smoluchowski kramers approximation of infinite dimensional systems abstract we prove the convergence in the small mass limit of statistically invariant states for a class of semi linear damped wave equations perturbed by an additive gaussian noise both with lipschitz continuous and with polynomial non linearities in particular we prove that the first marginals of any sequence of invariant measures for the stochastic wave equation converge in a suitable wasserstein metric to the unique invariant measure of the limiting stochastic semi linear parabolic equation obtained in the smoluchowski kramers approximation the wasserstein metric is associated to a suitable distance on the space of square integrable functions that is chosen in such a way that the dynamics of the limiting stochastic parabolic equation is contractive with respect to such a wasserstein metric this implies that the limiting result is a consequence of the validity of a generalized smoluchowski kramers limit at fixed times the proof of such a generalized limit requires new delicate bounds for the solutions of the stochastic wave equation that must be uniform with respect to the size of the mass

delay replacement in direct form structures a class of high order low sensitivity digital filter structures is generated by means of a direct transformation of a high order direct form df structure the proposed structures have low coefficient dynamic range and exhibit low coefficient frequency response sensitivity and roundoff noise characteristics yet require only 3n multiplications per output sample as compared to 2n in the direct form case

homogenization based interval analysis for structural acoustic problem involving periodical composites and multi scale uncertain but bounded parameters this paper presents a homogenization based interval analysis method for the prediction of coupled structural acoustic systems involving periodical composites and multi scale uncertain but bounded parameters in the structural acoustic system the macro plate structure is assumed to be composed of a periodically uniform microstructure the equivalent macro material properties of the microstructure are computed using the homogenization method by integrating the first order taylor expansion interval analysis method with the homogenization based finite element method a homogenization based interval finite element method hifem is developed to solve a periodical composite structural acoustic system with multi scale uncertain but bounded parameters the corresponding formulations of the hifem are deduced a subinterval technique is also introduced into the hifem for higher accuracy numerical examples of a hexahedral box and an automobile passenger compartment are given to demonstrate the efficiency of the presented method for a periodical composite structural acoustic system with multi scale uncertain but bounded parameters

estimation of continuous time ar process parameters from discrete time data the problem of estimating continuous time autoregressive process parameters from discrete time data is considered the basic approach used here is based on replacing the derivatives in the model by discrete time differences forming a linear regression and using the least squares method such a procedure is simple to apply computationally flexible and efficient and may have good numerical properties it is known however that all standard approximations of the highest order derivative such as repeated use of the delta operator gives a biased least squares estimate even as the sampling interval tends to zero some of our previous approaches to overcome this problem are reviewed then two new methods which avoid the shift in our previous results are presented one of them which is termed bias compensation is computationally very efficient finally the relationship of the above least squares approaches with an instrumental variable method is investigated comparative simulation results are also presented

efficient zero location tests for delta operator based polynomials two different kinds of stability tests or more generally zero location tests are proposed when a real polynomial formulated in the delta operator is given the method used is a simple linear transformation based on some known discrete time tests including the schur cohn test sct and the proposed algorithms are computationally efficient furthermore it is shown that as the sampling interval vanishes all new algorithms converge to their continuous time limits therefore providing smooth transitions from the shift operator based discrete time tests to the continuous time ones one of these limits is the classic routh test rt and the other is a new test closely related to the rt examples are given to demonstrate the tests which show clear numerical advantages over the traditional shift operator based ones such as the sct in case of fast sampling the significance of these new tests lies beyond the fact that they have provided efficient and reliable zero location tests directly in the delta domain these tests provide the missing links between the discrete time shift operator based tests and the continuous time ones as a consequence two separate and yet related families of zero location tests are established which include the well known rt and the sct

modified sub interval perturbation finite element method for 2d acoustic field prediction with large uncertain but bounded parameters abstract based on the sub interval perturbation analysis a modified sub interval perturbation finite element method is proposed to determine the bounds of sound pressure in the 2d acoustic field with large uncertain but bounded parameters in the proposed method the inversion of the invertible sub interval dynamic stiffness matrix is approximated by a modified approximate interval value sherman morrison woodbury formula to overcome the drawbacks arising from the dependency phenomenon of parameters and the unpredictable effect of neglecting the higher order terms in neumann series the modified sub interval perturbation procedures are implemented in a numerical finite element framework numerical results on a 2d acoustic tube and a 2d acoustic cavity of a car with large uncertain but bounded parameters evidence the remarkable accuracy and effectiveness of the proposed method

response variability due to randomness in poisson s ratio for plane strain and plane stress states summary in the ordinary structural materials one of the parameters that can be assumed to have spatial uncertainty is poisson s ratio therefore the independent evaluation of the effects of this parameter on the response variability is of importance the difficulties in obtaining the response variability due to randomness in poisson s ratio lie in the fact that the poisson s ratio enters the stiffness matrix as a non linear parameter in this paper a formulation to determine the response variability in plane strain and plane stress states due to the randomness in the poisson s ratio is given the formulation is accomplished by means of the stochastic decomposition of the constitutive matrix into several sub matrices taking into consideration of the polynomial expansion on the coefficients of constitutive relation to demonstrate the validity of the proposed formulation some example structures are chosen and the results are compared with those obtained by means of monte carlo simulation through the formulation proposed in this study it becomes possible for the weighted integral stochastic finite element analysis to consider all the uncertain material parameters in its application