estimating spectral correlations with simple nonlinear transformations two computationally efficient cyclic spectral analysis algorithms are compared using a computer simulation each algorithm replaces multiplications with sign changes and multiplexing operations compared with conventional frequency smoothing estimators the quadruplex and one bit spectral correlation algorithms suffered losses in output signal to noise ratio of approximately 0 6 db and 1 9 db respectively

absolutely continuous spectrum of dirac operators with square integrable potentials we show that the absolutely continuous part of the spectral function of the one dimensional dirac operator on a half line with a constant mass term and a real square integrable potential is strictly increasing throughout the essential spectrum 1 1 the proof is based on estimates for the transmission coefficient for the full line scattering problem with a truncated potential and a subsequent limiting procedure for the spectral function furthermore we show that the absolutely continuous spectrum persists when an angular momentum term is added thus also establishing the result for spherically symmetric dirac operators in higher dimensions

on the absolutely continuous spectrum of a vector matrix dirac system a dirac system is considered which has a matrix valued long range short range and oscillatory potentials the system has one singular endpoint at infinity additional conditions on the potential are given which guarantee particular asymptotic behaviour of an energy functional associated with a certain set of solutions this asymptotic behaviour guarantees the existence of a purely absolutely continuous spectrum outside a gap containing the origin

efficient methods of estimate correlation functions of gaussian processes and their performance analysis new efficient methods to estimate crosscorrelation functions of gaussian signals are studied in these methods the covariance property of the gaussian distribution is utilized such that the correlation estimates can be computed with only additions to evaluate the performances of the methods exact expressions for the bias and variance of these estimators are formulated and utilized in comparing these methods with the conventional correlation estimator as a result we point out that these new methods can give estimates which are comparable to the conventional approach

a fast digital method of estimating the autocorrelation of a guassian stationary process given a zero mean stationary gaussian process x n it is shown that the autocorrelation can be estimated by hat r xx j c n sum min i 1 max n x i sign x i j where c n frac pi 2n 2 sum min i 1 max n x i this method is attractive since c n needs to he computed only once and sum min i 1 max n x i sign x i j can be computed by additions only moreover the shape of the autocorrelation given by hat r xx j c n can be computed by additions only

correlation estimators based on simple nonlinear transformations the computational cost of estimating correlations may be reduced by employing sums of simple nonlinear functions of the data a quadruplex transformation is presented and the performance of the associated estimator is analyzed for real and complex gaussian processes with independent observations the variance of the estimator is approximately 14 higher than that obtained by averaging lag products

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

instability of the absolutely continuous spectrum of ordinary differential operators under local perturbations abstract it is shown that a potential q exists such that a selfadjoint realization of lu u q x u has singular continuous spectrum in an interval i while all the selfadjoint realizations of l u u q x v x u where v is a continuous function with compact support have absolutely continuous spectrum in i

transfer matrices hyperbolic geometry and absolutely continuous spectrum for some discrete schrodinger operators on graphs abstract we prove the existence of absolutely continuous spectrum for a class of discrete schrodinger operators on tree like graphs we consider potentials whose radial behaviour is subject only to an l bound in the transverse direction the potential must satisfy a condition such as periodicity the graphs we consider include binary trees and graphs obtained from a binary tree by adding edges possibly with weights our methods are motivated by the one dimensional transfer matrix method interpreted as a discrete dynamical system on the hyperbolic plane this is extended to more general graphs leading to a formula for the green s function bounds on the green s function then follow from the contraction properties of the transformations that arise in this generalization the bounds imply the existence of absolutely continuous spectrum

on a fast digital method of estimating the autocorrelation of a gaussian stationary process the zero mean stationary gaussian processes have the property that if they are input into an instantaneous nonlinear device the cross correlation of input and output is proportional to the auto correlation of the input this suggests an estimation procedure for the autocorrelation function based mainly on additions which is a modified type of the pcc polarity coincidence correlator the object of this paper is to compute the bias and the variance of such an estimator and to discuss some fundamental properties as a reference some examples are provided which compare the behavior of the modified ppc estimator to the classical one based on products and additions

efficient autocorrelation estimation using relative magnitudes the relative magnitude estimator computes the normalized autocorrelation of a stationary gaussian process using simple nonlinear functions to eliminate most multiplications approximate expressions for bias and variance of the estimate are presented along with the results of a computer simulation the estimator performs well when compared to similar techniques

dense point spectrum for the one dimensional dirac operator with an electrostatic potential for the one dimensional dirac operator examples of electrostatic potentials with decay behaviour arbitrarily close to coulomb decay are constructed for which the operator has a prescribed set of eigenvalues dense in the whole or part of its essential spectrum a simple proof that the essential spectrum of one dimensional dirac operators with electrostatic potentials is never empty is given in the appendix

evasion with weak superiority le but du poursuivant est de terminer le jeu en choisissant une commande convenable alors que le but de l echappant est d empecher la fin du jeu avec une commande appropriee

critical coupling constants and eigenvalue asymptotics of perturbed periodic sturm liouville operators perturbations of asymptotic decay c r 2 arise in the partial wave analysis of rotationally symmetric partial differential operators we show that for each end point 0 of the spectral bands of a perturbed periodic sturm liouville operator there is a critical coupling constant c crit such that eigenvalues in the spectral gap accumulate at 0 if and only if c c crit 1 the oscillation theoretic method used in the proof also yields the asymptotic distribution of the eigenvalues near 0

bounded solutions and absolute continuity of sturm liouville operators this work is a contribution to the theory of the absolutely continuous spectrum of one dimensional schriidinger operators i e sturm liouville operators generated by differential expressions of the form ru u qu in proofs of absolute continuity for such operators and also for the closely related dirac systems always asymptotic properties of solutions of zu lu for real or complex values of 1 have played an important role see for example 18 19 8 4 9 lo in these works and a number of others particular classes of potentials q were treated using properties of solutions in the course of the proof of absolute continuity somewhat more recently the connection between asymptotic properties of solutions and absolute continuity was given a theory i e results of the following form were proved let the solutions of zu lu satisfy some specific asymptotic property for a varying in some subset of r no or almost no a priori assumptions on q then operators generated by z are absolutely continuous in this set a first result of this type was given by carmona 3 who proved that local uniform boundedness of solutions together with their derivatives in some open a set implies pure absolute continuity in this set here we will mostly rely on the concept of non or racy of solutions which was shown by gilbert and pearson 7 12 61 to be a powerful tool in the investigation of the continuous spectrum of sturm liouville operators in section 2 we give some consequences of their results whi ch are useful in proofs of absolute continuity these consequences range from non existence of imbedded eigenvalues and the existence of absolutely continuous parts to pure absolute continuity and the existence of transient 210 0022 247x 92 5 00

methods for estimating the autocorrelation function of complex gaussian stationary processes new methods for estimating the autocorrelation function acf of a complex gaussian stationary process are presented these methods are based on a general invariance property for the autocorrelation of a common class of the above processes this property suggests estimation procedures based on magnitude hard limiting and phase quantization the procedures are an extension of the relay estimator currently employed for real processes the computational cost and the general properties of the methods are discussed in particular some estimators especially suited for very simple implementations are considered the performance of the complex hybrid sign estimator is evaluated and compared to that of the classical direct estimator the proposed methods are attractive for many applications in the field of digital signal processing

differential games of generalized pursuit and evasion differential games of generalized pursuit and evasion are studied by comparing them with differential games of fixed duration for which a theory already has been established it is shown that if the isaacs condition holds and the data satisfy reasonable hypotheses then the games have values which are continuous functions of the initial time and state if the data satisfy appropriate lipschitz conditions then the value is lipschitz continuous and satisfies the isaacs equation at all points of differentiability of the value

absolutely continuous spectrum of dirac operators for long range potentials abstract using the resolvent method and the technique of weighted l2 estimates we deduce the non existence of the singular continuous spectrum of the dirac operator p x on the interval 1 we assume that the hermitian matrix potential p x p1 x p2 x is divided into a long range part p 1 x o x e r r p 1 x o x e and a short range part p 2 x o x 1 e x with local singularities p x o x a j 1 of coulomb type for n nuclei a1 an r 3

on the evadable sets of differential evasion games abstract the notions of evasion strategies and evadable sets are introduced for a nonlinear differential game with information delay and results about the evadable sets and the strict evadability of the game are obtained a linear case is treated at the end