asymptotic behavior of an age structured fish population in this paper a model for the dynamics of an age structured population is considered in which the recruitment process is regulated by a density dependent factor the stability of the equilibrium age distributions is investagated and the region of attractivity is studied moreover some applications to fishery models are considered

an exact confidence band for one dimensional polynomial regression summary an exact piecewise polynomial simultaneous confidence band is described for onedimensional p i th order polynomial regression the band is constructed by placing intervals around the estimated response at the zeros of the pth order orthogonal polynomial with respect to the design points since under the usual assumptions the response estimates are uncorrelated at these zeros the construction of the exact band in the normal case is made easy

amplitude equations for time dependent solutions of the mckendrick equations the mckendrick equations model the dynamical behavior of age dependent populations these equations govern at time t the number of individuals of age a in a population known as the population density and arise from a conservation law subject to constitutive assumptions for the maternity and mortality rates in this paper we present a weakly nonlinear analysis of the mckendrick equations which describes the bifurcation to time dependent solutions whose amplitudes are governed by a complex landau stuart type equation the framework of the multiple scales approach is described for general assumptions on the maternity and mortality rates and the analysis is carried out in detail for an age independent mortality rate and a separable maternity function which includes a nonzero delay in the onset of maturation the resulting analysis indicates that the presence of the delay significantly affects the postbifurcational dynamics and introduces a codimension two bifurcation in the system

generalized luneburg canonical varieties and vector fields on quasicaustics some aspects of a particular class of bifurcation varieties which are provided by simple and unimodal boundary singularities are studied their correspondence to diffraction theory is established the generic caustics by diffraction on apertures are derived and their generating families for the corresponding lagrangian varieties are calculated it is proved that the quasicaustics associated to simple singularities are smooth hypersurfaces or whitney s cross caps the procedure for calculating the modules of logarithmic vector fields is given and the minimal sets of the corresponding generators are explicitly calculated the general boundary singularities are constructed and the structure of quasicaustics defined by parabolic singularities is investigated

stability analysis for equilibria in age specific population dynamics on considere une population de n especes dont les taux de vie dependent de l ge on etudie le comportement de stabilite a l equilibre pour les equations d evolution

nonparametric regression with predictors missing at random nonparametric regression with predictors missing at random mar where the probability of missing depends only on observed variables is considered univariate predictor is the primary case of interest a new adaptive orthogonal series estimator is developed large sample theory shows that the estimator is rate minimax and it is also sharp minimax whenever predictors are missing completely at random mcar furthermore confidence bands estimation of nuisance functions including conditional probability of observing the predictor design density and scale and multiple regression are also considered numerical study and a real example show feasibility of the proposed methodology for small samples supplementary materials containing results of the numerical study are available online

hopf bifurcation in a size structured population dynamic model with random growth abstract this paper is devoted to the study of a size structured model with ricker type birth function as well as random fluctuation in the growth process the complete model takes the form of a reaction diffusion equation with a nonlinear and nonlocal boundary condition we study some dynamical properties of the model by using the theory of integrated semigroups it is shown that hopf bifurcation occurs at a positive steady state of the model this problem is new and is related to the center manifold theory developed recently in p magal s ruan center manifold theorem for semilinear equations with non dense domain and applications to hopf bifurcation in age structured models mem amer math soc in press for semilinear equation with non densely defined operators

nonlinear hyperbolic partial differential equations for the dynamics of parasite populations abstract in the present paper we present a rigorous mathematical analysis of a general model for the dynamics of parasite populations which takes into account the following biological assumptions the host population is described by an immigration death process with age dependent death rates the parasites accumulate in the hosts according to an immigration death process where the immigration rate is an arbitrary function of the average parasite load in the total host population the presence of parasites in a host increases his death rate proportional to the number of parasites present after deriving a partial differential equation with a nonlinearity containing integrals of the unknown function we reduce the equation to an integral equation for the immigration rate of parasites we shall prove local existence and uniqueness under quite natural conditions there is a zero stationary solution and a bifurcating branch of positive solutions the zero solution is linearly stable below the bifurcation point for large transmission rate the asymptotic behavior of the average parasite load per host and of the life expectancy of the hosts and of the parasites is determined

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

an age dependent population model and its operator abstract an age dependent single population model in the form of a partial differential equation is discussed properties of the associated age dependent operator and the corresponding semigroup are obtained we then use these properties to discuss the stability of the null solution of this model the method proposed here may be useful for some other models

an age structured population model in a spatially heterogeneous environment existence and uniqueness theory abstract this paper considers the existence and uniqueness of solutions of an age structured population model in a spatially heterogeneous bounded environment the model describes individual organism movement of diffusion and advection in the older life stage but assumes stationarity of individuals in the embryonic stage the mathematical formulation is a nonlinear degenerate parabolic partial differential problem with non locally integro type initial boundary conditions

confidence bands in generalized linear models generalized linear models glm include many useful models this paper studies simultaneous confidence regions for the mean response function in these models the coverage probabilities of these regions are related to tail probabilities of maxima of gaussian random fields asymptotically and hence the so called tube formula is applicable without any modification however in the generalized linear models the errors are often non additive and non gaussian and may be discrete this poses a challenge to the accuracy of the approximation by the tube formula in the moderate sample situation here two alternative approaches are considered these approaches are based on an edgeworth expansion for the distribution of a maximum likelihood estimator and a version of skorohod s representation theorem which are used to convert an error term which is of order n 1 2 in one sided confidence regions and of n 1 in two sided confidence regions from the edgeworth expansion to a bias term the bias is then estimated and corrected in two ways to adjust the approximation formula examples and simulations show that our methods are viable and complementary to existing methods an application to insect data is provided code for implementing our procedures is available via the software parfit

bifurcation of time periodic solutions of the mckendrick equations with applications to population dynamics abstract a local two parameter bifurcation theorem concerning the bifurcation from steady states of time periodic solutions of a nonlinear system of partial integro differential equations is proved a hopf bifurcation theorem is derived as a corollary by means of independent and dependent variable changes this theorem is applicable to the general mckendrick equations governing the growth of an age structured population with the added feature here of a possible gestation period the theorem is based on a fredholm theory developed in the paper for the associated linear equations an application is given to an age structured population whose fecundity is density and age dependent and it is shown that for a sufficiently narrow age specific reproductive and resource consumption window steady state instabilities accompanied by sustained time periodic oscillations occur when the birth modulus surpasses a critical value

equidistributing principles in moving finite element methods abstract recently miller and his co workers proposed a moving finite element method based on a least squares principle this was followed by a similar method by the present authors using a petrov galerkin approach in this paper the two methods are compared in particular it is shown that both methods move their nodes according to an approximate equidistributing principle this observation leads to a criterion for the placement of the nodes it is also shown that the penalty function designed by miller may also be used with the petrov galerkin method finally numerical examples are given illustrating the performance of the two methods

global branches of equilibrium solutions of the mckendrick equations for age structured population growth abstract the existence of positive equilibrium solutions of the mckendrick equations for the dynamics of an age structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter under only continuity assumptions on the density dependent death and tertility rates it is shown that a global continuum of positive equilibria exists in a certain banach space this continuum connects from the trivial solution at n 1 to the boundary of the domain on which the problem is posed results concerning the spectrum are given in particular some circumstances are described under which positive equilibria exist for all n values greater than the critical value n 1

simultaneous confidence bounds in multiple regression using predictor variable constraints abstract this article presents a method for approximating the coverage probability of simultaneous confidence bounds for multiple regression functions when the vector of predictor variables is constrained to lie in a polyhedral convex set the method is useful because it allows one to construct simultaneous confidence intervals with prescribed coverage probability for the regression function evaluated at various settings of the predictor variables which are narrower than bounds obtained without using the predictor variable constraints for a family of two sided simultaneous confidence bounds that includes scheffe type and constant width bounds the probability of coverage is related to the distribution of the maximum euclidean norm of the projection onto a polyhedral cone for a pair of random vectors with known joint distribution an analogous relation holds for one sided bounds if an algorithm for computing the projection onto the cone is available then these results enable one to use the monte carlo

density dependent cellular growth in an age structured colony abstract the mckendrick von foerster model is often used to model cell colonies with both constant and arbitrarily varying generation times our purpose here is to extend the model by linking the fluctuation of the generation time to the history of the colony such a linkage is natural since for example when a colony grows large enough to severely tax its environment the generation time lengthens accordingly the resulting model consists of a pair of hyperbolic balance laws with a boundary condition of the form u 0 t 2 1 m t u m t t where m depends functionally on the solution u we show the model to be well posed and demonstrate its ability to duplicate observed biological phenomena in a simple case

the semigroup associated with nonlinear age dependent population dynamics abstract the solutions of the equations of nonlinear age dependent population dynamics may be associated with a strongly continuous semigroup of nonlinear operators in the banach space l 1 0 r n the infinitesimal generator of this nonlinear semigroup is characterized and an exponential representation formula for the nonlinear semigroup is obtained in terms of the infinitesimal generator

simultaneous confidence bands for linear regression with heteroscedastic errors abstract the scheffe method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space when the bands need only hold for a subset of that space previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence data with heteroscedastic errors occur often and unless some transformation is feasible there is no obvious way to construct bands using the current methods this article shows how to construct approximate simultaneous confidence bands when the errors are heteroscedastic and symmetric the method works when the weights are known or unknown and have to be estimated the region in which the bands must hold can be quite general and will work for any linear unbiased estimate of the regression surface the method can even be extended to linear estimates with a small amount of bias such as nonparametric kernel regression smoothers

logistic models of structured population growth abstract a general model of structured population dynamics with logistic type nonlinearity is considered the model consists of a semilinear hyperbolic partial differential equation with a linear boundary condition and an initial value the logistic nonlinearity corresponds to increased mortality as the population increases the problem is treated as an abstract semilinear evolution equation sufficient conditions are given for the solutions to converge to an equilibrium solution applications are made to age structured populations size structured populations multispecies structured populations and cell populations

on the qualitative behaviour of populations with age specific interactions abstract a mathematical model describing the age dependent dynamics of a population is studied under very general assumptions existence of nonzero equilibrium solutions is proven for some special kind of rate law it is shown that this model can asymptotically be described by means of a simpler system of ordinary differential equations an example is given where the model admits nonconstant time periodic solutions

on the equations of age dependent population dynamics the aim of this work is to give a direct and constructive proof of existence and uniqueness of a global solution to the equations of age dependent population dynamics introduced and considered by m e gurtin r c maccamy in 3 the linear theory was developed by f r sharpe a j lotka 10 and a g mckendrick 8 see also 1 9 and extended to the nonlinear case by m e gurtin r c maccamy in 3 see also 4 5 6 in 3 the key of the proof of existence and uniqueness was to reduce the problem to a pair of integral equations in fact as we shall see the problem can also be solved by a simple fixed point argument to outline more clearly the ideas of the proof we will first discuss the setting and the resolution of the linear case and then we will generalize the results of 3

stability of biochemical reaction tanks abstract in this paper we study the dynamics of a continuously fed chemical reaction tank in which a biological organism promotes the chemical reaction the mathematical model proposed takes the age structure of the organism into account an analytic procedure is used to compute the critical parameter ranges which lead to limit cycle oscillations of the population of the organism computer simulations are then used to confirm the shape of some of the limit cycles

lagrangian submanifolds in product symplectic spaces we analyze the global structure of lagrangian grassmannian in the product symplectic space and investigate the local properties of generic symplectic relations the cohomological symplectic invariant of discrete dynamical systems is generalized to the class of generalized canonical mappings lower bounds for the number of two point and three point symplectic invariants for billiard type dynamical systems are found and several examples of symplectic correspondences encountered from physics are presented

exact confidence bands for linear regression over intervals abstract exact simultaneous confidence intervals and bands for the regression line on a set cx in simple linear regression have been known only when cx is a finite set with one or two points or when cx is a finite or infinite interval otherwise conservative bands have been used in this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points also tables are provided for cases of finite cx with three points and of cx an interval

a class of nonlinear diffusion problems in age dependent population dynamics in this paper we study the existence the uniqueness and the asymptotic behaviour of a class of nonlinear diffusion problems these problems are motivated by models of age dependent population dynamics which originate in the article by gurtin maccamy ll only a few special cases of these models have been analyzed to date with the most recent published work being that of maccamy 17 gurtin maccamy 12 and langlais 15 161 the cases treated in 12 171 are restricted to special simple forms of the birth and death moduli that occur in these models and to a specific form of the nonlinear diffusion mechanism on the other hand langlais 16 considers a different nonlinear diffusion mechanism and obtains a type of generalized solution for general forms of the birth and death moduli in this work we consider a general form of the nonlinear diffusion mechanism and we develop a method for establishing the existence and uniqueness of solutions of the resulting equations our method allows us to obtain classical solutions even with general forms of the birth and death moduli we also describe the asymptotic behaviour of the solutions when the time variable becomes large and apply our results to some specific examples the equations that we study are motivated as follows consider a population that can disperse in a spatial domain r for simplicity we take q j where j is an open interval in r but it will be clear from the context that more general regions q of r can be considered let a t x denote the number of individuals per unit length and unit age that are of age a at time t and are located at the position x e j the total population per unit length at time t and at position x is given by