lower bounds for the perron root of a nonnegative matrix abstract new lower bounds frequently better than previous bounds and readily computable for the perron root r a of a nonnegative matrix a are obtained the theoretical comparison of new bounds with the known ones is supplemented with two numerical examples

jordanian deformation of sl 2 as a contraction of its drinfeld jimbo deformation we introduce a contraction procedure for obtaining the jordanian deformation of sl 2 from its drinfeld jimbo deformation to be specific we obtain slh 2 its differential geometry and its star product from their q deformed counterparts we also present a transformation of the generators of uq sl 2 which in a limit yield the generators of uh sl 2

blind adaptive fresh filtering for signal extraction a blind adaptive method called the ba fresh optimum frequency shift filtering technique is proposed and its convergence analyzed the ba fresh filter does not require training signals nor knowledge of the statistics of the desired signal it is capable of separating desired signals from spectrally overlapping interference by knowing only the cycle frequencies of the signals

spatial activity allocation modelling the dominant eigenvalue and its corresponding eigenvector for the garin lowry model criteria are derived for convergence and it is shown how the forecasts are affected by changes in the parameters of the model and by fluctuations in the exogenous variables convergence occurs if and only if the dominant eigenvalue is smaller than one expressing the upper and lower bounds for the dominant eigenvalue in terms of the parameters of the model yields interpretable convergence conditions for the sensitivity analysis the model is rewritten as an eigensystem in which the endogenous variables appear as the elements of the eigenvector corresponding with the dominant eigenvalue that is the perron vector the sensitivity of the forecasts is analyzed by examining the effects of perturbations in a matrix on the perron vector

a sequence of lower bounds for the spectral radius of nonnegatfve matrices abstract we present a sequence of progressively better lower bounds for the s pectral radius of a nonnegative matrix each element of the sequence is a function of the spectral radius of the geometric symmetrization of a power of the matrix as defined by schwenk each element provides a better approximation to the spectral radius than the elements in the sequences provided by other authors

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

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

adaptive fresh filters for compensation of cycle frequency errors this paper deals with the problem of uncertainties in the periodicities of linear almost periodically time variant laptv filters these filters are usually implemented as a set of branches each consisting of a frequency shifter followed by a linear time invariant lti filter this implementation is also known as fresh filters this paper is motivated by the fact that when there exist errors in the frequency shifts the optimum set of lti filters is obtained by canceling the outputs of the corresponding branches the purpose of this paper is to analyze the nonstationary behavior of adaptive filters in order to mitigate this problem our results show that an adaptive filter can offset the errors in the frequency shifts the reason is that the coefficients of the adaptive filter are updated so that the filter actually performs as a linear periodically time variant filter for each branch this allows to track the errors in the frequency shifts when the rate of convergence of the adaptive algorithm is suitably selected an analytical study of the convergence is presented which allows to compute the optimal rate of convergence and the mean squared error attained by the adaptive filter

nested bounds for the perron root of a nonnegative matrix abstract it is well known that for a nonnegative matrix a the smallest row sum r a and the largest row sum r a provide lower and upper bounds respectively for the perron root of a these bounds are generalized for a partitioned nonnegative matrix a the new bounds are better than r a and r a and they can be further improved by a refinement of the partition known monotonicity and convergence properties of r a and r a are generalized for the new bounds

differential calculi on the quantum group glp q 2 the author presents a systematical study of left covariant differential calculus on the quantum group glp q 2 a two parameter deformation of the general linear group in particular the author explicitly constructs the most general bicovariant calculus it depends on a new parameter s the corresponding lie algebra of left coinvariant vector fields is a two parameter deformation of the classical lie algebra p and q appear only in the combination r pq in the limit p q to 1 one obtains non standard bicovariant differential calculi on the classical lie group

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

the performance of time dependent adaptive filters for interference rejection time dependent adaptive filters tdafs that allow for the cyclostationary nature of communication signals by periodically changing the filter and adaptation parameters are examined the tdaf has an advantage over the conventional time independent adaptive filter in achieving better performance i e reduced mean square error mse for signals with periodic statistics the basic theory of the tdaf is presented the tdaf is shown to be more effective than the time independent adaptive filter for interference rejection this is verified by theoretical analysis and computer simulation of specific cases of extracting a signal in noise or interference the criteria for judging the performance of the tdaf for interference rejection are mse bit error rate measurements and constellation diagrams

multiparametric quantum deformation of the general linear supergroup in the work l d faddeev and his collaborators and subsequently v g drinfeld m jimbo s l woronowicz a new class of hopf algebras was constructed they can be considered as one parametric deformations of either group ring or the universal enveloping algebra of a simple algebraic group in this paper we define and investigate a multiparametric deformation of the general linear supergroup this is the simplest example of some general constructions described in 5 6

lower bounds for the perron root of a nonnegative matrix for an n n matrix a aij 0 we prove the perron root r a satisfies the inequality r a 1 i j n aijaji xixj i 1n aii q xi2 i 1nxi2 q for any x x1 xn t 0 with i 1nxi 1 and for any q min aii using this a necessary condition for a real n n matrix a with aii 0 and aij 0 i j i j 1 n to be an m matrix is presented viz 1 i j naijajiaiiajjxixj 1 q q i 1nxi2 i 1nxi2 for any x x1 xn t 0 with i 1nxi 1 and for any q 0

a lower bound for the perron root of a nonnegative matrix ii abstract this paper is a continuation of an earlier one by the author we obtain a new lower bound for the perron root r a of a nonnegative n n matrix a we show that for a with at least one principal submatrix of order two with different diagonal entries and with at least one positive off diagonal entry the bound is at least as good as the one from 7 and we determine a class of nonnegative matrices for which it is essentially better we also show that not every nonnegative square matrix is similar to a nonnegative square matrix with identical diagonal entries

the quantum group glh 2 among all quantum group structures on the space mat 2 of 2 by 2 matrices how many have a central quantum determinant so that one can define quantum sl 2 out of quantum gl 2 up to isomorphism there are two such structures glq 2 and glh 2 the former is well known the latter is described in this letter

tight bounds on the spectral radius of asymmetric nonnegative matrices abstract for an arbitrary asymmetric nonnegative n n matrix a we identify a pair of symmetric matrices whose largest eigenvalues bound the spectral radius of a furthermore we show that these bounding matrices are best possible by characterizing matrices a which attain equality with either the upper or the lower bounding matrix the lower bound may be extended to some matrices with negative entries provided they have no negative cycles

differential geometry of glh 1 1 we construct a differential calculus on the quantum supergroup glh 1 1 and obtain the h deformed superalgebra of glh 1 1

generalizations of the projection methods with application to sor theory for hermitian positive semidefinite linear systems ann n complex matrixb is calledparacontracting if b 2 1 and 0 x n i b bx 2 x 2 we show that a productb b k b k 1 b1 ofk paracontracting matrices is semiconvergent and give upper bounds on the subdominant eigenvalue ofb in terms of the subdominant singular values of theb i s and in terms of the angles between certain subspaces our results here extend earlier results due to halperin and due to smith solomon and wagner we also determine necessary and sufficient conditions forn numbers in the interval 0 1 to form the spectrum of a product of two orthogonal projections and hence characterize the subdominant eigenvalue of such a product in the final part of the paper we apply the upper bounds mentioned earlier to provide an estimate on the subdominant eigenvalue of the sor iteration matrix associated with ann n hermitian positive semidefinite matrixa none of whose diagonal entries vanish

adaptive filtering based on time averaged mse for cyclostationary signals adaptive filters are commonly used in many signal processing and communications systems in many practical digital communications scenarios including for example interference limited wireless and wireline communications as well as narrowband power line communications the considered signals are jointly cyclostationary yet most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals e g the least mean squares lms it is known that these algorithms may not converge for jointly cyclostationary signals in this paper we rigorously study the optimal adaptive filtering of jointly cyclostationary signals we first identify the relevant objective as the time averaged mean squared error criterion ta mse and obtain an adaptive algorithm as the stochastic approximation of the ta mse minimizer when the considered signals are jointly stationary the algorithm specializes to the standard lms algorithm we provide a comprehensive transient and steady state performance analysis without imposing a specific distribution on the considered signals and derive conditions for convergence and stability the algorithm which we call time averaged lms is applied to practical scenarios in a simulations study and an excellent agreement between the theoretical and the empirical performance is observed

cyclic wiener filtering theory and method conventional time and space filtering of stationary random signals which amounts to forming linear combinations of time translates and space translates exploits the temporal and spatial coherence of the signals by including frequency translates as well the spectral coherence that is characteristic of cyclostationary signals can also be exploited some of the theoretical concepts underlying this generalized type of filtering called frequency shift fresh filtering are developed the theory of optimum fresh filtering which is a generalization of wiener filtering called cyclic wiener filtering is summarized and the theory is illustrated with specific examples of separating temporally and spectrally overlapping communications signals including am bpsk and qpsk the structures and performances of optimum fresh filters are presented and adaptive adjustment of the weights in these structures is discussed also specific results on the number of digital qam signals that can be separated as a function of excess bandwidth are obtained