parity dependent squeezing of light a parity dependent squeezing operator is introduced which imposes different su 1 1 rotations on the even and odd subspaces of the harmonic oscillator hilbert space this operator is used to define parity dependent squeezed states which exhibit highly non classical properties such as strong antibunching quadrature squeezing strong oscillations in the photon number distribution etc in contrast to the usual squeezed states whose q and wigner functions are simply gaussians the parity dependent squeezed states have much more complicated q and wigner functions that exhibit an interesting interference in phase space the generation of these states by parity dependent quadratic hamiltonians is also discussed

kernel of star product for spin tomograms the spin state tomogram is presented as the modulus squared of the matrix element of the su 2 group irreducible representation for the spin system we established explicitly a realization of the set of operators defining for spin tomograms the star product formalism in terms of irreducible tensors on the set of spin tomograms the delta function and standard and moyal like kernels of the tomogram star product are calculated explicitly in terms of clebsch gordan and racah coefficients and matrix elements of the su 2 irreducible representation in the limit of infinite spin the spin tomogram is shown to become the tomogram of the harmonic oscillator state

the segal bargmann coherent state transform for compact lie groups abstract let k be an arbitrary compact connected lie group we describe on k an analog of the segal bargmann coherent state transform and we prove theorem 1 that this generalized coherent state transform maps l 2 k isometrically onto the space of holomorphic functions in l 2 g where g is the complexification of k and where is an appropriate heat kernel measure on g the generalized coherent state transform is defined in terms of the heat kernel on the compact group k and its analytic continuation to the complex group g we also define a k averaged version of the coherent state transform and we prove a similar result for it theorem 2 in the appendix we describe the coherent states which motivate the definitions of these transforms in section 9 we obtain inversion formulas for both the coherent state transform and the k averaged coherent state transform theorems 3 4 as a consequence we obtain formulas for certain bergman kernels on the complex group g theorems 5 6 in section 10 we derive a general paley wiener theorem for k and we exhibit a family of convolution transforms each of which is an isometric isomorphism of l 2 k onto a certain l 2 space of holomorphic functions on g these transforms include the k averaged coherent state transform as a special case we also discuss the analogous results for r 1 the results of section 10 are theorems 7 10 finally in section 11 we discuss the case of quotient spaces we prove theorem 11 that both the coherent state transform and the k averaged coherent state transform pass in a natural way from k to k h where h is a closed connected subgroup of k

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

coherent states for a quantum particle on a circle the coherent states for a quantum particle on a circle are introduced the bargmann representation within the actual treatment provides the representation of the algebra where u is unitary which is a direct consequence of the heisenberg algebra but it is more adequate for the study of circular motion

unconditional stabilization of linear discrete systems via adaptive control this paper deals with the conditions of overall deterministic stability of the adaptive control schemes which may be obtained by associating any usual identification and control methods e g recursive minimum square stochastic approximation extended kalman filter for identification model reference pole placement quadratic optimization for control the deterministic and time invariance hypotheses are introduced here only for the analysis of the above schemes but not for their synthesis there are no assumptions of sufficiently exciting input or any requirement for parameter convergence nor an hypothesis of bounded input and output signals

equipartition of the eigenfunctions of quantized ergodic maps on the torus we give a simple proof of the equipartition of the eigenfunctions of a class of quantized ergodic area preserving maps on the torus examples are the irrational translations the skew translations the hyperbolic automorphisms and some of their perturbations

infrared singular fields and nonregular representations of canonical commutation relation algebras infrared singular variables which often enter in the formulation of models in quantum field theory many body theory and quantum statistical mechanics are described in terms of nonregular representations of canonical commutation relations algebras general properties of such representations are discussed in this way one also obtains insight into the construction and representation of charged field algebras a as canonical extensions of a neutral observable algebra a0 the charged state representations of a0 are obtained through nonregular vacuum representations of the extended field algebra a the above structures are proven to work in several explicit models

barut girardello coherent states for and and their macroscopic superpositions the barut girardello bg coherent states cs representation is extended to the noncompact algebras and in reducible quadratic boson realizations the bg cs take the form of multimode ordinary schr dinger cat states macroscopic superpositions of cs canonical cs n 1 2 are pointed out which are overcomplete in the n mode hilbert space and the relation between the canonical cs and the bg type cs representations is established the sets of and bg cs and their discrete superpositions contain many states studied in quantum optics even and odd n mode cs pair cs and provide an approach to quadrature squeezing alternative to that of intelligent states new subsets of weakly and strongly nonclassical states are pointed out and their statistical properties first and second order squeezing photon number distributions are discussed for specific values of the angle parameters and small amplitude of the canonical cs components these states approach multimode fock states with one two or three bosons photons it is shown that eigenstates of a squared non hermitian operator generalized cat states can exhibit squeezing of the quadratures of a

generalized coherent states for su n systems generalized coherent states are developed for su n systems for arbitrary n this is done by first iteratively determining explicit representations for the su n coherent states and then determining parametric representations useful for applications for su n the set of coherent states is isomorphic to a coset space su n su n 1 and thus shows the geometrical structure of the coset space these results provide a convenient 2n 1 dimensional space for the description of arbitrary su n systems we further obtain the metric and measure on the coset space and show some properties of the su n coherent states

holomorphic discrete series and harmonic series unitary irreducible representations of non compact lie groups sp 2n r u p q and so 2n generalised characters of the infinite dimensional holomorphic discrete series unitary irreducible representations of the non compact groups u p q sp 2n r and so 2n are explicitly expressed in terms of characters of finite dimensional unitary group representations these formulae are remarkably succinct despite involving certain infinite series of schur functions similar formulae are derived for harmonic series unitary representation of both u p q and sp 2n r consideration of the branching rules from u p q to u q p and from sp 2n r to u n enables holomorphic representations to be identified as a subset of the harmonic representations the branching rules are established in full generality and are then used in the evaluation of tensor products of both holomorphic and harmonic representations in the case of the former a known result is recast in terms of closed formulae involving schur functions and for the latter various generalisations of these formulae are given a conjecture is also made regarding what might be the simplest possible formulae covering all holomorphic and harmonic representations of sp 2n r and u p q illustrative examples are presented

identification of linear stochastic systems via second and fourth order cumulant matching the identification problem for time invariant single input single output linear stochastic systems driven by non gaussian white noise is considered the system is not restricted to be minimum phase and it is allowed to contain all pass components a least squares criterion that involves matching the second and the fourth order cumulant functions of the noisy observations is proposed knowledge of the probability distribution of the driving noise is not required an order determination criterion that is a modification of the akaike information criterion is also proposed strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are presented to illustrate the method

the barut girardello coherent states it is shown that the completeness problem of the sl 2 r coherent states proposed by barut and girardello leads to a moment problem not a mellin transform this moment problem which also appears in the theory of para bose oscillators has been solved following the sharma mehta mukunda sudarshan solution of the problem the matrix element of finite transformation in the coherent state basis is shown to satisfy a quasiorthogonality condition analogous to the orthogonality condition of the matrix element in the canonical basis finally the barut girardello hilbert space of entire analytic functions of growth 1 1 turns out to be only a subspace of bargmann s well known hilbert space of analytic functions this subspace which has been called the reduced bargmann space in a previous paper is an invariant subspace of sl 2 r with this identification the generators of the group in this realization turn out to be the well known boson operators of holman and biedenharn

evaluation of the coulomb force via the fredholm integral equation the electrostatic force between two conducting spheres is solved exactly from coulomb s law the force is evaluated in two steps i the charge distribution on each of the spheres is calculated as a function of separation distance by way of a solution to the fredholm integral equation ii the effect of the known charge distribution is integrated to obtain the electrostatic force evaluation of the electrostatic force is fast because the series expression for the charge distribution is super converging a characteristic trait for some fredholm type equations

precision tracking control of non minimum phase systems with zero phase error in this paper a method is proposed for designing the command feedforward controller for zero phase error tracking control of systems having unacceptable zeros the unacceptable zeros include both non minimum phase zeros and lightly damped zeros in the proposed approach a digital preview filter along with the acceptable part of the system s inverse model is designed to form the command feedforward controller using preview information of the input trajectory the designed tracking controller guarantees zero phase error and high precision tracking performance in the proposed design the best tracking performance can be achieved by minimizing a weighted penalty function which controls the gain error between the desired output and the actual output two design cases were examined the first is the design based on a uniform weighting function in this study the optimal solution of the design can be analytically obtained and three prior approaches were shown to be the special cases of the proposed solutio

resolutions of the identity in terms of line integrals of su 1 1 coherent states resolutions of the identity in terms of contour integrals that involve coherent states and their complementary states are derived the complementary states are auxiliary states that help in the formulation of these resolutions of the identity since the coherent states are normalizable inside the unit disc and the complementary states are normalizable outside the unit disc enlargements of the hilbert space are considered which allow the construction of resolutions of the identity in terms of contour integrals in rings several examples of our formalism are presented

an analysis of finite difference and finite volume formulations of conservation laws abstract finite difference and finite volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws a new coordinate free formulation of systems of conservation laws is developed which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system the analysis considers general types of equations potential euler and navier stokes three dimensional unsteady flows with time varying grids are described using a single consistent nomenclature for both formulations grid motion due to a non inertial reference frame as well as flow adaptation is covered in comparing the two formulations it is found useful to distinguish between differences in numerical methods and differences in grid definition the former plays a role for non cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled the differences in grid definition for the two formulations is found to be more important since it affects the manner in which boundary conditions zonal procedures and grid singularities are handled at computational boundaries the proper interpretation of strong and weak conservation law forms for quasi one dimensional and axisymmetric flows is brought out

chaotic analytic zero points exact statistics for those of a random spin state a natural statistical ensemble of 2j points on the unit sphere can be associated via the majorana representation with a random quantum state of spin j and an exact expression is obtained here for the general k point correlation function in this ensemble the pair correlation in the large j limit takes the relatively simple form where and is the angular separation of the pair of points on the sphere it appears from the numerical work of others that in this limit these statistics are typical of the zero points of analytic functions associated with chaotic quantum dynamical systems

the bakerian lecture 1987 quantum chaology bounded or driven classical systems often exhibit chaos exponential instability that persists but their quantum counterparts do not nevertheless there are new regimes of quantum behaviour that emerge in the semiclassical limit and depend on whether the classical orbits are regular or chaotic and this motivates the following definition definition quantum chaology is the study of semiclassical but nonclassical behaviour characteristic of systems whose classical motion exhibits chaos this is illustrated by the statistics of energy levels on scales comparable with the mean level spacing of order h n for n freedoms these fall into universality classes for classically chaotic systems the statistics are those of random matrices real symmetric or complex hermitian depending on the presence or absence of time reversal symmetry for classically regular ones the statistics are poisson on larger scales of order h i e classically small but semiclassically large universality breaks down these phenomena are being explained by representing spectra in terms of classical closed orbits universal spectral behaviour has its origin in very long orbits non universal behaviour depends only on short ones

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

poincare contraction of su 1 1 fock bargmann structure some aspects of the contraction process so0 1 2 to poincare are studied the starting point is the choice of a suitable parametrization for the de sitterian phase space so0 1 2 so 2 approximately su 1 1 u 1 the authors show that the contraction to poincare must be realized by restricting the fock bargmann space to a specific subspace this constraint is necessary to make the divergent terms disappear in particular the classical result according to which the discrete series representation of su 1 1 contracts onto the wigner representation p m is described at a global level

a new coherent paired state with possible applications to fluctuation dissipation phenomena the authors extend their previous work on coherent paired states associated with the lie group su 1 1 whereas the earlier states were defined with respect to a single type of canonical boson or linear quantum harmonic oscillator the new states are defined in terms of two distinct types of bosons or oscillators the new coherent states may again on the one hand be viewed as ordinary glauber coherent states in the two boson hilbert space spanned by arbitrary numbers of two distinct bogoliubov quasiparticles associated with the original bosons via a generalised bogoliubov transformation alternatively expressed wholly in terms of the original bosons these new coherent states are reached from the ordinary coherent states via a unitary pairing transformation which is shown to be associated with the entire so called discrete series of representations of the group su 1 1 as an important illustration of the use of these states and transformations they study in detail a rather general class of quantum lagrangians which includes the damped linear harmonic oscillator they thereby illustrate their possible usefulness in applications to quantum many body or field theoretic processes involving fluctuation dissipation phenomena in general

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

brief paper on the stabilizability condition in indirect adaptive control many recent studies on overall stability of adaptive control systems require among other conditions that the identified model be stabilizable at least asymptotically in fact the usual identification methods do not guarantee this property in the passive approach without exciting extra signals or if the model order is subject to over estimation in order to solve this problem it is shown in this paper that certain classical identification algorithms can be easily modified in order to ensure the above stabilizability condition without affecting the other properties

technical communique on adaptive minimum variance regulation for non minimum phase plants adaptive minimum variance control is applied to nonminimum phase plants augmented with adaptive compensators the objective of the compensators is to achieve asymptotically a minimum phase property for the augmented plant with this property the minimum variance controller gives a stabilizing control signal the scheme proposed has interpretations as an adaptive quadratic index minimizing procedure and also as an adaptive pole assignment algorithm the advantage over other adaptive quadratic index minimizing procedures is simply that the weightings are made adaptive so as to guarantee convergence one feature not shared by other adaptive pole assignment schemes is that they conveniently specialize to simple minimum variance schemes when for these control energy constraints are not violated this paper presents only the discrete time adaptive regulator version companion papers give a full global convergence theory and pre processing augmentations for the stochastic tracking scheme versions

matrix elements of operators in symmetrical u 6 u 3 u 2 u 1 and u 6 su 3 so 3 so 2 basis in this paper we consider a basis for n boson states classified by the chain of groups u 6 u 3 u 2 u 1 we determine analytical expressions for the matrix elements of the boson creation and annihilation operators as well as for the u 6 generators with respect to that basis for such purpose we use the wigner eckart theorem with respect to u 3 and calculate the reduced matrix elements of the appropriate irreducible tensors from their matrix elements between highest weight states then we apply the transformation brackets from the chain u 6 u 3 u 2 u 1 to the physical chain u 6 su 3 so 3 so 2 to obtain the matrix elements of the above mentioned operators in a basis corresponding to the latter the matrix elements so determined can be used either in the nuclear interacting boson model of arima and iachello or in the microscopic nuclear collective model of vanagas et al

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

generalized intelligent states and squeezing the robertson schrodinger uncertainty relation for two observables a and b is shown to be minimized in the eigenstates of the operator a ib being a complex number such states called generalized intelligent states gis can exhibit arbitrarily strong squeezing of a or b the time evolution of gis is stable for hamiltonians which admit linear in a and b invariants systems of gis for the su 1 1 and su 2 groups are constructed and discussed it is shown that su 1 1 gis contain all the perelomov coherent states cs and the barut and girardello cs while the spin cs are a subset of su 2 gis cs for an arbitrary semisimple lie group can be considered as a gis for the quadratures of the weyl generators

extended cahill glauber formalism for finite dimensional spaces i fundamentals the cahill glauber approach for quantum mechanics on phase space is extended to the finite dimensional case through the use of discrete coherent states all properties and features of the continuous formalism are appropriately generalized the continuum results are promptly recovered as a limiting case the jacobi theta functions are shown to have a prominent role in the context

analytic and contour representations in the unit disk based on su 1 1 coherent states a contour representation in the unit disk based on su 1 1 coherent states is introduced the scalar product is given by a contour integral the regions of convergence of the functions representing ket and bra states are studied an analytic representation in the unit disk is also considered where the scalar product is represented by an integral over the unit disk with the lobachevsky measure various relations which connect these analytic functions with other phase space quantities are derived

analytical expressions for the matrix elements of the non compact symplectic algebra analytic matrix elements are derived for all the lowest weight representations of the noncompact symplectic algebra sp 3 r it is shown that the expressions are exact for representations of the type sigma 1 sigma 2 sigma 3 and for all states of an arbitrary representation that are multiplicity free with respect to the u 3 subalgebra furthermore they are remarkably accurate in general

navier stokes simulations of slender axisymmetric shapes in supersonic turbulent flow computational fluid dynamics is used to study flows about slender axisymmetric bodies at very high speeds numerical experiments are conducted to simulate a broad range of flight conditions mach number is varied from 1 5 to 8 and reynolds number is varied from 1 x 106 m to 2 x 108 m the primary objective is to develop and validate a computational methodology for the accurate simulation of a wide variety of flow structures accurate results are obtained for detached bow shocks recompression shocks corner point expansions base flow recirculations and turbulent boundary layers accuracy is assessed through comparison with theory and experimental data computed surface pressure shock structure base flow structure and velocity profiles are within measurement accuracy throughout the range of conditions tested the methodology is both practical and general general in its applicability and practical in its performance to achieve high accuracy modifications to previously reported techniques are implemented in the scheme these modifications improve computed results in the vicinity of symmetry lines and in the base flow region including the turbulent wake

the growth of bargmann functions and the completeness of sequences of coherent states the growth of bargmann functions is intimately connected to the density of the zeros of these functions and to the completeness of sequences of coherent states using these ideas we find the least density that a sequence of coherent states must have in order to be overcomplete within the space of bargmann functions of an order not exceeding and of a type not exceeding if of order these results generalize known results on the completeness of von neumann lattices the practical significance of this formalism in the context of quantum optics is also discussed

classical limits for quantum maps on the torus we provide a rigorous canonical quantization for the following toral automorphisms cat maps generalized kicked maps and generalized harper maps for each of these systems we construct a unitary propagator and prove the existence of a well defined classical limit we also provide an alternative derivation of hannay and berry results for the cat map propagator on the plane

adaptive control with finite time persistency of excitation an adaptive control algorithm for discrete time siso systems is presented the main feature is the fact that it requires an external persistently exciting signal for a finite interval of time in this way tracking of a class of signals such as set points can be achieved within an arbitrarily small error

quantum riemann surfaces i the unit disc we construct a non commutative algebra c mu bar u which is a quantum deformation of the algebra of continuous functions on the closed unit disc bar u c mu bar u is generated by the toeplitz operators on a suitable hilbert space of holomorphic functions onu

the stratonovich weyl correspondence for one dimensional kinematical groups the stratonovich weyl correspondence is a restatement of the moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively the first and most important step is to define a mapping from the manifold into the set of self adjoint operators on a hilbert space under suitable conditions this mapping is called a stratonovich weyl kernel the construction of this mapping is discussed on coadjoint orbits of the one dimensional galilei poincare and newton hooke groups as well as the two dimensional euclidean group

representation and properties of para bose oscillator operators ii coherent states and the minimum uncertainty states the energy position and momentum eigenstates of a para bose oscillator system were considered in paper i here we consider the bargmann or the analytic function description of the para bose system this brings in in a natural way the coherent states z defined as the eigenstates of the annihilation operator the transformation functions relating this description to the energy position and momentum eigenstates are explicitly obtained possible resolution of the identity operator using coherent states is examined a particular resolution contains two integrals one containing the diagonal basis z z and the other containing the pseudodiagonal basis z z we briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations the problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible dependence of this minimum value is considered

towards a globally stable direct adaptive control scheme for not necessarily minimum phase systems a direct adaptive control scheme for not necessarily minimum phase systems is presented the algorithm is based on simultaneous identification of input and output prediction models this leads to a bilinear parameter estimation problem for which a least squares criterion minimization is proposed this framework makes it possible to establish global convergence without any extra condition we give an example to illustrate the practical features

global convergence for adaptive one step ahead optimal controllers based on input matching this paper establishes global convergence for adaptive one step ahead optimal controllers applied to a class of linear discrete time single input single output systems the class of systems includes all stable systems whether they are minimum phase or not all minimum phase systems whether they are stable or not and some unstable nonminimum phase systems the key substantive assumption is that the one step ahead optimal controller designed using the true system parameters leads to a stable closed loop system subject to this natural restriction it is shown that a simple adaptive control algorithm based on input matching is globally convergent in the sense that the system inputs and outputs remain bounded for all time and the input converges to the one step ahead optimal input both deterministic and stochastic cases are treated

almost exact modelling assumption in adaptive linear control modem adaptive controllers are known to give bounded solutions when the system normalized unmodelled effects are bounded by a small constant this paper studies this unusual characterization of uncertainties we show it encompasses more classical approaches we discuss how feedback and by passing may allow this assumption to be satisfied we conclude by proposing the notion of almost exactly linearly modelled systems

bargmann transform zak transform and coherent states it is well known that completeness properties of sets of coherent states associated with lattices in the phase plane can be proved by using the bargmann representation or by using the kq representation which was introduced by j zak in this paper both methods are considered in particular in connection with expansions of generalized functions in what are called gabor series the setting consists of two spaces of generalized functions tempered distributions and elements of the class s which appear in a natural way in the context of the bargmann transform also a thorough mathematical investigation of the zak transform is given this paper contains many comments and complements on existing literature in particular connections with the theory of interpolation of entire functions over the gaussian integers are given

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

effective treatment of the singular line boundary problem for three dimensional grids three dimensional grids of rotation contain a singular line where the radial grid planes meet when the flow equations are transformed into generalized coordinates a mathematical singularity is introduced into the governing equations specifically the grid jacobian j becomes infinite along the singular line this can introduce nonphysical perturbations in the flow solution particularly if a finite difference solution algorithm is used a number of recent publications1 5 have discussed problems associated with the singular line this paper presents a method for eliminating the axis singularity the governing equations are reformulated using a redefined grid jacobian that can be evaluated at the singular line this allows a finite difference algorithm to compute a smooth continuous solution in the region of the singular line contents

the bargmann representation for the quantum mechanics on a sphere the bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in kowalski and rembielinski j phys a 33 6035 2000 the connection is discussed between the introduced formalism and the standard approach based on the hilbert space of square integrable functions on a sphere s2

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

coherent states and the classical limit on irreducible representations we give an explicit construction of the coherent states for an arbitrary irreducible representation we also construct the symplectic structure on the manifold of coherent states find canonical variables and discuss various classical limits of quantum mechanical systems with relevant observables that obey commutation relations

factorization of analytic representations in the unit disc and number phase statistics of a quantum harmonic oscillator the inner outer part factorization of analytic representations in the unit disc is used for an effective characterization of the number phase statistical properties of a quantum harmonic oscillator it is shown that the factorization is intimately connected with the number phase weyl semigroup and its properties in the barut girardello analytic representation the factorization is implemented as a convolution several examples are given which demonstrate the physical significance of the factorization and its role for quantum statistics in particular we study the effect of phase space interference on the factorization properties of a superposition state

moyal quantization with compact symmetry groups and noncommutative harmonic analysis the phase space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles covariance and traciality this generalizes results and methods already implemented for spin systems j c varilly and j m gracia bondia ann phys 190 107 1989 the twisted product of phase space functions is shown to be the image of group convolution in the context of a novel fourier theory on the coadjoint orbits

coherent state realizations of su n 1 on the n torus we obtain a new family of coherent state representations of su n 1 in which the coherent states are wigner functions over a subgroup of su n 1 for representations of su n 1 of the type 0 0 the basis functions are simple products of n exponential the corresponding coherent state representations of the algebra su n 1 are also obtained and provide a polar decomposition of su n 1 for any n 1 the su n 1 modules thus obtained are useful in understanding contractions of su n 1 and su n 1 phase states of quantum optics

quantum mechanical path integrals with wiener measures for all polynomial hamiltonians we construct arbitrary matrix elements of the quantum evolution operator for a wide class of self adjoint canonical hamiltonians including those which are polynomial in the heisenberg operators as the limit of well defined path integrals involving wiener measure on phase space as the diffusion constant diverges a related construction achieves a similar result for an arbitrary spin hamiltonian

generalised coherent states and group representations on hilbert spaces of analytic functions using the example for the group su 1 1 the author obtains the basis functions of a hilbert space of analytic functions from the perelomov 1972 definition of generalised coherent states the lie algebra in this space has the form of a holstein primakoff representation appropriate for su 1 1

persistency of excitation in the presence of possibly unbounded signals this note develops an explicit characterization of the concept of persistency of excitation for time invariant linear systems in the presence of possibly unbounded signals this result can be used to establish exponential convergence for a range of adaptive control algorithms a feature of our proof is a particular technique for dealing with the initial condition response

adaptive pole placement without excitation probing signals this paper presents an indirect adaptive control scheme for linear systems which may possibly be a nonminimum phase the control scheme achieves asymptotical pole placement without either introducing persistent excitation probing signals into the systems or assuming any a priori knowledge on the plant parameters the system order is the only a priori knowledge required on the plant the adaptive control law is free from singularities in the sense that the estimated plant model is always controllable the singularities are overcome by a suitable parameter estimates modification which is based upon standard least squares covariance matrix properties the analysis of the stability and the global convergence of a closed loop system is given in detail for both discrete time and continuous time systems

heisenberg weyl algebras of symmetric and antisymmetric bosons all the polynomials in symmetric 2 and antisymmetric 11 u n bosons are constructed in u n bases and u n reduced matrix elements for the bosons between polynomial basis states are computed applications to representation theory of lie groups paired fermion and boson physics are briefly discussed

coherent states on the m sheeted covering group of su 1 1 coherent states associated with the m sheeted covering group of su 1 1 are considered and such properties as overcompleteness and resolution of the identity are studied they are used to define analytic representations in which the transformations of the m sheeted covering group of su 1 1 are implemented as extended mobius conformal mappings applications of this formalism in the study of hamiltonians that describe m particle clustering are also considered

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

spectral functions special functions and the selberg zeta function the functional determinant of an eigenvalue sequence as defined by zeta regularization can be simply evaluated by quadratures we apply this procedure to the selberg trace formula for a compact riemann surface to find a factorization of the selberg zeta function into two functional determinants respectively related to the laplacian on the compact surface itself and on the sphere we also apply our formalism to various explicit eigenvalue sequences reproducing in a simpler way classical results about the gamma function and the barnesg function concerning the latter our method explains its connection to the selberg zeta function and evaluates the related glaisher kinkelin constanta

infinite statistics and the su 1 1 phase operator a few years ago agarwal 1991 phys rev a 44 8398 showed that the susskind glogower phase operators expressible in terms of bose operators provide a realization of the algebra for particles obeying infinite statistics in this paper we show that the su 1 1 phase operators constructed in terms of the elements of the su 1 1 lie algebra also provide a realization of the algebra for infinite statistics there are many realizations of the su 1 1 algebra in terms of single or multimode bose operators three of which are discussed along with their corresponding phase states the susskind glogower phase operator is a special case of the su 1 1 phase operator associated with the holstein primakoff realization of su 1 1

beurling type density theorems in the unit disk we consider two equivalent density concepts for the unit disk that provide a complete description of sampling and interpolation ina n the banach space of functionsf analytic in the unit disk with 1 z 2 n f z bounded this study reveals a nyquist density a sequence of points is roughly speaking a set of sampling if and only if its density in every part of the disk is strictly larger thann and it is a set of interpolation if and only if its density in every part of the disk is strictly smaller thann similar density theorems are also obtained for weighted bergman spaces

extended self tuning algorithm this article concerns the practical implications of an extended self tuning property the extension represents a refinement of existing asymptotic self tuning properties in the sense that it allows the designer to make arbitrary assumptions concerning the disturbance dynamics the important practical consequence of this is that a simple pole assignment self tuner may now be designed which combines servo tracking and regulatory closed loop criteria in the pure regulation case a priori parametrization of the noise dynamics can be used to aid convergence of the self tuning algorithm in addition an implicit pole assignment regulator is easily formulated from the extended self tuner

an integral transform related to quantization ii some mathematical properties we study in more detail the mathematical properties of the integral transform relating the matrix elements between coherent states of a quantum operator to the corresponding classical function explicit families of hilbert spaces are constructed between which the integral transform is an isomorphism

hilbert spaces of analytic functions and representations of the positive discrete series of sp 6 r hilbert spaces of analytic functions are constructed which carry irreducible representations of the positive discrete series of sp 6 r

analytic representations based on su 3 coherent states and robertson intelligent states robertson intelligent states which minimize the schrodinger robertson uncertainty relation are constructed as eigenstates of a linear combination of weyl generators of the su 3 algebra the construction is based on the analytic representations of su 3 coherent states new classes of coherent and squeezed states are explicitly derived

singularity free adaptive pole placement for second order systems abstract this paper proposes a new adaptive pole placement control scheme which overcomes the crucial singularity problem in indirect adaptive control that is it guarantees the controllability of the estimated plant model allowing the calculation of the controller parameters without introducing persistency of excitation into the system the control scheme is applicable to either minimum or non minimum phase systems and guarantees the closed loop stability of the controlled system detailed analysis is given for second order systems

extension of the barut girardello coherent state and path integral we extend the barut girardello coherent state for the representation of su 1 1 to the coherent state for a representation of u n 1 and construct the measure we also construct a path integral formula for some hamiltonian

quantum algebras and q special functions related to coherent states maps of the disc the quantum algebras generated by the coherent states maps of the disc are investigated it is shown that the analytic realization of these algebras leads to a generalized analysis which includes standard analysis as well as q analysis the applications of the analysis to star product quantizations and q special functions theory are given among others the meromorphic continuation of the generalized basic hypergeometric series is found and a reproducing measure is constructed when the series is treated as a reproducing kernel

adaptive control of nonminimum phase systems recent papers have established global convergence for a class of adaptive control algorithms for discrete time linear dynamic systems however in most cases studied to date it has been assumed that the system is stably invertible this assumption plays a major role in the proofs of convergence in this paper we consider the more general case in which it is not assumed that the system is either stable or stably invertible we establish local convergence for a class of adaptive control algorithms applied to general discrete deterministic linear time invariant systems by convergence in this context we mean that the system inputs and outputs remain bounded for all time and the closed loop poles are effectively assigned in the limit for a given desired trajectory

rational von neumann lattices a rational von neumann lattice is defined as a lattice in phase space with the constants a and b in the x and p directions given by a ratio of integers zeros of harmonic oscillator functions in the kq representation on such lattices are found it is shown that the number of zeros of the kq function determines the number of states by which a set on a von neumann lattice is overcomplete interesting relations between theta functions are derived on the basis of their connection with the harmonic oscillator states in the kq representation

su 2 coherent states on an m sheeted covering of the sphere su 2 coherent states on an m sheeted covering of the sphere are introduced and properties like overcompleteness and resolution of the identity are studied operators j m j m jz m that obey the su 2 algebra but shift the jn states by m steps are considered and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the standard su 2 coherent states with respect to the usual angular momentum operators j j jz an extended su 2 bargmann representation on an m sheeted sphere is introduced in which the transformations of an m sheeted covering of the su 2 group are implemented as extended mobius conformal mappings the formalism is applied in the study of hamiltonians that contain the operators j m j m jz m and describe processes where the state of a particle is shifted by m steps the method is also used in the context of both the holstein primakoff and schwinger representation of su 2

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

the continuum random tree iii let mathscr r k k geq 1 be random trees with k leaves satisfying a consistency condition removing a random leaf from mathscr r k gives mathscr r k 1 then under an extra condition this family determines a random continuum tree mathscr l which it is convenient to represent as a random subset of l 1 this leads to an abstract notion of convergence in distribution as n rightarrow infty of rescaled random trees mathscr j n on n vertices to a limit continuum random tree mathscr l the notion is based upon the assumption that for fixed k the subtrees of mathscr j n determined by k randomly chosen vertices converge to mathscr r k as our main example under mild conditions on the offspring distribution the family tree of a galton watson branching process conditioned on total population size equal to n can be rescaled to converge to a limit continuum random tree which can be constructed from brownian excursion

coherent states on the m sheeted complex plane coherent states on the m sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied operators am am which create and annihilate clusters of m particles are considered and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the ordinary glauber coherent states with respect to a a an extended bargmann representation in the m sheeted complex plane and p and q representations with respect to our coherent states are studied applications of this formalism in the study of hamiltonians that describe m particle clustering are also considered