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

rich dynamics in a spatial predator prey model with delay in this paper we study the spatiotemporal dynamics of a diffusive holling tanner predator prey model with discrete time delay via analytically and numerically analysis we unveil six types of patterns with and without time delay among them of particular novel is the observation of linear pattern consisting of a series of parallel lines whose formation is closely related with the temporal hopf bifurcation threshold moreover we also find that larger time delay or diffusion of predator may induce the extinction of both prey and predator theoretical analysis and numerical simulations validate the well known conclusion diffusion is usually beneficial for stabilizing pattern formation yet discrete time delay plays a destabilizing role in the generation of pattern

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

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

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

chaos revealing multiplicative representation of quantum eigenstates the quantisation of the two dimensional toric and spherical phase spaces is considered in analytic coherent state representations every pure quantum state admits therein a finite multiplicative parametrisation by the zeros of its husimi function for eigenstates of quantised systems this description explicitly reflects the nature of the underlying classical dynamics in the semiclassical regime the distribution of the zeros in the phase space becomes one dimensional for integrable systems and highly spread out conceivably uniform for chaotic systems this multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems

testing for a treatment effect in the presence of nonresponders good 1979 biometrics 35 483 489 introduced a new randomization test for the two sample problem where a proportion 1 p of the treatment group does not respond to the treatment and suggested that the wilcoxon test is not effective for this situation we show to the contrary that the wilcoxon test is quite useful when p greater than or equal to 6 and point out an error in his definition of a one tailed randomization test

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

asymptotic properties of censored linear rank tests a conjecture of prentice is established which states that for censored linear rank test exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function we show that under minimal conditions asymptotically equivalent tests are obtained when either the kaplan meier altshuler or moment estimator of the survival function is used asymptotic normality is also established for a general random censorship model under the null hypothesis and for contiguous alternatives this is used to calculate efficacies and when the censoring times are i i d an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests 1 introduction prentice 1978 has constructed a general class of linear rank tests for a regression model with censored data his approach was to specify a score function for a classical linear rank test in the absence of censoring chernoff and savage 1958 hajek and sidak 1967 to construct all possible rankings of the unobserved uncensored values which were consistent with observed censored sample and then to assign to each observation the average of all possible scores it could have received in the absence of censoring giving equal weighting to each possible uncensored ranking except for a few special scoring functions notably logarithmic or power law scores these averages are unwieldy when there is appreciable censoring and prentice suggested that asymptotically equivalent tests might arise if the score function was evaluated at some suitable estimate of the survivor function this is well known to be true for uncensored data but requires further justification when censoring is present because the estimate of the survivor function is more complicated in this work we show that prentice s conjecture is true under minimal conditions and also we show that it remains true if prentice s moment estimator of the survivor function is replaced by either the kaplan meier estimator or altshuler s estimator asymptotic normality of these tests is established under a random censorship model for the null hypothesis and contiguous alternatives by martingale methods this is used to compute efficacies for a general random censorship model and asymptotic relative efficiencies for i i d potential censoring times where fully efficient linear rank tests exist asymptotic normality for general alternatives has been established in cuzick 1982 by more complicated methods

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

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

analytic representations based on su 1 1 coherent states and their applications we consider two analytic representations of the su 1 1 lie group the representation in the unit disc based on the su 1 1 perelomov coherent states and the barut girardello representation based on the eigenstates of the su 1 1 lowering generator we show that these representations are related through a laplace transform a weak resolution of the identity in terms of the perelomov su 1 1 coherent states is presented which is valid even when the bargmann index k is smaller than various applications of these results in the context of the two photon realization of su 1 1 in quantum optics are also discussed

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

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

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

phase space approach to quantum dynamics replaces the schrodinger equation for the time propagation of states of a quantized 2d spherical phase space by the dynamics of a system of n particles lying in phase space this is done through factorization formulae of an analytic function theory arising in a coherent state representation the particles being the zeroes of the quantum state for linear hamiltonians like a spin in a uniform magnetic field the motion of the particles is classical however nonlinear terms induce interactions between the particles their time propagation is studied and it is shown that contrary to integrable systems for chaotic maps they tend to fill as their classical counterpart the whole phase space in a uniform way

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

effects of demographic noise on the synchronization of a metapopulation in a fluctuating environment we use the theory of noise induced phase synchronization to analyze the effects of demographic noise on the synchronization of a metapopulation of predator prey systems within a fluctuating environment moran effect treating each local predator prey population as a stochastic urn model we derive a langevin equation for the stochastic dynamics of the metapopulation assuming each local population acts as a limit cycle oscillator in the deterministic limit we use phase reduction and averaging methods to derive the steady state probability density for pairwise phase differences between oscillators which is then used to determine the degree of synchronization of the metapopulation

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

a relationship between two forms of linear rank procedures for censored data summary this paper gives a useful relationship between two popular classes of linear rank statistics for arbitrarily right censored data the relationship allows a linear rank procedure with certain optimal properties to be transformed into the form of a procedure having established asymptotic properties under proportional hazards alternatives

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

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

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

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

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

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

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

generating kernel for the boson realisation of symplectic algebras the discussion of boson realisations of symplectic algebras requires as an essential ingredient an operator k needed for the passage from the dyson to the holstein primakoff realisation in previous papers the matrix form of k2 was derived through appropriate recursion relations in the present analysis the authors show that k2 can be determined in explicit and closed form as the overlap of coherent states of the symplectic group the matrix elements of k2 can then be obtained by expanding this overlap in terms of appropriate eigenstates

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

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

dynamics and absorption properties of stochastic equations with holder diffusion coefficients abstract in this article we characterize the dynamics and absorption properties of a class of stochastic differential equations around singular points where both the drift and diffusion functions vanish according to the holder coefficient of the diffusion function around the singular point we identify different regimes a regime where the solutions almost surely reach the singular point in finite time and regimes of exponential attraction or repulsion from the singular point stability of the absorbing state large deviations for the absorption time existence of stationary or quasi stationary distributions are discussed in particular we show that quasi stationary distributions only exist for 3 4 and for 3 4 1 no quasi stationary distribution is found and numerical simulations tend to show that the process conditioned on not being absorbed initiates an almost sure exponential convergence towards the absorbing state as is demonstrated to be true for 1 these results have several implications in the understanding of stochastic bifurcations and we completely unfold two generic situations the pitchfork and saddle node bifurcations and discuss the hopf bifurcation in the appendix

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

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

generalized hypergeometric coherent states we introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions we call them generalized hypergeometric states in general and generalized hypergeometric coherent states in particular if they allow a resolution of unity depending on the domain of convergence of the generalized hypergeometric functions we distinguish generalized hypergeometric states on the plane the open unit disc and the unit circle all states are eigenstates of suitably defined lowering operators we then study their photon number statistics and phase properties as revealed by the husimi and pegg barnett phase distributions on the basis of the generalized hypergeometric coherent states we introduce new analytic representations of arbitrary quantum states in bargmann and hardy spaces as well as generalized hypergeometric husimi distributions and corresponding phase distributions

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

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

competition between one and two photon absorption processes we obtain an exact analytical solution to the master equation for the diagonal density matrix elements of the one mode quantized field when both one and two photon absorption processes are present explicit expressions for the time dependences of the factorial moments are found the special cases of the initial fock s binomial negative binomial thermal and coherent states as well as of their even odd counterparts are considered in detail the existence of the universal time dependent distribution of initially highly excited states is discovered and simple explicit expressions are given for some specific values of parameters this distribution holds for times exceeding the transition time of the order of being the two photon absorption coefficient and the initial mean photon number respectively the transition time from any initial state to the ground state is shown to be finite even for highly excited states provided that although the final stage of evolution is characterized by the sub poissonian statistics for any initial state mandel s parameter is shown to be very sensitive to small differences in high order initial factorial moments at the intermediate stage

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

linear rank tests for the nonresponders problem with censored data summary in a two sample setting a two parameter mixture model is postulated for the treated patients where a proportion of the patients improve and the remaining proportion of nonresponders behave like the control patients the response is subject to random censoring censored data versions of linear rank statistics are developed in order to detect improvement due to treatment the tests are compared to standard tests such as the logrank test in terms of asymptotic relative efficiency empirical power and performance on real data

two sample rank tests for detecting changes that occur in a small proportion of the treated population in the course of studying a biological phenomenon thought to be a precursor to chromosome breakage researchers have found that treatments sometimes produce a higher proportion of outliers than do controls our examples pertain to smokers and patients undergoing chemotherapy although the statistical methods developed here would apply to subjects exposed to any other health hazard we formulate the problem in a nonparametric setting locally most powerful rank tests are obtained for mixture alternatives in one instance the approximate scores test has the simple form of counting the number of treatment responses above a combined sample percentile our test statistics are compared to the wilcoxon and normal scores tests using empirical power studies and asymptotic efficiencies

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

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

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

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

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

the holomorphic discrete series for affine symmetric spaces i abstract let x g h be an affine symmetric space we study part of the discrete spectrum of l2 x for x of hermitian type a notion we define in analogy with the group case in particular we find intertwining operators from the scalar holomorphic discrete series of g which is automatically of hermitian type into l2 x the multiplicity of this series is then shown to be one by a uniqueness result for the intertwining operators finally we investigate the complexification x c of x and show that the discrete series in question admits holomorphic continuation into a certain domain in x c

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