dynamical noether invariants for time dependent nonlinear systems dynamical invariants are derived for time dependent systems with nonlinear equations of motion including nonharmonic damped systems the concept of a dynamical algebra is discussed and its utility for the construction of dynamical invariants for nonharmonic systems is demonstrated finally we show the existence of dynamical invariants for some nonlinear quantum systems

comment on a note on the construction of the ermakov lewis invariant we show that the basic results in the paper referred to in the title moyo s and leach p g l 2002 j phys a math gen 35 5333 45 concerning the derivation of the ermakov invariant from noether symmetry methods are not new

gauge transformation approach to the exact solution of a generalized harmonic oscillator the exact solution and the invariant operator of a generalized harmonic oscillator are obtained by performing three consecutive gauge transformations on the time dependent schrodinger equation in contrast to previous results they depend only on solutions of a linear differential equation for the associated classical harmonic oscillator non adiabatic and adiabatic berry phases for the system are calculated on the basis of the exact solution

multiparticle susy quantum mechanics and representations of the permutation group the method of multidimensional susy quantum mechanics is applied to the investigation of supersymmetrical n particle systems on a line for the case of separable centre of mass motion new decomposition of the super hamiltonian into block diagonal form with elementary matrix components is constructed matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreducible representations of the permutation group sn which correspond to the young tableaux n m 1m the connections with known generalizations of n particle calogero and sutherland models are established

the barrier transmission problem treated by the amplitude phase method and expressed in terms of an invariant of the ermakov lewis type transmission and reflection of a quantal particle by a single hump potential barrier are analysed by means of an amplitude phase decomposition of the wavefunction on both sides of the barrier the amplitude phase analysis of the wavefunction provides a particular invariant of the ermakov lewis type which originates in the matching process the transmission and reflection coefficients turn out to be simple functions of this invariant numerical calculations of the invariant for an eckart epstein potential barrier provide very accurate results

integrability in time dependent systems with one degree of freedom the notion of integrability is discussed for classical nonautonomous systems with one degree of freedom the analysis is focused on models which are linearly spanned by finite lie algebras by constructing the autonomous extension of the time dependent hamiltonian we prove the existence of two invariants in involution which are shown to obey the criterion of functional independence the implication of this result is that chaotic motion cannot exist in these systems in addition if the invariant manifold is compact then the system is liouville integrable as an application we discuss regimes of integrability in models of dynamical tunneling and parametric resonance and in the dynamics of two level systems under generic classical fields a corresponding quantum algebraic structure is shown to exist which satisfies analog conditions of liouville integrability and reproduces the classical dynamics in an appropriate limit within the weyl wigner formalism the quantum analog is then conjectured to be integrable as well

the algebraic structure of generalized ermakov systems in three dimensions the characteristic algebra of generalized ermakov systems is sl 2 r the structure of these systems in three dimensions is obtained a subset in the form of an equation of motion with the additional requirement of so 3 symmetry is studied it includes the classical equation of the magnetic monopole the existence of three vectors of poincare type is established consideration is given to weak generalized ermakov systems in which the symmetry breaking occurs in the radial equation

explanatory and pragmatic estimates of the treatment effect when deviations from allocated treatment occur abstract in a randomized clinical trial comparing two treatments it can happen that certain patients receive the treatment other than that determined by random allocation significance testing is usually performed by intention to treat that is comparison of groups as determined by random allocation the difference between the mean values of the outcome variable for these two groups estimates the difference in practical use between two treatment policies corresponding to a pragmatic approach an attenuation factor can then be used to obtain an estimate of the underlying difference in effectiveness between the two treatments corresponding to an explanatory paradigm thus two distinct estimates are obtained in many instances both are valid but have distinct interpretations correspondingly in planning sample size requirements when deviations from allocated treatment can be anticipated the target treatment difference may be understood in either an explanatory or a pragmatic sense for the sample size assessment method it is necessary to take this distinction into account

thermodynamics of the standard quantum harmonic oscillator of time dependent frequency with and without inverse quadratic potential making use of a dynamical invariant operator we obtain a quantum mechanical solution of a damped harmonic oscillator having time dependent frequency with and without inverse quadratic potential we confirm that the uncertainty relation is always larger than 2 in both the number and thermal state we obtain a density operator satisfying the liouville von neumann equation and use its diagonal elements to calculate various expectation values in the thermal state

on the hamiltonian structure of ermakov systems a canonical hamiltonian formalism is derived for a class of ermakov systems specified by several different frequency functions this class of systems comprises all known cases of hamiltonian ermakov systems and can always be reduced to quadratures the hamiltonian structure is explored to find exact solutions for the calogero system and for a non central potential with dynamic symmetry some generalizations of these systems possessing exact solutions are also identified and solved

lie families theory and applications we analyze the families of non autonomous systems of first order ordinary differential equations admitting a common time dependent superposition rule i e a time dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants we next study the relations of these families called lie families with the theory of lie and quasi lie systems and apply our theory to provide common time dependent superposition rules for certain lie families

an exact propagator for a time dependent harmonic oscillator with a time dependent inverse square potential using feynman s polygonal paths for path integrals the exact evaluation of the propagator for a time dependent harmonic oscillator with a time dependent inverse square potential becomes possible the propagator at and beyond caustics is then evaluated by including the maslov correction factor finally the authors obtain the wavefunctions for the propagator obtained

closed form approximations to the reml estimator of a variance ratio or heritability in a mixed linear model in this article we estimate heritability or intraclass correlation in a mixed linear model having two sources of variation in most applications the commonly used restricted maximum likelihood reml estimator can only be obtained via an iterative approach in some cases the algorithm used to compute reml estimates may be slow or may even fail to converge we develop a set of closed form approximations to the reml estimator and the performance of these estimators is compared with that of the reml estimator we provide guidelines regarding how to choose the estimator that best approximates the reml estimator examples presented in the article suggest that the closed form estimators compete with and in some cases outperform the reml estimator

feynman propagator for time dependent lagrangians possessing an invariant quadratic in momentum a class of time dependent classical lagrangians possessing an invariant quadratic in momentum is considered from a quantal point of view quantum mechanics is introduced through the feynman propagator defined as a path integral involving the classical action it is shown without carrying out an explicit path integration that the propagator for such a time dependent system is related to the propagator of an associated time independent problem the expansion of the propagator in terms of the eigenfunctions of the invariant operator is derived and the equivalence of the present theory to that of lewis and reisenfeld 1969 is discussed explicit analytic forms of propagators are obtained for some cases to illustrate the application of the present approach

exact solutions for the general nonstationary oscillator with a singular perturbation three linearly independent hermitian invariants for the nonstationary generalized singular oscillator so are constructed and their complex linear combination is diagonalized the constructed family of eigenstates contains as subsets all previously obtained solutions for the so and includes all robertson and schrodinger intelligent states for the three invariants it is shown that the constructed analogues of the su 1 1 group related coherent states for the so minimize the robertson and schrodinger uncertainty relations for the three invariants and for every pair of them simultaneously the squeezing properties of the new states are briefly discussed

generalized hamiltonian structures for ermakov systems we construct poisson structures for ermakov systems using the ermakov invariant as the hamiltonian two classes of poisson structures are obtained one of them is degenerate in which case we derive the casimir functions in some situations the existence of casimir functions can give rise to superintegrable ermakov systems finally we characterize the cases where linearization of the equations of motion is possible

partially solvable quantum many body problems in d dimensional space d 1 2 3 a simple technique employed almost three decades ago to manufacture partially solvable quantum many body problems is revisited a quantum problem is partially solvable if only some of its eigenvalues and eigenfunctions can be exhibited the models thereby generated are characterized by hamiltonians of normal form i e standard kinetic plus momentum independent potential energy in most cases the latter features three body in addition to two body and one body interactions the setting refers to d dimensional space the examples focus on d 1 d 2 and d 2 and include generalizations of and additional results on cases recently discussed in the literature as well as new models

on analysis of variance in the mixed model an analysis of variance anova is defined to be a partition of the total sum of squares into independent terms which when suitably scaled are chisquared variables a partition of less than the total sum of squares but with these properties will often suffice and is referred to as a partial anova conditions for an anova and for partial anovas selected to contain only specific parameters are given implications for estimation of variance components from an anova are also discussed these results are largely an extension of work by graybill and hultquist 1961 with unbalanced data conditions for an anova and the number of terms in it both can depend on which effects in the model are fixed and which are random this is not taken into account by those procedures for partitioning a sum of squares which distinguish between random and fixed effects only in the calculation of expected mean squares several examples are given

confidence intervals for a variance ratio or for heritability in an unbalanced mixed linear model a procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects this procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability the confidence interval can be defined in terms of the output of a least squares analysis it can be computed by a graphical or iterative technique requiring the diagonalization of an m x m matrix or alternatively the inversion of a number of m x m matrices confidence intervals that are approximate can be obtained with much less computational burden using either of two approaches the various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects corresponding to each interval procedure is a significance test and one or more estimators

two stage instrumental variable methods for estimating the causal odds ratio analysis of bias we present closed form expressions of asymptotic bias for the causal odds ratio from two estimation approaches of instrumental variable logistic regression i the two stage predictor substitution 2sps method and ii the two stage residual inclusion 2sri approach under the 2sps approach the first stage model yields the predicted value of treatment as a function of an instrument and covariates and in the second stage model for the outcome this predicted value replaces the observed value of treatment as a covariate under the 2sri approach the first stage is the same but the residual term of the first stage regression is included in the second stage regression retaining the observed treatment as a covariate our bias assessment is for a different context from that of terza j health econ 2008 27 3 531 543 who focused on the causal odds ratio conditional on the unmeasured confounder whereas we focus on the causal odds ratio among compliers under the principal stratification framework our closed form bias results show that the 2sps logistic regression generates asymptotically biased estimates of this causal odds ratio when there is no unmeasured confounding and that this bias increases with increasing unmeasured confounding the 2sri logistic regression is asymptotically unbiased when there is no unmeasured confounding but when there is unmeasured confounding there is bias and it increases with increasing unmeasured confounding the closed form bias results provide guidance for using these iv logistic regression methods our simulation results are consistent with our closed form analytic results under different combinations of parameter settings

characteristic uncertainty relations new uncertainty relations for n observables are established the relations take the invariant form of inequalities between the characteristic coefficients of order r rd 1 2 n of the uncertainty matrix and the matrix of mean commutators of the observables it is shown that the second and third order characteristic inequalities for the three generators of su 1 1 and su 2 are minimized in the corresponding group related coherent states with maximal symmetry

bayesian inference for causal effects in randomized experiments with noncompliance for most of this century randomization has been a cornerstone of scientific experimentation especially when dealing with humans as experimental units in practice however noncompliance is relatively common with human subjects complicating traditional theories of inference that require adherence to the random treatment assignment in this paper we present bayesian inferential methods for causal estimands in the presence of noncompliance when the binary treatment assignment is random and hence ignorable but the binary treatment received is not ignorable we assume that both the treatment assigned and the treatment received are observed we describe posterior estimation using em and data augmentation algorithms also we investigate the role of two assumptions often made in econometric instrumental variables analyses the exclusion restriction and the monotonicity assumption without which the likelihood functions generally have substantial regions of maxima we apply our procedures to real and artificial data thereby demonstrating the technology and showing that our new methods can yield valid inferences that differ in practically important ways from those based on previous methods for analysis in the presence of noncompliance including intention to treat analyses and analyses based on econometric instrumental variables techniques finally we perform a simulation to investigate the operating characteristics of the competing procedures in a simple setting which indicates relatively dramatic improvements in frequency operating characteristics attainable using our bayesian procedures

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

unitary transformation approach to the exact solution for the singular oscillator by performing unitary transformations the exact solution of the time dependent singular oscillator is obtained the invariant operator and the auxiliary equation are rigorously established the non adiabatic berry s phase is calculated

coupled channel scattering and separation of coupled differential equations by generalized darboux transformations general methods for separation of coupled differential equations are applied in coupled channel scattering theory with appropriate asymptotic conditions it is shown that the problems with thresholds cannot be separated finally it is pointed out that separation of the coupled channel s wave problem without thresholds can be realized by the use of generalized darboux transformations

can milne s method work well for the coulomb like potentials we extend the improved milne s milne spline method for obtaining eigenvalues and eigenfunctions to the cases of long range and singular potentials for which we have conjectured that it is difficult to apply the method contrary to our conjecture it turned out that the method is valid also for coulomb potential and repulsive 1 xn n 2 3 type potential further we applied the method for two cases for which the solutions are not known in order to investigate the stability of the multi dimensional universe it has been shown that the extra dimensional internal space of our universe is not stable in classical einstein gravity as well as canonically quantized one two possibilities for stabilization were investigated i noncanonically quantized einstein gravity and ii canonically quantized higher curvature gravity it has been suggested that the space is stable by qualitative and approximate methods exact analytical treatment is very difficult so that numerical investigation is highly desirable numerical investigation shows that the space is stable with sufficient reliability

on the effect of treatment among would be treatment compliers an analysis of the multiple risk factor intervention trial abstract the multiple risk factor intervention trial mrfit was a major trial that examined the efficacy of a multifactor intervention on reducing coronary heart disease mortality after a mean follow up of 7 years treatment was not significantly different from control and extensive investigation was undertaken to explain the result this article examines how the effect of treatment varies with compliance with treatment the basic idea is that the binary characteristic would comply with treatment is balanced between groups by randomization even though it is unobservable before randomization and only observed after randomization in the treatment group using baseline covariates a prediction model for this observed characteristic is developed in the treatment group and estimated probabilities of treatment compliance are calculated for all patients in both groups the assumption that patients who would not comply with treatment must have the same mean response in both groups is avoided two methods f

dissipative quantum dynamics solution of the generalized von neumann equation for the damped harmonic oscillator a recently proposed generalized von neumann equation describing dissipative time evolution of quantum systems is applied to a damped and driven harmonic oscillator utilizing lie algebraic methods the nonlinear operator equation is solved and from this solution the behaviour of the mean value x is extracted including both amplitude and phaseshift relative to the driving force a differential equation for x is derived and the damping constant is identified

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

estimating efficacy in trials with selective crossover when one arm in a trial has a worse early endpoint such as recurrence a data monitoring committee might recommend that all participants are offered the apparently superior treatment the resultant crossover makes it difficult to measure differences between arms thereafter including for longer term endpoints such as mortality and disease specific mortality in this paper we consider estimators of the efficacy of treatment on those who would not cross over if randomised to the apparently inferior arm binomial and proportional hazards maximum likelihood estimators are developed the binomial estimator is applied to analysis of a breast cancer treatment trial and compared with intention to treat and inverse probability weighting estimators full and partial likelihood proportional hazard model estimators are assessed through computer simulations where they had similar bias and variance the new efficacy estimators extend those for all or none compliance to this important problem 2017 the authors statistics in medicine published by john wiley sons ltd

semi canonical quantisation of dissipative equations in order to avoid the known problems of canonical quantisation of the dissipative equation mx alpha xn delta v delta x 0 a modified approach is proposed it is based on the classically conserved quantity e mx2 2 v x alpha integral xndx rather than on a hamilton function linear quadratic and cubic damping n 1 2 and 3 are discussed explicitly for n 1 and n 3 normalisable one particle states cannot be stable however for quadratic friction which is classically a reversible process the author shows using the example of the harmonic oscillator that stable normalisable eigenstates can exist

on geometric phases and dynamical invariants a formalism is developed for calculating berry phases for nonadiabatic time periodic quantum systems when a dynamical invariant is known it is found that when the invariant is periodic and has a nondegenerate spectrum this method allows a convenient way to obtain generalized berry phases and the proper cyclic initial states the method is applied to the generalized harmonic oscillator and the two level system where the invariant operators are explicitly constructed formulae for the conventional berry s phases are readily obtained by taking the adiabatic limit of the exact results

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

robertson intelligent states the diagonalization of the uncertainty matrix and the minimization of robertson inequality for n observables are considered it is proved that for even n this relation is minimized in states which are eigenstates of n 2 independent complex linear combinations of the observables in the case of canonical observables this eigenvalue condition is also necessary such minimizing states are called robertson intelligent states ris the group related coherent states cs with maximal symmetry for semisimple lie groups are a particular case of ris for the quadratures of weyl generators explicit constructions of ris are considered for operators of su 1 1 su 2 and sp n r algebras unlike the group related cs ris can exhibit strong squeezing of group generators multimode squared amplitude squeezed states are naturally introduced as sp n r ris it is shown that the uncertainty matrices for quadratures of q deformed boson operators q 0 and of any k power of are positive definite and can be diagonalized by symplectic linear transformations

model selection criterion for causal parameters in structural mean models based on a quasi likelihood summary structural mean models smms have been proposed for estimating causal parameters in the presence of nonignorable non compliance in clinical trials to obtain a valid causal estimate we must impose several assumptions one of these is the correct specification of the structural model building on pan s work 2001 biometrics 57 120 125 on developing a model selection criterion for generalized estimating equations we propose a new approach for model selection of smms based on a quasi likelihood we provide a formal model selection criterion that is an extension of akaike s information criterion using subset selection of baseline covariates our method allows us to understand whether the treatment effect varies across the available baseline covariate levels and or to quantify the treatment effect on a specific covariates level to target specific individuals to maximize treatment benefit we present simulation results in which our method performs reasonably well compared to other testing methods in terms of both the probability of selecting the correct model and the predictive performances of the individual treatment effects we use a large randomized clinical trial of pravastatin as a motivation

correlation functions of the nonstationary quantum singular oscillator the exact density matrix elements and the correlation functions of the one dimensional non stationary singular oscillator the potential u x t omega 2 t x2 2 g x2 excited from the thermodynamic equilibrium states are obtained generating functions for rho nm and also for transition probabilities are constructed

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

regaining power lost by non compliance via full probability modelling non compliance or non receipt of randomized intervention is a common problem in randomized controlled trials an intention to treat itt analysis which compares individuals as randomized under estimates the efficacy of the intervention and leads to a loss of power we explore the possibility of regaining some of this power in a setting with all or nothing compliance without making any assumptions about the comparability of compliers and non compliers efficacy may be specified as the complier average causal effect cace which is the difference in mean outcome among compliers compliance is only partially observed but under an exclusion restriction assumption the cace may be estimated using maximum likelihood in order to quantify the possible gain in power we derive an expression for the asymptotic relative efficiency are of the cace relative to the itt effect with a normally distributed outcome under the assumption of a common cace across covariate strata the cace estimate is at least as powerful as itt analysis the inclusion of covariates that predict compliance enables an additional gain in power which is investigated algebraically using data from three clinical trials we obtain values of the are ranging up to 1 05 due to covariates alone and 1 13 due to cace modelling alone corresponding to gains in power of up to 5 per cent this implies that a large gain in power obtained using as treated or per protocol analyses is likely to be due to the strong and often implausible assumptions such analyses require to be valid

a note on generalization of the lewis invariant and the ermakov systems in this paper we examine several possible generalizations of the well known lewis invariant and the ermakov systems the analysis relies on the application of the theorem of emmy noether the problem of constructing lewis type invariants is reduced to a problem of solving a single partial differential equation the so called potential equation within this approach the role of the auxiliary equation is clarified by an analysis of linear systems generalization of the ermakov type procedure for derivation of the lewis invariant is also discussed moreover different forms of general solution of the problem will be provided which extend the range of possible applications of the analysis

on the quantization of linearly damped harmonic oscillator using the equation of motion for a linearly damped harmonic oscillator as fundamental equation a condition has been obtained that must be satisfied by its lagrangian and a number of functional forms has been critically investigated the lagrangians that successfully describe a classical damped oscillator have been quantized using feynman s elegant path integral method however it is found that the expectation value of energy of the damped oscillator in all the cases becomes infinitely large for t ruling out the possibility of treating the damped quantum system as a one body problem

nonlinear schrodinger type field equation for the description of dissipative systems iii frictionally damped free motion as an example for an aperiodic motion a new theory for the description of dissipative systems by nonlinear schrodinger type field equations nlse s with logarithmic nonlinearity which has been recently developed by the authors is applied to investigate the frictionally damped free motion and similar spatially unrestricted aperiodic problems wave packet solutions as well as time dependent wave function solutions are derived and discussed in the limit of vanishing friction friction constant 0 these solutions turn into the well known solutions of the respective linear schrodinger field equation the same applies to the mean values of position momentum and energy as well as to the uncertainty product of position and momentum for 0 however interesting new effects appear in contrast to the linear theory the uncertainty product of position and momentum does not diverge any more for infinitely long times t but asymptotically approaches a definite constant value which depends on characteristic parameters of the system like its ma

dynamical algebraic approach and invariants for time dependent hamiltonian systems in two dimensions dynamical invariants for time dependent td oscillator systems in two dimensions are derived the applications of the dynamical algebraic approach known already for one dimensional td systems r s kaushal and h j korsch j math phys 22 1904 1981 are now carried out to two dimensional td systems a possible generalization of ermakov systems to higher dimensions is discussed

fiducial intervals for variance components in an unbalanced two component normal mixed linear model in this article we propose a new method for constructing confidence intervals for 2 2 and the intraclass correlation 2 2 e2 in a two component mixed effects linear model this method is based on an extension of r a fisher s fiducial argument we conducted a simulation study to compare the resulting interval estimates with other competing confidence interval procedures from the literature our results demonstrate that the proposed fiducial intervals have satisfactory performance in terms of coverage probability as well as shorter average confidence interval lengths overall we also prove that these fiducial intervals have asymptotically exact frequentist coverage probability the computations for the proposed procedures are illustrated using real data examples

the ermakov lewis invariants for coupled linear oscillators we consider n coupled linear oscillators with time dependent coefficients an exact complex amplitude real phase decomposition of the oscillatory motion is constructed this decomposition is further used to derive n exact constants of motion which generalize the so called ermakov lewis invariant of a single oscillator in the floquet problem of periodic oscillator coefficients we discuss the existence of periodic complex amplitude functions in terms of existing floquet solutions

exactly solvable three body systems with internal degrees of freedom the approach of multi dimensional susy quantum mechanics is used in an explicit construction of exactly solvable three body and quasi exactly solvable n body matrix problems on a line from intertwining relations with time dependent operators we build exactly solvable non stationary scalar and 2 2 matrix three body models which are time dependent extensions of the calogero model finally we investigate the invariant operators associated with these systems

ermakov and non ermakov systems in quantum dissipative models via the hydrodynamical formulation of quantum mechanics a unified protocol to treat the quantum time dependent harmonic oscillator with friction is presented described by two different models an explicitly time dependent linear schrodinger equation caldirola kanai model and a logarithmic nonlinear schrodinger equation kostin model for the former model an ermakov system that makes it possible to obtain an invariant of ermakov lewis type is derived for the latter model a non ermakov system is derived instead and it is shown that neither an exact nor an approximate invariant of ermakov lewis type exists

time dependent normal form hamiltonian for dynamical equilibria a new time dependent normal form procedure for dynamical equilibria undergoing parametric excitation of one dimensional 1d hamiltonian systems is developed with the method of lie transforms the expansion is based on the lewis invariant for the linearized motion the time dependent hamiltonian normal form reduces smoothly to the usual representation in the autonomous limit illustrative examples of the formalism are focused on time periodic systems and the dynamics of hamiltonian switching

intertwining relations for the matrix calogero like models supersymmetry and shape invariance we investigate the intertwining relations for n particle calogero like models with internal degrees of freedom starting from the well known dunkl polychronakos operators we construct a new type of local without exchange operation differential operator these operators intertwine the matrix hamiltonians corresponding to irreducible representations of the permutation group sn in particular cases this method allows us to construct a new class of exactly solvable dirac like equations and a new class of matrix models with shape invariance we establish a connection with the approach of multi dimensional supersymmetric quantum mechanics

note on invariants for uncoupled ermakov systems several invariants for an ermakov system consisting of a parametric oscillator and a milne oscillator in one dimension are derived this system appears in amplitude phase analysis of parametric oscillator solutions first and second order invariants for such a system are derived using the wronskian relations of a fundamental pair of parametric oscillator solutions in this way wronskian invariants of the parametric oscillator system alone imply ermakov lewis type invariants for the combined ermakov system as well as invariants for the milne oscillator alone

time dependent invariant associated to nonlinear schrodinger langevin equations via the quantum hydrodynamical method a time dependent invariant associated to the quantum dissipative time dependent harmonic oscillator tdho described by two classes of nonlinear schrodinger langevin equations with the following frictional nonlinear terms is constructed i w1 i ln ln which is the schuch chung hartman frictional nonlinear term and ii w2 x x cp 1 c p 1 2 i c which includes the sussmann c 1 the hasse c 1 2 and the albrecht kostin c 0 frictional nonlinear operators the associated invariant found is exact for the schuch chung hartman and hasse models and only approximate for the sussman and albrecht kostin models

simultaneous confidence intervals for functions of variance components in random models abstract interval estimation of certain functions of variance components is of interest to research workers in all fields of applications in which the variance component model is used confidence intervals for linear functions and ratios of variance components have been proposed by several authors for the most part these intervals are approximate with unknown exact probabilities associated with their coverage in this article a technique is given for the construction of simultaneous confidence intervals for the values of all continuous functions of the variance components in a balanced general random linear model these confidence intervals are conservative that is the actual confidence level cannot be less than any preset value the proposed technique is easy to apply as it only requires the optimization of a given continuous function of the variance components over a bounded region several examples of continuous functions are considered including linear functions and ratios of variance components

exact invariants for a class of time dependent nonlinear hamiltonian systems a method of generalizing a class of invariants for a time dependent linear oscillator is developed for the motion of a mass point in one dimension with a general time dependent nonlinear potential formulas are derived for the allowable time dependent potentials and for the corresponding invariants the method by which these conclusions are reached is interesting theoretically and is explained in detail

exact confidence sets for variance components in unbalanced mixed linear models we present a general procedure for obtaining an exact confidence set for the variance components in a mixed linear model the procedure can be viewed as a generalization of the anova method used with balanced models our procedure uses as pivotal quantities quadratic forms that are distributed independently as chi squared variables these quadratic forms are constructed with reference to spaces that are orthogonal with respect to the covariance matrix of the observation vector which is a function of the variance components for balanced models these pivotal quantities simplify to multiples of the sums of squares used in the anova method an exact confidence set for the vector of ratios of the effect variances to the error variance is also presented based on the same collection of quadratic forms computing formulas for calculating approximations to these confidence sets are presented and the results of their application to several two way data sets are given

semiclassical narrow tube quantizations of time periodic hamiltonian systems an approximate semiclassical quantization procedure for time periodic hamiltonians is formulated which applies to motion near stable periodic orbits of the system corresponding to elliptic islands of the period map the theory involves canonical transformations and the use of a particular dynamical lewis invariant the basic assumption in the narrow tube approximation is the localization of the quantal wavefunction inside the elliptic islands

bounds on causal effects in three arm trials with non compliance summary the paper considers the analysis of three arm randomized trials with non compliance in these trials the average causal effects of treatments within principal strata of compliance behaviour are of interest for better understanding the effect of the treatment unfortunately even with the usual assumptions the average causal effects of treatments within principal strata are not point identified however the observable data do provide useful information on the bounds of the identification regions of the parameters of interest under two sets of assumptions we derive sharp bounds for the causal effects within principal strata for binary outcomes and construct confidence intervals to cover the identification regions the methods are illustrated by an analysis of data from a randomized study of treatments for alcohol dependence

new two dimensional quantum models partially solvable by the supersymmetrical approach new solutions for second order intertwining relations in two dimensional susy qm are found via repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation potentials obtained by this method two dimensional generalized poschl teller potentials appear to be shape invariant the recently proposed method of susy separation of variables is implemented to obtain a part of their spectra including the ground state explicit expressions for energy eigenvalues and corresponding normalizable eigenfunctions are given in an analytic form intertwining relations of higher orders are discussed

scattering s matrix derived from invariants of the ermakov lewis type an amplitude phase formula for the s matrix due to a central potential is derived the derivation makes use of invariants of the ermakov lewis type

canonical transformations and exact invariants for dissipative systems a simple treatment to the problem of finding exact invariants and related auxiliary equations for time dependent oscillators with friction is presented the treatment is based on the use of a time dependent canonical transformation and an auxiliary transformation

quasi exactly solvable problems and sl 2 algebra recently discovered quasi exactly solvable problems of quantum mechanics are shown to be related to the existence of the finite dimensional representations of the groupsl 2 q whereq r c it is proven that the bilinear formh a j j b j stand for the generators allows one to generate a set of quasi exactly solvable problems of different types including those that are already known we get in particular problems in which the spectral riemannian surface containing an infinite number of sheets is split off one or two finite sheet pieces in the general case the transitionh h d2 dx2 v x is realized with the aim of the elliptic functions all known exactly solvable quantum problems with known spectrum and factorized riemannian surface can be obtained in this approach

intertwining relations of non stationary schrodinger operators general first and higher order intertwining relations between non stationary one dimensional schrodinger operators are introduced for the first order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in an r separation of variables the fokker planck and diffusion equations are briefly considered second order intertwining operators are also discussed within a general approach however due to its complicated structure only particular solutions are given in some detail

nonlinear time dependent anharmonic oscillator asymptotic behavior and connected invariants the motion of a particle in a potential decreasing with time as x n is considered different time and space rescaling are considered in order to obtain the asymptotic solutions the validity of adiabatic invariants is discussed the classical critical case corresponds to the obtainment of self similar solutions for the quantum problem

a note on the construction of the ermakov lewis invariant we use noether symmetries to discuss the source of the ermakov lewis invariant and show that it comes from a generalized symmetry this symmetry is a lie symmetry of the invariant furthermore we use liouville s theorem to construct two integrals of the ermakov system and compute the poisson brackets of all the integrals of the system to see which ones are in involution with each other interesting observations are made

exact wavefunctions for a time dependent coulomb potential the one dimensional schrodinger equation associated with a time dependent coulomb potential is studied the invariant operator method lewis and riesenfeld and unitary transformation approach are employed to derive quantum solutions of the system we obtain an ordinary second order differential equation whose analytical exact solution has been unknown it is confirmed that the form of this equation is similar to the radial schrodinger equation for the hydrogen atom in a arbitrary strong magnetic field the qualitative properties for the eigenstates spectrum are described separately for the different values of the parameter 0 appearing in the x2 term x being the position i e 0 0 0 0 and 0 0 for the 0 0 case the eigenvalue equation of invariant operator reduces to a solvable form and consequently we have provided exact eigenstates of the time dependent hamiltonian system

weighting in instrumental variables and g estimation we propose here a simple scheme to use information on compliance and prerandomization covariates to improve analysis of randomized trials with non compliance we use the data to determine the effect of randomization on treatment received among various strata defined by pretreatment covariates when the effect of treatment received on the outcome of interest is the same across strata and pretreatment covariates predict non compliance weighting the estimating functions by the effect of randomization on treatment received can improve the precision of explanatory estimates of treatment effect and can increase the power of intent to treat tests of the null hypothesis efficiency gains under the weighting scheme are a simple increasing function of the variability of these weights such weighting schemes will often lead to improvements even when these conditions are not met we use a randomized trial of cholestyramine to illustrate these points