blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

global existence and exponential growth of solution for the logarithmic boussinesq type equation abstract in this paper we consider the boussinesq type equation associated with logarithmic nonlinear term and initial boundary value conditions by using potential well method combined with the logarithmic sobolev inequality we obtain the existence of global solution at last we show that the l 2 norm of the solution will grow up as an exponential function as time goes to infinity under some suitable conditions for initial data the result shows that the polynomial nonlinearity is a critical condition of blow up in finite time for the solutions of boussinesq equations

pseudo hermiticity versus pt symmetry iii equivalence of pseudo hermiticity and the presence of antilinear symmetries we show that a diagonalizable non hermitian hamiltonian h is pseudo hermitian if and only if it has an antilinear symmetry i e a symmetry generated by an invertible antilinear operator this implies that the eigenvalues of h are real or come in complex conjugate pairs if and only if h possesses such a symmetry in particular the reality of the spectrum of h implies the presence of an antilinear symmetry we further show that the spectrum of h is real if and only if there is a positive definite inner product on the hilbert space with respect to which h is hermitian or alternatively there is a pseudo canonical transformation of the hilbert space that maps h into a hermitian operator

application of the sturm liouville theorem and shape invariance formalism to the dirac equation with hyperbolic like potential abstract we use a simple algebraic formalism i e based on the sturm liouville theorem and shape invariance formalism to study the energy spectra for dirac equation with scalar and vector hyperbolic like potentials the rosen morse and eckart potentials as typical models are performed to show the advantage of this method

construction of exact solutions to eigenvalue problems by the asymptotic iteration method we apply the asymptotic iteration method aim ciftci hall and saad 2003 j phys a math gen 36 11807 to solve new classes of second order homogeneous linear differential equation in particular solutions are found for a general class of eigenvalue problems which includes schrodinger problems with coulomb harmonic oscillator or poschl teller potentials as well as the special eigenproblems studied recently by bender et al 2001 j phys a math gen 34 9835 and generalized in the present paper to arbitrary dimension

global existence and blow up of solutions for cauchy problem of generalized boussinesq equation abstract we study the cauchy problem of generalized boussinesq equation u t t u x x u x x f u x x 0 where f u u p or u p 1 u p 1 by introducing a family of potential wells we obtain invariant sets vacuum isolating and threshold result of global existence and nonexistence of solution

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

asymptotic iteration method solutions to the relativistic duffin kemmer petiau equation a simple exact analytical solution of the relativistic duffin kemmer petiau equation within the framework of the asymptotic iteration method is presented exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the coulomb potentials as a nontrivial example the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method

any l state solutions of the hulthen potential in arbitrary dimensions the energy spectra of the hulthen effective potential in d dimensions are obtained within the new quantization rule approach for any l states the interdimensional degeneracies among states are also presented in the case of d 3 the agreement between our results and those obtained by other methods is excellent

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

the initial boundary value problems for a class of nonlinear wave equations with damping term abstract in this paper we study the existence and uniqueness of the global generalized solution and the global classical solution the blowup of the solution and the energy decay of the solutions of the initial boundary value problems for a class of nonlinear wave equations

analytical approximations of scattering states to the l wave solutions for the schrodinger equation with the eckart potential the scattering state solutions of the schrodinger equation for the eckart potential with the centrifugal term are obtained approximately it is shown that the solutions can be expressed in terms of the generalized hypergeometric functions 2f1 a b c z the normalized radial wave functions of scattering states on the k 2 scale and the calculation formula of phase shifts are also derived three special cases for l 0 0 and r0 are also studied briefly

blind identification of fir systems driven by markov like input signals we propose a new algorithm for the blind identification and equalization of finite impulse response fir systems using the second order statistics of the received signal the new algorithm is set in the same context as the algorithms of tong et al 1994 and moulines et al 1995 however unlike those earlier approaches it is designed to allow correlated input signals specifically the algorithm accommodates finite memory sources and sources whose autocorrelation function decays exponentially numerical simulations compare the equalization performance of the new algorithm to those of tong and moulines it is shown that our algorithm yields consistently lower bit error rates at a wide variety of signal to noise ratios and at various equalizer lengths moreover the algorithm maintains this advantage even if it has no a priori information of source correlation or if source symbols are uncorrelated

mapping of shape invariant potentials under point canonical transformations the authors give explicit point canonical transformations which map twelve types of shape invariant potentials which are known to be exactly solvable into two potential classes the eigenfunctions in these two classes are given by hypergeometric and confluent hypergeometric functions respectively

existence and nonexistence of global solutions for a class of nonlinear wave equations of higher order abstract in this paper we investigate the existence and uniqueness of the solution to the cauchy problem for a class of nonlinear wave equations of higher order and prove the existence and nonexistence of global solutions to this problem by a potential well method

the asymptotic iteration method for the eigenenergies of the schrodinger equation with the potential v r z r gr λr2 the eigenenergies of the schrodinger equation with coulomb potential plus linear and harmonic radial terms are investigated using the perturbation technique within the framework of the asymptotic iteration method the obtained eigenenergies are compared with those obtained from the shifted 1 n expansion method the moment method and also with the exact values obtained from the super symmetric method it is found that asymptotically this method gives accurate results for arbitrary g z and

any l state solutions of the hulthen potential by the asymptotic iteration method in this paper we present the analytical solution of the radial schrodinger equation for the hulthen potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states we obtain the energy eigenvalues and corresponding eigenfunctions for different screening parameters the wavefunctions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different values in order to demonstrate this the results of the asymptotic iteration method are compared with the results of the supersymmetry numerical integration variational and shifted 1 n expansion methods

a weakly nonlinear analysis of elasto plastic microstructure models at certain critical values of the hardening modulus the governing equations of elasto plastic flow may lose their hyperbolicity and exhibit two modes of ill posedness shear band and flutter ill posedness these modes of ill posedness are characterized by the uncontrolled growth of modes at infinitely fine scales which ultimately violates the continuum assumption in previous work l an and a peirce siam j appl math 54 1994 pp 708 730 a continuum model accounting for microscale deformations was built linear analysis demonstrated the regularizing effect of the microstructure and provided a relationship between the width of the localized instabilities and the microlength scale in this paper a weakly nonlinear analysis is used to explore the immediate post critical behavior of the solutions for both one dimensional and anti plane shear models post critical deformations in the plastic regions are shown to be governed by the boussinesq equation one of the completely integrable pdes having so

comment on the asymptotic iteration method for polynomial potentials it is shown that polynomial potentials can be treated by a method which cuts out most of the complications of the popular aim approach several examples are given to show how expectation values and resonance energies can be calculated using the simplified approach

blind and semi blind fir multichannel estimation global identifiability conditions two channel estimation methods are often opposed training sequence methods that use the information induced by known symbols and blind methods that use the information contained in the received signal and possibly hypotheses on the input symbol statistics but without integrating the information from known symbols if present semi blind methods combine both training sequence and blind information and are more powerful than the two methods separately we investigate the identifiability conditions for blind and semi blind finite impulse response fir multichannel estimation in terms of channel characteristics received data length and input symbol excitation modes as well as number of known symbols for semi blind estimation two models corresponding to two different cases of a priori knowledge on the input symbols are studied the deterministic model in which the unknown symbols are considered as unknown deterministic quantities and the gaussian model in which they are considered as gaussian random variables this last model includes the methods using the second order statistics of the received data semi blind methods appear superior to blind and training sequence methods and allow the estimation of any channel with only few known symbols furthermore the gaussian model appears more robust than the deterministic one as it leads to less demanding identifiability conditions

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

the asymptotic iteration method for the angular spheroidal eigenvalues the asymptotic iteration method is applied to calculate the angular spheroidal eigenvalues ml c it is shown that this method asymptotically gives accurate results over the full range of parameter values l m and c

pt symmetric quantum mechanics this paper proposes to broaden the canonical formulation of quantum mechanics ordinarily one imposes the condition h h on the hamiltonian where represents the mathematical operation of complex conjugation and matrix transposition this conventional hermiticity condition is sufficient to ensure that the hamiltonian h has a real spectrum however replacing this mathematical condition by the weaker and more physical requirement h h where represents combined parity reflection and time reversal pt one obtains new classes of complex hamiltonians whose spectra are still real and positive this generalization of hermiticity is investigated using a complex deformation h p2 x2 ix e of the harmonic oscillator hamiltonian where e is a real parameter the system exhibits two phases when e 0 the energy spectrum of h is real and positive as a consequence of pt symmetry however when 1 e 0 the spectrum contains an infinite number of complex eigenvalues and a finite number of real positive eigenvalues b

strict identifiability of multiple fir channels driven by an unknown arbitrary sequence the problem of blind identification of multiple finite impulse response fir channels driven by a common input arises in a wide range of applications it has received increasing attention in the signal processing community a system of multiple fir channels driven by an unknown input is said to be strictly identifiable if in the absence of noise the given channel outputs can only be realized by a unique up to a constant system impulse response and a unique input sequence we show necessary and sufficient conditions for strict identifiability and establish a connection among strict identifiability a cross relation based cr based identifiability and a fisher information based fi based identifiability

explicit wavefunctions for shape invariant potentials by operator techniques the authors obtain explicit expressions for the wavefunctions of all the known shape invariant potentials by using the operator method

identification of 2 d noncausal gauss markov random fields parameter identification of multidimensional noncausal markov random fields is an important paradigm in multidimensional signal processing and modeling and the solutions to this problem are employed in many areas of image processing an original procedure for estimating the model parameters of discrete index 2 d noncausal gauss markov random fields gmrfs from noisy observations is proposed valid for both finite and infinite lattices and for any kind of boundary conditions starting from a suitable local representation of the gmrf and taking into account the symmetry property of so called field potentials a linear equation set relating the model parameters to the 2 d autocorrelation function known or estimated of the observed field is derived its solution gives the parameter estimates of the gmrf together with the estimate of the possibly unknown variance of the observation noise

the stability of nonlinear least squares problems and the cramer rao bound a number of problems of interest in signal processing can be reduced to nonlinear parameter estimation problems the traditional approach to studying the stability of these estimation problems is to demonstrate finiteness of the cramer rao bound crb for a given noise distribution we review an alternate deterministic notion of stability for the associated nonlinear least squares nls problem from the realm of nonlinear programming i e that the global minimizer of the least squares problem exists and varies smoothly with the noise furthermore we show that under mild conditions identifiability of the parameters along with a finite crb for the case of gaussian noise is equivalent to the deterministic stability of the nls problem finally we demonstrate the application of our result which is general to the problems of multichannel blind deconvolution and sinusoid retrieval to generate new stability results for these problems with little additional effort

on an iteration method for eigenvalue problems we discuss a recently proposed asymptotic iteration method for eigenvalue problems we analyse its rate of convergence the use of adjustable parameters to improve it and the relationship with an alternative method based on the same ideas

a systematic study on the exact solution of the position dependent mass schrodinger equation an algebraic method of constructing potentials for which the schrodinger equation with position dependent mass can be solved exactly is presented a general form of the generators of su 1 1 algebra has been employed with a unified approach to the problem our systematic approach reproduces a number of earlier results and also leads to some novelties we show that the solutions of the schrodinger equation with position dependent mass are free from the choice of parameters for position dependent mass two classes of potentials are constructed that include almost all exactly solvable potentials

data efficient blind ofdm channel estimation using receiver diversity we investigate non data aided channel estimation for cyclically prefixed orthogonal frequency division multiplexing ofdm systems by exploiting channel diversity using only two receive antennas a blind deterministic algorithm is proposed identifiability conditions are derived that guarantee the perfect channel retrieval in the absence of noise in the presence of noise the proposed method has the desired property of being data efficient only a single ofdm block is needed to achieve good estimation performance for a wide range of snr values the algorithm is also robust to input symbols as it does not have any restriction on the input symbols with regard to their constellation or their statistical properties in addition this diversity based algorithm is computationally efficient and its performance compares favorably to most existing blind algorithms

a recurrence formula for obtaining certain matrix elements in the base of eigenfunctions of the hamiltonian for a particular screened potential a recurrence formula for obtaining matrix elements of products of powers of exp nu r and 1 exp nu r is derived the matrix elements are calculated in the base of eigenfunctions of the hamiltonian for the effective potential lambda exp nu r 1 exp nu r mu exp nu r 1 exp nu r 2 where lambda nu and mu are positive constants this potential can be considered as a generalisation of a potential suggested by hylleraas and risberg 1941 and by hulthen 1942 in the limit of the parameter nu tending to zero the recurrence formula is transformed into a recurrence formula is transformed into a recurrence formula given by badawi et al 1973 for matrix elements of powers of r for the hydrogen atom

poschl teller paradoxes in the well known poschl teller trigonometric potential well a symmetric regularization x x ie of the impenetrable end point barriers is performed this leads to the four different solvable generalizations of the model as a byproduct the scheme clarifies certain apparent paradoxes encountered in the classically forbidden coupling regime

sufficient conditions for regularity and strict identifiability in mimo systems we consider regularity and identifiability of convolutive multi input multi output mimo systems with additive white gaussian noise modeling the source and finite impulse response fir channel sequences as deterministic unknowns in the blind context the mimo system is not locally identifiable hence its fisher information matrix fim is not regular in fact the dimension of the complex valued blind fim null space is at least the number of sources squared because the fim is singular additional information about the system is required to resolve the degrees of uncertainty and thereby obtain a valid cramer rao bound crb therefore it is of interest to know under what conditions the blind fim nullity reaches its lower bound we develop sufficient conditions for the complex fim to attain its minimum nullity refining previous necessary conditions and extending single input multi output simo results we show that the sufficient conditions for the complex fim to have minimum nullity are also equivalent to sufficient conditions for mimo strict identifiability these provide sufficient conditions on the richness of the sources the required diversity and the source lengths under these conditions additional constraints such as training may be employed to yield an identifiable system with no ambiguities remaining

mapping of the five parameter exponential type potential model into trigonometric type potentials we choose the five parameter exponential type potential model as input and construct five trigonometric type potentials via point canonical transformations their energy spectra and wavefunctions are obtained in a unified manner by using the expressions for the energy spectra and wavefunctions of the five parameter exponential type potential model

systematic search for symmetric potentials with real energy spectra changes of coordinates represent one of the most effective ways of deriving solvable potentials from ordinary differential equations for separate special functions here we relax the standard hermiticity requirement and find an innovative construction which leads to unusual complex potentials their energy spectrum is shown to stay real after a weakening of the hermiticity of the schr dinger equation to its mere invariance under the combined parity and time reversal symmetry this ultimately results in richer bound state spectra some of our new exactly solvable potentials generalize the current textbook models details are given for constructions based on the hypergeometric and confluent hypergeometric special functions

pseudo hermiticity versus pt symmetry ii a complete characterization of non hermitian hamiltonians with a real spectrum we give a necessary and sufficient condition for the reality of the spectrum of a non hermitian hamiltonian admitting a complete set of biorthonormal eigenvectors

analytical approximations to the l wave solutions of the schrodinger equation with the eckart potential the bound state solutions of the schrodinger equation with the eckart potential with the centrifugal term are obtained approximately it is shown that the solutions can be expressed in terms of the generalized hypergeometric functions 2f1 a b c z the intractable normalized wavefunctions are also derived to show the accuracy of our results we calculate the eigenvalues numerically for arbitrary quantum numbers n and l it is found that the results are in good agreement with those obtained by other methods for short range potential large a two special cases for l 0 and 0 are also studied briefly

arbitrarily positive initial energy blowup and blowup time for some fourth order viscous wave equation abstract this paper is devoted to the finite time blowup phenomena for a class of fourth order wave equation with viscous damping term it is shown that the high initial energy finite time blowup associated with the upper bound of the blowup time is established by introducing a new auxiliary function and employing an adapted concavity method

global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth order in this paper we focus on the cauchy problem for a nonlinear wave equation of fourth order in n dimensional space n 1 the decay structure of which is of regularity loss property based on the decay estimate of solutions to the linear problem we introduce a set of time weighted sobolev spaces by using the contraction mapping theorem we obtain the global in time existence and the optimal decay estimates of solutions to the cauchy problem under smallness assumption on the initial data

fourth order wave equations with nonlinear strain and source terms abstract in this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms first we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions then we obtain a threshold result of global existence and nonexistence finally we discuss the global existence of solutions for the problem with critical initial condition i u 0 0 e 0 d so the esquivel avila s results are generalized and improved

regularity and strict identifiability in mimo systems we study finite impulse response fir multi input multi output mimo systems with additive noise treating the finite length sources and channel coefficients as deterministic unknowns considering both regularity and identifiability in blind estimation the ambiguity set is large admitting linear combinations of the sources we show that the fisher information matrix fim is always rank deficient by at least the number of sources squared and develop necessary and sufficient conditions for the fim to achieve its minimum nullity tight bounds are given on the required source data lengths to achieve minimum nullity of the fim we consider combinations of constraints that lead to regularity i e to a full rank fim and thus a meaningful cramer rao bound exploiting the null space of the fim we show how parameters must be specified to obtain a full rank fim with implications for training sequence design in multisource systems together with constrained cramer rao bounds crbs this approach provides practical techniques for obtaining appropriate mimo crbs for many cases necessary and sufficient conditions are also developed for strict identifiability id the conditions for strict id are shown to be nearly equivalent to those for the fim nullity to be minimized

global existence asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term abstract the paper studies the global existence asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term it proves that under rather mild conditions on nonlinear terms and initial data the above mentioned problem admits a global weak solution and the solution decays exponentially to zero as t respectively in the states of large initial data and small initial energy in particular in the case of space dimension n 1 the weak solution is regularized to be a unique generalized solution and if the conditions guaranteeing the global existence of weak solutions are not valid then under the opposite conditions the solutions of above mentioned problem blow up in finite time and an example is given

on the initial and terminal value problem for a class of semilinear strongly material damped plate equations abstract we study the semilinear strongly damped plate equation by considering its two different problems for initial value problem we prove the local well posedness and blow up results of solution for the problem with polynomial nonlinear source terms for terminal value problem given the ill posedness in the sense of hadamard we propose a regularization method for the problem with logarithmic nonlinearities under the a priori assumption on the exact solution belonging to a gevrey space we propose the fourier truncation method to stabilize the ill posed problem also by establishing some stability estimates of logarithmic type in l q space

potential well method for cauchy problem of generalized double dispersion equations abstract in this paper we study cauchy problem of generalized double dispersion equations u t t u x x u x x t t u x x x x f u x x where f u u p p 1 or u 2 k k 1 2 by introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions but also obtain the invariance of some sets and vacuum isolating of solutions in addition the global existence and finite time blow up of solutions for problem with critical initial conditions e 0 d i u 0 0 or i u 0 0 are proved

a search for shape invariant solvable potentials the author investigates a simple method of constructing potentials which is related to the work of bhattacharjie and sudarshan 1962 and for which the schrodinger equation can be solved in terms of known special functions it turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions satisfying linear homogeneous second order differential equations can be solutions of the schrodinger equation with potentials of the form v x w2 x w x the author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape invariant potentials

multistep linear predictors based blind identification and equalization of multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider the estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers we extend the multistep linear prediction approach to mimo channels where the multichannel transfer function need not be column reduced moreover we allow infinite impulse response iir channels as well as the case where the subchannel transfer functions have common zeros in the past this approach has been confined to simo finite impulse response fir channels with no common subchannel zeros a related existing approach applicable to mimo channels is restricted to fir column reduced systems with equal length subchannels in our approach the knowledge of the nature of the underlying model fir or iir or the model order is not required our approach works when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data illustrative computer simulation examples are provided

deterministic linear prediction methods for blind channel estimation based on dual concept of zero forcing equalization this paper investigates a class of second order blind channel estimation algorithms based on deterministic linear prediction which includes double sided as well as forward and backward single sided for single input multiple output simo finite impulse response fir channels by introducing the dual problem of well known zero forcing equalization concept we first derive a double sided deterministic linear prediction d dlp algorithm that has good channel estimation performance with the knowledge of exact channel order by further exploiting the interference subspace cancellation technique and the triangular block toeplitz structure of a portion of the channel filtering matrix upper left or lower right part we obtain the forward and backward single sided deterministic linear prediction fs dlp and bs dlp algorithms that can work in the absence of knowledge of channel order with a cost of relatively poor channel estimate moreover a channel order estimation method is also studied based on results from both fs dlp and bs dlp simulation examples are finally presented to demonstrate the potential of the proposed methods

new class of conditionally exactly solvable potentials in quantum mechanics motivated by an idea of dutra 1993 we obtain a new class of one dimensional conditionally exactly solvable potentials for which the entire spectra can be obtained in an algebraic manner provided one of the potential parameters is assigned a fixed negative value it is shown that using shape invariant potentials as input one may generate different classes of such potentials even in more than one dimension we also illustrate that wkb and supersymmetry inspired wkb methods provide very good approximations for these potentials with the latter doing comparatively better

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

cross relation based blind simo identifiability in the presence of near common zeros and noise the blind identification of single input multiple output simo systems is often performed by exploiting a cross relation cr between channel pairs it has been shown that this property allows an estimation of channel impulse responses up to a common gain factor if certain identifiability conditions are met in this case the estimated channels can be evaluated by a gain compensated system distance known as normalized projection misalignment npm current algorithms for blind channel identification however suffer in the presence of insufficient channel diversity and observation noise in this paper we first demonstrate that in the absence of noise the cr identification error for channels with exact common zeros is given by a single channel pole zero transfer function next we extend our analysis to the realistic case of near common zeros and noise for which we show that the effective error can still be approximated by a common transfer function as long as the distance between the channel zeros remains below a signal to noise ratio dependent threshold a finite impulse response fir modeling of the error then enables us to define a common filter error compensated system distance termed normalized filter projection misalignment nfpm which establishes a natural extension to the npm analysis by finally considering realistic channels which we blindly estimate with the adaptive multichannel least mean square mclms algorithm we demonstrate that the nfpm reliably reaches the noise floor confirming that the effective error can be approximated by a common fir filter

a class of fourth order wave equations with dissipative and nonlinear strain terms we study the initial boundary value problem for a class of fourth order wave equations with dissipative and nonlinear strain terms by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence and nonexistence of solutions

arbitrary l state solutions of the rotating morse potential by the asymptotic iteration method for non zerovalues we present an analytical solution of the radial schr odinger equation for the rotating morse potential using the pekeris approximation within the framework of the asymptotic iteration method the bound state energy eigenvalues and corresponding wavefunctions are obtained for a number of diatomic molecules and the results are compared with the findings of the super symmetry the hypervirial perturbation the nikiforov uvarov the variational the shifted 1 n and the modified shifted 1 n expansion methods

a blind approach to closed loop identification of hammerstein systems this paper is a continuing study of the blind approach for the hammerstein identification in sun et al 1999 and bai and fu 2002 in the framework of a closed loop sampled data system the output is sampled faster than the updating period of the input the parameters of the linear dynamics are consistently estimated from the information of the output only after which the unmeasurable inner signal is uniquely reconstructed the noise effect is explicitly considered in both the parameter and inner signal estimation the estimation of the system orders and time delay are studied on the basis of two groups of basic equations obtained by polyphase decomposition the proposed blind approach is validated and illustrated by a simulated numerical example

asymptotic iteration method for eigenvalue problems an asymptotic iteration method for solving second order homogeneous linear differential equations of the form y 0 x y s0 x y is introduced where 0 x 0 and s0 x are c functions applications to schrodinger type problems including some with highly singular potentials are presented