stability theorem for delay differential equations with impulses abstract in this paper we obtain sufficient conditions for the stability of the zero solution of the delay differential equation with impulses formula

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

characterizing the statistical properties of mutual information in mimo channels we consider gaussian multiple input multiple output mimo frequency selective spatially correlated fading channels assuming that the channel is unknown at the transmitter and perfectly known at the receiver for gaussian codebooks using results from multivariate statistics we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal to noise ratio snr we show that our bound is tighter than previously reported analytical lower bounds and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity based on a closed form approximation of the variance of mutual information in correlated flat fading mimo channels we provide insights into the multiplexing diversity tradeoff for gaussian code books furthermore for a given total number of antennas we consider the problem of finding the optimal ergodic capacity maximizing number of transmit and receive antennas and we reveal the snr dependent nature of the maximization strategy finally we present numerical results and comparisons between our capacity bounds and previously reported bounds

invex equilibrium problems in this paper we introduce a new class of equilibrium problems known as invex equilibrium problems in the setting of invexity this class of equilibrium problems includes equilibrium problems variational inequalities and variational like inequalities as special cases we use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under some mild conditions we also consider the concept of well posedness for invex equilibrium problems our results represent significant and important refinements of the previously known results

an asymptotically efficient arma estimator based on sample covariances an asymptotically efficient autoregressive moving average arma spectral estimator is presented based on the sample covariances of observed time series the estimate of the autoregressive ar part is shown to be identical to the optimal instrumental variable iv estimator in 7 although derived here using a different approach the moving average ma spectral parameter estimate is new

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

estimating the number of sinusoids in additive white noise the test proposed uses the eigenvector decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis the estimator is shown to be able to resolve closely spaced sinusoids at lower signal to noise ratios than heuristic tests simulation results for two closely spaced sinusoids are detailed several unanswered questions are discussed

stability with respect to part of the variables in systems with impulse effect abstract effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect the approach presented is based on the specially introduced piecewise continuous ljapunov functions

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

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

generalized invex monotonicity abstract in this paper the generalized invex monotone functions are defined as an extension of monotone functions a series of sufficient and necessary conditions are also given that relate the generalized invexity of the function with the generalized invex monotonicity of its gradient function this new class of functions will be important in order to characterize the solutions of the variational like inequality problem and mathematical programming problem

uniform stability theorems for delay differential equations with impulses abstract in the paper we obtain sufficient conditions for the uniform stability of the zero solution of the delay differential equation with impulses x t h t x t f t x t t t 0 t t k x t k x t k i k x t k k n

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

the generalized quasi variational inequality problem over non compact sets abstract in this note we shall prove new existence results for the generalized quasi variational inequality problem which includes as particular cases all the existing generalizations of the classical variational inequality problem

global stability of sets for impulsive differential systems by lyapunov s direct method abstract in the present paper the question of global stability of sets of sufficiently general type with respect to systems of impulsive differential equations is considered it is proved that with the existence of piecewise continuous functions of the type of lyapunov s functions with certain properties is a sufficient condition for various types of global asymptotic stability

generalized nash games and quasi variational inequalities abstract a generalized nash game is an n person noncooperative game with nondisjoint strategy sets other names for this game form include social equilibria and pseudo nash games this paper explores both the qualitative and quantitative properties of such games through the use of quasi variational inequality theory several interesting relationships between the variational and quasi variational inequality forms of this class of games are described and the practical implementation of generalized nash games are explored at length

on vector quasivariational inequalities in this paper we consider the vector quasivariational inequalities and the vector quasivariational like inequalities for multifunctions with vector values and prove some existence theorems of solutions for our inequalities also we give the relationship between a kind of the vector variational inequality for multifunctions and a vector optimization problem involving nondifferentiable lipschitz functions

iterative algorithm for completely generalized set valued strongly nonlinear mixed variational like inequalities a class of completely generalized set valued strongly nonlinear mixed variational likeinequalities is introduced the auxiliary principle technique is extended to study this new class of mixed variational like inequalities the existence of a solution of the auxiliary problem for this new class of mixed variational like inequalities is shown the iterative algorithm for this new class of mixed variational like inequalities is given by virtue of this existence result moreover the existence of a solution of this new class of mixed variational like inequalities and the strong convergence of iterative sequences generated by the algorithm are shown the convergence criteria are different from some early and recent ones presented in the literature

a variational inequality approach for the determination of oligopolistic market equilibrium this paper presents an alternative approach to that by murphy sherali and soyster 13 for computing market equilibria with mathematical programming methods this approach is based upon a variational inequality representation of the problem and the use of a diagonalization relaxation algorithm

on the general variational inequality abstract in this paper we investigate the general variational inequality which extends the classical variational inequality in finite dimensional spaces necessary and sufficient conditions for the existence of a solution of this problem are obtained some existence results are derived using the fixed point theory uniqueness of the solution is also discussed application of these existence results to the implicit complementarity problem is given

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

frequency domain prony method for autoregressive model identification and sinusoidal parameter estimation in this study the weighted integral method for identifying differential equation models is extended to a discrete time system with a difference equation de model and a finite length sampled data sequence and obtain a frequency domain algorithm for short time signal analysis and frequency estimation the derivation consists of three steps 1 provide the de autoregressive model with unknown coefficients which is satisfied in a finite observation interval 2 discrete fourier transform dft the de to obtain algebraic equations aes among the fourier coefficients two mathematical techniques are introduced to maintain the circulant nature of time shifts 3 simultaneously solve a sufficient number of aes with least squares criterion to obtain unknowns exactly when the driving term is absent or to obtain unknowns that minimize the driving power when it is present the methods developed enable a decomposed processing of identification and estimation in the frequency domain thus they will be suitable for maximizing statistical efficiency smallness of estimation error variance reducing the computational cost and use in a resolution enhanced time frequency analysis of real world signals the performance of the proposed methods are compared with those of several dft based methods and cramer rao lower bound also the interference effect and its reduction in frequency decomposed processing are examined

a note on the existence of traffic equilibria this note presents an alternative proof of the existence of a solution to the network equilibrium problem which is based on the recent work in complementarity theory by t smith 11

further results and insights on subspace based sinusoidal frequency estimation subspace based methods for parameter identification have received considerable attention in the literature starting with a scalar valued process it is well known that subspace based identification of sinusoidal frequencies is possible if the scalar valued data is windowed to form a low rank vector valued process music and esprit like estimators have for some time been applied to this vector model in addition a statistically attractive markov like procedure for this class of methods has been proposed herein the markov like procedure is reinvestigated several results regarding rank performance and structure are given in a compact manner the large sample equivalence with the approximate maximum likelihood method by stoica et al 1988 is also established

estimation of the parameters of a random amplitude sinusoid by correlation fitting we consider the best asymptotic accuracy that can be achieved when estimating the parameters of a random amplitude sinusoid from its sample covariances an estimator based on matching in a weighted least squares sense the sample correlation sequence to the theoretical sequence is presented the asymptotic properties of the estimator are analyzed a lower bound on the estimation of the parameters from sample covariances is derived this bound is shown to be attainable by appropriately choosing the weighting matrix however the unweighted nonlinear least squares estimate performance is shown to come close to the lower bound the influence of the number of samples the number of correlation samples and the lowpass envelope characteristics are studied finally a comparison with yule walker yw methods is given

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

the persistence of nonoscillatory solutions of delay differential equations under impulsive perturbations abstract we obtain a sufficient condition for the persistence of nonoscillatory solutions of the delay differential equation under impulsive perturbations

abstract variational inequality problems and a basic theorem of complementarity abstract in this paper a basic theorem of complementarity is established for an abstract variational inequality problem in particular we obtain a basic theorem of complementarity for a class of generalized variational inequality problems studied by parida and sen 1 we also obtain some sufficient conditions for the existence of a solution of this class of problems

existence of solutions for lower semicontinuous quasi equilibrium problems in this paper we deal with the following quasi equilibrium problem given a nonempty subset c of a topological vector space x a nonempty set d two functions t c d f x d r and a multifunction s c 2x find x x such that x c x s x and f x tx f x tx for all x s x such a problem recently introduced in 1 extends and unifies several variational inequality problems generalized complementarity problems and nash equilibrium problems we prove several existence results in which the upper semicontinuity of the multifunction s is not assumed

paper optimization with respect to covariance sequence parameters a general problem involving optimization of a covariance sequence is considered in the paper one difficulty with this class of problems is to ensure that the covariance sequence is nonnegative definite in other words realizable it is suggested that this difficulty can be overcome by reformulating the optimization problem in terms of the partial autocorrelation coefficients pac one need only constrain these coefficients to lie in the range 1 1 to guarantee that the corresponding covariance sequence is nonnegative definite the synthesis of a signal realizing the optimizing covariance sequence is also discussed special emphasis is given to the case when some of the pacs are either 1 or 1

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

generalized quasi variational like inequality problem this paper gives some very general results on the generalized quasi variational like inequality problem since the problem includes all the existing extensions of the classical variational inequality problem as special cases our existence theorems extend the previous results in the literature by relaxing both continuity and concavity of the functional the approach adopted in this paper is based on continuous selection type arguments and thus is quite different from the berge maximum theorem or hahn banach theorem approach used in the literature

some existence results for multivalued complementarity problems this paper presents some new results for the existence of a solution to a multivalued complementary problem these results are derived under a upper limiting homogeneity ulh property on the multifunction defining the complementarity problem and on a certain closedness interiority condition the closedness condition seems to be new in the context of existence proof for the multivalued complementarity problem we show that this closedness condition is satisfied by the class of polyhedral multifunctions

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

on the generalized quasi variational inequality problems the purpose of this paper is to study the existence problem of solutions for some kinds of abstract generalized quasi variational inequality problems by using a new kind of fixed point approach

a general theorem of complementarity for the implicit gqvi problem abstract in this paper we prove a basic theory of complementarity for the implicit generalized quasi variational inequality problem our result widely extends many known results established in the literature an application to the quasi equilibrium problem is also given

a further generalization of yannelis prabhakar s continuous selection theorem and its applications abstract in this article we first prove one improved version of the yannelis prabhakar continuous selection theorem and next as its applications a fixed point theorem in noncompact product spaces a nonempty intersection theorem some existence theorems of solutions for the generalized quasi variational inequalities and some equilibrium existence theorems for the abstract economies are given

data throughputs of noise limited mimo cellular systems we present the closed form approximated expressions of the cumulative distribution function of the spectral efficiency for noise limited multiple input multiple output mimo cellular systems with minimum mean square error based ordered successive interference cancellation mmse osic or zero forcing zf receivers in a composite channel model which includes both rayleigh and log normal fading when the users have independent and identically distributed i i d channels we analyze the spectral efficiency of the mimo time division multiple access tdma systems with maximum data rate scheduler numerical experiments show that these results can consistently produce highly accurate results

covariance sequence approximation for parametric spectrum modeling parametric methods of spectrum analysis are founded on finite dimensional models for covariance sequences rational spectrum approximants for continuous spectra are based on autoregressive ar moving average ma or autoregressive moving average arma models for covariance sequences line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences in this paper we make the point that a wide variety of spectrum types admit to modal analysis wherein the modes are characterized by amplitudes frequencies and damping factors the associated modal decomposition is appropriate for both continuous and discrete components of the spectrum the domain of attraction for the decomposition includes arma sequences harmonically or nonharmonically related sinusoids damped sinusoids white noise and linear combinations of these the parametric spectrum analysis problem now becomes one of identifying mode parameters this we achieve by solving two modified least squares problems numerical results are presented to illustrate the identification of mode parameters and corresponding spectra from finite records of perfect and estimated covariance sequences the results for sinusoids and sinusoids in white noise are interpreted in terms of in phase and quadrature effects attributable to the finite record length

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

new razumikhin type theorems for impulsive functional differential equations in this paper we investigate stability and boundedness for a class of impulsive functional differential equations by using liapunov functions and razumikhin technique some new razumikhin type theorems on stability and boundedness are obtained the corresponding results obtained recently in j shen j yan nonlinear anal 33 1998 519 531 x liu j shen to appear are improved

discontinuous quasivariational like inequalities in this note we deal with the following problem given x rn a multification gg x 2x two single valued maps f x rn x x rn find a point x x such that x x and f x x x 0 for all x x we prove an existence theorem in which in particular the function f is not supposed to be continuous

information tradeoffs in using the sample autocorrelation function in arma parameter estimation this paper considers bounds on the statistical efficiency of estimators of the poles and zeros of an arma process based on estimates of the process autocorrelation function acf special attention is paid to autoregressive ar and ar plus white noise processes it is seen that reducing the arma process data to a given set of consecutive lags of the popular lagged product acf estimates prior to parameter estimation increases cramer rao bounds on the generalized error covariance a parametric study of the bound deterioration for some illustrative signal and noise situations reveals some empirical strategies for choosing acf estimate lags to preserve statistical information analysis is based on the relative information index rii 2 and derivations of the large sample fisher s information matrix for the raw data and for the lagged product acf estimate of an arma process are included

a class of nonconvex functions and pre variational inequalities abstract a class of nonconvex functions is introduced called semi preinvex function which includes the classes of preinvex functions and arc connected convex functions the fritz john conditions of the mathematical programming problem are derived for these kinds of functions the pre variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions the type i function related to unconstrained problems is given as an equivalent form of the pre variational inequality existence theorems for the solution of the pre variational inequality are also proved

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

a robust spectral estimation by modeling an estimated autocovariance with an arma model the development analysis simulation results and comparison of techniques for estimating spectral peaks of stationary signals in environments with low signal to noise ratio are discussed unlike traditional parametric methods the proposed method estimates parameters of a model which best approximates the estimated autocovariance lag rather than the received signal this technique is studied and evaluated in three different respects using a performance index in the spectral domain suppression of the moving average ma portion and in terms of effective signal to noise ratio this estimation technique demonstrates outstanding robustness and resolution for estimating both spectral peaks and amplitudes of multiple sinusoids embedded in white gaussian noise compared to traditional methods when used in conjunction with cadzow s autoregressive moving average arma method using singular value decomposition svd the technique extracts frequencies and amplitudes of existing sinusoids down to 17 db while the arma method alone achieves only 10 db on average

impulsive stabilization of functional differential equations via liapunov functionals abstract in this paper we consider the impulsive stabilization problems for a class of impulsive functional differential equation of the form x t f t x t t t 0 x i k t x t t t k k z our method is based on the application of the liapunov second method together with liapunov functionals

generalized quasi variational like hemivariational inequalities abstract in this paper we introduce and study a new class of generalized quasi variational like hemivariational inequalities with multi valued pseudomonotone operators in banach spaces some new existence theorems of solutions for this class of generalized quasi variational like hemivariational inequalities are proved the results presented in this paper generalize and extend some known results

an exact direct method of sinusoidal parameter estimation derived from finite fourier integral of differential equation in this paper we propose a novel method for estimating the parameters frequency amplitude and phase of real sinusoids to derive the estimator we start from the characteristic differential equation of a sinusoid to remove differentials and obtain an algebraic relation for frequency we introduce finite period weighted integrals of the differential equation which become equivalent to the differential equation when a sufficient number of weight functions are applied as weight functions we show that fourier kernels have excellent properties terms related to integral boundaries are readily eliminated observations are provided by fourier coefficients and the relation becomes independently accurate for multiple sinusoids if they are sufficiently spaced we solve the obtained equations in two ways one is for approaching to the cramer rao lower bound crlb and the other is for enhancing the interference rejection capability also methods are proposed to calculate the weighted integrals from sampled signals with an improved accuracy proposed algorithms are examined under noise and sinusoidal interference error variances are compared with the crlb and other fast fourier transform fft based methods

bounds on the accuracy of gaussian arma parameter estimation methods based on sample covariances the asymptotic accuracy of gaussian arma parameter estimation methods based on a fixed number of sample covariances is considered several key results are briefly reviewed including i a general asymptotic expression for the error covariance of the arma parameter estimates ii the fact that this error covariance is always greater than a certain lower bound iii the fact that this lower bound is strictly greater than the cramer rao bound iv an explicit arma estimation technique that asymptotically achieves the bound the key result of this note is a proof that this lower bound approaches the cramer rao bound as the number of sample covariances tends to infinity

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

the generalized quasi variational inequality problem with applications a new problem called the generalized quasi variational inequality problem is introduced this new problem extends all the existing variational inequality problems in finite dimensional spaces and enlarges the class of problems that can be approached by the variational inequality theory some existence results without convexity assumptions are presented applications to mathematical and equilibrium programming are given

a basic theorem of complementarity for the generalized variational like inequality problem abstract in this paper a basic theorem of complementarity is established for generalized variational like inequality problems introduced by parida and sen some existence results for both generalized variational inequality and complementarity problems are established by employing this basic theorem of complementarity in particular some sets of conditions that are normally satisfied by a nonsolvable generalized complementarity problem are investigated

a bundle type auxiliary problem method for solving generalized variational like inequalities for generalized variational like inequalities by combining the auxiliary principle technique with the bundle idea for nonconvex nonsmooth minimization we present an implementable iterative method to make the subproblem easier to solve even though the preinvex function may not be convex we still consider using the model similar to the one in r mifflin a modification and extension of lemarechal s algorithm for nonsmooth minimization mathematical programming 17 1982 77 90 which may not be under the preinvex function to approximate locally the involved preinvex function and prove that this local approximation is well defined at each iteration of the algorithm i e the construction of this local approximation can terminate in finite steps at each iteration of the proposed algorithm we not only explain how to construct the approximation but also prove the weak convergence of the sequence generated by the corresponding algorithm under some conditions the proposed algorithm is a generalization of the existing algorithm for generalized variational inequalities to generalized variational like inequalities in some sense see t t hue j j strodiot v h nguyen convergence of the approximate auxiliary problem method for solving generalized variational inequalities journal of optimization theory and applications 121 2004 119 145

approximate maximum likelihood frequency estimation the high resolution frequency estimators most commonly used such as music esprit and yule walker determine estimates of the sinusoidal frequencies from the sample covariances of noise corrupted data in this paper a frequency estimation method termed approximate maximum likelihood aml is derived from the approximate likelihood function of sample covariances the statistical performance of aml is studied both analytically and numerically and compared with the cramer rao bound as well as the statistical performance corresponding to the aforementioned methods of frequency estimation aml is shown to provide the minimum asymptotic error variance in the class of all estimators based on a given set of covariances the implementation of the aml frequency estimator is discussed in detail the paper also introduces an aml based procedure for estimating the number of sinusoidal signals in the measured data which is shown to possess high detection performance

stability of sets of functional differential equations with impulse effect abstract in this paper we investigate stability of sets for a class of impulsive functional differential equations by using piecewise continuous lyapunov functions with razumickhin techniques some sufficient conditions for stability of sets are established and some known stability theorems also are generalized

lyapunov functions on product spaces and stability theory of delay differential equations if we examine the lyapunov functionals constructed for all the examples that have been discussed so far in the literature we find that the investigators inadvertently employ a combination of a lyapunov function and a functional in such a way that the corresponding derivative can be estimated suitably without demanding minimal classes of functions or the knowledge of solutions as in the case of lyapunov functions or lyapunov functionals respectively 3 61 the method of lyapunov functionals however demands the knowledge of solutions of delay differential equations considered and consequently the discussion of examples is not really in the spirit of the method this observation leads us to develop the method of lyapunov functions on product spaces for studying stability properties of equations with delay where except conceptually the knowledge of solutions is not demanded we shall also develop stability theory in terms of two measures which unifies several known stability concepts our presentation demonstrates the advantage of utilizing lyapunov functions on product spaces 391 0022 247x 91 3 00