existence and large time behavior to coupled chemotaxis fluid equations in besov morrey spaces abstract the paper deals with the cauchy problem of coupled chemotaxis fluid equations by taking advantage of a coupling structure of the equations and using the semigroup approach we show existence and asymptotic stability with small initial data and external force u 0 n 0 c 0 c 0 n r 1 1 n r 2 2 n r 3 3 l m n for certain technical assumptions for the embedded relationship between function spaces we show that our initial data class is larger than that of kozono et al 2016 11 and covers physical cases of initial aggregation at points diracs and on filaments as an application we obtain a class of asymptotically existence of a basin of attraction for each self similar solutions with homogeneous initial data

a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

global regular and singular solutions for a model of gravitating particles the existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of generalized pseudomeasures this approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem

deterministic cca based algorithms for blind equalization of fir mimo channels in this paper a new deterministic technique for blind equalization of multiple input multiple output mimo channels is presented the proposed method relies on the channel order diversity of the finite impulse response mimo channel and it does not make any assumption about the spectra or the finite alphabet property of the sources assuming that the lengths of the single input multiple output channels are known or estimated a priori it is able to extract the sources up to a scale and rotation matrix ambiguity which only affects to those sources associated to single input multiple output simo channels with equal lengths unlike previously proposed techniques the method described in this paper obtains the equalizers and the best linear combination of their outputs in a single step and thus optimally the reformulation of the proposed method as a set of nested canonical correlation analysis problems is exploited to obtain efficient batch and adaptive equalization algorithms finally the performance of the proposed algorithms is evaluated by means of some simulation examples

a conservative discretization of the poisson nernst planck equations on adaptive cartesian grids in this paper we present a novel hybrid finite difference finite volume method for the numerical solution of the nonlinear poisson nernst planck pnp equations on irregular domains the method is described in two spatial dimensions but can be extended to three dimensional problems as well the boundary of the irregular domain is represented implicitly via the zero level set of a signed distance function and quadtree data structures are used to systematically generate adaptive grids needed to accurately capture the electric double layer near the boundary to handle the nonlinearity in the pnp equations efficiently a semi implicit time integration method is utilized an important feature of our method is that total number of ions in the system is conserved by carefully imposing the boundary conditions by utilizing a conservative discretization of the diffusive and more importantly the nonlinear migrative flux term several numerical experiments are conducted which illustrate that the presented method is first order accurate in time and second order accurate in space moreover these tests explicitly indicate that the algorithm is also conservative finally we illustrate the applicability of our method in the study of the charging dynamics of porous supercapacitors

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

quadratic higher order criteria for iterative blind separation of a mimo convolutive mixture of sources this paper deals with the problem of source separation in the case when the observations result from a multiple input multiple output convolutive mixing system in a blind framework higher order contrast functions have been proved to be efficient for extracting sources inspired by a semiblind approach we propose new contrast functions for blind signal separation that make use of reference signals the main advantage of this approach consists in the quadratic form of these criteria the extraction of one source hence reduces to a simple optimization task for which fast and efficient algorithms are available the separation of the other sources from the mixture is then carried out by an iterative deflation method furthermore these contrasts are shown to be valid for both independent identically distributed i i d and non i i d source signals the performance offered by these criteria is investigated through simulations they appear as very appealing tools compared with some classical contrast functions

design of a multichannel two dimensional delta domain lattice filter for noise removal in this paper a multichannel form of the two dimensional 2 d delta domain lattice filter has been designed motivated by the success of 2 d delta domain lattice filters delta domain concepts are generalized to the multichannel case by a good choice of the transformation matrix that relates the q domain and delta domain filters the channels can be handled independently which makes the algorithm simple and attractive however it is capable of handling multichannel problems even if the noise is correlated between channels resulting in extremely low snr values the proposed algorithm provides the ability of handling multichannel image frames and colored images in the so called delta domain that is known to be always better than the traditional q domain in handling ill conditioned problems on line image frames carrying gaussian and multiplicative noise simultaneously on different channels as well as color images are taken into consideration and successful results are obtained in terms of noise removal

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

subspace based channel shortening for the blind separation of convolutive mixtures a novel subspace based channel shortening procedure is proposed based on the structure of the delayed autocorrelation matrices of the observation process this purely second order approach applies to overdetermined multiple input multiple output mimo channels with independent white sources the channel may be sparse and its length is assumed to be unknown through successive deflations the problem can be transformed into an instantaneous blind source separation bss problem which is simpler to solve using for example independent component analysis ica techniques the algorithm is computationally fast although it requires large input datasets such data can be acquired either through large numbers of sensors or by using increased data sampling rate when not enough data are available the method can still be used for reducing the channel length thus simplifying the problem for subsequent treatment

convergence analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

blind equalization of simo fir channels driven by colored signals with unknown statistics we consider the blind equalization of single input multiple output finite impulse response channel driven by colored signals the statistics of the input colored signals are unknown a priori by exploiting the inherent structural relationship between the source autocorrelation matrices of different delay lags the closed form zero forcing and minimum mean square error equalizers of desired delays are estimated from the second order statistics of the received data the blind equalizability conditions of the proposed method are investigated numerical simulation results are presented to illustrate the performance of the proposed algorithm

the small convection limit in a two dimensional chemotaxis navier stokes system this paper deals with an initial boundary value problem for the chemotaxis navier stokes system begin aligned left begin array lcll n t u cdot nabla n delta n nabla cdot n nabla c qquad quad x in omega t 0 c t u cdot nabla c delta c nc qquad quad x in omega t 0 u t kappa u cdot nabla u delta u nabla p n nabla phi qquad quad x in omega t 0 nabla cdot u 0 qquad quad x in omega t 0 end array right end aligned in a bounded convex domain omega subset mathbb r 2 with smooth boundary with kappa in mathbb r and a given smooth potential phi omega rightarrow mathbb r it is known that for each kappa in mathbb r and all sufficiently smooth initial data this problem possesses a unique global classical solution n kappa c kappa u kappa the present work asserts that these solutions stabilize to n 0 c 0 u 0 uniformly with respect to the time variable more precisely it is shown that there exist mu 0 and c 0 such that whenever kappa in 1 1 begin aligned big vert n kappa cdot t n 0 cdot t big vert l infty omega big vert c kappa cdot t c 0 cdot t big vert l infty omega quad big vert u kappa cdot t u 0 cdot t big vert l infty omega le c kappa e mu t end aligned for all t 0 this result thereby provides an example for a rigorous quantification of stability properties in the stokes limit process as frequently considered in the literature on chemotaxis fluid systems in application contexts involving low reynolds numbers

symmetrization techniques on unbounded domains application to a chemotaxis system on rn the authors study the parabolic elliptic system on rn u t u u v 0 v v u u 0 u0 a version of the mathematical model of chemotaxis proposed by keller and segel a differential inequality for the quantity s0u t d where u is the decreasing rearrangement of the solution u t with respect to the spatial variable is obtained as a consequence they obtain e g lp bounds of the solution u v on r2 and global in time existence of solutions under the condition r2u0 8 then the solution u v blows up in a finite time compared to the previous work of diaz diaz and nagai adv math sci appl 5 1995 no 2 659 680 mr1361010 96j 35246 where this problem has been considered on bounded domains of rn there are some additional technical difficulties connected with the regularity of the derivative u t

existence and uniqueness theorem on mild solutions to the keller segel system coupled with the navier stokes fluid abstract we consider the keller segel system coupled with the navier stokes fluid in the whole space and prove the existence of global mild solutions with the small initial data in the scaling invariant space our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions for the initial data as a byproduct we show the asymptotic stability of solutions as the time goes to infinity since we may deal with the initial data in the weak l p spaces the existence of self similar solutions provided the initial data are small homogeneous functions

global strong solution to the semi linear keller segel system of parabolic parabolic type with small data in scale invariant spaces abstract we shall show existence of global strong solution to the semi linear keller segel system in r n n 3 of parabolic parabolic type with small initial data u 0 h n r 2 r r n and v 0 h n r r r n for max 1 n 4 r n 2 our method is based on the perturbation of linealization together with the l p l q estimates of the heat semigroup and the fractional powers of the laplace operator as a by product of our method we shall prove the decay property of solutions as the time goes to infinity

adaptive subspace algorithm for blind separation of independent sources in convolutive mixture the advantage of the algorithm proposed in this article is that it reduces a convolutive mixture to an instantaneous mixture by using only second order statistics but more sensors than sources furthermore the sources can be separated by using any algorithm applicable to an instantaneous mixture otherwise to ensure the convergence of our algorithm we assume some classical assumptions for blind separation of sources and some added subspace assumptions finally the assumptions concerning the subspace model and their properties are emphasized

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

adaptive spectral estimation by the conjugate gradient method this paper proposes an alternative technique for adaptive spectral estimation the new technique applies the method of conjugate gradient which is used for iteratively finding the generalized eigenvector corresponding to the minimum generalized eigenvalue of a semidefinite hermitian matrix to the adaptive spectral analysis problem computer simulations have been performed to compare the new method to existing ones from the limited examples presented it is seen that the new method is computationally more efficient at the expense of more core storage also this method is effective for small data records and can implement noise correction to yield unbiased spectral estimates if an estimate of the noise covariance matrix is available the technique performs well for both narrow band and wide band signals

tracking of fast fading channels in long code cdma a new technique for blind tracking of fast fading channels in long code code division multiple access cdma is proposed by exploiting multipath diversity based on a linear interpolation channel model the proposed method blindly identifies a time varying channel at arbitrary estimating points within a block up to a scale factor and increases bandwidth efficiency allowing only one pilot symbol within a block which is much larger than channel coherence time the proposed method can be implemented using an efficient state space inversion technique for multiuser cases the mean square error mse performance of the proposed estimator is compared with the cramer rao bound crb for interpolated channel modeling error and bit error rate ber are also evaluated using monte carlo simulations and compared with the block fading model and a decision directed tracking technique

time global existence and finite time blow up criterion for solutions to the keller segel system coupled with the navier stokes fluid abstract we will deal with the chemotaxis model under the effect of the navier stokes fluid i e the incompressible viscous fluid we shall show the existence of a local mild solution for large initial data and a global mild solution for small initial data in the scale invariant class demonstrating that n 0 l 1 r 2 and u 0 l 2 r 2 our method is based on the perturbation of linearization together with the l p l q estimates of the heat semigroup as a by product of our method we shall prove the smoothing effect and uniqueness of our mild solution in addition we shall show a blow up criterion which almost covers the well known threshold number 8 of the size n 0 l 1 r 2 under the rest state of the fluid motion furthermore the blow up rate will be also discussed

optimum blind multichannel equalization using the linear prediction algorithm the linear prediction lp algorithm estimates a zero forcing zf equalizer from the channel output s second order statistics sos we show that it allows in fact to determine a whole subspace of but not all zf equalizers the one obtained by maximizing the signal to noise ratio snr at the equalizer output not only outperforms the original lp equalizer but also attains the lowest achievable by any no delay zf equalizer mean square error mse the increase in complexity is only marginal but equalization performance can be enhanced significantly especially in the practical case of a small leading channel coefficient

lag windowing and multiple data windowing are roughly equivalent for smooth spectrum estimation there is no fundamental difference between lag windowing a correlation sequence and multiple windowing a data sequence when the objective is to reduce the mean squared error of a spectrum estimator by analyzing the approximate low rank factorization of a bandlimiting toeplitz operator we find that lag windowed or spectrally smoothed spectrum estimators have multiple data windowed implementations this makes the blackman tukey grenander rosenblatt spectrogram equivalent to the thomson spectrum estimator and vice versa meaning btgr spectrograms may be implemented in a multichannel filterbank version of the thomson estimator

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

blind decision feedback equalization of time varying channels with dpsk inputs this paper presents a new method to the blind equalization of a class of linear time varying mobile channels for differentially encoded channel input signals through reparameterization the equivalent discrete system can be modeled as a single input multiple output system unlike some existing methods this new algorithm does not require prior knowledge on the cyclic frequency of the channel response the algorithm is simple and relies only on a decision feedback structure and the differential encoding nature of the channel input signals the convergence analysis of the decision feedback system is presented along with simulation examples

on eigenstructure based direct multichannel blind image restoration existing eigenstructure based direct multichannel blind image restoration techniques include nullspace based and direct deconvolver estimation techniques the nullspace based approach can be formulated as an optimization problem we show that this formulation implies a new subspace based approach that uses matrix operations this new approach has the same advantages as the nullspace based one but requires less computational complexity under some mild conditions its complexity is equal to that of the fft furthermore the relation among the nullspace based approach the direct deconvolver estimation and the new subspace based approach is studied

joint channel and symbol estimation by oblique projections the problem of simultaneous blind channel and symbol estimation of a single input multiple output simo communication channel is considered it is shown that the outer product of the channel vector and the channel input sequence can be obtained by a linear estimator that has the finite sample convergence property furthermore this estimator can be obtained by the use of oblique projections an order detection algorithm that avoids the use of subjective thresholding is also proposed applications to multiuser detection are also considered

mimo blind second order equalization method and conjugate cyclostationarity the blind identification of vector valued fir transfer functions using exclusively second order statistics of the output has become conventional the so called subspace method provides a nice and efficient way of solving the problem however the extension to the multi input multi output mimo case is not that straightforward and for instance some indetermination drawbacks may occur we show in this correspondence that the introduction of some cyclostationarity at the input which still leads to feasible systems may lead to an algorithm that is far more satisfactory because for both it is less prone to indetermination problems and the required assumptions are not too sophisticated

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

modular and numerically stable fast transversal filters for multichannel and multiexperiment rls the authors present scalar implementations of multichannel and multiexperiment fast recursive least squares algorithms in transversal filter form known as fast transversal filter ftf algorithms by processing the different channels and or experiments one at a time the multichannel and or multiexperiment algorithm decomposes into a set of intertwined single channel single experiment algorithms for multichannel algorithms the general case of possibly different filter orders in different channels is handled geometrically this modular decomposition approach corresponds to a gram schmidt orthogonalization of multiple error vectors algebraically this technique corresponds to matrix triangularization of error covariance matrices and converts matrix operations into a regular set of scalar operations modular algorithm structures that are amenable to vlsi implementation on arrays of parallel processors naturally follow from the present approach numerically the resulting algorithm benefits from the advantages of triangularization techniques in block processing

blind channel identification via stochastic approximation constant step size algorithms this work is devoted to the study of a class of recursive algorithms for blind channel identification using weak convergence methods the convergence of the algorithm is obtained and the rate of convergence is ascertained the technique discussed can also be used in the analysis of rates of convergence for decreasing step size algorithms

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

global existence and stabilization in a degenerate chemotaxis stokes system with mildly strong diffusion enhancement abstract a class of chemotaxis stokes systems generalizing the prototype n t u n n m 1 n n c c t u c c n c u t p u n u 0 is considered in bounded convex three dimensional domains where w 2 is given the paper develops an analytical approach which consists in a combination of energy based arguments and maximal sobolev regularity theory and which allows for the construction of global bounded weak solutions to an associated initial boundary value problem under the assumption that 0 1 m 9 8 moreover the obtained solutions are shown to approach the spatially homogeneous steady state 1 n 0 0 0 in the large time limit this extends previous results which either relied on different and apparently less significant energy type structures or on completely alternative approaches and thereby exclusively achieved comparable results under hypotheses stronger than 0 1

low complexity equalization of time varying channels with precoding this correspondence deals with time varying tv single input multiple output simo channels which are both frequency selective due to high data rate and time selective due to mobility a complex exponential basis expansion model ce bem is used to model the channel we consider a block transmission system where on the transmit side a precoder is employed to enable the maximum available diversity for a ce bem channel after direct decoding on the receive side the resulting channel resembles a finite impulse response fir filter on both block and symbol level we therefore propose an equalizer that bears a structure analogous to the effective channel in comparison with a standard block minimum mean square error decision feedback equalizer bmmse dfe that involves the inversion of a large size matrix the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available the equalizer taps and the information symbol estimates are refined recursively by means of normalized least mean squares nlms adaptation

eventual smoothness of generalized solutions to a singular chemotaxis stokes system in 2d abstract we study the chemotaxis fluid system n t u n n n c c x t 0 c t u c c n c x t 0 u t p u n x t 0 u 0 x t 0 under homogeneous neumann boundary conditions for n and c and homogeneous dirichlet boundary conditions for u where r 2 is a bounded domain with smooth boundary and c 2 from recent results it is known that for suitable regular initial data the corresponding initial boundary value problem possesses a global generalized solution we will show that for small initial mass n 0 these generalized solutions will eventually become classical solutions of the system and obey certain asymptotic properties moreover from the analysis of certain energy type inequalities arising during the investigation of the eventual regularity we will also derive a result on global existence of classical solutions under assumption of certain smallness conditions on the size of n 0 in l 1 and in l log l u 0 in l 4 and of c 0 in l 2