nonexistence of formal first integrals for nonlinear systems under the case of resonance in this paper by using the normal form theory we give some criteria of the nonexistence of formal first integrals for nonlinear systems under resonance as application we also give a criterion for nonintegrability of a family of higher order perturbation systems of certain integrable hamiltonian systems

equivalence of hardy submodules generated by polynomials abstract in this paper we obtain a complete classification under unitary equivalence for hardy submodules on the polydisk which are generated by ideals of polynomials let i be an ideal of polynomials in n variables since i is generated by finitely many polynomials i has a greatest common divisor p so i can be uniquely written as i p l which is called the beurling form of i let i 1 p 1 l 1 i 2 p 2 l 2 we prove that i 1 and i 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n and p 1 l 1 p 1 l 2 consequently two principal submodules p 1 and p 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n furthermore we give a complete similarity classification for submodules generated by homogeneous ideals finally we point out that in the case of the hardy module on the unit ball i 1 and i 2 are unitarily equivalent if and only if they are equal if i 1 and i 2 are homogeneous ideals then i 1 and i 2 are quasi similar if and only if i 1 i 2

nonparametric inference for periodic sequences this article proposes a nonparametric method for estimating the period and values of a periodic sequence when the data are evenly spaced in time the period is estimated by a leave out one cycle version of cross validation cv and complements the periodogram a widely used tool for period estimation the cv method is computationally simple and implicitly penalizes multiples of the smallest period leading to a virtually consistent estimator of integer periods this estimator is investigated both theoretically and by simulation we also propose a nonparametric test of the null hypothesis that the data have constant mean against the alternative that the sequence of means is periodic finally our methodology is demonstrated on three well known time series the sunspots and lynx trapping data and the el nino series of sea surface temperatures

defect operators defect functions and defect indices for analytic submodules abstract this paper mainly concerns defect operators and defect functions of hardy submodules bergman submodules over the unit ball and hardy submodules over the polydisk the defect operator function carries key information about operator theory function theory and structure of analytic submodules the problem when a submodule has finite defect is attacked for both hardy submodules and bergman submodules our interest will be in submodules generated by polynomials the reason for choosing such submodules is to understand the interaction of operator theory function theory and algebraic geometry

characteristic spaces and rigidity for analytic hilbert modules abstract it is well known that a polynomial in one variable is completely determined by its zeros counting multiplicities we generalize this result to an ideal of polynomials in several variables by introducing the characteristic spaces of the ideal one finds that the ideal is completely determined by its characteristic spaces on a characteristic set in particular a primary ideal is completely determined by its characteristic space at any zero point some straightforward applications of the above results yield the algebraic reduction theorem for analytic hilbert modules in several variables also we obtain some general rigidity results for analytic hilbert modules by using the techniques of af envelopes of analytic hilbert modules

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

period function for a class of hamiltonian systems abstract this paper studies the period function of the class of hamiltonian systems x h y y h x where h x y has the special form h x y f x g y and the origin is a non degenerate center more concretely if t h denotes the period of the periodic orbit contained in h x y h we solve the inverse problem of characterizing all systems with a given function t h we also characterize the limiting behaviour of t at infinity when the origin is a global center and apply this result to prove among other results that there are no nonlinear polynomial isochronous centers in this family

operator theory in the hardy space over the bidisk iii this paper is a continuation of a project of developing a systematic operator theory inh2 d2 a large part of it is devoted to a study ofevaluation operator which is a very useful tool in the theory a number of elementary properties of the evaluation operator are exhibited and these properties are used to derive results in other topics such as interpretation of characteristic opertor function inh2 d2 spectral equivalence compactness compressions of shift operators etc even though some results reflect the two variable nature ofh2 d2 the goal of this paper is to manifest a close tie between the operator theory inh2 d2 and classical single operator theory the unilateral shift of a finite multiplicity and the bergman shift will be used as examples to illustrate some of the results

incorporating prior theory in covariance structure analysis a bayesian approach a bayesian approach to the testing of competing covariance structures is developed the method provides approximate posterior probablities for each model under consideration without prior specification of individual parameter distributions the method is based on ayesian updating using cross validated pseudo likelihoods given that the observed variables are the samefor all competing models the approximate posterior probabilities may be obtained easily from the chi square values and other known constants using only a hand calculator the approach is illustrated using and example which illustrates how the prior probabilities can alter the results concerning which model specification is preferred

on the distributional properties of model selection criteria abstract it is commonly accepted that statistical modeling should follow the parsimony principle namely that simple models should be given priority whenever possible but little quantitative knowledge is known concerning the amount of penalty for complexity regarded as allowable we try to understand the parsimony principle in the context of model selection in particular the generalized final prediction error criterion is considered and we argue that the penalty term should be chosen between 1 5 and 5 for most practical situations applying our results to the cross validation criterion we obtain insights into how the partition of data should be done we also discuss the small sample performance of our methods

nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems abstract the aim of this paper is to study the normal forms of nonautonomous differential systems for doing so we first investigate the nonuniform dichotomy spectrum of the linear evolution operators that admit a nonuniform exponential dichotomy where the linear evolution operators are defined by nonautonomous differential equations x a t x in r n using the nonuniform dichotomy spectrum we obtain the normal forms of the nonautonomous linear differential equations finally we establish the finite jet normal forms of the nonlinear differential systems x a t x f t x in r n which is based on the nonuniform dichotomy spectrum and the normal forms of the nonautonomous linear systems

a note on local integrability of differential systems abstract for an n dimensional local analytic differential system x a x f x with f x o x 2 the poincare nonintegrability theorem states that if the eigenvalues of a are not resonant the system does not have an analytic or a formal first integral in a neighborhood of the origin this result was extended in 2003 to the case when a admits one zero eigenvalue and the other are non resonant for n 2 the system has an analytic first integral at the origin if and only if the origin is a non isolated singular point for n 2 the system has a formal first integral at the origin if and only if the origin is not an isolated singular point however the question of whether the system has an analytic first integral at the origin provided that the origin is not an isolated singular point remains open

convergence versus integrability in birkhoff normal form we show that any analytically integrable hamiltonian system near an equilibrium point admits a convergent birkhoff normalization the proof is based on a new geometric approach to the topic

model selection criteria an investigation of relative accuracy posterior probabilities and combinations of criteria we investigate the performance of empirical criteria for comparing and selecting quantitative models from among a candidate set a simulation based on empirically observed parameter values is used to determine which criterion is the most accurate at identifying the correct model specification the simulation is composed of both nested and nonnested linear regression models we then derive posterior probability estimates of the superiority of the alternative models from each of the criteria and evaluate the relative accuracy bias and information content of these probabilities to investigate whether additional accuracy can be derived from combining criteria a method for obtaining a joint prediction from combinations of the criteria is proposed and the incremental improvement in selection accuracy considered based on the simulation we conclude that most leading criteria perform well in selecting the best model and several criteria also produce accurate probabilities of model superiority computationally intensive criteria failed to perform better than criteria which were computationally simpler also the use of several criteria in combination failed to appreciably outperform the use of one model the schwarz criterion performed best overall in terms of selection accuracy accuracy of posterior probabilities and ease of use thus we suggest that general model comparison model selection and model probability estimation be performed using the schwarz criterion which can be implemented given the model log likelihoods using only a hand calculator

test theory without an answer key a general model is presented for homogeneous dichotomous items when the answer key is not known a priori the model is structurally related to the two class latent structure model with the roles of respondents and items interchanged for very small sets of respondents iterative maximum likelihood estimates of the parameters can be obtained by existing methods for other situations new estimation methods are developed and assessed with monte carlo data the answer key can be accurately reconstructed with relatively small sets of respondents the model is useful when a researcher wants to study objectively the knowledge possessed by members of a culturally coherent group that the researcher is not a member of

hilbert polynomials and arveson s curvature invariant abstract we define and study hilbert polynomials for certain holomorphic hilbert spaces we obtain several estimates for these polynomials and their coefficients our estimates inspire us to investigate the connection between the leading coefficients of hilbert polynomials for invariant subspaces of the symmetric fock space and arveson s curvature invariant for coinvariant subspaces we are able to obtain some formulas relating the curvature invariant with other invariants in particular we prove that arveson s version of the gauss bonnet chern formula is true when the invariant subspaces are generated by any polynomials

limits for the precision and value of information from dependent sources in many inferential and decision making situations information is obtained from a number of information sources and the separate pieces of information are often not independent this paper investigates the impact of dependence on the precision and value of information the results indicate that positive dependence among information sources can have a serious detrimental effect on the precision and value of the information differences in precision between the dependent and independent cases can be remarkably large with dependence the incremental value of information can decrease very rapidly and the limiting value of information as more sources are considered can be considerably less than the expected value of perfect information the results of this paper have implications for the acquisition and use of information in decision making problems

analytic normalization of analytically integrable differential systems near a periodic orbit abstract for an analytic differential system in r n with a periodic orbit we will prove that if the system is analytically integrable around the periodic orbit i e it has n 1 functionally independent analytic first integrals defined in a neighborhood of the periodic orbit then the system is analytically equivalent to its poincare dulac type normal form this result is an extension of analytically integrable differential systems around a singularity to the ones around a periodic orbit

analytic normalization of analytic integrable systems and the embedding flows abstract this paper provides the normal forms of analytic integrable differential systems and diffeomorphisms via analytic normalizations furthermore we consider the existence of embedding flows of an analytic integrable diffeomorphism

varieties and analytic normalizations of partially integrable systems abstract for analytic differential systems x a x f x in f n with f r or c we study the varieties of their partial integrability in a neighborhood of the origin we also prove the existence of analytic normalizations of partially integrable differential systems

nominal scale agreement among observers experiments are considered where each of a sample of subjects is assigned to one of c categories separately by each of a fixed or varying group of observers building on earlier publications general procedures are proposed to analyze agreements and disagreements among observers in the case of a varying group of observers it is shown that it is not necessary to demand a constant number of observers per subject in the case of a fixed group of observers the problem of missing data is considered the procedures are illustrated within the context of two clinical diagnosis examples in the first example it is investigated which categories are relatively hard to distinguish from one another a new theorem is applied that shows a useful property of the statistic kappa in the second example it is investigated if a subgroup of observers can be found with a significantly higher degree of interobserver agreement

testing the fit of a parametric function abstract general methods for testing the fit of a parametric function are proposed the idea underlying each method is to accept the prescribed parametric model if and only if it is chosen by a model selection criterion several different selection criteria are considered including one based on a modified version of the akaike information criterion and others based on various score statistics the tests have a connection with nonparametric smoothing because they use orthogonal series estimators to detect departures from a parametric model an important aspect of the tests is that they can be applied in a wide variety of settings including generalized linear models spectral analysis the goodness of fit problem and longitudinal data analysis implementation using standard statistical software is straightforward asymptotic distribution theory for several test statistics is described and the tests are shown to be consistent against essentially any alternative hypothesis simulations and a data exampl

analytic integrable systems analytic normalization and embedding flows abstract in this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems more details we will prove that any complete analytic integrable diffeomorphism f x b x f x in c n 0 with b having eigenvalues not modulus 1 and f x o x 2 is locally analytically conjugate to its normal form meanwhile we also prove that any complete analytic integrable differential system x a x f x in c n 0 with a having nonzero eigenvalues and f x o x 2 is locally analytically conjugate to its normal form furthermore we will prove that any complete analytic integrable diffeomorphism defined on an analytic manifold can be embedded in a complete analytic integrable flow we note that parts of our results are the improvement of moser s one in j moser the analytic invariants of an area preserving mapping near a hyperbolic fixed point comm pure appl math 9 1956 673 692 and of poincare s one in h poincare sur l integration des equations differentielles du premier order et du premier degre ii rend circ mat palermo 11 1897 193 239 these results also improve the ones in xiang zhang analytic normalization of analytic integrable systems and the embedding flows j differential equations 244 2008 1080 1092 in the sense that the linear part of the systems can be nonhyperbolic and the one in n t zung convergence versus integrability in poincare dulac normal form math res lett 9 2002 217 228 in the way that our paper presents the concrete expression of the normal form in a restricted case

the core operator and congruent submodules abstract the hardy spaces h 2 d 2 can be conveniently viewed as a module over the polynomial ring c z 1 z 2 submodules of h 2 d 2 have connections with many areas of study in operator theory a large amount of research has been carried out striving to understand the structure of submodules under certain equivalence relations unitary equivalence is a well known equivalence relation in set of submodules however the rigidity phenomenon discovered in douglas et al algebraic reduction and rigidity for hilbert modules amer j math 117 1 1995 75 92 and some other related papers suggests that unitary equivalence being extremely sensitive to perturbations of zero sets lacks the flexibility one might need for a classification of submodules in this paper we suggest an alternative equivalence relation namely congruence the idea is motivated by a symmetry and stability property that the core operator possesses the congruence relation effectively classifies the submodules with a finite rank core operator near the end of the paper we point out an essential connection of the core operator with operator model theory

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

how many forecasters do you really have mahalanobis provides the intuition for the surprising clemen and winkler result how to combine expert opinions is an issue that has many aspects and even more answers the problem addressed here is the incremental information an additional expert brings when he or she is correlated with the existing experts r t clemen and r l winkler derive an algebraic formula that gives the surprising answer usually very little in this paper we provide the geometrical intuition behind the clemen and winkler result we also show how the clemen and winkler formula breaks down i e gives bizarre results as the error covariance structure approaches singularity

formal first integrals for periodic systems in the present paper we give an elementary proof for the result of li et al 2003 6 about nonexistence of formal first integrals for periodic systems in a neighborhood of a constant solution moreover we present a criterion about partial existence of formal first integrals for the periodic system by using the floquet s theory

the structure of inner multipliers on spaces with complete nevanlinna pick kernels let k be the reproducing kernel for a hilbert space h k of analytic functions on bd the open unit ball in cd d 1 k is called a complete np kernel if k0 1 and if 1 1 k z is positive definite on bd bd let d be a separable hilbert space and consider h k d h k d and think of it as a space of d valued h k functions a theorem of mccullough and trent j funct anal 178 2000 226 249 partially extends the beurling lax halmos theorem for the invariant subspaces of the hardy space h2 d they show that if k is a complete np kernel and if d is a separable hilbert space then for any scalar multiplier invariant subspace m of h k d there exists an auxiliary hilbert space e and a multiplication operator h k e h k d such that is a partial isometry and m h k e such multiplication operators are called inner multiplication operators and they satisfy the orthogonal projection onto m in this paper we shall show that for many interesting complete np kernels the analogy with the beurling lax halmos theorem can be strengthened we show that for almost every z bd the nontangential limit z of the multiplier bd b e d associated with an inner multiplication operator is a partial isometry and that rank z is equal to a constant almost everywhere the result applies to certain weighted dirichlet spaces and to the space h2d which is determined by the kernel k z 11 z d z bd in particular our result implies that the curvature invariant of arveson proc natl acad sci usa96 1999 11 096 11 099 of a pure contractive hilbert module of finite rank is an integer this answers a question of w arveson proc natl acad sci usa96 1999 11096 11099

reliability and expected loss a unifying principle we provide a unified theoretical basis on which measures of data reliability may be derived or evaluated for both quantitative and qualitative data this approach evaluates reliability as the proportional reduction in loss prl that is attained in a sample by an optimal estimator the resulting measure is between 0 and 1 linearly related to expected loss and provides a direct way of contrasting the measured reliability in the sample with the least reliable and most reliable data generating cases the prl measure is a generalization of many of the commonly used reliability measures

towards data driven selection of a penalty function for data driven neyman tests the data driven neyman statistic consists of two elements a score statistic in a finite dimensional submodel and a selection rule to determine the best fitted submodel for instance schwarz bic and akaike aic rules are often applied in such constructions for moderate sample sizes aic is sensitive in detecting complex models while bic works well for relatively simple structures when the sample size is moderate the choice of selection rule for determining a best fitted model from a number of models has a substantial influence on the power of the related data driven neyman test this paper proposes a new solution in which the type of penalty aic or bic is chosen on the basis of the data the resulting refined data driven test combines the advantages of these two selection rules

on model selection and the arc sine laws generalizations of the arc sine laws are shown to provide insight into the operating characteristics of certain techniques for selecting models to fit a given data set when the available models are nested as a corollary one sees that a popular technique may be expected to include about one superfluous parameter even if the sample size is large

using the conditional grade of membership model to assess judgment accuracy consider the case wherej instruments are used to classify each ofi objects relative tok nominal categories the conditional grade of membership gom model provides a method of estimating the classification probabilities of each instrument or judge when the objects being classified consist of both pure types that lie exclusively in one ofk nominal categories and mixtures that lie in more than one category classification probabilities are identifiable whenever the sample of gom vectors includes pure types from each category when additional relatively mild assumptions are made about judgment accuracy the identifiable correct classification probabilities are the greatest lower bounds among all solutions that might correspond to the observed multinomial process even when the unobserved gom vectors do not include pure types from each category estimation using the conditional gom model is illustrated on a simulated data set further simulations show that the estimates of the classification probabilities are relatively accurate even when the sample contains only a small percentage of approximately pure objects

generalized rational first integrals of analytic differential systems abstract in this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances the main results extend some of the previous related ones for instance the classical poincare s one poincare 1891 1897 16 the furta s one furta 1996 8 part of chen et al s ones chen et al 2008 4 and the shi s one shi 2007 18 the key point in the proof of our main results is that functionally independence of generalized rational functions implies the functionally independence of their lowest order rational homogeneous terms

first integrals and normal forms for germs of analytic vector fields abstract for a germ of analytic vector fields the existence of first integrals resonance and the convergence of normalization transforming the vector field to a normal form are closely related in this paper we first provide a link between the number of first integrals and the resonant relations for a quasi periodic vector field which generalizes one of the poincare s classical results h poincare sur l integration des equations differentielles du premier order et du premier degre i and ii rend circ mat palermo 5 1891 161 191 11 1897 193 239 on autonomous systems and theorem 5 of weigu li j llibre xiang zhang local first integrals of differential systems and diffeomorphism z angew math phys 54 2003 235 255 on periodic systems then in the space of analytic autonomous systems in c 2 n with exactly n resonances and n functionally independent first integrals our results are related to the convergence and generic divergence of the normalizations lastly for a planar hamiltonian system it is well known that the system has an isochronous center if and only if it can be linearizable in a neighborhood of the center using the euler lagrange equation we provide a new approach to its proof

total convergence or general divergence in small divisors we study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic the characteristic features are delicate problems of convergence of formal power series due to small divisors we prove the following dichotomy we have convergence for all parameter values or divergence everywhere except for an exceptional pluri polar set of parameters we illustrate this general principle in different problems of small divisors as an application we obtain new richer families of non linearizable examples in the siegel problem when the bruno condition is violated generalizing and extending to higher dimension previous results of yoccoz and the author

notes on ordered reproducing hilbert spaces over the complex plane abstract let f g be entire functions if there exist m 1 m 2 0 such that f z m 1 g z whenever z m 2 we say that f g let x be a reproducing hilbert space with an orthogonal basis z n n 0 we say that x is an ordered reproducing hilbert space or x is ordered if f g and g x imply f x in this note we show that if lim inf n z n 1 z n then x is ordered if lim inf n z n 1 z n 0 then x is not ordered in the case lim inf n z n 1 z n l 0 there are examples to show that x can be of order or opposite

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

convergence or generic divergence of the birkhoff normal form we prove that the birkhoff normal form of hamiltorlian flows at a nonresonant singular point with given quadratic part is always convergent or generically divergent the same result is proved for the normalization mapping and any formal first integral

general estimators for the reliability of qualitative data we study a proportional reduction in loss prl measure for the reliability of categorical data and consider the general case in which each ofn judges assigns a subject to one ofk categories this measure has been shown to be equivalent to a measure proposed by perreault and leigh for a special case when there are two equally competent judges and the correct category has a uniform prior distribution we consider a general framework where the correct category is assumed to have an arbitrary prior distribution and where classification probabilities vary by correct category judge and category of classification in this setting we consider prl reliability measures based on two estimators of the correct category the empirical bayes estimator and an estimator based on the judges consensus choice we also discuss four important special cases of the general model and study several types of lower bounds for prl reliability

nonexistence of isochronous centers in planar polynomial hamiltonian systems of degree four abstract in this paper we study centers of planar polynomial hamiltonian systems and we are interested in the isochronous ones we prove that every center of a polynomial hamiltonian system of degree four that is with its homogeneous part of degree four not identically zero is nonisochronous the proof uses the geometric properties of the period annulus and it requires the study of the hamiltonian systems associated to a hamiltonian function of the form h x y a x b x y c x y 2 d x y 3

varieties of local integrability of analytic differential systems and their applications abstract in this paper we provide a characterization of local integrability for analytic or formal differential systems in r n or c n via the integrability varieties our result generalizes the classical one of poincare and lyapunov on local integrability of planar analytic differential systems to any finitely dimensional analytic differential systems as an application of our theory we study the integrability of a family of four dimensional quadratic hamiltonian systems

extension of floquet s theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows this paper has two parts in the first one we generalize the floquet theory to nonlinear periodic differential systems in the second part we apply the first one to obtain a sufficient condition in order that a germ of diffeomorphism can be embedded in a differential flow