permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

permanence for a two species gause type ratio dependent predator prey system with time delay in a two patch environment this paper is devoted to a two species periodic gause type ratio dependent predator prey system with time delay in a two patch environment by using the comparison theorem of differential equations we establish sufficient conditions for the permanence of the system as corollaries some applications are listed in particular our results generalize and improve some known ones

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

a theory of exact and approximate configurational invariants abstract a theory of integrable hamiltonian systems in two dimensions is formulated and applied the four dimensional phase space problem that is the vanishing of the poisson bracket between another invariant and the hamiltonian is here reduced to the solution of a series of two dimensional configuration space equations the theory is also applicable to more than two dimensions the constraints are found which admit to integrability of the orbits for magnetic or coriolis forces as well as for forces derivable from a potential when a system admits a given invariant the invariant is found for example by quadrature a number of examples including known and apparently previously unknown invariants are given the theory of exact integrals of the motion also can be extended to the derivation of approximate invariants the orbital structure of integrable or approximately integrable systems correlates with the degree maximum power of the velocity of a standardized invariant the theory admits a variational principle among other approximation techniques for the computation of a best approximate invariant the problem of the general cubic potential with one symmetric coordinate v 1 2 ax 2 1 2 by 2 cx 2 y 1 3 dy 3 of which the well studied henon heiles potential is the special case for a b and c d is examined in detail

schrodinger equation with time dependent boundary conditions a schrodinger equation for a well potential with varying width is studied generalized canonical transformations are shown to transform the problem into a time dependent harmonic oscillator problem submitted to fixed boundary conditions this transformed problem is solved by a perturbation technique and gives the evolution of the average energy of the system according to the motion of the well motions corresponding to a renormalization or compaction group are shown to be solvable by separation of variables

non parametric analysis of a proportional wearout model for accelerated degradation data abstract in analyzing the reliability of a product the quantity of interest is usually the time to failure however many products may degrade before failure and it is possible to record the actual degradation on units as a function of time the time to failure is defined as the time when a unit reaches a particular level of degradation this paper focuses on accelerated degradation models in life testing a new model for accelerated degradation data called a proportional wearout model is proposed the mean degradation curve and the acceleration factor for each stress level are estimated non parametrically a point estimate and a bootstrap confidence interval for the time to failure of the mean degradation curve under the usual use condition t0 are obtained a goodness of test that may be applied to this model and other degradation models is proposed the proportional wearout model is fit to sliding metal wear data w meeker l escobar statistical methods for reliability data john wiley and sons 1998 and the results are compared to the fit of the time scale model used in j shaiu h lin analyzing accelerated degradation data by non paramateric regression ieee transactions on reliability 48 1999 149 158 it is shown that the proportional wearout model fits these data well but the time scale model does not

the spectral geometry of the hopf fibration we study the spectral geometry of the hopf fibration and determine the right invariant metrics on for which there exist eigenforms of the laplacian on which pull back to eigenforms of the laplacian on we show that the pull back of the volume form on can be an eigenform of the laplacian on with non zero eigenvalue we show that if is a principal bundle with a bundle metric and that if then eigenvalues cannot change thus eigenvalues do not change for the fibrations and if we also study the corresponding questions in the complex category for the fibration of the hopf manifold

estimation of reliability in field performance studies likelihood based methods are developed for the analysis of field performance studies with particular attention centered on the estimation of regression coefficients in parametric models failure record data are those in which the time to failure and the regressor variables are observed only for those items that fail in some prespecified follow up or warranty period 0 t it is noted that for satisfactory inference about baseline failure rates or regression effects it is usually necessary to supplement the failure record data either by incorporating specific prior information about x or by taking a supplementary sample of items that survive t general methods are outlined and specific formulas for various likelihood based methods are obtained when the failure time model is exponential or weibull in these models the methods are compared with respect to asymptotic efftciency of estimation several extensions to more complicated sampling plans are considered

the inverse of a singular linear transformation and some applications in constrained mechanics we extend the notion of the moore penrose inverse of a matrix to the case of a morphism between vector bundles and a more general concept is used to develop the geometric theory of udwadia and kalaba s approach to constrained lagrangian mechanics

non noether constants of motion mathematical tools of modern differential geometry are used to derive in an intrinsic formulation more general results about non noether constants of motion a relation between two different ways of obtaining such constants is found by making use of leverrier s method of determining the characteristics polynomial of a matrix in terms of the traces of its increasing powers

positive periodic solution of two species ratio dependent predator prey system with time delay in two patch environment in this paper we are concerned with the existence of positive periodic solution to a class of two species ratio dependent predator prey diffusion model with time delay by using the continuation theorem of coincidence degree theory we transform this problem into a problem of calculating the topological degree of a continuous mapping and then some sufficient conditions of the existence of positive periodic solution is established for the system

invariance of second order ordinary differential equations under two dimensional affine subalgebras of ermakov pinney lie algebra abstract using the only admissible rank two realisations of the lie algebra of the affine group in one dimension in terms of the lie algebra of lie symmetries of the ermakov pinney ep equation some classes of second order nonlinear ordinary differential equations solvable by reduction method are constructed one class includes the standard ep equation as a special case a new ep equation with a perturbed potential but admitting the same solution formula as ep itself arises the solution of the dissipative ep equation is also discussed

statistical inference of a time to failure distribution derived from linear degradation in the study of semiconductor degradation records of transconductance loss or threshold voltage shift over time are useful in constructing the cumulative distribution function cdf of the time until the degradation reaches a specified level in this article we propose a model with random regression coefficients and a standard deviation function for analyzing linear degradation data both analytical and empirical motivations of the model are provided we estimate the model parameters the cdf and its quantiles by the maximum likelihood ml method and construct confidence intervals from the bootstrap from the asymptotic normal approximation and from inverting likelihood ratio tests simulations are conducted to examine the properties of the ml estimates and the confidence intervals analysis of an engineering dataset illustrates the proposed procedures

persistence and stability for a two species ratio dependent predator prey system with time delay in a two patch environment abstract a two species ratio dependent predator prey diffusion model with time delay is investigated it is shown that the system is permanent under some appropriate conditions and sufficient conditions are obtained for the local and global stability of the positive equilibrium of the system

the nonlinear mixed effects model with a smooth random effects density summary the fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood the density of the random effects is assumed to be smooth but is otherwise unrestricted the method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood standard algorithms are used for optimization empirical bayes estimates of random coefficients are obtained by computing posterior modes the method is applied to data from pharmacokinetics and properties of the method are investigated by application to simulated data

on the determination of non local symmetries the importance of non local symmetries of differential equations lies in their manifestation as lie point symmetries of the equations resulting from reduction of order the reason for the determination of these symmetries in second order equations with only one lie point symmetry is self evident however the disadvantage of non local symmetries is that no systematic approach to their determination exists we present such an approach applicable to differential equations of any order and apply it to some second order ordinary differential equations and show that they have a rich occurrence we also look at possible generalizations of the concept of non local symmetries

lie symmetries and invariants of the lotka volterra system in this paper we use the lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3d lotka volterra system

an exact invariant for a class of time dependent anharmonic oscillators with cubic anharmonicity an exact invariant is constructed for a class of time dependent anharmonic oscillators using the method of the lie theory of extended groups the presence of the anharmonic term imposes a constraint on the nature of the time dependence for a subclass it is possible to obtain an energy like integral and a condition under which the motion is bounded

lie transformation group solutions of the nonlinear one dimensional vlasov equation the solution of the exact nonlinear one dimensional vlasov equation with a space and time dependent electric field is reduced to the solution of a nonlinear first order ordinary differential equation with two subsidiary equations the reduction holds for any electric field nonlinear in the spatial coordinate or for a subclass of electric fields linear in the spatial coordinate and is equivalent to the solution of a generalized bernstein greene kruskal bgk vlasov equation with a velocity dependent lorentz force the lie method for the solution of differential equations invariant under a transformation group has been used to calculate the group generator the canonical variables and the generalized bgk vlasov equation analytical forms for the functional dependence of the vlasov equation one particle distribution function are given

invariants for dissipative nonlinear systems by using rescaling a rescaling transformation of space and time is introduced in the study of nonlinear dissipative systems that are described by a second order differential equation with a friction term proportional to the velocity t v the transformation is of the form x t where x c t t d dt a2 t this rescaling is used to find each potential for which there exists an exact invariant quadratic in the velocity and to find the invariant the invariants are found explicitly for a power law potential t xm 1 m 1 and an arbitrary coefficient of friction t we show in an example how the rescaling transformation can be chosen to give an asymptotic solution of the equation in cases where the exact invariant does not exist for certain parameters the asymptotic solution is a self similar solution that is an attractor for all initial conditions the technique of applying a rescaling transformation has been useful in other problems and may have additional practical applications

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

classification scheme for two dimensional ermakov type systems and generalizations we describe a classification scheme for certain pairs of coupled nonlinear second order ordinary differential equations having a first integral which can be obtained by an ermakov type elimination procedure the classification produces a hierarchy of systems having different levels of generality different cases within the same level are distinguished by the integrability of a certain one form which is related to a nonlinear superposition law between the two equations the study of these one forms and the classification are made systematic by using the general reduction theorem of pfaffian forms the paper contains illustrations of the way previous examples fit into the classification scheme and a discussion of its generalization to higher dimensions

periodicity in a logistic type system with several delays with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of the following several delays logistic type system du t dt u t a t j 1mb j t u t t j t q j where a t b j t are positive periodic continuous functions with periodic w 0 t j t are nonnegative continuous periodic functions with periodic w 0 after that by constructing a suitable lyapunov functional some sufficient conditions which guarantee the stability of the positive periodic solutions are obtained

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

sl 3 r as the group of symmetry transformations for all one dimensional linear systems iii equivalent lagrangian formalisms the sl 3 r theory of projective transformations of the plane is applied to the lagrangians of all one dimensional newtonian linear systems noether and non noether equivalent lagrangians as well as the associated noether and non noether constants of motion are thus obtained in a completely general and systematic way complete unification is achieved by this group theoretic approach to lagrangians of one dimensional linear systems

canonoid transformations from a geometric perspective the concept of canonoid transformation for a locally hamiltonian vector field is introduced and its relation with the existence of non noether constants of the motion is shown from a geometrical viewpoint the equations determining generating functions for such canonoid transformations are obtained and applications to some particular problems given

canonical transformations theory for presymplectic systems we develop a theory of canonical transformations for presymplectic systems reducing this concept to that of canonical transformations for regular coisotropic canonical systems in this way we can also link these with the usual canonical transformations for the symplectic reduced phase space furthermore the concept of a generating function arises in a natural way as well as that of gauge group

hamiltonian structure and integrability of the stationary kuramoto sivashinsky equation in this article the stationary kuramoto sivashinsky ks equation is studied it is shown first that this equation can be transformed into a one dimensional hamiltonian system describing the motion of a particle in a time dependent potential second working with this formalism and coming back then to the initial ks equation a subset of initial conditions is derived for which the corresponding solutions u x will behave like the dominant pole 120 x x0 3 deduced from the painleve analysis and will explode in a finite time finally special attention is given to the well known kuramoto tsuzuki solution and it is shown that provided the independent variable x is initialized in a specified domain this solution explodes also like 120 x x0 3

lie algebras under constraints and non bijective canonical transformations the concept of a lie algebra under constraints is developed in connection with the theory of non bijective canonical transformations a finite dimensional vector space m carrying a faithful linear representation of a lie algebra l is mapped into a lower dimensional space m in such a manner that a subalgebra l0 of l is mapped into d l0 0 the lie algebra l under the constraint d l0 0 is the largest subalgebra l1 of l that can be represented faithfully on m if l0 is semisimple then l1 is shown to be the centraliser cent ll0 if l is semisimple and l0 is a one dimensional diagonal subalgebra of a cartan subalgebra of l then l1 is shown to be the factor algebra cent ll0 l0 the later two results are applied to non bijective canonical transformations generalising the kustaanheimo stiefel transformation

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

arma covariance structures with time heteroscedasticity for repeated measures experiments abstract rochon and helms 1989 presented a model for analyzing repeated measures experiments the general linear model was used to assess the influence of covariate information and arma time series models were put forward to characterize the covariance matrix among the repeated measures practical experience has suggested however that the arma assumption of constant variances and autocovariances over time is too restrictive for many applications for example observations may be relatively stable toward the beginning of the study but become more variable toward the end this article presents a modification to this structure which provides for heteroscedasticity over time maximum likelihood ml estimation procedures are considered and the estimators are found to enjoy optimal large sample properties a scoring algorithm is described for iterating to a solution of the ml equations the model is illustrated with data from a clinical trial investigating human erythropoietin for treating anemia in end

berry s phase and wavefunctions for time dependent hamilton systems an alternative derivation of berry s phase 1985 to that given by morales 1988 is given for non autonomous hamiltonian systems which admit an energy like first integral the generality of the problems treated is greater

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

bootstrap confidence intervals for a class of parametric problems summary we consider the following class of problems having observed a multivariate normal data vector y with unknown mean vector q covariance matrix the identity find an approximate confidence interval for 0 t q a real valued function of q a simple geometric construction is given which leads to highly accurate solutions this construction shows that the standard approximation based on maximum likelihood theory 04 cz00 can be quite misleading when 0 is nonlinear in q we discuss bootstrap based confidence intervals which remove most of the error in the standard approximation at the expense of considerably more calculation the bootstrap intervals are invariant under transformation of both y and i and so they automatically produce accurate solutions in problems which can be transformed to multivariate normality without requiring knowledge of the normalizing transformation

the effect of dispersal on permanence in a predator prey population growth model abstract in this paper we consider a periodic predator prey system where the prey can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation we assume a volterra within patch dynamic under the assumption that the average of dispersal rate from patch 1 to patch 2 is less than that of the intrinsic growth rate of prey in patch 1 we provide a sufficient and necessary condition to guarantee the prey and predator species to be permanent by using the main techniques in 1

sl 3 r as the group of symmetry transformations for all one dimensional linear systems the converse problem of similarity analysis is solved in general for the finite symmetry transformations of any inhomogeneous ordinary linear differential equation of the second order x f2 t x f1 t x f0 t the eight parameter realizations of the symmetry group are obtained in the form f 1p2 f where f stands for transformations of t x that depend exclusively on the fundamental solutions of the equation and where p2 is an arbitrary projective transformation in the plane thus it is shown that the full point symmetry group corresponds to sl 3 r indeed without recourse to the lie algebra also a technique is obtained for calculating the finite point symmetry realization of sl 3 r for any given one dimensional linear system some miscellaneous examples are given

geometric theory of the equivalence of lagrangians for constrained systems the lagrangian description of a system is analysed from a geometric viewpoint in order to find a concept for equivalence of singular lagrangians generalising that of the regular case geometric and gauge equivalence of singular lagrangians are studied and the authors also give some conditions in which second order differential equations exist satisfying the dynamical equation on the final constraint submanifold

a time discrete and zero adjusted gamma process model with application to degradation analysis abstract the standard gamma process is widely used for degradation modelling when the degradation paths are always positive and strictly increasing nevertheless the standard gamma process is considered inappropriate if the observed sample paths are horizontal over several time intervals motivated by this phenomenon we develop a time discrete and zero adjusted gamma process model statistical inference method of this model is then proposed to illustrate our proposed model both simulation study and real data analysis are conducted whose results demonstrate that the proposed model has satisfactory fit performance and predictive performance

on a nonlinear nonautonomous predator prey model with diffusion and distributed delay in this paper a nonlinear nonautonomous predator prey model with diffusion and continuous distributed delay is studied where all the parameters are time dependent the system which is composed of two patches has two species the prey can diffuse between two patches but the predator is confined to one patch we first discuss the uniform persistence and global asymptotic stability of the model after that by constructing a suitable lyapunov functional some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained an example shows the feasibility of our main results

periodic solutions and permanence for a delayed nonautonomous ratio dependent predator prey model with holling type functional response by using the continuation theorem of coincidence degree theory the existence of positive periodic solutions for a delayed ratio dependent predator prey model with holling type iii functional response x t x t a t b t t k t s x s ds c t x2 t y t m2y2 t x2 t y t y t e t x2 t m2y2 t x2 t d t is established where a t b t c t e t and d t are all positive periodic continuous functions with period 0 m 0 and k s is a measurable function with period is a nonnegative constant the permanence of the system is also considered in particular if k s 0 s where 0 s is the dirac delta function at s 0 our results show that the permanence of the above system is equivalent to the existence of positive periodic solution

on certain canonoid transformations and invariants for the parametric oscillator in classical mechanics a transformation in phase space is said to be canonoid if it maps only some hamiltonian systems into hamiltonian systems once canonoid transformations are considered these systems can be classically described by means of lagrangians or hamiltonians other than the conventional ones in this context a basic role is played by the dynamical invariants generated through the poisson brackets of the new independent variables in phase space here we obtain the explicit form of special canonoid transformations of the polynomial type for systems which can be classically described by an equation of the parametric oscillator type and discuss some algebraic properties shown by the associated dynamical invariants

extended legendre transformation approach to the time dependent hamiltonian formalism the hamiltonian formalism for time dependent systems is developed using vector fields defined in the extended cotangent bundle t q r the extended hamiltonian h is obtained using the extended legendre transformation associated to an extended lagrangian l previously defined in t q r and then the techniques of symplectic mechanics are employed in t q r to study the properties of the extended hamiltonian system finally this approach is related with the multisymplectic formalism and other extended approaches

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

on the inverse problem of the calculus of variations in field theory the inverse problem of the calculus of variations is investigated in the case of field theory uniqueness of the action principle is demonstrated for the vector laplace equation in a non decomposable riemannian space as well as for the harmonic map equation

non symplectic symmetries and bi hamiltonian structures of the rational harmonic oscillator the existence of bi hamiltonian structures for the rational harmonic oscillator non central harmonic oscillator with rational ratio of frequencies is analysed by making use of the geometric theory of symmetries we prove that these additional structures are a consequence of the existence of dynamical symmetries of non symplectic non canonical type the associated recursion operators are also obtained

first integrals for the modified emden equation q α t q qn 0 it is shown that the modified emden equation q t q qn 0 possesses first integrals for functions t other than kt 1 the function t is obtained explicitly in the case n 3 and parametrically for other n 2 the case n 2 is seen to be particularly difficult to solve

periodicity in a delayed ratio dependent predator prey system abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio dependent predator prey system in a periodic environment

a direct approach to finding exact invariants for one dimensional time dependent classical hamiltonians for a classical hamiltonian h 1 2 p2 v q t with an arbitrary time dependent potential v q t exact invariants that can be expressed as series in positive powers of p i q p t n 0pnfn q t are examined the method is based on direct use of the equation di dt i t i h 0 a recursion relation for the coefficients fn q t is obtained all potentials that admit an invariant quadratic in p are found and for those potentials all invariants quadratic in p are determined the feasibility of extending the analysis to find invariants that are polynomials in p of higher degree than quadratic is discussed the systems for which invariants quadratic in p have been found are transformed to autonomous systems by a canonical transformation

effect of weak prey in leslie gower predator prey model a leslie gower prey predator model incorporating partial prey protection is proposed prey densities are divided into two groups strong and weak the special dynamic of each group is considered the condition of existence and uniqueness of the equilibrium point in the positive octant is determined and by constructing a suitable lyapunov function it is shown that the unique equilibrium point is stable in the positive octant the effects of strong prey becoming weak prey is studied and it is shown that it has no influence on the persistent property of the system and can enhance the co existence of the prey predator

global stability for a class of predator prey systems this paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator prey systems the dulac s criterion is applied and liapunov functions are constructed to establish the global stability

extended tangent bundle formalism for time dependent lagrangian systems the lagrangian formalism for time dependent systems is developed using vector fields defined in the extended tangent bundle t q r the definition of the time independent extended lagrangian function l associated to a time dependent lagrangian l is given and then the techniques of symplectic mechanics are used to prove some properties of the equations determining the euler lagrange vector field the relations between the time independent and the time dependent helmholtz conditions are analyzed from a geometric perspective and finally the noether theorem for the extended lagrangian l is considered

generalized canonical transformations for time dependent systems we introduce the concept of generalized canonical transformations as symplectomorphisms of the extended phase space we prove that any such transformation factorizes in a standard canonical transformation times another one that changes only the time variable the theory of generating functions as well as that of hamilton jacobi is developed some further applications are developed

lagrangian submanifolds and higher order mechanical systems higher order lagrangian and hamiltonian systems time dependent or independent are interpreted in terms of lagrangian submanifolds of sympletic higher order tangent bundles the relation between both formalisms is given

cooperative systems of differential equations with concave nonlinearities on considere le systeme dynamique discret engendre par une application monotone concave t r n r n on etudie ensuite des systemes d equations differentielles cooperatifs periodiques x f t x a non linearites concaves

on a periodic multi species ecological model a periodic predator prey model with m predators and n preys is proposed in this paper which can be seen as the modification of the traditional lotka volterra model by using comparison theorem the ultimately bounded region of the system is obtained by using comparison theorem and brouwer fixed point theorem sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained finally by constructing a suitable lyapunov function some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system the results obtained here generalized the main results of j d zhao w c chen global asymptotic stability of a periodic ecological model applied mathematics and computation 147 3 2004 881 892

theory of nonbijective canonical transformations in mechanics application to the coulomb problem it is shown that the study of nonbijective transformation requires a fiber bundle formulation of mechanics the conditions upon which nonbijective canonical point transformations can be defined are given then as an example we apply that theory to the study of the coulomb problem in two and three dimensions the hopf fibration leads to an inverse harmonic oscillator problem since the completion of this work a paper by g h ringwood and j t devreese has been published in j math phys 21 1390 1980 dealing with the same problem their work is based on the construction of propagators in quotient spaces the identity between the propagator prescriptions and nonlinear canonical transformations is not automatically fulfilled therefore it seems that the reliability of their results is not due to their method which in general is not correct but to an underlying property of the transformation used namely the kustaanheimo stiefel map see our results

first integrals for a general linear system of two second order odes via a partial lagrangian the partial noether operators and first integrals of a general system of two linear second order ordinary differential equations odes with variable coefficients are studied by means of a partial lagrangian the canonical form for the general system of two second order ordinary differential equations is invoked and all cases of this system are discussed with respect to partial noether operators we also tabulate the results for the special case b x c x of the system which was considered elsewhere using a lagrangian and a partial lagrangian the first integrals are obtained explicitly by exploiting a noether like theorem with the help of partial noether operators this study gives a new way to construct first integrals for systems without a variational principle as not all linear equations have a lagrangian physical applications to conservative and oscillator mechanical systems are given

the effect of diffusion on the time varying logistic population growth abstract in this paper we consider the effect of diffusion on the species that live in changing patches environment different from the former studies 1 4 we pay attention to the more important situation in conservation biology that species live in a weak patches environment in the sense that species in some of the isolated patches will be extinct without the contribution from other patches we obtain an interesting result the identical species can persist for some diffusion rates and can also vanish for another set of restriction on diffusion rates

some simple methods for estimating intraindividual variability in nonlinear mixed effects models methods are proposed to improve both population and individual inference within the nonlinear random coefficient regression framework by incorporating possible heterogeneity in the intraindividual variance structure these methods extend existing variance function estimation techniques by pooling information across individuals the methods are appropriate when it is reasonable to assume that there exists a common intraindividual variance structure

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

extension of giacomini s results concerning invariants for one dimensional time dependent potentials one dimensional time dependent potentials are considered for which an invariant can be expressed in terms of the potential and the momentum according to the formulation of giacomini new solutions of giacomini s equations are derived in addition possibilities are discussed for extending giacomini s approach to more general systems

poisson maps and canonoid transformations for time dependent hamiltonian systems after a new presentation of the geometric theory of time dependent systems in the hamiltonian formulation using poisson structures a characterization of canonoid transformations with respect to a dynamical vector field is given the associated constants of motion and the generating functions of canonoid transformations are also studied the theory is illustrated with several examples

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

models for longitudinal data with random effects and ar 1 errors abstract for longitudinal data on several individuals linear models that contain both random effects across individuals and autocorrelation in the within individual errors are studied a score test for autocorrelation in the within individual errors for the conditional independence random effects model is first developed an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and autoregressive ar 1 errors is then derived empirical bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with ar 1 errors model are also considered a numerical example is presented to illustrate these methods

one dimensional nonautonomous dynamical systems with exact transcendental invariants new classes of dynamical systems for nonautonomous particle motion in one dimension are exactly solved in terms of arbitrary functions of both space and time besides extending considerably the class of mechanical systems with known exact solutions the explicit dependence on space represents an improvement on previous results such as those obtained by lewis and leach this might be helpful for extending the lewis and symon technique of constructing the bgky type of solutions for the vlasov poisson equations

an algebraic and geometric approach to non bijective quadratic transformations this work is concerned with an extension of the so called levi civita and kustaanheimo stiefel transformations the extension is achieved along two lines firstly the authors examine the latter transformations in other dimensions than the ones originally considered by on the one hand levi civita and on the other hand by kustaanheimo and stiefel secondly they pass from the compact to the non compact case this leads to quadratic non bijective transformations that they refer to as hurwitz or kustaanheimo stiefel like and quasihurwitz or levi civita like transformations the hurwitz and quasihurwitz transformations are introduced and studied in an algebraic framework which relies on the use of eight dimensional cayley dickson algebras an explicit formulation of the hurwitz and quasihurwitz transformations is also given in terms of clifford algebras the hurwitz transformations are investigated from a geometrical viewpoint indeed they are connected to hopf and pseudohopf fibrations finally some differential aspects of the hurwitz and to a lesser extent quasihurwitz transformations are developed in view of future physical applications

equivalent lagrangians multidimensional case we generalize a theorem known for one dimensional nonsingular equivalent lagrangians l and to the multidimensional case in particular we prove that the matrix which relates the left hand sides of the euler lagrange equations obtained from l and is such that the trace of all its integer powers are constants of the motion we construct several multidimensional examples in which the elements of are functions of position velocity and time and prove that in some cases equivalence prevails even if det 0

canonical equivalence of integrable systems their associated semi groups and moment systems abstract by exhibiting the canonical transformation that does the job we prove that all integrable systems on r 2n are canonically equivalent this equivalence has a unitary counterpart in the quantum mechanical set up and a nonunitary counterpart transforming the semigroups associated to classical systems it can also be used to transform the monet system moment and cross sequences associated to each hamiltonian onto each other

a separability theorem for dynamical systems admitting alternative lagrangian descriptions by generalising earlier results the authors prove that whenever a lagrangian dynamical system can be associated with a 1 1 type tensor field which is left invariant by the dynamics satisfies the nijenhuis condition and is compatible with the tangent bundle structure the system necessarily decomposes into a collection of lower dimensional mutually non interacting lagrangian subsystems

the qualitative analysis of n species nonlinear prey competition systems in this paper we consider an n species nonlinear prey competition system using the differential inequality theorem and the v function method we obtain some sufficient conditions for the permanence and global asymptotic stability of the system

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

blow up regularization of singular lagrangians we propose a method for regularizing singular lagrangians by adding new degrees of freedom we illustrate this regularization method with some particular examples this procedure is shown to be very useful when the lagrangian is homogeneous of degree one in the velocities giving rise to an identically vanishing hamiltonian

hamiltonian dynamics on the symplectic extended phase space for autonomous and non autonomous systems we will present a consistent description of hamiltonian dynamics on the symplectic extended phase space that is analogous to that of a time independent hamiltonian system on the conventional symplectic phase space the extended hamiltonian h1 and the pertaining extended symplectic structure that establish the proper canonical extension of a conventional hamiltonian h will be derived from a generalized formulation of hamilton s variational principle the extended canonical transformation theory then naturally permits transformations that also map the time scales of the original and destination system while preserving the extended hamiltonian h1 and hence the form of the canonical equations derived from h1 the lorentz transformation as well as time scaling transformations in celestial mechanics will be shown to represent particular canonical transformations in the symplectic extended phase space furthermore the generalized canonical transformation approach allows us to directly map explicitly time dependent hamiltonians into time independent ones an extended generating function that defines transformations of this kind will be presented for the time dependent damped harmonic oscillator and for a general class of explicitly time dependent potentials in the appendix we will re establish the proper form of the extended hamiltonian h1 by means of a legendre transformation of the extended lagrangian l1

on a delayed nonautonomous ratio dependent predator prey model with holling type functional response and diffusion abstract a two species periodic ratio dependent predator prey model with holling type functional response and diffusion is investigated three different sets of sufficient conditions one set is diffusive independent and the other two sets are diffusive dependent which ensure the permanence of the system and a set of sufficient condition which ensure the extinction of the predator species are obtained examples together with their numeric simulations show the feasibility of the main results

permanence and extinction of a three species ratio dependent food chain model with delay and prey diffusion abstract in this paper we study a diffusive three species ratio dependent food chain model using differential inequality to obtain sufficient conditions that ensure the permanence of the system and the extinction of predator species our results reinforce the main result of sun wen shihua chen and huihai mei positive periodic solution of a more realistic three species lotka volterra model with delay and density regulation chaos solitons and fractals in press

frobenius method and invariants for one dimensional time dependent hamiltonian systems we apply the frobenius integrability theorem in the search for invariants for one dimensional hamiltonian systems with a time dependent potential we obtain several classes of potential functions for which the frobenius method ensures the existence of a two dimensional foliation to which the motion is constrained in particular we derive a new infinite class of potentials for which the motion is assuredly restricted to a two dimensional foliation in some cases the frobenius method allows the explicit construction of an associated invariant the inverse result is proven that if an invariant is known then it can always be furnished by the frobenius method

existence of four periodic solutions for a generalized delayed ratio dependent predator prey system in this paper by using the continuation theorem of coincidence degree theory we obtain the existence condition of at least four periodic solutions for a delayed ratio dependent predator prey system an example is represented to illustrate the feasibility of our main result