whitening rotation based semi blind mimo channel estimation this paper proposes a whitening rotation wr based algorithm for semi blind estimation of a complex flat fading multi input multi output mimo channel matrix h the proposed algorithm is based on decomposition of h as the matrix product h wq sup h where w is a whitening matrix and q is unitary rotation matrix the whitening matrix w can be estimated blind using only received data while q is estimated exclusively from pilot symbols employing the results for the complex constrained cramer rao bound cc crb it is shown that the lower bound on the mean square error mse in the estimate of h is directly proportional to its number of unconstrained parameters utilizing the bounds the semi blind scheme is shown to be very efficient when the number of receive antennas is greater than or equal to the number of transmit antennas closed form expressions for the crb of the semi blind technique are presented algorithms for channel estimation based on the decomposition are also developed and analyzed in particular the properties of the constrained maximum likelihood ml estimator of q for an orthogonal pilot sequence is examined and the constrained estimator for a general pilot sequence is derived in addition a gaussian likelihood function is considered for the joint optimization of w and q and its performance is studied simulation results are presented to support the algorithms and analysis and they demonstrate improved performance compared to exclusively training based estimation

aharonov bohm quantum systems on a punctured 2 torus this paper deals with aharonov bohm a b quantum systems on a punctured two dimensional torus from the geometric and the operator theoretic point of view first flat connections on the u 1 bundles over the punctured 2 torus are studied which serve as vector potentials for a b effect magnetic fields it is proved that the moduli space of flat connections is identified with the n 1 dimensional torus tn 1 if the punctured torus has n 0 pinholes at which solenoids are assumed to penetrate the 2 torus for a given point of tn 1 an associated flat connection is constructed in terms of the weierstrass zeta function on c together with an inhomogeneous linear function on r2 a b quantum systems are defined in terms of position operators and momentum operators coupled with the a b potentials necessary and sufficient conditions are given for two a b quantum systems to be unitarily equivalent further the a b hamiltonian is defined and analysed from the viewpoint of operator theory the deficiency indices of the a b hamiltonian are determined to be n m n m where m is the number of solenoids whose fluxes are not quantized finally the eigenvalue problem is studied for the a b hamiltonian with all fluxes quantized to obtain eigenvalues together with eigenfunctions which are described in terms of the weierstrass sigma functions

gauge theory on a non simply connected domain and representations of canonical commutation relations a quantum system of a particle interacting with a non abelian gauge field on the non simply connected domain m r2 an nn 1 is considered where an n 1 n are fixed isolated points in r2 the gauge potential a of the gauge field is a p p anti hermitian matrix valued 1 form on m and may be strongly singular at the points an n 1 n if a is flat then the physical momentum and the position operators pj qj 2j 1 of the particle satisfy the canonical commutation relations ccr with two degrees of freedom on a suitable dense domain of the hilbert space l2 r2 cp a necessary and sufficient condition for this representation to be the schrodinger 2 system is given in terms of the wilson loops of the rectangles not intersecting an n 1 n this also gives a characterization for the representation to be non schrodinger it is proven that for a class of gauge potentials which is not necessarily flat pj is essentially self adjoint moreover an example which gives a class of non schrodinger repres

momentum operators with gauge potentials local quantization of magnetic flux and representation of canonical commutation relations commutation properties of two dimensional momentum operators with gauge potentials are investigated a notion of local quantization of magnetic flux is introduced to characterize physically the strong commutativity of the momentum operators in terms of the notion a necessary and sufficient condition is given for the position and the momentum operators to be equivalent to the schrodinger representation of the canonical commutation relations

fundamental solution of the heat and schrodinger equations with point interaction abstract we find explicit formulae for the fundamental solution for the heat and time dependent schrodinger equations with point interaction in dimension n 3 we discuss in detail the small time asymptotics of these fundamental solutions the case n 2 has the peculiarity of involving logarithmic terms in the expansion

blind mai and isi suppression for ds cdma systems using hos based inverse filter criteria cumulant based inverse filter criteria ifc using second and higher order statistics hos proposed by tugnait et al 1993 have been widely used for blind deconvolution of discrete time multi input multi output mimo linear time invariant systems with non gaussian measurements through a multistage successive cancellation procedure but the deconvolved signals turn out to be an unknown permutation of the driving inputs a multistage blind equalization algorithm mbea is proposed for multiple access interference mai and intersymbol interference isi suppression of multiuser direct sequence code division multiple access ds cdma systems in the presence of multipath the proposed mbea which processes the chip waveform matched filter output signal without requiring any path delay information includes blind deconvolution processing using ifc followed by identification of the estimated symbol sequence with the associated user through a user identification algorithm uia then some simulation results are presented to support the proposed mbea and uia finally some conclusions are drawn

a mathematical aspect of a tunnel junction for spintronic qubit abstract we consider the dirac particle that lives in the 1 dimensional configuration space consisting of two quantum wires and a junction between the two we regard the spin of a dirac particle as spintronic qubit we give concrete formulae explicitly expressing the one to one correspondence between every self adjoint extension of the minimal dirac operator and its corresponding boundary condition of the wave functions of the dirac particle we then show that all the boundary conditions can be classified into just two types the two types are characterized by whether the electron passes through the junction or not we also show how the tunneling produces its own phase factor and what is the relation between the phase factor and the spintronic qubit in the tunneling boundary condition

on the blow up rate and the blow up set of breaking waves for a shallow water equation we consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation blow up can occur only in the form of wave breaking i e the solution remains bounded but its slope becomes unbounded in finite time a quite detailed description of the wave breaking phenomenon is given there is at least a point in general depending on time where the slope becomes infinite exactly at breaking time the precise blow up rate is established and for a large class of initial data we also determine the blow up set

canonical commutation relations the weierstrass zeta function and infinite dimensional hilbert space representations of the quantum group uq sl2 a two dimensional quantum system of a charged particle interacting with a vector potential determined by the weierstrass zeta function is considered the position and the physical momentum operators give a representation of the canonical commutation relations with two degrees of freedom if the charge of the particle is not an integer the case corresponding to the aharonov bohm effect then the representation is inequivalent to the schrodinger representation it is shown that the inequivalent representation induces infinite dimensional hilbert space representations of the quantum group uq sl some properties of these representations of uq sl are investigated

blind separation of independent sources for virtually any source probability density function the blind source separation bss problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure in the bss scenario of two noiseless real valued instantaneous linear mixtures of two sources an approximate maximum likelihood ml approach has been suggested in the literature which is only valid under certain constraints on the probability density function pdf of the sources in the present paper the expression for this ml estimator is reviewed and generalized to include virtually any source distribution an intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved an asymptotic performance analysis is then carried out yielding a closed form expression for the estimator asymptotic pdf simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis in addition an extension of the method to the general bss scenario of more than two sources and two sensors is successfully implemented

initial boundary value problems for nonlinear dispersive wave equations in this paper we study initial value boundary problems of two types of nonlinear dispersive wave equations on the half line and on a finite interval subject to homogeneous dirichlet boundary conditions we first prove local well posedness of the rod equation and of the b equation for general initial data furthermore we are able to specify conditions on the initial data which on the one hand guarantee global existence and on the other hand produce solutions with a finite life span in the case of finite time singularities we are able to describe the precise blow up scenario of breaking waves our approach is based on sharp extension results for functions on the half line or on a finite interval and several symmetry preserving properties of the equations under discussion

adaptive blind source separation for virtually any source probability density function blind source separation bss aims to recover a set of statistically independent source signals from a set of linear mixtures of the same sources in the noiseless real mixture two source two sensor scenario once the observations are whitened decorrelated and normalized only a givens rotation matrix remains to be identified in order to achieve the source separation in this paper an adaptive estimator of the angle that characterizes such a rotation is derived it is shown to converge to a stable valid separation solution with the only condition that the sum of source kurtosis be distinct from zero an asymptotic performance analysis is carried out resulting in a closed form expression for the asymptotic probability density function of the proposed estimator it is shown how the estimator can be incorporated into a complete adaptive source separation system by combining it with an adaptive prewhitening strategy and how it can be useful in a general bss scenario of more than two signals by means of a pairwise approach a variety of simulations assess the accuracy of the asymptotic results display the properties of the estimator such as its robust fast convergence and compare this on line bss implementation with other adaptive bss procedures

canonical quantization on a doubly connected space and the aharonov bohm phase abstract we consider the canonical quantization schrodinger representation on a doubly connected space r r 2 x y x2 y2 r2 r 0 we show that when we employ 2 dimensional orthogonal coordinates ox1x2 there are uncountably many different self adjoint extensions puj of pj i xj j 1 2 and none of the pairs pj qj j j 1 2 qj xj satisfies the weyl relation then we construct a new canonical pair of canonical momentum and position operators so that the pair can satisfy the weyl relation by using the streamline coordinates as its application in the weyl relation with respect to the pair of the mv momentum and position operators by the above new canonical pair we find the aharonov bohm phase

fourth order criteria for blind sources separation various criteria based on contrast functions as well as higher order statistics are used for solving the problem of blind separation of sources in the paper for the case of instantaneous mixtures of two sources it is proved that the minimization or the cancellation of a really simple criterion a fourth order cross cumulant leads to a set of solutions whose spurious ones can be simply cancelled by using a decorrelation

optimal pairwise fourth order independent component analysis blind source separation bss aims at the reconstruction of unknown mutually independent signals so called sources from their mixtures observed at the output of a sensor array the bss of instantaneous linear mixtures which finds application in numerous fields can be solved through the statistical tool of independent component analysis ica this paper concentrates on the analytic solutions for the fundamental two signal ica scenario a novel estimation class so called general weighted fourth order estimator gwfoe is put forward which is based on the fourth order statistics of the whitened sensor output by means of a weight parameter the gwfoe is able to unify a variety of apparently disparate estimation expressions previously scattered throughout the literature including the well known jade method in the two signal case a theoretical asymptotic performance analysis is carried out resulting in the gwfoe large sample mean square error and the source dependent weight value of the most efficient estimator in the class to extend the pairwise estimators to the general scenario of more than two sources an improved jacobi like optimization technique is proposed the approach consists of calculating the necessary sensor output fourth order statistics at the initialization stage of the algorithm which can lead to significant computational savings when large sample blocks are processed based on this idea adaptive algorithms are also devised showing very satisfactory convergence characteristics experiments illustrate the good performance of these optimal pairwise ica strategies in both off and on line processing modes

a remark concerning canonical commutation relations an elementary quantum mechanical example of canonical commutation relations not equivalent to the schrodinger representation is discussed it demonstrates that the nelson phenomenon occurs in a natural situation

representation theoretic aspects of two dimensional quantum systems in singular vector potentials canonical commutation relations quantum algebras and reduction to lattice quantum systems some representation theoretic aspects of a two dimensional quantum system of a charged particle in a vector potential a which may be singular on an infinite discrete subset d of r2 are investigated for each vector v in a set v d r2 0 the projection pv of the physical momentum operator p p a to the direction of v is defined by pv v p as an operator acting in l2 r2 where p idx idy x y r2 with dx resp dy being the generalized partial differential operator in the variable x resp y and r is a parameter denoting the charge of the particle it is proven that pv is essentially self adjoint and an explicit formula is derived for the strongly continuous one parameter unitary group eitpv t r generated by the self adjoint operator pv the closure of pv i e the magnetic translation to the direction of the vector v the magnetic translations along curves in r2 d are also considered conjugately to pv and pw w v d a self adjoint multiplication operator qv w is introduced which is a

well posedness global existence and blowup phenomena for a periodic quasi linear hyperbolic equation we establish the local well posedness of a recently derived model for small amplitude shallow water waves for a large class of initial data we prove global existence of the corresponding solution criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained and an existence and uniqueness result for a class of global weak solutions is also given c 1998 john wiley sons inc

adaptive modal identification of structures with equivariant adaptive separation via independence approach abstract an efficient output only blind source separation bss method was recently introduced for the modal identification of structures bss procedures recover a set of independent sources from their unknown linear mixtures when only mixtures are observed batch data is required for the separation in traditional blind source separation methods these algorithms are however unfavorable as some sets of data are observed one after another in this paper an adaptive blind source separation technique equivariant adaptive separation via independence easi is introduced to overcome the mentioned disadvantage within the structures the easi algorithm is beneficial as it can provide solutions to real time problems while also update the un mixing matrix for each step easi not only avoids increases in size of the relevant matrices and vectors but also decreases the analysis time a synthetic example and a benchmark structure have been used in this paper to better investigate the efficiency of the proposed method the simulation results demonstrate the effectiveness of the easi algorithm in on line identification of modal parameters of structures

singular solutions of a modified two component camassa holm equation the camassa holm ch equation is a well known integrable equation describing the velocity dynamics of shallow water waves this equation exhibits spontaneous emergence of singular solutions peakons from smooth initial conditions the ch equation has been recently extended to a two component integrable system ch2 which includes both velocity and density variables in the dynamics although possessing peakon solutions in the velocity the ch2 equation does not admit singular solutions in the density profile we modify the ch2 system to allow a dependence on the average density as well as the pointwise density the modified ch2 system mch2 does admit peakon solutions in the velocity and average density we analytically identify the steepening mechanism that allows the singular solutions to emerge from smooth spatially confined initial data numerical results for the mch2 system are given and compared with the pure ch2 case these numerics show that the modification in the mch2 system to introduce the average density has little short time effect on the emergent dynamical properties however an analytical and numerical study of pairwise peakon interactions for the mch2 system shows a different asymptotic feature namely besides the expected soliton scattering behavior seen in overtaking and head on peakon collisions the mch2 system also allows the phase shift of the peakon collision to diverge in certain parameter regimes

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

blind separation using convex functions in this paper the problem of how to conveniently estimate independence from observations is addressed random variables rvs are transformed by their respective distribution functions and quantized then the uniformity of the joint probability of the obtained discrete rvs is evaluated using a strictly convex function an infinite class of new independence measures named quasientropy qe is thus proposed unbiased estimates of the values of the distribution functions at the observations are directly utilized in estimating qe the linear instantaneous blind source separation bss algorithm based on qe can separate signals with arbitrary continuous distributions

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

point interactions in two dimensions basic properties approximations and applications to solid state physics on etudie rigoureusement l operateur de schrodinger formellement donne par h y dans l 2 r 2 et on montre comment l approcher en termes d hamiltoniens a courte portee transformes d echelles on considere des questions semblables pour l operateur h j 1 n j y j n n on etudie les proprietes spectrales du modele a un electron d un cristal a 2 dimensions avec des interactions ponctuelles

magnetic translation groups in an n dimensional torus and their representations a charged particle in a uniform magnetic field in a two dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry we study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions the magnetic translation group mtg is defined as a group of translations that leave the gauge field invariant we show that the mtg in an n dimensional torus is isomorphic to a central extension of a cyclic group z 1 z 2l tm by u 1 with 2l m n we construct and classify irreducible unitary representations of the mtg in a three torus and apply the representation theory to three examples we briefly describe a representation theory for a general n torus the mtg in an n torus can be regarded as a generalization of the so called noncommutative torus

a multidimensional phase locked loop for blind multiuser detection this paper concerns the problem of blind multiuser detection a special case of the blind source separation problem in which the source signals have finite alphabets specifically we address the problem of identifying and resolving the n spl times n unitary matrix ambiguity u that results from whitening the receiver observations where n is the number of sources we propose the multidimensional phase locked loop mpll as a generalization of a scalar decision directed pll to vector valued signals the mpll adapts an estimate of u according to the recursion u spl circ sub k 1 u spl circ sub k r sub k where r sub k is an n dimensional householder like rotation depending on only the kth receiver observation the o n sup 2 complexity of an efficient implementation of the algorithm is extremely low nevertheless simulation results demonstrate good convergence properties and superior steady state performance when compared with prior techniques the algorithm is also able to accommodate large alphabets and shaped alphabets

global existence and blow up phenomena for an integrable two component camassa holm shallow water system abstract this paper is concerned with global existence and blow up phenomena for an integrable two component camassa holm shallow water system a new global existence result and several new blow up results of strong solutions to the system are presented our obtained results for the system are sharp and improve considerably earlier results

retracted blow up and global existence for a modified two component camassa holm equation the present work is mainly concerned with blow up phenomena and global existence for a modified two component camassa holm equation firstly a new blow up criterion and the precise blow up rate are presented then a new global existence result for strong solutions to the equation is given