uniform l1 stability estimate of the boltzmann equation near a local maxwellian abstract we consider the boltzmann equation describing the spacial temporal evolution of the velocity distribution function in a near exponential local maxwellian regime we present two robust nonlinear functionals measuring possible future collisions and l 1 distance between two mild solutions through the explicit local cancellation of the collision mechanism due to the special structure of an exponential local maxwellian solution we show that the nonlinear functionals in s y ha nonlinear functionals of the boltzmann equation and uniform stability estimates j differential equations 215 2005 178 205 satisfy uniform stability estimates these functionals can be employed to the study of l 1 scattering and uniform l 1 stability estimate of mild solutions for the boltzmann equation with inverse power intermolecular potentials

lp stability of solutions of boltzmann equation with external force in soft potentials in this paper we present a uniform lp stability theory for the solutions to boltzmann equation with small or large external forces in vacuum in soft potentials we assume that the initial data are sufficiently small and a fast decay in space and velocity our stability analysis is divided into two parts for small external forces we first consider the time derivative of the pth power of lp norm of the distance between two mild solutions f and g then define nonlinear functionals and apply the gronwall s inequality to obtain the lp stability for large external forces we make use of the constructive assumptions on external force minkowski s inequality and gronwall s inequality to derive the lp stability estimate

uniform stability of solutions of boltzmann equation for soft potential with external force abstract the study of cauchy problem of the boltzmann equation is important in both theory and applications existence of global solutions to the equation and uniform stability of solutions in the absence of external force were introduced in the previous work on the boltzmann equation in this paper we will investigate the uniform stability of solutions in l 1 for the cauchy problem of the boltzmann equation when there is an external force for the case of soft potentials

l1 and bv type stability of the boltzmann equation with external forces abstract based on the existence theory on the boltzmann equation with external forces in infinite vacuum in this paper we will study the l 1 and bv type stability of the classical solutions for small initial data the stability results generalize those for the boltzmann equation without force to the case with external force in particular we show that the stability can be established for the soft potentials directly while the stability for the hard potentials and hard sphere model is obtained through the construction of some nonlinear functionals the functionals thus constructed generalize those constructed in s y ha nonlinear functionals of the boltzmann equation and uniform stability estimates j differential equations 215 2005 178 205 for the case without force to capture the effect of the force term on the time evolution of the solutions

the same class of stationary solutions to some multidimensional kinetic systems with extensive background density abstract in this study we investigate the existence and uniqueness of the same class of stationary solutions for some kinetic systems comprising the vlasov poisson fokker planck system vlasov poisson boltzmann system and vlasov maxwell boltzmann system in arbitrary space dimensions n n 3 essentially the problem can be reduced to solving the problem of a second order elliptic equation with exponential nonlinearity this result had been proved in three spatial dimensions but the extension to a higher dimensional setting makes the existence proof nontrivial in particular it necessary to highlight that the requirement regarding the background density function is relaxed compared with previous studies in the case of three spatial dimensions

energy method for boltzmann equation abstract a basic simple energy method for the boltzmann equation is presented here it is based on a new macro micro decomposition of the boltzmann equation as well as the h theorem this allows us to make use of the ideas from hyperbolic conservation laws and viscous conservation laws to yield the direct energy method as an illustration we apply the method for the study of the time asymptotic nonlinear stability of the global maxwellian states previous energy method starting with grad and finishing with ukai involves the spectral analysis and regularity of collision operator through sophisticated weighted norms

l 1 stability of the boltzmann equation for the hard sphere model we study the l1 stability of classical solutions to the boltzmann equation for a hard sphere model when initial datum is a small perturbation of a vacuum and tends to zero exponentially fast at infinity in the phase space for this we introduce nonlinear functionals measuring potential interactions between particles with different velocities and l1 distance between classical solutions we use pointwise estimates for a solution and the gain term of a collision operator to control the time evolution of nonlinear functionals

global existence of classical solutions to the vlasov poisson boltzmann system with given magnetic field abstract this paper considers the vlasov poisson boltzmann system with given magnetic field the global existence of classical solutions was obtained when the initial data is a small perturbation around a global maxwellian the proof is based on the theory of compressible navier stokes poisson equations with forcing and the macro microdecomposition of the solution to the boltzmann equation with respect to the local maxwellian introduced in t p liu t yang s h yu energy method for the boltzmann equation physica d 188 3 4 2004 178 192 and elaborated in t yang h j zhao a new energy method for the boltzmann equation j math phys 47 2006 the result shows that the existence of solutions is independent of the magnetic field

hydrodynamic limit of the boltzmann equation with contact discontinuities the hydrodynamic limit for the boltzmann equation is studied in the case when the limit system that is the system of euler equations contains contact discontinuities when suitable initial data is chosen to avoid the initial layer we prove that there exist a family of solutions to the boltzmann equation globally in time for small knudsen number and this family of solutions converge to the local maxwellian defined by the contact discontinuity of the euler equations uniformly away from the discontinuity as the knudsen number e tends to zero the proof is obtained by an appropriately chosen scaling and the energy method through the micro macro decomposition

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a covariance approximation method for near field direction finding using a uniform linear array most narrowband high resolution bearing estimation algorithms were proposed based on the assumption of a far field source environment when this assumption is violated i e some sources are in the near field these algorithms generally provide unsatisfactory performances a new algorithm is proposed to handle this near field problem using a uniform linear array the received signal covariance matrix for near field sources is viewed as a corrupted measurement of the ideal signal covariance matrix for far field sources located at the same bearings taking this viewpoint the authors reconstruct a far field approximation ffa covariance matrix from the received covariance matrix to reduce the corruptions therefore existing high resolution bearing estimation techniques can be directly applied to estimate the bearings of the near field sources the properties of the proposed approach are investigated in detail simulation results demonstrating the effectiveness of this approach are included

efficient wideband source localization using beamforming invariance technique a novel scheme for wideband direction of arrival doa estimation is proposed the technique performs coherent signal subspace transformation by a set of judiciously constructed beamforming matrices the beamformers are chosen to transform each of the narrowband array manifold vectors into the one corresponding to the reference frequency regardless of the actual spatial distribution of the sources the focused data correlation matrix can thus be obtained without any preliminary doa estimation or iteration a simplified version of the beamspace root music algorithm is developed and used in conjunction with the proposed method to efficiently localize multiple wideband sources with a linear equally spaced array numerical simulations are conducted to demonstrate the efficacy of the new scheme

fast rls type algorithm for unbiased equation error adaptive iir filtering based on approximate inverse power iteration in this paper a fast approximate inverse power aip iteration is applied to compute recursively the total least squares tls solution for unbiased equation error adaptive infinite impulse response iir filtering which is established by approximating the well known inverse power iteration with galerkin method the aip algorithm is based on an interesting modification of the inverse power iteration in which the first entry of the parameter vector is constrained to the negative one the distinctive feature of the proposed algorithm lies in its high computational efficiency which is characterized by efficient computation of the fast gain vector fgv adaptation of the interesting modification of the inverse power iteration and rank one update of the augmented correlation matrix the shift structure of the input data vector is exploited to develop a fast algorithm for computing the gain vector this fgv algorithm can be implemented at a numerical cost lower than the well known fast kalman algorithm since the first entry of the parameter vector has been fixed as the negative one and the weight vector is updated along the input data vector a very efficient aip algorithm is obtained by using the fgv algorithm the proposed aip algorithm is of computational complexity o l per iteration moreover with no need to use the well known matrix inversion lemma the aip algorithm has another attractive feature of numerical stability the proposed algorithm is shown to have global convergence simulation examples are included to demonstrate the effectiveness of the proposed aip algorithm

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

an algorithm for efficient unbiased equation error infinite impulse response adaptive filtering an algorithm for efficiently adjusting the coefficients of equation error infinite impulse response iir adaptive filters is described unlike the recursive least squares rls algorithm the proposed algorithm yields unbiased filter coefficients simulations involving the identification of unknown pole zero systems demonstrate the algorithm s improved performance over the equation error rls algorithm

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

conjugate gradient eigenstructure tracking for adaptive spectral estimation a conjugate gradient iteration is derived that converges to the set of r dominant subdominant eigenpairs this iteration is used to construct two eigenstructure tracking algorithms that track the r dimensional dominant or subdominant subspaces of time varying data or data covariance matrices the two eigenstructure tracking algorithms have update complexities o m sup 2 r and the other o mr sup 2 where m is the data dimension the algorithms are customized to solve high resolution temporal and spatial frequency tracking problems they are compared with existing techniques by tying into published simulation based performance tests the algorithms demonstrate rapid convergence and tracking characteristics at a competitive cost

an adaptive nulling system for a narrow band signal with a look direction constraint utilizing the conjugate gradient method the problem of iterative adjustments of the weights of a phased array with a look direction constraint in the presence of jammers is presented the technique described uses the adaptive conjugate method instead of the popularly used method of steepest descent to eliminate the jammer components thus minimizing the error between the received signal and the actual one this iterative method minimized the l sub 2 norm the mean square error and is guaranteed to converge in a finite number of steps which is not available for the present techniques utilized to solve this problem improvement in rate of convergence is thus achieved at the expense of algorithmic complexity

global existence to boltzmann equation with external force in infinite vacuum in this paper we give a condition on the bicharacteristic which guarantees the global existence of the mild solution to the boltzmann equation with an external force for the hard sphere model and potentials with angular cutoff in infinite vacuum this generalizes the previous results to the case when the force can have arbitrary strength the constructive condition on the bicharacteristic is used to obtain the pointwise estimates on the collision operator so that the global existence comes from the contraction mapping theorem

a fast recursive total least squares algorithm for adaptive fir filtering this paper proposes a new fast recursive total least squares n rtls algorithm to recursively compute the tls solution for adaptive finite impulse response fir filtering the n rtls algorithm is based on the minimization of the constrained rayleigh quotient c rq in which the last entry of the parameter vector is constrained to the negative one as analysis results on the convergence of the proposed algorithm we study the properties of the stationary points of the c rq the high computational efficiency of the new algorithm depends on the efficient computation of the fast gain vector fgv and the adaptation of the c rq since the last entry of the parameter vector in the c rq has been fixed as the negative one a minimum point of the c rq is searched only along the input data vector and a more efficient n rtls algorithm is obtained by using the fgv as compared with davila s rtls algorithms the n rtls algorithm saves the 6m number of multiplies divides and square roots mads the global convergence of the new algorithm is studied by lasalle s invariance principle the performances of the relevant algorithms are compared via simulations and the long term numerical stability of the n rtls algorithm is verified

a half space problem for the boltzmann equation with specular reflection boundary condition there are many open problems on the stability of nonlinear wave patterns to the boltzmann equation even though the corresponding stability theory has been comparatively well established for the gas dynamical systems in this paper we study the nonlinear stability of a rarefaction wave profile to the boltzmann equation with the boundary effect imposed by specular reflection for both the hard sphere model and the hard potential model with angular cut off the analysis is based on the property of the solution and its derivatives which are either odd or even functions at the boundary coming from specular reflection and the decomposition on both the solution and the boltzmann equation introduced in 24 26 for energy method

an efficient recursive total least squares algorithm for fir adaptive filtering an algorithm for recursively computing the total least squares tls solution to the adaptive filtering problem is described this algorithm requires o n multiplications per iteration to effectively track the n dimensional eigenvector associated with the minimum eigenvalue of an augmented sample covariance matrix it is shown that the recursive least squares rls algorithm generates biased adaptive filter coefficients when the filter input vector contains additive noise the tls solution on the other hand is seen to produce unbiased solutions examples of standard adaptive filtering applications that result in noise being added to the adaptive filter input vector are cited computer simulations comparing the relative performance of rls and recursive tls are described

using the em algorithm to increase the number of signals estimable by 2 d parametric techniques this paper provides an easy method for increasing the number of modes estimable by 2 d parameter estimation schemes which use a single snapshot of the data for data of size m sub 1 spl times m sub 2 few of these techniques allow the number of modes to exceed m sub 1 and or m sub 2 as these restrictions are not inherent to the model but the algorithms themselves this problem is circumvented by treating the observed data as an incomplete version of a larger data set an existing 2 d parameter estimation scheme is then used for the maximization m step of the expectation maximization em algorithm in this way one can increase the number of modes the scheme can estimate without changing the scheme itself

plane rotation based evd updating schemes for efficient subspace tracking we present new algorithms based on plane rotations for tracking the eigenvalue decomposition evd of a time varying data covariance matrix these algorithms directly produce eigenvectors in orthonormal form and are well suited for the application of subspace methods to nonstationary data after recasting evd tracking as a simplified rank one evd update problem computationally efficient solutions are obtained in two steps first a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transform which is represented in exponential matrix form in terms of a reduced set of small unconstrained parameters second two approximate decompositions of this exponential matrix into products of plane or givens rotations are derived one of which being previously unknown these decompositions lead to new plane rotation based evd updating schemes proteus whose main feature is the use of plane rotations for updating the eigenvectors thereby preserving orthonormality finally the proteus schemes are used to derive new evd trackers whose convergence and numerical stability are investigated via simulations one algorithm can track all the signal subspace evd components in only o lm operations where l and m respectively denote the data vector and signal subspace dimensions while achieving a performance comparable to an exact evd approach and maintaining perfect orthonormality of the eigenvectors the new algorithms show no signs of error buildup

a decoupled approach for optimal estimation of transfer function parameters from input output data a theoretical and algorithmic framework is proposed for optimal identification of rational transfer function parameters of discrete time linear systems from input output io data the nonlinear criterion is theoretically decoupled into a purely linear problem for estimating the optimal numerator and a nonlinear problem for the optimal denominator the proposed decoupled approach has reduced computational requirements when compared with existing algorithms that estimate the parameters simultaneously

nonlinear stability of rarefaction waves for the boltzmann equation it is well known that the boltzmann equation is related to the euler and navier stokes equations in the field of gas dynamics the relation is either for small knudsen number or for dissipative waves in the time asymptotic sense in this paper we show that rarefaction waves for the boltzmann equation are time asymptotic stable and tend to the rarefaction waves for the euler and navier stokes equations our main tool is the combination of techniques for viscous conservation laws and the energy method based on micro macro decomposition of the boltzmann equation the expansion nature of the rarefaction waves and the suitable microscopic version of the h theorem are essential elements of our analysis

diffusive expansion for solutions of the boltzmann equation in the whole space this paper is concerned with the diffusive expansion for solutions of the rescaled boltzmann equation in the whole space 0 1 tf v xf 1 q f f x rn v rn t 0 with prescribed initial data 0 2 f t x v t 0 f0 x v x rn v rn our main purpose is to justify the global validity of the diffusive expansion 0 3 f t x v f1 t x v 2f2 t x v n 1fn 1 t x v nfn t x v for a solution f t x v of the rescaled boltzmann equation 0 1 in the whole space rn for all t 0 with initial data f0 x v satisfying the initial expansion 0 4 f0 x v f1 0 x v 2f2 0 x v n 1fn 1 0 x v nfn 0 x v x v r2n here v 2 n2exp v 22 is a normalized global maxwellian under the assumption that the fluid components of the coefficients fm 0 x v 1 m n of the initial expansion f0 x v have divergence free velocity fields um0 x as well as temperature fields m0 x if we assume further that the velocity temperature fields u10 x 10 x of f1 0 x v have small amplitude in hs rn s 2 n n 2 we can determine these coefficients fm t x v 1 m n in the diffusive expansion 0 3 uniquely by an iteration method and energy method the hydrodynamic component of these coefficients fm t x v 1 m n satisfies the incompressible condition the boussinesq relations and or the navier stokes fourier system respectively while the microscopic component of these coefficients is determined by a recursive formula compared with the corresponding problem inside a periodic box studied in y guo 2006 18 the main difficulty here is due to the fact that poincare s inequality is not valid in the whole space rn and this difficulty is overcome by using the lp lq estimate on the riesz potential moreover by exploiting the energy method we can also deduce certain the space time energy estimates on these coefficients fm t x v 1 m n once the coefficients fm t x v 1 m n in the diffusive expansion 0 3 are uniquely determined and some delicate estimates have been obtained the uniform estimates with respect to on the remainders fn t x v are then established via a unified nonlinear energy method and such an estimate guarantees the validity of the diffusive expansion 0 3 in the large provided that 0 5 n 2n 2 notice that for m 2 um t x is no longer a divergence free vector and it is worth to pointing out that for m 3 it was in deducing certain estimates on pm t x by the lp lq estimate on the riesz potential that we need to require that n 2n 2

data recursive algorithms for blind channel identification in oversampled communication systems data recursive algorithms are presented for performing blind channel identification in oversampled communication systems novel on line solutions with complexities that are only linear in the oversampling rate are considered and mean convergence conditions are provided numerical results are presented for a binary phase shift keyed bpsk system

on the zeros of the linear prediction error filter for deterministic signals the zeros of a linear prediction error filter polynomial for a class of deterministic signals that are a sum of samples of m exponentially damped undamped sinusoids is studied it is assumed that n samples are available for processing and that they are uncorrupted by noise it is shown that the exponent parameters of the m signals can be determined from m zeros called signal zeros of an lth degree prediction error filter polynomial l m if l lies in between m and n m n m 2 in a special case the rest of the l m zeros of the filter polynomial switch are called extraneous zeros are shown to be approximately uniformly distributed with in the unit circle regardless of the type of exponentials in the signal if the prediction filter coefficients are chosen to have minimum euclidean length the results obtained provide insight into the estimation problem with noisy data

on frequency estimation with the iqml algorithm a popular implementation of the kiss iqml algorithm for frequency estimation applies an inappropriate constraint to the parameter vector this results in high thresholds for certain frequency configurations by applying a consistent constraint a better estimator can be obtained

cauchy problem for the vlasov poisson boltzmann system the dynamics of dilute electrons can be modelled by the fundamental vlasov poisson boltzmann system which describes mutual interactions of the electrons through collisions in the self consistent electric field in this paper it is shown that any smooth perturbation of a given global maxwellian leads to a unique global in time classical solution when either the mean free path is small or the background charge density is large moreover the solution converges to the global maxwellian when time tends to infinity the analysis combines the techniques used in the study of conservation laws with the decomposition of the boltzmann equation introduced in 17 19 by obtaining new entropy estimates for this physical model

the vlasov maxwell boltzmann system near maxwellians perhaps the most fundamental model for dynamics of dilute charged particles is described by the vlasov maxwell boltzmann system in which particles interact with themselves through collisions and with their self consistent electromagnetic field despite its importance no global in time solutions weak or strong have been constructed so far it is shown in this article that any initially smooth periodic small perturbation of a given global maxwellian which preserves the same mass total momentum and reduced total energy 22 leads to a unique global in time classical solution for such a master system the construction is based on a recent nonlinear energy method with a new a priori estimate for the dissipation the linear collision operator l not its time integration is positive definite for any solutionf t x v with small amplitude to the vlasov maxwell boltzmann system 8 and 12 as a by product such an estimate also yields an exponential decay for the simpler vlasov poisson boltzmann system 24

existence of stationary solutions to the vlasov poisson boltzmann system abstract in this paper we study the existence of stationary solutions to the vlasov poisson boltzmann system when the background density function tends to a positive constant with a very mild decay rate as x in fact the stationary vlasov poisson boltzmann system can be written into an elliptic equation with exponential nonlinearity under the assumption on the decay rate being ln e x for some 0 it is shown that this elliptic equation has a unique solution this result generalizes the previous work r glassey j schaeffer y zheng steady states of the vlasov poisson fokker planck system j math anal appl 202 1996 1058 1075 where the decay rate 1 x 1 2 is assumed

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

least squares type algorithm for adaptive implementation of pisarenko s harmonic retrieval method pisarenko s harmonic retrieval method involves determining the minimum eigenvalue and the corresponding eigenvector of the covariance matrix of the observed random process recently thompson 9 suggested a constrained gradient search procedure for obtaining an adaptive version of pisarenko s method and his simulations have verified that the frequency estimates provided by his procedure were unbiased however the main cost of this technique was that the initial convergence rate could be very slow for certain poor initial conditions restating the constrained minimization as an unconstrained nonlinear problem we derived an alternative gauss newton type recursive algorithm which also used the second derivative matrix or hessian this algorithm may also be viewed as an approximate least squares algorithm simulations have been performed to compare this algorithm to a slight variant of thompson s original algorithm the most important conclusions are that the least squares type algorithm has faster convergence in the beginning while its convergence rate close to the true parameters depends on the signal to noise ratio of the input signal the approximate least squares algorithm resolves the sinusoids much faster than the gradient version

contact discontinuity with general perturbations for gas motions the contact discontinuity is one of the basic wave patterns in gas motions the stability of contact discontinuities with general perturbations for the navier stokes equations and the boltzmann equation is a long standing open problem general perturbations of a contact discontinuity may generate diffusion waves which evolve and interact with the contact wave to cause analytic difficulties in this paper we succeed in obtaining the large time asymptotic stability of a contact wave pattern with a convergence rate for the navier stokes equations and the boltzmann equation in a uniform way one of the key observations is that even though the energy norm of the deviation of the solution from the contact wave may grow at the rate it can be compensated by the decay in the energy norm of the derivatives of the deviation which is of the order of thus this reciprocal order of decay rates for the time evolution of the perturbation is essential to close the a priori estimate containing the uniform bounds of the l8 norm on the lower order estimate and then it gives the decay of the solution to the contact wave pattern

the vlasov poisson boltzmann system without angular cutoff this paper is concerned with the vlasov poisson boltzmann system for plasma particles of two species in three space dimensions the boltzmann collision kernel is assumed to be angular non cutoff with 3 2s and 1 2 s 1 where s are two parameters describing the kinetic and angular singularities respectively we establish the global existence and convergence rates of classical solutions to the cauchy problem when initial data is near maxwellians this extends the results in duan et al j diff eqs 252 12 6356 6386 2012 math models methods appl sci 23 6 927 2013 for the cutoff kernel with 2 1 to the case 3 2 as long as the angular singularity exists instead and is strong enough i e s is close to 1 the proof is based on the time weighted energy method building also upon the recent studies of the non cutoff boltzmann equation in gressman and strain j amer math soc 24 3 771 847 2011 and the vlasov poisson landau system in guo j amer math soc 25 759 812 2012

on a boundary layer problem for the nonlinear boltzmann equation this article deals with a boundary layer problem arising in the kinetic theory of gases when the mean free path of molecules tends to zero the model considered here is the stationary nonlinear boltzmann equation in one dimension with a slightly perturbed reflection boundary condition we restrict our attention to the case of hard spheres collisions with grad s cutoff assumption existence uniqueness and asymptotic behavior are derived by means of energy estimates

two dimensional angle of arrival estimation in the presence of finite distance sources when sources are a finite distance away from an array system most high resolution bearing estimation techniques exhibit unsatisfactory performance due to the invalidity of the planar wavefront assumption this problem has been addressed by a far field approximation ffa method based on a preprocessing scheme by exploiting favorable characteristics of a uniform linear array the method constructs a ffa covariance matrix which is toeplitz and approximates to the far field data covariance matrix from the observed data covariance matrix then eigenstructure methods can be applied to perform bearing estimation without revising the planar wavefront assumption this method is extended to the problem of two dimensional angle of arrival aoa estimation using a uniform planar array in the presence of finite distance sources a procedure is derived for reconstructing the 2 d ffa covariance matrix with block toeplitz structure using the 2 d ffa covariance matrix eigenstructure methods can be applied in conjunction with a 2 d aoa search to solve the problem simulation results confirm the theoretical work

maximum likelihood estimation of multiple frequencies with constraints to guarantee unit circle roots an approximate maximum likelihood estimator mle of multiple exponentials converts the frequency estimation problem into a problem of estimating the coefficients of a z polynomial with roots at the desired frequencies theoretically the roots of the estimated polynomial should fall on the unit circle but mle as originally proposed does not guarantee unit circle roots this drawback sometimes causes merged frequency estimates especially at low snr if all the sufficient conditions for the z polynomial to have unit circle roots are incorporated the optimization problem becomes too nonlinear and it loses the desirable weighted quadratic structure of mle in the present paper the exact constraints are imposed on each of the first order factors corresponding to individual frequencies for ensuring unit circle roots the constraints are applied during optimization alternately for each frequency in the absence of any merged frequency estimates the rms values more closely approach the theoretical cramer rao cr bound at low snr levels

estimating the bearings of near field cyclostationary signals by exploiting favorable characteristics of a uniform linear array ula the far field approximation ffa method reduces the deterioration of most high resolution bearing estimation techniques due to the invalidity of the planar wavefront assumption when near field sources exist we first present a new technique that provides better performance than existing bearing estimation techniques for cyclostationary signals then the proposed technique incorporating with the ffa method is proposed to estimate signal bearings in the presence of near field sources without revising the planar wavefront assumption several simulation examples confirm the theoretical work and show the effectiveness of the proposed technique

fast approximate inverse power iteration algorithm for adaptive total least squares fir filtering the presence of contaminating noises at both the input and the output of an finite impulse response fir system constitutes a major impediment to unbiased parameter estimation the total least squares tls method is known to be effective in achieving unbiased estimation in this correspondence we develop a fast recursive algorithm with a view to finding the tls solution for adaptive fir filtering given the fact that the tls solution is obtainable via inverse power iteration we introduce a novel but approximate inverse power iteration in combination with galerkin method so that the tls solution can be updated adaptively at a lower computational cost we also take advantage of the regular form of the tls solution to constrain the last element of the filter parameter vector to the negative one we further reduce the computational complexity of the developed algorithm by making efficient computation of the fast gain vector defined in and using rank one update of the augmented autocorrelation matrix the developed algorithm saves seven m mad s number of multiplies divides and square roots when compared with the recursive tls algorithm in moreover unlike the algorithms given in and the developed algorithm does not deal with the solution to a one variable quadratic equation and it avoids square root operation therefore it has the simpler structure and may be more easily implemented we then make a careful investigation into global convergence of the developed algorithm simulation results are provided that clearly illustrate appealing performance of the developed algorithm including its good long term numerical stability

superresolution by structured matrix approximation the bearing estimation problem is formulated as a matrix approximation problem the columns of a matrix x are formed by the snapshot vectors from an n element array the matrix x is then approximated by a matrix in the least square sense the rank as well as the partial structure of the space spanned by the columns of the approximated x matrix are prespecified after the approximated x matrix is computed the bearings of the sources and consequently the spatial correlation of the source signals are estimated the performance of the proposed technique is compared with two existing methods using simulation the comparison is made in terms of bias mean squared error failure rates and confidence intervals for the mean and the variance estimates for all three methods at different signal to noise ratios when the sources are moving slowly and the number of snapshot vectors available for processing is large a simple online adaptive algorithm is suggested

optimal large time behavior of the vlasov maxwell boltzmann system in the whole space in this paper we study the large time behavior of classical solutions to the two species vlasov maxwell boltzmann system in the whole space input amssym bbb r 3 the existence of global in time nearby maxwellian solutions is known from strain in 2006 however the asymptotic behavior of these solutions has been a challenging open problem building on our previous work on time decay for the simpler vlasov poisson boltzmann system we prove that these solutions converge to the global maxwellian with the optimal decay rate of o t 3 2 3 2r in the l l norm for any 2 r if initial perturbation is smooth enough and decays in space velocity fast enough at infinity moreover some explicit rates for the electromagnetic field tending to 0 are also provided 2011 wiley periodicals inc

a generalized information criterion for generalized minor component extraction generalized minor component analysis gmca is an essential technique in data classification and signal processing in this paper we propose an information criterion for gmca and derive a fast gmca algorithm for extracting the first generalized minor component gmc by using quasi newton method to this information criterion in order to extract multiple gmcs through the weighed matrix method this information criterion is extended into a weighted one which has a unique global maximum attained if and only if its state matrices converge to the gmcs of the matrix pencil composed of the autocorrelation matrices of two stochastic processes a gradient algorithm is also derived based on this weighted information criterion theoretical analysis shows that the gradient algorithm has self stabilizing property and does not need the normalization operation required in other algorithms the global convergence analysis of the proposed algorithm is accomplished through the lyapunov method numerical simulations and real application are carried out to further demonstrate the accuracy and speed advantages of the proposed algorithms

a survey of conjugate gradient algorithms for solution of extreme eigen problems of a symmetric matrix a survey of various conjugate gradient cg algorithms is presented for the minimum maximum eigen problems of a fixed symmetric matrix the cg algorithms are compared to a commonly used conventional method found in imsl it is concluded that the cg algorithms are more flexible and efficient than some of the conventional methods used in adaptive spectrum analysis and signal processing

asymptotic stability of traveling wave solutions of systems for one dimensional gas motion the asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics 1 the solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet for some 0 ast provided that the initial disturbance is small and of integral zero and in addition decays at an algebraic rate for x 2 the traveling wave solution with nishida and smoller s condition of the system of a viscous heat conductive ideal gas is asymptotically stable provided the initial disturbance is small and of integral zero 3 the traveling wave solution with weak shock profile of the broadwell model system of the boltzmann equation is asymptotically stable provided the initial disturbance is small and its hydrodynamical moments are of integral zero each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one the property of integral zero of the initial disturbance plays a crucial role in this procedure

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

initial boundary value problems for the boltzmann equation global existence of weak solutions for an open set of 3 bounded or not we consider initial boundary value problems for the boltzmann equation for general gas surface interaction laws and for hard potentials we prove a global existence result for weak solutions the proof uses the regularization of the collision operator and the renormalization method for the regularized problem by using weak compactness in l1 and averaged stability ofq f f we prove the existence of weak solutions of our problem

fast iterative algorithm for real time array processing an online iterative conjugate gradient algorithm for array processing is presented the basic idea is to recast the array processing problem into a form so that the iterative method can be applied to compute the array weights vector recursively to speed up the rate of convergence of the iterative process the conjugate gradient method is used under moderate signal to noise ratios the algorithm converges to the minimum euclidean norm least squares solution in p iterations for p number of signals it does not require eigendecomposition of the covariance matrix and prior information regarding the number of signals it is capable of handling fully coherent sources and is effective for a small number of snapshots numerical examples are presented to illustrate the performance achievable

global hilbert expansion for the vlasov poisson boltzmann system the dynamics of an electron gas in a constant ion background can be decribed by the vlasov poisson boltzmann system at the kinetic level or by the compressible euler poisson system at the fluid level we prove that any solution of the vlasov poisson boltzmann system near a smooth local maxwellian with a small irrotational velocity converges global in time to the corresponding solution to the euler poisson system as the mean free path e goes to zero we use a recent l2 l framework in the boltzmann theory to control the higher order remainder in the hilbert expansion uniformly in e and globally in time

steady states of the vlasov poisson fokker planck system abstract the form of steady state solutions to the vlasov poisson fokker planck system is known from the works of dressler and others in these papers an external potential is present which tends to infinity as x it is shown here that this assumption is needed to obtain nontrivial steady states this is achieved by showing that for a given nonnegative background density satisfying certain integrability conditions only the trivial solution is possible this result is sharp and exactly matches the known existence criteria of f bouchut and j dolbeault differential integral equations 8 1995 487 514 and others these steady states are solutions to a nonlinear elliptic equation with an exponential nonlinearity for a given background density which is asymptotically constant it is directly shown by elementary means that this nonlinear elliptic equation possesses a smooth and uniquely determined global solution

a deconvolution approach to source localization due to its low resolution the conventional beamformer cbf has generally been neglected in the recent literature on array processing and considerable attention devoted to the high resolution hr techniques applying a deconvolution approach to the output of the cbf the authors obtain a source localization procedure whose performances are comparable to those of the most efficient hr techniques the scheme moreover also furnishes estimates of the source powers and comprises a test that detects the number of sources present it can indeed be seen as a means to obtain maximum likelihood estimates mle when the cbf output is taken as the observed data

on the cauchy problem for the inelastic boltzmann equation with external force in this paper the cauchy problem for the inelastic boltzmann equation with external force is considered for near vacuum data under the assumptions on the bicharacteristic generated by external force which can be arbitrarily large we prove the global existence of mild solution for initial data small enough with respect to the sup norm with exponential weight by using the contraction mapping theorem furthermore we prove the uniform l1 stability of the mild solution following from the exponential decay estimate and the gronwall s inequality for the case of soft potentials

a new energy method for the boltzmann equation an energy method for the boltzmann equation was proposed by liu yang and yu physica d 188 178 192 2004 based on the decomposition of the boltzmann equation and its solution around the local maxwellian the main idea is to rewrite the boltzmann equation as a fluid type dynamics system with the nonfluid component appearing in the source terms coupled with an equation for the time evolution of the nonfluid component in this paper we will elaborate this method and our main observation is that the microscopic projection of the local maxwellian with respect to a given global maxwellian is not linear but quadratic based on this and by analyzing the fluid type system using the analytic techniques for the system of conservation laws we can indeed control the conserved quantities u and 12u2 e of the boltzmann equation by the microscopic projection of the solution of the boltzmann equation with respect to the global maxwellian which is sufficient to deduce the energy estimates for the solution of

optimal identification of discrete time systems from impulse response data an optimal method om for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented the multidimensional nonlinear fitting error minimization problem has been theoretically decoupled into two subproblems of reduced computational complexities the proposed approach is applicable for identifying rational models with arbitrary numbers of poles and zeros the nonlinear denominator subproblem possesses weighted quadratic structure which is utilized to formulate an efficient iterative minimization algorithm the optimal numerator is found noniteratively with a linear least squares approach that utilizes the optimized denominator both the decoupled subcriteria of om posses global optimality properties the steiglitz mcbride 1960 sm method is also decoupled for arbitrary numbers of poles and zeros dsm g it is demonstrated that the denominator subproblem of dsm g is theoretically optimal for another existing decoupled sm method dsm j it has been shown that only the numerator is theoretically optimal

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

pigeons do not jump high abstract the infinite pigeonhole principle for 2 partitions asserts the existence for every set a of an infinite subset of a or of its complement in this paper we develop a new notion of forcing enabling a fine analysis of the computability theoretic features of the pigeonhole principle we deduce various consequences such as the existence for every set a of an infinite subset of it or its complement of non high degree we also prove that every 0 3 set has an infinite low3 solution and give a simpler proof of liu s theorem that every set has an infinite subset in it or its complement of non pa degree

global existence of classical solutions to the vlasov poisson boltzmann system the time evolution of the distribution function for the charged particles in a dilute gas is governed by the vlasov poisson boltzmann system when the force is self induced and its potential function satisfies the poisson equation in this paper we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global maxwellian moreover the convergence rate in time to the global maxwellian is also obtained through the energy method the proof is based on the theory of compressible navier stokes equations with forcing and the decomposition of the solutions to the boltzmann equation with respect to the local maxwellian introduced in 23 and elaborated in 31

boltzmann equation micro macro decompositions and positivity of shock profiles we introduce an elementary energy method for the boltzmann equation based on a decomposition of the equation into macroscopic and microscopic components the decomposition is useful for the study of time asymptotic stability of nonlinear waves the wave location is determined by the macroscopic equation the microscopic component has an equilibrating property the coupling of macroscopic and microscopic components gives rise naturally to the dissipations similar to those obtained by the chapman enskog expansion our main result is the establishment of the positivity of shock profiles for the boltzmann equation this is shown by the time asymptotic approach and the maximal principle for the collision operator

on a class of finite step iterative methods conjugate directions for the solution of an operator equation arising in electromagnetics a class of finite step iterative methods for the solution of linear operator equations is presented specifically the basic principles of the method of conjugate directions are developed gaussian elimination and the method of conjugate gradients are then presented as two special cases with an arbitrary initial guess the method of conjugate gradient always converges to the solution in at most n iterations where n is the number of independent eigenvalues for the operator in the finite dimensional space in which the problem is being solved the conjugate gradient method requires much less storage sim 5n than the conventional matrix methods sim n 2 in the solution of problems of higher complexity also after each iteration the quality of the solution is known in the conjugate gradient method the conjugate gradient method is also superior to the spectral iterative method as the latter does not always converge and it doubles the complexity of a given problem unnecessarily four versions of the conjugate gradient method are presented in detail and numerical results for a thin wire scatterer are given to illustrate various properties of each version

the cramer rao bound on frequency estimates of signals closely spaced in frequency unconditional case the paper analyzes the cramer rao cr bound on frequency estimation covariance for the unconditional or stochastic signal model it addresses the problem of n signals closely spaced in temporal or spatial frequency the main result is that for this regime the cr bound decomposes into a product of simple scalar factors that individually reflect frequency separation signal powers and covariances data sampling grid and sample size the factored expression provides useful insight into the behavior of the bound for closely spaced frequencies the result also leads to a new formula for the signal to noise snr threshold at which an unbiased frequency estimator can resolve signals closely spaced in frequency interestingly with a simple modification the formulae are identical to those recently obtained for the conditional or deterministic signal model

the metamathematics of stable ramsey s theorem for pairs we show that over the base theory rca0 stable ramsey s the orem for pairs implies neither ramsey s theorem for pairs nor 0 induction

nonlinear functionals of the boltzmann equation and uniform stability estimates abstract we present nonlinear functionals measuring physical space variation and l 1 distance between two classical solutions for the boltzmann equation with a cut off inverse power potential in the case that initial datum is a small smooth perturbation of vacuum and decays fast enough in the phase space we show that these functionals satisfy stability estimates which lead to bv type estimates and a uniform l 1 stability

some logically weak ramseyan theorems abstract we study four families of consequences of ramsey s theorem from the viewpoint of reverse mathematics the first which we call the achromatic ramsey theorem is from a partition relation introduced by erd s hajnal and rado c d r which asserts that for every f r c there exists an infinite h with f h r d the second and third are the free set theorem and the thin set theorem which were introduced by harvey friedman and the last is the rainbow ramsey theorem we show that most theorems from these families are quite weak i e they are strictly weaker than aca 0 over rca 0 interestingly these families turn out to be closely related we establish the so called strong cone avoidance property of most instances of the achromatic ramsey theorem by an induction of exponents then apply this and a similar induction to obtain the strong cone avoidance property of the free set theorem from the strong cone avoidance property of the achromatic ramsey theorem and the free set theorem we derive the strong cone avoidance property of the thin set theorem and the rainbow ramsey theorem it follows easily that a theorem with the strong cone avoidance property does not imply aca 0 over rca 0