blind deconvolution of multi input single output systems with binary sources the problem of blind source separation for multi input single output miso systems with binary inputs is treated in this paper our approach exploits the constellation properties of the successor values for each output sample in the absence of noise the successors of each output value form a characteristic finite set of clusters successor constellation the shape of this constellation is invariant of the predecessor value and it only depends on the last filter tap consequently the localization of the successors constellation can lead to the removal of the last filter tap thus reducing the length of the filter a process we call channel deflation based on the successor observation clustering soc we develop two algorithms for blind source separation soc 1 and soc 2 differing mainly on the required size of the data set furthermore the treatment of the system in the presence of noise is described using data clustering and data correction the problem of noise is attacked using a statistical mode based method moreover we correct the problem of misclassified observations using an iterative scheme based on the viterbi algorithm for the decoding of a hidden markov model hmm

minimum resistance shapes in linear continuum mechanics a necessary optimality condition for the problem of the minimum resistance shape for a rigid three dimensional inclusion displaced in an unbounded isotropic elastic medium subject to a constraint o

on the large time galerkin approximation of the navier stokes equations in this article we are interested in the difficult problem of relating the large time behaviour of the navier stokes equations to the large time behaviour of their galerkin approximation we restrict ourselves to the simplest situation dealing with stationary solutions and the question is the following one if the computed approximation of the time dependent equations seems to converge to some limit as t to infty is the same true for the exact problem and are the limits related we give here some sufficient conditions reasonably easy to verify which guarantee a positive answer to this question

cauchy integral formula for generalized analytic functions in hydrodynamics it is shown that for several classes of generalized analytic functions arising in linearized equations of hydrodynamics and magnetohydrodynamics the cauchy integral formulae follow from the one for generalized holomorphic vectors in a uniform fashion if hydrodynamic fields velocity pressure and vorticity admit representations in terms of corresponding generalized analytic functions those representations and the cauchy integral formulae form two essential parts of the generalized analytic function approach which readily yields either closed form solutions or boundary integral equations this approach is demonstrated for problems of axisymmetric and asymmetric stokes flows two phase axisymmetric stokes flows two dimensional and axisymmetric oseen flows

linear prediction methods for blind fractionally spaced equalization we describe adaptive methods for estimating fir zero forcing blind equalizers with arbitrary delay directly from the linear predictions of the observations while most current methods require inversion or singular value decomposition svd of the correlation matrix our methods need only to solve two linear prediction problems they can be implemented as rls or lms algorithms to recursively update the equalizer estimation they are computationally efficient the computational complexity in each recursion can be less than 15 ln sup 2 in the rls case where ln equals the equalizer length and 3l ln in the lms case where l is the number of subchannels the performance of the proposed methods and comparisons with existing approaches are shown by simulation to demonstrate their effectiveness

hilbert formulas for r analytic functions in the domain exterior to spindle hilbert formulas for an r analytic function defined by a generalized cauchy riemann system in the domain exterior to the contour of a spindle in the meridional cross section plane have been derived the derivation is based on the theory of riemann boundary value problems for analytic functions for numerical calculations fourier integrals with hilbert formulas representing the real and imaginary parts of the r analytic function have been reduced to the form of regular integrals the problem of the axially symmetric steady motion of a rigid spindle shaped body in a stokes fluid has been solved and the pressure in the fluid has been expressed analytically based on a hilbert formula as an illustration streamlines about the body vortex and pressure functions at the contour of the body and the drag force exerted on the body by the fluid have been calculated

qr factorization based blind channel identification with second order statistics most eigenstructure based blind channel identification and equalization algorithms with second order statistics need svd or evd of the correlation matrix of the received signal in this paper we address new algorithms based on qr factorization of the received signal directly without calculating the correlation matrix this renders the qr factorization based algorithms more robust against ill conditioned channels i e those channels with almost common zeros among the subchannels first we present a block algorithm that performs the qr factorization of the received data matrix as a whole then a recursive algorithm is developed based on the qr factorization by updating a rank revealing ulv decomposition compared with existing algorithms in the same category our algorithms are computationally more efficient the computation in each recursion of the recursive algorithm is on the order of o m sup 2 if only equalization is required where m is the dimension of the received signal vector our recursive algorithm preserves the fast convergence property of the subspace algorithms thus converging faster than other adaptive algorithms such as the super exponential algorithm with comparable computational complexities moreover our proposed algorithms do not require noise variance estimation numerical simulations demonstrate the good performance of the proposed algorithms

common periodic behavior in larger and larger truncations of the navier stokes equations the periodic behavior ofn mode truncations of the navier stokes equations on a two dimensional torus is studied forn 44 60 80 and 98 significant common features are found particularly for not too high reynolds numbers in all models periodicity ends giving rise though at quite different parameter values to quasiperiodicity

blind channel estimation using the second order statistics asymptotic performance and limitations we consider the asymptotic performance and fundamental limitations of the class of blind estimators that use second order statistics an achievable lower bound of the asymptotic normalized mean square error anmse is derived it is shown that the achievable anmse is lower bounded by the condition number of the jacobian matrix of the correlation function with respect to the channel parameters it is shown next that the jacobian matrix is singular if and only if the subchannels share common conjugate reciprocal zeros this condition is different from the existing channel identification conditions asymptotic performance of some existing eigenstructure based algorithms is analyzed closed form expressions of anmse and their lower bounds are derived for the least squares ls and the subspace ss blind channel estimators when there are two subchannels asymptotic efficiency of ls ss algorithms is also evaluated showing that significant performance improvement is possible when the information of the source correlation is exploited

time dependent periodic navier stokes flows on a two dimensional torus the dynamical behaviour of an incompressible viscous fluid flow on a two dimensional torus externally excited by a spatially periodic force is investigated the flow field described by navier stokes equations is found to possess a sequence of time periodic solutions which bifurcate from a single steady state solution i e hopf bifurcations this result is based on a combination of analysis and computations and each provides corroborative evidence to the findings of the other

bifurcation computations on an approximate inertial manifold for the 2d navier stokes equations abstract we compare the minimum number of modes needed to capture certain bifurcations of the 2d navier stokes equations by a certain nonlinear galerkin method and by the traditional galerkin method the boundary conditions are periodic and the forcing is in a single mode two different choices of the forcing mode are tested we introduce and implement a homotopy which allows continuation between approximations of different size

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

instability for the navier stokes equations on the 2 dimensional torus and a lower bound for the hausdorff dimension of their global attractors we prove instability of stationary solutions of the navier stokes equations on the domain 0 2 0 2 with periodic boundary condition for a class of external forces for large reynolds number moreover we give a lower bound for the hausdorff dimension of the global attractors

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

global solutions of the navier stokes equations in thin three dimensional domains this paper is concerned with the spatially periodic navier stokes equations in a thin three dimensional domain it is shown that the classical solution exists globally when the initial velocityu0and the external forcefare chosen in the set significantly larger than those presented in earlier works what is more it is shown that these global solutions which seem large in a function space are small in nature

blind channel estimation using the second order statistics algorithms most second order moment based blind channel estimators belong to two categories i optimal correlation spectral fitting techniques and ii eigenstructure based techniques these two classes of algorithms have complementary advantages and disadvantages a new optimization criterion referred to as the joint optimization with subspace constraints josc is proposed to unify the two types of approaches based on this criterion a new algorithm is developed to combine the strength of the two classes of blind channel estimators among a number of attractive features the josc algorithm does not require the accurate detection of the channel order when compared with existing eigenstructure based techniques the josc performs better especially when the channel is close to being unidentifiable when compared with correlation spectral fitting schemes the josc is less affected by the presence of local minima

long time behavior of navier stokes flow on a two dimensional torus excited by an external sinusoidal force in this paper we study the navier stokes flow on the two dimensional toruss1 s1 excited by the external force k2 sinky 0 and find the long time behavior for the flow starting from some states wheres1 0 2 mod 2 especially for the casek 2 it follows from an analysis and computation that the navier stokes flow with the initial state cos mx ny or sin mx ny will likely evolve through at most one step bifurcation to either a steady state solution or a time dependent periodic solution for any reynolds number and integersm andn

asymmetric creeping motion of a rigid spindle shaped body in a viscous fluid exact solutions to the three dimensional problems of asymmetric creeping translation and rotation of a rigid spindle shaped body in a viscous incompressible fluid have been obtained in both problems the velocity field has been represented in the form of dean and o neill and under certain conditions the equation of continuity has been reduced to a three contour equation for an analytic function related to the density in a fourier integral representing the pressure in bispherical coordinates then the three contour equation has been reduced to a fredholm integral equation of the second kind with a quasi difference kernel by the complex fourier transform as an illustration for the obtained solutions the pressure at the surface of the body has been calculated and analyzed the resisting force and torque have been obtained for an arbitrary body of revolution via limits of certain harmonic functions at infinity and as an example have been computed for various values of a geometrical parameter of the s

an example of absence of turbulence for any reynolds number ii we study a viscous incompressible fluid moving in a two dimensional flat torus 0 l 0 2 l 2 we show a set of external forces for which the stationary state is attractive for any reynolds numberr moreover the size of this set and the basin of attraction are independent ofr

on a criterion for locating stable stationary solutions to the navier stokes equations on donne une estimation superieure uniforme explicite a la borne de constantin foias ternam et on donne une forme applicable explicite aux conditions suffisantes on considere seulement le cas a 2 dimensions

on updating signal subspaces the authors develop an algorithm for adaptively estimating the noise subspace of a data matrix as is required in signal processing applications employing the signal subspace approach the noise subspace is estimated using a rank revealing qr factorization instead of the more expensive singular value or eigenvalue decompositions using incremental condition estimation to monitor the smallest singular values of triangular matrices the authors can update the rank revealing triangular factorization inexpensively when new rows are added and old rows are deleted experiments demonstrate that the new approach usually requires o n sup 2 work to update an n n matrix and that it accurately tracks the noise subspace

blind channel identification subspace tracking method without rank estimation subspace ss methods are an effective approach for blind channel identification however these methods also have two major disadvantages 1 they require accurate channel length estimation and or rank estimation of the correlation matrix which is difficult with noisy channels and 2 they require a large amount of computation for the singular value decomposition svd which makes it inconvenient for adaptive implementation although many adaptive subspace tracking algorithms can be applied the computational complexity is still o m sup 3 where m is the data vector length in this paper we introduce new recursive subspace algorithms using ulv updating and successive cancellation techniques the new algorithms do not need to estimate the rank of the correlation matrix furthermore the channel length can be overestimated initially and be recovered at the end by a successive cancellation procedure which leads to more convenient implementations the adaptive algorithm has computations of o m sup 2 in each recursion the new methods can be applied to either the single user or the multiuser cases simulations demonstrate their good performance

asymmetric three dimensional stokes flows about two fused equal spheres exact solutions to three dimensional stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates the problems have been reduced to three contour equations for meromorphic functions from a certain class and then the latter have been reduced to fredholm integral equations of the second kind by the mehler fock transform of order 1 for the specified class of functions the equivalence of the corresponding three contour and fredholm equations has been established in the framework of riemann boundary value problems for analytic functions as an illustration for the obtained solutions the pressure has been calculated at the surface of the body for both problems and resisting force and torque experienced by the body in asymmetric translation and rotation have been computed as functions of a geometrical parameter of the body

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed