waveform correlation by tree matching a waveform correlation scheme is presented the scheme consists of four parts 1 the representation of waveforms by trees 2 the definition of basic operations on tree nodes and tree distance 3 a tree matching algorithm and 4 a backtracking procedure to find the best node to node correlation this correlation scheme has been implemented results show that the scheme has the capability of handling distortions that result from stretching or shrinking of intervals or from missing intervals

compatible conditional distributions abstract consider two families of candidate conditional densities or probability mass functions f x y y s y and f y x x s x this article investigates necessary and sufficient conditions for the existence of a joint density or joint probability mass function f x y with the given families as its associated conditional densities this supplements previous work that has addressed the question of uniqueness of f x y assuming its existence

quadratic systems with center and their perturbations abstract we study the quadratic systems on a plane z i z az2 b z 2 cz2 z x iy we give a simple algebraic proof of the center conditions 0 and b 0 or a 1 2 b 1 or a b 1 c c or a 2 b 1 c 1 and of the theorem of bautin that the number of small amplitude limit cycles bifurcating from a center or a focus is not greater than 3 we present the bifurcational diagrams and phase portraits of the systems with center and describe the cyclicity precisely in each case here one mistake in bautin s work is revealed and some questions concerning focus numbers are answered we study also global not small limit cycles for a small perturbation of the center case with two invariant lines the lotka volterra system using abelian integrals we show that the number of zeroes of the corresponding abelian integral is 0 1 or 2 some attention is devoted to the problem of limit cycles for a small perturbation of a system with a two fold center when two center conditions hold the problem turns out to be equivalent to the problem of zeroes of some integral with polynomial coefficients

algebraic and analytical tools for the study of the period function abstract in this paper we consider analytic planar differential systems having a first integral of the form h x y a x b x y c x y 2 and an integrating factor x not depending on y our aim is to provide tools to study the period function of the centers of this type of differential system and to this end we prove three results theorem a gives a characterization of isochronicity a criterion to bound the number of critical periods and a necessary condition for the period function to be monotone theorem b is intended for being applied in combination with theorem a in an algebraic setting that we shall specify finally theorem c is devoted to study the number of critical periods bifurcating from the period annulus of an isochrone perturbed linearly inside a family of centers four different applications are given to illustrate these results

association models and the bivariate normal for contingency tables with ordered categories summary association models considered by goodman 1979 for contingency tables with ordered categories are presented here in a somewhat different form to facilitate comparison with the bivariate normal association models can be applied when an underlying bivariate normal is assumed and also under more general conditions and they provide alternatives to tetrachoric and polychoric correlation these models agree more closely with the bivariate normal than does plackett s model 1965 when the row and column classifications arise from underlying univariate normal distributions the general utility of the association models is illustrated here

non isochronicity of the center at the origin in polynomial hamiltonian systems with even degree nonlinearities abstract in 2002 x jarque and j villadelprat proved that no center in a planar polynomial hamiltonian system of degree 4 is isochronous and raised a question is there a planar polynomial hamiltonian system of even degree which has an isochronous center in this paper we give a criterion for non isochronicity of the center at the origin of planar polynomial hamiltonian systems moreover the orders of weak centers are determined our results answer a weak version of the question proving that there is no planar polynomial hamiltonian system with only even degree nonlinearities having an isochronous center at the origin

characterizing isochronous points and computing isochronous sections abstract we consider two dimensional autonomous systems of differential equations x y x p x y y x y q x y where is a real constant and p and q are smooth functions of order greater than or equal to two these systems so called centre focus type systems have either a centre or a focus at the origin we characterize the systems with a weak isochronous focus at the origin by means of their radial and azimuthal coefficients we prove in this case the existence of a normalized vector field and an isochronous section which arrives at the origin with defined direction we also provide algorithms that compute the radial and azimuthal coefficients terms of normalized vector field and of isochronous section of a system as applications we analyze the weak isochronous foci for quadratic systems and for systems with cubic non linearities and we give a three parameter family of rayleigh equations with four local critical periods

distance between populations using mixed continuous and categorical variables summary a general form of the location model is considered for mixed continuous and categorical variables observed in a number of different populations and some special cases of practical interest are cited the distance between any two populations is derived for each of these models estimation of parameters in these distance measures is discussed and the methods are illustrated by application to previously published data

loglinear multidimensional irt models for polytomously scored items a loglinear irt model is proposed that relates polytomously scored item responses to a multidimensional latent space the analyst may specify a response function for each response indicating which latent abilities are necessary to arrive at that response each item may have a different number of response categories so that free response items are more easily analyzed conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear irt models

fuzzy approach to solve the recognition problem of handwritten chinese characters abstract a method based on the concept of fuzzy set for handwritten chinese character hcc recognition is proposed in this paper chinese characters can be viewed as a collection of line segments called strokes since the strokes under consideration here are fuzzy in nature the concept of fuzzy set is utilized in the similarity measure two membership functions are defined for the location measure and type measure between two strokes and a function of fuzzy entropy is used in information measure although the recognition problem can be reduced to the assignment problem some modifications are still necessary all the similarities between the corresponding strokes can be chosen by solving the assignment problem using the cost function of fuzzy entropy and then are averaged to derive the score of similarity between two chinese characters 881 classes of chinese characters in etl 8 160 variations class are used as the test patterns and the recognition rate is about 96 in addition experiments about the effects of the membership function based on the class separability are also discussed in this paper

pseudo isochronicity in a class of septic differential systems this paper deals with the pseudo isochronicity for a class of septic differential systems in this paper we transform infinity into the origin so that the properties of infinity can be investigated with the methods developed for finite critical points by calculating the singular point quantities and period constants of the origin the problem of infinity being a pseudo isochronous center has been solved in this case

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

improving dynamic programming to solve image registration a new method of dynamic programming dp is presented a picture is paired with a reference map in order to arrive at picture registration an ordered sequence of primitive patterns is formed from the map an attempt is made to locate a similar sequence from the picture using classical picture processing methods this yields a distorted and unordered sequence marked by noise dp is then used to search for a common match to the two sequences both the initial and final registration states are however unknown moreover the continuity of the path is frequently interrupted due to shortcomings in detection or perhaps occlusions thus classical dp algorithms appear to give only poor results under practical conditions when well adapted to treat signals issued from a first order markovian process they can be used as this method shows to treat kth order processes the concept of the virtual state kept in memory suspends broken paths until they can be reconnected thus bridging the existing gaps between the different parts of the path the proposed algorithm has been applied to satellite images with their contours sectioned by clouds the result leads to the guarantee of very good registration in spite of image contours badly hampered by noise and or clouds

linearizability conditions for lotka volterra planar complex quartic systems having homogeneous nonlinearities in this paper we investigate the linearizability problem for the two dimensional lotka volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials i e we consider systems of the form email protected x 1 a 3 0x 3 a 2 1x 2y a 1 2xy 2 a 0 3y 3 email protected y 1 b 3 0x 3 b 2 1x 2y b 1 2xy 2 b 0 3y 3 the necessary and sufficient conditions for the linearizability of this system are found from them the conditions for isochronicity of the corresponding real system can be derived

the asymptotic posterior normality of the latent trait in an irt model it has long been part of the item response theory irt folklore that under the usual empirical bayes unidimensional irt modeling approach the posterior distribution of examinee ability given test response is approximately normal for a long test under very general and nonrestrictive nonparametric assumptions we make this claim rigorous for a broad class of latent models

linearizability conditions for a cubic system we obtain the necessary and sufficient conditions for linearizability of an eight parameter family of two dimensional system of differential equations in the form of linear canonical saddle perturbed by polynomials with four quadratic and four cubic terms

on the period function of lienard systems abstract we study the period functiontof a centeroof a lienard system a sufficient condition for the monotonicity oft or for the isochronicity ofo is given such a condition is also necessary whenfandgare analytic andgis odd in this case a characterization of isochronous centers of lienard systems is given strict monotonicity and global monotonicity oftare also investigated

on the upper bound of the criticality of potential systems at the outer boundary using the roussarie ecalle compensator abstract this paper is concerned with the study of the criticality of families of planar centers more precisely we study sufficient conditions to bound the number of critical periodic orbits that bifurcate from the outer boundary of the period annulus of potential centers in the recent years the new approach of embedding the derivative of the period function into a collection of functions that form a chebyshev system near the outer boundary has shown to be fruitful in this issue in this work we tackle with a remaining case that was not taken into account in the previous studies in which the roussarie ecalle compensator plays an essential role the theoretical results we develop are applied to study the bifurcation diagram of the period function of two different families of centers the power like family x x q x p p q r with p q and the family of dehomogenized loud s centers

on the period function in a class of generalized lotka volterra systems in this note motivated by the recent results of wang et al wang et al local bifurcations of critical periods in a generalized 2d lv system appl math comput 214 2009 17 25 we study the behaviour of the period function of the center at the point 1 1 of the planar differential systemu u p 1 v q v email protected q u p 1 where p q email protected r with pq 0 and m 0 our aim is twofold firstly we determine regions in the parameter space for which the corresponding system has a center with a monotonic period function secondly by taking advantage of the results of wang et al we show some properties of the bifurcation diagram of the period function and we make some comments for further research the differential system under consideration is a generalization proposed by farkas and noszticzius of the lotka volterra model

asymptotic expansion of the period function abstract let p be a not necessarily bounded polycycle of an analytic vector field on an open set of the plane suppose that the singularities which appear after desingularization of the vertices of p are formally linearizable consider the function t defined by the return time near p it is shown that the function t and its derivative t have asymptotic expansions in x r and x log x r it is also shown that under some other conditions imposed on the polycycle vertices the asymptotic expansions of t and t converge absolutely and uniformly to these functions respectively these results are applied to the polycycles of the analytic vector fields which have a darboux first integral in particular it is obtained that if p is a polycycle of a hamiltonian vector field with an analytic polynomial if p is unbounded hamiltonian function t is a nonoscillating function another application concerns the nilpotent centers or focus since the singularities which appear after desingularization of such a singularity have analytic first integrals

isochronicity for a class of reversible systems abstract this paper deals with the relation between isochronicity and first integral for a class of reversible systems x u x y y f x y which associates to the first integral of the form h x y f x y 2 g x two necessary and sufficient conditions are given to characterize isochronicity for these systems moreover we apply these results to show that there exists a class of polynomial reversible systems of degree n with isochronous center for any n

the monotonicity of period function for codimension four quadratic system q4 abstract in this paper we study the codimension four quadratic system q 4 z iz 4 z 2 2 z 2 b ic z 2 where b and c are real constants i 2 1 z x iy b ic 2 it is proved that the period function of periodic trajectories for q 4 is monotone the content of this paper can be viewed as a contribution to the proof of chicone s conjecture cf mr 94h 58072

latent class and discrete latent trait models similarities and differences introduction log linear models and latent class analysis latent class measurement models latent trait models discretized latent trait models estimation in latent trait models

isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials in this work we study isochronous centers of two dimensional autonomous system in the plane with linear part of center type and nonlinear part given by homogeneous polynomials of fifth degree a complete classification of the necessary conditions for the time reversible systems of this class is given in order to have an isochronous center at the origin an open problem is stated for the sufficient conditions moreover we find two nonreversible isochronous families from the center cases known all the computations in order to obtain necessary conditions for such isochronous centers are given in polar coordinates and we give a proof of the isochronicity of these systems by using different methods

isochronicity into a family of time reversible cubic vector fields in this work we study necessary and sufficient conditions for the existence of isochronous centers into a family of cubic time reversible systems this class of reversible systems is characterized by the existence of an inverse integrating factor which is a certain power of an invariant straight line

the asymptotic posterior normality of the latent trait for polytomous irt models chang and stout 1993 presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous irt models this paper presents an extention of their results to polytomous irt models in a fairly straightforward manner in addition a global information function is defined and the relationship between the global information function and the currently used information functions is discussed an information index that combines both the global and local information is proposed for adaptive testing applications

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

properties of the period function for some hamiltonian systems and homogeneous solutions of a semilinear elliptic equation abstract in this work we study the period function t of solutions to the conservative equation x t f x t 0 we present conditions on f that imply the monotonicity and convexity of t as a consequence we obtain the criterium established by c chicone and find conditions easier to apply we also get a condition obtained by cima gasull and manosas about monotonicity and following some of their calculations present results on the period function of hamiltonian systems where h x y f x n 1 y n using the monotonicity of t we count the homogeneous solutions to the semilinear elliptic equation u u 1 in two dimensions

characterizing a joint probability distribution by conditionals summary we derive conditions under which a set of conditional and marginal probability distributions will uniquely specify an all positive joint distribution our theoretical result may yield insights into the construction and simulation of multivariate probability models

on line recognition of cursive korean characters using dp matching and fuzzy concept abstract this paper proposes an on line recognition method of cursive korean characters based on dynamic programming dp matching and fuzzy concept the proposed algorithm invariant to rotation and size reduces greatly the computational requirement of dp matching by matching phonemes rather than character patterns where the angle difference and the ratio of lengths between input and reference patterns are adopted as matching features correct matching of poorly written cursive characters becomes possible by introducing the fuzzy concept in representing phoneme features and the positional relationships between adjacent phonemes computer simulation results show the effectiveness of the proposed algorithm

on holland s dutch identity conjecture the manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear holland 1990a gives a quadratic form for the log manifest probabilities by using the dutch identity further holland conjectures that this special quadratic form is a limiting one for all smooth unidimensional item response models as test length tends to infinity the purpose of this paper is to give three counterexamples to demonstrate that holland s dutch identity conjecture does not hold in general the counterexamples suggest that only under strong assumptions can it be true that the limits of log manifest probabilities are quadratic three propositions giving sets of such strong conditions are given

a new method for dealing with measurement error in explanatory variables of regression models we introduce a new method moment reconstruction of correcting for measurement error in covariates in regression models the central idea is similar to regression calibration in that the values of the covariates that are measured with error are replaced by adjusted values in regression calibration the adjusted value is the expectation of the true value conditional on the measured value in moment reconstruction the adjusted value is the variance preserving empirical bayes estimate of the true value conditional on the outcome variable the adjusted values thereby have the same first two moments and the same covariance with the outcome variable as the unobserved true covariate values we show that moment reconstruction is equivalent to regression calibration in the case of linear regression but leads to different results for logistic regression for case control studies with logistic regression and covariates that are normally distributed within cases and controls we show that the resulting estimates of the regression coefficients are consistent in simulations we demonstrate that for logistic regression moment reconstruction carries less bias than regression calibration and for case control studies is superior in mean square error to the standard regression calibration approach finally we give an example of the use of moment reconstruction in linear discriminant analysis and a nonstandard problem where we wish to adjust a classification tree for measurement error in the explanatory variables

isochronicity of a z2 equivariant quintic system abstract the main purpose of this paper is to study the problem of simultaneous existence of two isochronous centers in some families of planar polynomial differential systems with symmetry more precisely we present conditions for a family of z 2 equivariant systems of degree 5 to have an isochronous bi center we also study their global phase portraits in the poincare disk and present considerations about the number of simultaneous centers in z 2 equivariant systems of degree 3 and 5 this study provides examples of quintic systems possessing three and five isochronous centers simultaneously

linearization of analytic isochronous centers from a given commutator in this paper we propose an algorithmic way to get the change of variables that linearizes an analytic isochronous center from a given commutator moreover we use this method in order to obtain the linearization of some isochronous centers of the existent literature

isochronicity for several classes of hamiltonian systems abstract in this paper we study isochronous centers of analytic hamiltonian systems giving special attention to the polynomial case we first revisit the potential systems and we show the connection between isochronicity and involutions we then study a more general system namely the ones associated to hamiltonians of the form h x y a x b x y c x y 2 as an application we classify the cubic polynomial hamiltonian isochronous centers and we give examples of nontrivial and nonglobal polynomial hamiltonian isochronous centers

darboux linearization and isochronous centers with a rational first integral abstract in this paper we study isochronous centers of polynomial systems it is known that a center is isochronous if and only if it is linearizable we introduce the notion of darboux linearizability of a center and give an effective criterion for verifying darboux linearizability if a center is darboux linearizable the method produces a linearizing change of coordinates most of the known polynomial isochronous centers are darboux linearizable moreover using this criterion we find a new two parameter family of cubic isochronous centers and give the linearizing changes of coordinates for centers belonging to that family we also determine all hamiltonian cubic systems which are darboux linearizable in the second part of this work we restrict to the study of isochronous centers having a rational first integral we prove that under certain conditions the cycle vanishing at the isochronous center is either zero homologous in the closure of a generic fiber or the function obtained from the first integral by eliminating the indeterminacy points has several critical points in the singular fiber passing through the isochronous center

computing center conditions for vector fields with constant angular speed we investigate the planar analytic systems which have a center focus equilibrium at the origin and whose angular speed is constant the conditions for the origin to be a center in fact an isochronous center are obtained concretely we find conditions for the existence of a cw commutator of the field we cite several subfamilies of centers and obtain the centers of the cuartic polynomial systems and of the families y x h1 hm x y h1 hm t and y x h2 h2n x y h2 h2n t with hi homogeneous polynomial in x y of degree i in these cases the maximum number of limit cycles which can bifurcate from a fine focus is determined

log multiplicative association models as item response models log multiplicative association lma models which are special cases of log linear models have interpretations in terms of latent continuous variables two theoretical derivations of lma models based on item response theory irt arguments are presented first we show that anderson and colleagues anderson vermunt 2000 anderson bockenholt 2000 anderson 2002 who derived lma models from statistical graphical models made the equivalent assumptions as holland 1990 when deriving models for the manifest probabilities of response patterns based on an irt approach we also present a second derivation of lma models where item response functions are specified as functions of rest scores these various connections provide insights into the behavior of lma models as item response models and point out philosophical issues with the use of lma models as item response models we show that even for short tests lma and standard irt models yield very similar to nearly identical results when data arise from standard irt models log multiplicative association models can be used as item response models and do not require numerical integration for estimation

linearizability conditions for lotka volterra planar complex cubic systems in this paper we investigate the linearizability problem for the two dimensional planar complex system the necessary and sufficient conditions for the linearizability of this system are found from them the conditions for isochronicity of the corresponding real system can be derived

graphical regression models for polytomous variables when modeling the relationship between two nominal categorical variables it is often desirable to include covariates to understand how individuals differ in their response behavior typically however not all the relevant covariates are available with the result that the measured variables cannot fully account for the associations between the nominal variables under the assumption that the observed and unobserved variables follow a homogeneous conditional gaussian distribution this paper proposesrc m regression models to decompose the residual associations between the polytomous variables based on goodman s 1979 1985 rc m association model a distinctive feature ofrc m regression models is that they facilitate the joint estimation of effects due to manifest and omitted continuous variables without requiring numerical integration therc m regression models are illustrated using data from the high school and beyond study tatsuoka lohnes 1988

the period function of the generalized lotka volterra centers abstract the present paper deals with the period function of the quadratic centers in the literature different terminologies are used to classify these centers but essentially there are four families hamiltonian reversible q 3 r codimension four q 4 and generalized lotka volterra systems q 3 lv chicone c chicone review in mathscinet ref 94h 58072 conjectured that the reversible centers have at most two critical periods and that the centers of the three other families have a monotonic period function with regard to the second part of this conjecture only the monotonicity of the hamiltonian and q 4 families w a coppel l gavrilov the period function of a hamiltonian quadratic system differential integral equations 6 1993 1357 1365 y zhao the monotonicity of period function for codimension four quadratic system q 4 j differential equations 185 2002 370 387 has been proved concerning the q 3 lv family no substantial progress has been made since the middle 80s when several authors showed independently the monotonicity of the classical lotka volterra centers f rothe the periods of the volterra lokta system j reine angew math 355 1985 129 138 r schaaf global behaviour of solution branches for some neumann problems depending on one or several parameters j reine angew math 346 1984 1 31 j waldvogel the period in the lotka volterra system is monotonic j math anal appl 114 1986 178 184 by means of the first period constant one can easily conclude that the period function of the centers in the q 3 lv family is monotone increasing near the inner boundary of its period annulus i e the center itself thus according to chicone s conjecture it should be also monotone increasing near the outer boundary which in the poincare disc is a polycycle in this paper we show that this is true in addition we prove that except for a zero measure subset of the parameter plane there is no bifurcation of critical periods from the outer boundary finally we show that the period function is globally i e in the whole period annulus monotone increasing in two other cases different from the classical one

characterizing the manifest probability distributions of three latent trait models for accuracy and response time in this paper we study the statistical relations between three latent trait models for accuracies and response times the hierarchical model hm of van der linden psychometrika 72 3 287 308 2007 the signed residual time model sm proposed by maris and van der maas psychometrika 77 4 615 633 2012 and the drift diffusion model dm as proposed by tuerlinckx and de boeck psychometrika 70 4 629 650 2005 one important distinction between these models is that the hm and the dm either assume or imply that accuracies and response times are independent given the latent trait variables while the sm does not in this paper we investigate the impact of this conditional independence property or a lack thereof on the manifest probability distribution for accuracies and response times we will find that the manifest distributions of the latent trait models share several important features such as the dependency between accuracy and response time but we also find important differences such as in what function of response time is being modeled our method for characterizing the manifest probability distributions is related to the dutch identity holland in psychometrika 55 6 5 18 1990

period function monotonicity of planar vector fields in this paper we study planar differential systems possessing a center at the origin we introduce functional conditions for centers and obtain sufficient conditions for monotonicity of period function and isochronicity of the center of systems of ode reducible to the equation email protected email protected f x email protected these criteria are applied to obtain sufficient conditions for isochronicity of some special important systems

the period function for quadratic integrable systems with cubic orbits this paper is concerned with the monotonicity of the period function for families of quadratic systems with centers whose orbits lie on cubic planar curves it is proved that each such system has a period function with at most one critical point

area preserving normalizations for centers of planar hamiltonian systems abstract it is well known that a nondegenerate center of an analytic hamiltonian planar system can be brought to normal form by means of an analytic canonical change of coordinates this normal form that we denote by cnf does not depend on the coordinate transformation in this paper we give an elementary proof of these facts and we show some interesting applications of the machinery that we develop in order to prove them for instance we describe the space of coordinate transformations that bring a hamiltonian nondegenerate center to its cnf and we prove that they are all canonical when the center is non isochronous we also show that two hamiltonian systems with a nondegenerate center are canonically conjugated if and only if both centers have the same period function

periodic solutions of a quartic nonautonomous equation on considere des equations de la forme z z 4 t z 3 t z 2 t z on donne un ensemble qui a au moins huit solutions periodiques les coefficients sont des polynomes quadratiques en cost et sint

the criticality of centers of potential systems at the outer boundary abstract the number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied we call this number the criticality at the outer boundary our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1 we apply them to study the bifurcation diagram of the period function of x y x x 1 p x 1 q y with q p this family was previously studied for q 1 by y miyamoto and k yagasaki

isochronicity and linearizability of a planar cubic system abstract in this paper we investigate the problem of linearizability for a family of cubic complex planar systems of ordinary differential equations we give a classification of linearizable systems in the family obtaining conditions for linearizability in terms of parameters we also discuss coexistence of isochronous centers in the systems

linearizability conditions of a time reversible quartic like system in this paper we study the linearizability problem of polynomial like complex differential systems we give a reduction of linearizability problem of such non polynomial systems to the problem of polynomial systems applying this reduction we find some linearizability conditions for a time reversible quartic like complex system and derive from them conditions of isochronous center for the corresponding real system

a class of reversible cubic systems with an isochronous center abstract we study cubic polynomial differential systems having an isochronous center and an inverse integrating factor formed by two different parallel invariant straight lines such systems are time reversible we find nine subclasses of such cubic systems see theorem 8 we also prove that time reversible polynomial differential systems with a nondegenerate center have half of the isochronous constants equal to zero see theorem 3 we present two open problems

algebraic particular integrals integrability and the problem of the center in this work we clarify the global geometrical phenomena corresponding to the notion of center for plane quadratic vector fields we first show the key role played by the algebraic particular integrals of degrees less than or equal to three in the theory of the center these curves control the changes in the systems as parameters vary the bifurcation diagram used to prove this result is realized in the natural topological space for the situation considered namely the real four dimensional projective space next we consider the known four algebraic conditions for the center for quadratic vector fields one of them says that the system is hamiltonian a condition which has a clear geometric meaning we determine the geometric meaning of the remaining other three algebraic conditions i ii iii

an approach to solving systems of polynomials via modular arithmetics with applications the objective of this paper is twofold first we describe a method to solve large systems of polynomial equations using modular arithmetics then we apply the approach to the study of the problem of linearizability for a quadratic system of ordinary differential equations

study of the period function of a two parameter family of centers abstract in this paper we study the period function of x 1 x p 1 x q with p q r and p q we prove three independent results the first one establishes some regions in the parameter space where the corresponding center has a monotonous period function this result extends the previous ones by miyamoto and yagasaki for the case q 1 the second one deals with the bifurcation of critical periodic orbits from the center the third one is addressed to the critical periodic orbits that bifurcate from the period annulus of each one of the three isochronous centers in the family when perturbed by means of a one parameter deformation these three results together with the ones that we obtained previously on the issue lead us to propose a conjectural bifurcation diagram for the global behaviour of the period function of the family

the period function of generalized loudʼs centers abstract in this paper a three parameter family of planar differential systems with homogeneous nonlinearities of arbitrary odd degree is studied this family is an extension to higher degree of loud s systems the origin is a nondegenerate center for all values of the parameter and we are interested in the qualitative properties of its period function we study the bifurcation diagram of this function focusing our attention on the bifurcations occurring at the polycycle that bounds the period annulus of the center moreover we determine some regions in the parameter space for which the corresponding period function is monotonous or it has at least one critical period giving also its character maximum or minimum finally we propose a complete conjectural bifurcation diagram of the period function of these generalized loud s centers

limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems abstract in this paper we consider the quadratic isochronous centers perturbed inside piecewise polynomial differential systems of arbitrary degree n with the straight line of discontinuity x 0 the main concerns are the number of zeros of the first order melnikov functions and the estimate of the number of limit cycles bifurcating from the period annuli for quadratic isochronous centers s 1 s 2 and s 3 we will provide a sharp upper bound for the number of zeros of the first order melnikov functions for quadratic isochronous center s 4 we give a rough estimate however when the problem is reduced to perturbations inside polynomial differential systems our result for s 4 will improve that in li et al 2000 12 significantly moreover we will reveal out some equivalence between the first order melnikov function method and the first order averaging method for investigating the number of limit cycles of piecewise polynomial differential systems

linearization of isochronous centers abstract in this paper we study isochronous centers of polynomial systems we first discuss isochronous centers of quadratic systems cubic symmetric systems and reduced kukles system all these systems have rational first integrals we give a unified proof of the isochronicity of these systems by constructing algebraic linearizing changes of coordinates we then study two other classes of systems with isochronous centers namely the class of complex systems z ip z and the class of cubic systems symmetric with respect to a line and satisfying 1 both classes consist of darboux integrable systems we discuss their geometric properties and construct the linearizing changes of coordinates we show that the class of polynomial isochronous systems carries a very rich geometry finally we discuss the geometry of the linearizing changes of coordinates in the complex plane

isochronous centers of polynomial hamiltonian systems and a conjecture of jarque and villadelprat abstract we study the conjecture of jarque and villadelprat stating that every center of a planar polynomial hamiltonian system of even degree is nonisochronous this conjecture has already been proved for quadratic and quartic systems using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields we are able to describe a very large class of nonisochronous hamiltonian systems of even arbitrarily large degree

isochronicity and linearizability of planar polynomial hamiltonian systems in this paper we study isochronicity and linearizability of planar polynomial hamiltonian systems first we prove a theorem which supports a negative answer to the following open question stated by jarque and villadelprat in 15 do there exist planar polynomial hamiltonian systems of even degree having an isochronous center additionally we obtain some conditions for linearizability of complex cubic hamiltonian systems

bayesian model comparison for the order restricted rc association model association models constitute an attractive alternative to the usual log linear models for modeling the dependence between classification variables they impose special structure on the underlying association by assigning scores on the levels of each classification variable which can be fixed or parametric under the general row column rc association model both row and column scores are unknown parameters without any restriction concerning their ordinality however when the classification variables are ordinal order restrictions on the scores arise naturally under such restrictions we adopt an alternative parameterization and draw inferences about the equality of adjacent scores using the bayesian approach to achieve that we have constructed a reversible jump markov chain monte carlo algorithm for moving across models of different dimension and estimate accurately the posterior model probabilities which can be used either for model comparison or for model averaging the proposed methodology is evaluated through a simulation study and illustrated using actual datasets

non autonomous equations related to polynomial two dimensional systems periodic solutions of certain one dimensional non autonomous differential equations are investigated equation 1 4 the independent variable is complex the motivation which is explained in the introductory section is the connection with certain polynomial two dimensional systems several classes of coefficients are considered in each case the aim is to estimate the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients in particular we need to know when there is a full neighbourhood of periodic solutions we give a number of sufficient conditions and investigate the implications for the corresponding two dimensional systems

linearizability conditions of time reversible quartic systems having homogeneous nonlinearities abstract in this paper we investigate the linearizability problem for the two dimensional time reversible complex system x x p x y y y q x y where p and q are homogeneous quartic polynomials the necessary and sufficient conditions for the linearizability of this system are found as a corollary the necessary and sufficient conditions for the origin to be an isochronous center of the planar time reversible real system u v f u v v u g u v where f and g are homogeneous quartic polynomials are obtained

centers with degenerate infinity and their commutators abstract we study polynomial systems with degeneracy at infinity and a center focus equilibrium at the origin we give some general properties related to the existence of polynomial commutators and use these properties in order to characterize uniformly isochronous polynomial centers with polynomial commutator and also we show that the commutator of the centers of the analytic systems whose angular speed is constant can be chosen of radial form finally we characterize the systems y ps j kn 1xhj x qs j kn 1yhj t with polynomial commutator with pj qj hj and kj homogeneous polynomials

a second order analysis of the periodic solutions for nonlinear periodic differential systems with a small parameter abstract we deal with nonlinear t periodic differential systems depending on a small parameter the unperturbed system has an invariant manifold of periodic solutions we provide the expressions of the bifurcation functions up to second order in the small parameter in order that their simple zeros are initial values of the periodic solutions that persist after the perturbation in the end two applications are done the key tool for proving the main result is the lyapunov schmidt reduction method applied to the t poincare andronov mapping

kukles revisited advances in computing techniques we revisit the kukles system to show how advances in computer hardware and software have improved symbolic calculations we confirm directly that there are no non persistent centres for the kukles system we also prove an earlier conjecture regarding the isochronous centres for the extended kukles system we introduce a technique whereby modular resultants can be used to investigate the properties of resultants that cannot be readily calculated using the existing software

completely integrable hamiltonian systems with weak lyapunov instability or isochrony the aim of this paper is to introduce a class of hamiltonian autonomous systems in dimension 4 which are completely integrable and their dynamics is described in all details they have an equilibrium point which is stable for some rare elements of the class and unstable in most cases anyhow it is linearly stable all orbits of the linearized system are bounded and no motion is asymptotic in the past namely no non constant solution has the equilibrium as limit point as time goes to minus infinity in the unstable cases there is a sequence of initial data which converges to the equilibrium point whose corresponding solutions are unbounded and the motion is slow so instability is quite weak and perhaps no such explicit examples of instability are known in the literature the stable cases are also interesting since the level sets of the 2 first integrals independent and in involution keep being non compact and stability is related to the isochronous periodicity of all orbits near the equilibrium point and the existence of a further first integral hopefully these superintegrable hamiltonian systems will deserve further research

on the classification of lienard systems with amplitude independent periods abstract we consider conditions under which the second order differential equation x f x x g x 0 has a family of periodic orbits with constant period this condition is equivalent to seeking conditions under which the two dimensional autonomous system x y y g x f x y has a center with constant period i e an isochronous center in turn this is equivalent to the latter system being locally linearizable we give a simple necessary and sufficient condition for this when f and g are analytic functions in the case where when f and g are polynomials we show that this reduces to a finitely determinable system of equations a complete classification is given of all such systems of degree 34 or less

algorithmic derivation of isochronicity conditions abstract this paper is concerned with obtaining the conditions under which the origin is an isochronous centre for certain planar polynomial systems the necessity of these conditions is proved using a computer implementation of an algorithm first proposed by i i pleshkan their sufficiency is then proved using various methods

on the critical points of the flight return time function of perturbed closed orbits abstract we deal here with planar analytic systems x x x e which are small perturbations of a period annulus for each transversal section to the unperturbed orbits we denote by t q e the time needed by a perturbed orbit that starts from q to return to we call this the flight return time function we say that the closed orbit of x x x 0 is a continuable critical orbit in a family of the form x x x e if for any q and any that passes through q there exists q e a critical point of t e such that q e q as e 0 in this work we study this new problem of continuability in particular we prove that a simple critical periodic orbit of x x x 0 is a continuable critical orbit in any family of the form x x x e we also give sufficient conditions for the existence of a continuable critical orbit of an isochronous center x x x 0

linearizability and local bifurcation of critical periods in a cubic kolmogorov system since chicone and jacobs investigated local bifurcation of critical periods for quadratic systems and newtonian systems in 1989 great attention has been paid to some particular forms of cubic systems having special practical significance but less difficulties in computation this paper is devoted to the linearizability and local bifurcation of critical periods for a cubic kolmogorov system we use the darboux method to give explicit linearizing transformations for isochronous centers investigating the finite generation for the ideal of all period constants which are of the polynomial form in six parameters we prove that at most two critical periods can be bifurcated from the interior equilibrium if it is an isochronous center moreover we prove that the maximum number of critical periods is reachable

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