asymptotic pattern for a partial neutral functional differential equation abstract in the present article the asymptotic speed of spread and traveling wavefronts of a partial neutral functional differential equation pnfde are investigated a variable transform yields to a partial retarded functional differential equation prfde with infinite number of constant delays the relation between the above pnfde and prfde is studied and an equivalence in a certain meaning of these two equations is verified using this equivalence we in fact obtain the existence and uniqueness of solution for the initial value problem of the pnfde we then consider the truncated system of the above prfde which is a partial retarded functional differential equation with finite number of constant delays we establish the existence of the traveling wave solution and the spreading speed for this truncated system a limit argument and the method of finite delay approximation are used to obtain the existence of the traveling wave solutions and the spreading speed for the prfde with infinite number of constant delays this leads to the existence of the traveling wave solution and the spreading speed for the considered pnfde by the above equivalence at last we confirm that the spreading speed is coincidental with the minimal wave speed for all equations an example is given to illustrate the application of our results

identification and estimation of nonlinear dynamic panel data models with unobserved covariates abstract this paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved covariates including such unobserved covariates may control for both the individual specific unobserved heterogeneity and the endogeneity of the explanatory variables without specifying the distribution of the initial condition with the unobserved variables we show that the models are nonparametrically identified from two periods of the dependent variable y i t and three periods of the covariate x i t the main identifying assumptions include high level injectivity restrictions and require that the evolution of the observed covariates depends on the unobserved covariates but not on the lagged dependent variable we also propose a sieve maximum likelihood estimator mle and focus on two classes of nonlinear dynamic panel data models i e dynamic discrete choice models and dynamic censored models we present the asymptotic properties of the sieve mle and investigate the finite sample properties of these sieve based estimators through a monte carlo study an intertemporal female labor force participation model is estimated as an empirical illustration using a sample from the panel study of income dynamics psid

traveling waves solutions for partial neutral differential equations abstract using monotonicity techniques and the schauder fixed point theorem we study the existence of traveling waves for neutral partial differential equations in the last section we illustrate our results on the neutral versions of the kpp fisher and the kobayashi equations

travelling wavefronts in the diffusive single species model with allee effect and distributed delay in this paper we consider the diffusive single species model with allee effect and distributed delay time special attention is paid to the existence of travelling wavefront solutions first we shall show that such fronts exist when the convolution kernel assumes the strong generic delay kernel and the delay is sufficiently small then in the non local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times we shall show that such fronts still exist for the weak generic delay kernel and small delay the approach used in this paper is the geometric singular perturbation theory

semiparametric analysis of random effects linear models from binary panel data andersen 1970 considered the problem of inference on random effects linear models from binary response panel data he showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution and if the observed explanatory variables vary over time a conditional maximum likelihood estimator consistently estimates the model parameters up to scale the present paper shows that inference remains possible if the disturbances for each panel member are known only to be time stationary with unbounded support and if the explanatory variables vary enough over time a conditional version of the maximum score estimator manski 1975 1985 consistently estimates the model parameters up to scale

the incidental parameter problem since 1948 this paper was written to mark the 50th anniversary of neyman and scott s econometrica paper defining the incidental parameter problem it surveys the history both of the paper and of the problem in the statistics and econometrics literature

on travelling wavefronts of nicholson s blowflies equation with diffusion this paper is devoted to the study of nicholson s blowflies equation with diffusion a kind of time delayed reaction diffusion for any travelling wavefront with speed c c c is the minimum wave speed we prove that the wavefront is time asymptotically stable when the delay time is sufficiently small and the initial perturbation around the wavefront decays to zero exponentially in space as x but it can be large in other locations the result develops and improves the previous wave stability obtained by mei et al in 2004 the new approach developed in this paper is the comparison principle combined with the technical weighted energy method numerical simulations are also carried out to confirm our theoretical results

existence of traveling wave solutions for a reaction diffusion equation with distributed delays abstract in this paper we consider a reaction diffusion equation with distributed delays special attention is paid to the existence of traveling wave solutions for special delay kernels using the linear chain trick and the geometric singular perturbation theory we investigate a natural connection between the existence of traveling wave solutions for the reaction diffusion equation with distributed delays and the existence of traveling wave solutions for the corresponding undelayed reaction diffusion equation we show that if the corresponding undelayed reaction diffusion equation has a traveling wave solution then for any sufficiently small delay the delayed reaction diffusion equation also has a traveling wave solution

nonparametric identification in nonseparable panel data models with generalized fixed effects abstract this paper extends the familiar notion of fixed effects to nonlinear structures with infinite dimensional unobservables like preferences the main result is that a generalized version of differencing identifies local average responses lars in nonseparable structures in contrast to existing results this does not require either substantial restrictions on functional form or independence between the persistent unobservables and the explanatory variables of interest and it requires only two time periods on the other hand the results are confined to the subpopulation of stayers chamberlain 1982 i e the population for which the explanatory variables do not change over time we extend the basic framework to include time trends and dynamics in the explanatory variables and we show how distributional effects as well as average partial effects are identified our approach also allows endogeneity in the transitory unobservables furthermore we show that this new identification principle can be applied to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects finally we suggest estimators for the local average response and average partial effect and we analyze their large and finite sample behavior

global stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate nonlinearity abstract this paper is concerned with the global stability of wavefronts with minimal speeds for degenerate nonlocal dispersal equations by the method of super and subsolutions and a squeezing technique the wavefront with minimal speed is proved to be globally asymptotically stable with phase shift

travelling wave and global attractivity in a competition diffusion system with nonlocal delays in this paper we are concerned with a two competition model described by a reaction diffusion system with nonlocal delays which account for the drift of individuals to their present position from their possible positions at previous times by using the iterative technique recently developed in wang et al 2006 14 the sufficient conditions are established for the existence of travelling wave solutions connecting the semi trivial steady state to the coexistence steady state of the considered system when the domain is bounded we investigate the global attractivity of the coexistence steady state of the system under homogeneous neumann boundary conditions as well the approach used is the upper lower solutions and monotone iteration technique

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

stability of steady states and existence of travelling waves in a vector disease model in this paper a host vector model is considered for a disease without immunity in which the current density of infectious vectors is related to the number of infectious hosts at earlier times spatial spread in a region is modelled in the partial integro differential equation by a diffusion term for the general model we first study the stability of the steady states using the contracting convex sets technique when the spatial variable is one dimensional and the delay kernel assumes some special form we establish the existence of travelling wave solutions by using the linear chain trick and the geometric singular perturbation method

efficiency of weighted average derivative estimators and index models weighted average derivatives are useful parameters for semiparametric index models and nonparametric demand analysis this paper gives efficiency results for average derivative estimators including formulating estimators that have high efficiency our analysis is carried out in three steps first we derive the efficiency bound for weighted average derivatives of conditional location functionals such as the conditional mean and median second we derive the efficiency bound for semiparametric index models where the location measure depends only on indices or linear combinations of the regressors third we compare the bound for index models with the asymptotic variance of weighted average derivative estimators of the index coefficients we characterize the form of the optimal weight function when the distribution of the regressors is elliptically symmetric in more general cases we discuss how to combine estimators with different weight functions to achieve efficiency we derive a general condition for approximate efficiency of pooled minimum chi square estimators for index model coefficients based on weighted average derivatives finally we discuss ways of selecting the type and number of weighting functions to achieve high efficiency

spreading speed and wavefronts for parabolic functional differential equations with spatio temporal delays the existence of traveling wavefronts and the spreading speed for a kind of general reaction diffusion system with spatio temporal delays are investigated we obtain the conclusion that there is c 0 being the asymptotic speed of spread and the minimal speed for the system some more delicate analysis techniques have been developed to make the forms of the kernel function g t x and the function f more flexible in our paper a pair of super solution and sub solution have been constructed in order that the existence of traveling wavefronts can be guaranteed there is a biological model as an example in this article which is coincident with this system

traveling wavefronts for a time delayed non newtonian filtration equation abstract this paper is concerned with traveling wavefronts for the evolutionary p laplacian with time delay we first establish some necessary and sufficient conditions for the existence of monotone nondecreasing and nonincreasing traveling wavefronts which correspond to definite wave speeds c 1 and c 2 respectively moreover special attention is also paid to the asymptotic behavior of traveling fronts connecting two uniform steady states

traveling waves for nonlinear cellular neural networks with distributed delays abstract in this paper we will establish the existence and nonexistence of traveling waves for nonlinear cellular neural networks with finite or infinite distributed delays the dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells where delays exist in self feedback and left or right neighborhood interactions our approach is to use schauder s fixed point theorem coupled with upper and lower solutions of the integral equation in a suitable banach space further we obtain the exponential asymptotic behavior in the negative infinity and the existence of traveling waves for the minimal wave speed by the limiting argument our results improve and cover some previous works

on the minimum probability of error of classification with incomplete patterns abstract some expected features of sample patterns in a classification system may be missing immeasurable or obscured when a sample pattern with such an incomplete set of features is presented to a classifier how reliable is the decision thus made by the classifier what is the effect of those absent features to the accuracy and correctness of the classification how to evaluate or estimate the probability of error of such a decision compared to that made on the use of more features or a supposedly complete set of features we derive the solutions of above problems from a point of view of bayes classifier the traditional decision theory is extended to the classifications with incomplete feature sets it shows that in case of classifying incomplete patterns the bayes classifier constructed on the marginal distributions of presented features also minimizes the probability of error we then use bhattacharyya bound to obtain an analytic form for estimating the error probabilities of classifications made on the partially available features with respect to that using more or a complete set of features directions are given to decision making on problems of in which situation the effect of missing or obscured features can be neglected or must be seriously considered experimental results have shown consistence with the theoretical analysis

travelling waves for a biological reaction diffusion model with spatio temporal delay in this paper we consider the reaction diffusion equations with spatio temporal delay which models the microbial growth in a flow reactor nonlocal spatial term a weighted average in space arises when the individuals have not necessarily been at the same point in space at previous time by employing linear chain technique geometric singular perturbation and the center manifold theorem we prove that the steady travelling wave does not only persist but also it looks qualitatively the same as it do with no delay at all under the introduction of delays at least for small delay

direct estimation of the index coefficient in a single index model single index modeling is widely applied in for example econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models by such modeling the statistical analysis usually focuses on estimating the index coefficients the average derivative estimator ade of the index vector is based on the fact that the average gradient of a single index function f x t is proportional to the index vector unfortunately a straightforward application of this idea meets the so called curse of dimensionality problem if the dimensionality d of the model is larger than 2 however prior information about the vector can be used for improving the quality of gradient estimation by extending the weighting kernel in a direction of small directional derivative the method proposed in this paper consists of such iterative improvements of the original ade the whole procedure requires at most 2 log n iterations and the resulting estimator is n consistent under relatively mild assumptions on the model independently of the dimensionality d

nonparametric identification in panels using quantiles abstract this paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity the effects of interest are derivatives of the average and quantile structural functions of the model we find that these derivatives are identified with two time periods for stayers i e for individuals with the same regressor values in two time periods we show that the identification results carry over to models that allow location and scale time effects we propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects the bootstrap proposed allows inference for function valued parameters such as quantile effects uniformly over a region of quantile indices and or regressor values an empirical application to engel curve estimation with panel data illustrates the results

on the existence of traveling waves for delayed reaction diffusion equations abstract we study the existence of traveling wave solutions for reaction diffusion equations with nonlocal delay where reaction terms are not necessarily monotone the existence of traveling wave solutions for reaction diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the schauder fixed point theorem the smoothness of upper and lower solutions is not required in this paper

stability analysis of heat flow with boundary time varying delay effect abstract in this paper we investigate the stabilization of heat flow with boundary time varying delay effect under some assumptions we prove exponential stability of the solution applying variable norm technique and modified lyapunov functional approach

nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species abstract this paper is concerned with nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species it is proved that all traveling wavefronts with speed c c are exponentially stable in l space by the weighted energy method and comparison principle moreover the time decay rates are obtained by weighted energy estimates

asymptotic patterns of a structured population diffusing in a two dimensional strip abstract in this paper we derive a population model for the growth of a single species on a two dimensional strip with neumann and robin boundary conditions we show that the dynamics of the mature population is governed by a reaction diffusion equation with delayed global interaction using the theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows we obtain the spreading speed c the non existence of traveling waves with wave speed 0 c c and the existence of monotone traveling waves connecting the two equilibria for c c

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

rank estimation of a generalized fixed effects regression model abstract this paper considers estimation of a fixed effects version of the generalized regression model of han 1987 journal of econometrics 35 303 316 the model allows for censoring places no parametric assumptions on the error disturbances and allows the fixed effects to be correlated with the covariates we introduce a class of rank estimators that consistently estimate the coefficients in the generalized fixed effects regression model the maximum score estimator for the binary choice fixed effects model is part of this class like the maximum score estimator the class of rank estimators converge at less than the n rate smoothed versions of these estimators however converge at rates approaching the n rate in a version of the model that allows for truncated data a sufficient condition for consistency of the estimators is that the error disturbances have an increasing hazard function

existence and nonexistence of monotone traveling waves for the delayed fisher equation abstract in this paper a new approach based on a shooting method in a half line coupled with the technique of upper lower solution pair is used to study the existence and nonexistence of monotone waves for one form of the delayed fisher equation that does not have the quasimonotonicity property a necessary and sufficient condition is provided this new method can be extended to investigate many other nonlocal and non monotone delayed reaction diffusion equations

leapfrog estimation of a fixed effects model with unknown transformation of the dependent variable abstract this paper considers a fixed effects panel version of the linear transformation model in which the dependent variable is h yt for an unspecified strictly monotonic h examples of the model include the multiple spell proportional hazards model and dependent variable transformation models e g the box cox model with fixed effects a semiparametric estimator called the leapfrog estimator is introduced and shown to be n consistent and asymptotically normal the leapfrog estimator allows for h to vary over time and for heteroskedasticity across observational units related semiparametric estimators are considered and a general covariance result for estimators based on second order u processes is presented

automatic pattern recognition a study of the probability of error a test sequence is used to select the best rule from a class of discrimination rules defined in terms of the training sequence the vapnik chervonenkis and related inequalities are used to obtain distribution free bounds on the difference between the probability of error of the selected rule and the probability of error of the best rule in the given class the bounds are used to prove the consistency and asymptotic optimality for several popular classes including linear discriminators nearest neighbor rules kernel based rules histogram rules binary tree classifiers and fourier series classifiers in particular the method can be used to choose the smoothing parameter in kernel based rules to choose k in the k nearest neighbor rule and to choose between parametric and nonparametric rules

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

jackknife and analytical bias reduction for nonlinear panel models fixed effects estimators of panel models can be severely biased because of the well known incidental parameters problem we show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large t we give bias corrections for averages over the fixed effects as well as model parameters we find large bias reductions from using these approaches in examples we consider asymptotics where t grows with n as an approximation to the properties of the estimators in econometric applications we show that if t grows at the same rate as n the fixed effects estimator is asymptotically biased so that asymptotic confidence intervals are incorrect but that they are correct for the panel jackknife we show t growing faster than n 1 3 suffices for correctness of the analytic correction a property we also conjecture for the jackknife

average and quantile effects in nonseparable panel models nonseparable panel models are important in a variety of economic settings including discrete choice this paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument partial identification results for average and quantile effects are given for discrete regressors under static or dynamic conditions in fully nonparametric and in semiparametric models with time effects it is shown that the usual linear fixed effects estimator is not a consistent estimator of the identified average effect and a consistent estimator is given a simple estimator of identified quantile treatment effects is given providing a solution to the important problem of estimating quantile treatment effects from panel data bounds for overall effects in static and dynamic models are given the dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity the impact of t the number of time periods is shown by deriving shrinkage rates for the identified set as t grows we also consider semiparametric discrete choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds computationally convenient methods for semiparametric models are presented we propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples we give empirical illustrations

delay induced traveling wave fronts in reaction diffusion equations of kpp fisher type this paper explores the impact of delay on the existence of traveling wave fronts in reaction diffusion equations of kpp fisher type for two such equations one being local and the other with nonlocal effect arising from the age structure of the population we show that delay can induce slow traveling wave fronts

variable bandwidth and local linear regression smoothers in this paper we introduce an appealing nonparametric method for estimating the mean regression function the proposed method combines the ideas of local linear smoothers and variable bandwidth hence it also inherits the advantages of both approaches we give expressions for the conditional mse and mise of the estimator minimization of the mise leads to an explicit formula for an optimal choice of the variable bandwidth moreover the merits of considering a variable bandwidth are discussed in addition we show that the estimator does not have boundary effects and hence does not require modifications at the boundary the performance of a corresponding plug in estimator is investigated simulations illustrate the proposed estimation method

identification and estimation of nonseparable single index models in panel data with correlated random effects the identification in a nonseparable single index models with correlated random effects is considered in panel data with a fixed number of time periods the identification assumption is based on the correlated random effects structure under this assumption the parameters of interest are identified up to a multiplicative constant and could be estimated by an average difference of derivatives estimator based on the local polynomial smoothing we suggest to linearly combine the estimators obtained for different orders of differences and derive the variance minimizing weighting scheme the asymptotic distribution of the proposed estimators is derived both for stationary and non stationary explanatory variables along with a test of the stationarity finally monte carlo experiments reveal finite sample properties of the proposed estimator

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

kernel classification rules from missing data nonparametric kernel classification rules derived from incomplete missing data are studied a number of techniques of handling missing observation in the training set are taken into account in particular the straightforward approach of designing a classifier only from available data deleting missing values is considered the class of imputation techniques is also taken into consideration in the latter case one estimates missing values and then calculates classification rules from such a completed training set consistency and speed of convergence of proposed classification rules are established results of simulation studies are presented

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

travelling waves for delayed reaction diffusion equations with global response we develop a new approach to obtain the existence of travelling wave solutions for reaction diffusion equations with delayed non local response the approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain banach space coupled with an index formula of the associated fredholm operator and some careful estimation of the nonlinear perturbation the general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non local and delayed response for the matured population

generalized jackknife estimators of weighted average derivatives with the aim of improving the quality of asymptotic distributional approximations for nonlinear functionals of nonparametric estimators this article revisits the large sample properties of an important member of that class namely a kernel based weighted average derivative estimator asymptotic linearity of the estimator is established under weak conditions indeed we show that the bandwidth conditions employed are necessary in some cases a bias corrected version of the estimator is proposed and shown to be asymptotically linear under yet weaker bandwidth conditions implementational details of the estimators are discussed including bandwidth selection procedures consistency of an analog estimator of the asymptotic variance is also established numerical results from a simulation study and an empirical illustration are reported to establish the results a novel result on uniform convergence rates for kernel estimators is obtained the online supplemental material to this article includes details on

stability of traveling waves in a population dynamics model with spatio temporal delay abstract in this paper we are concerned with the stability of all traveling waves for a population dynamics model with spatio temporal delay by the weighted energy method combining comparison principle the global exponential stability of all traveling waves for the model is established even including the slower waves whose wave speed is close to the critical speed

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

traveling wave solutions in a delayed diffusive competition system abstract in this paper we first investigate the existence of traveling wave fronts in a delayed diffusive competition system by constructing a pair of upper and lower solutions then we consider the asymptotic behavior of traveling wave solutions at the minus plus infinity by means of the bilateral laplace transform finally the monotonicity and uniqueness up to the translation of traveling wave solutions are also obtained by the strong comparison principle and the sliding method

estimation of a panel data sample selection model we consider the problem of estimation in a panel data sample selection model where both the selection and the regression equation of interest contain unobservable individual specific effects we propose a two step estimation procedure which differences out both the sample selection effect and the unobservable individual effect from the equation of interest in the first step the unknown coefficients of the selection equation are consistently estimated the estimates are then used to estimate the regression equation of interest the estimator proposed in this paper is consistent and asymptotically normal with a rate of convergence that can be made arbitrarily close to n 1 2 depending on the strength of certain smoothness assumptions the finite sample properties of the estimator are investigated in a small monte carlo simulation

pyramidal traveling fronts in a nonlocal delayed diffusion equation abstract recently there have been great progresses on the study of nonplanar traveling wave solutions of reaction diffusion equations in this paper we study the pyramidal traveling fronts of nonlocal delayed diffusion equation in r n with n 2 by using the comparison principle and establishing super and subsolution since the effect of nonlocal delay we show that nonlocal delayed diffusion equation in n dimensional space has a pyramidal traveling front u t x v x x n s t toward x n axis for each s c 0 in particular two dimensional traveling curved front and three dimensional pyramidal fronts for nonlocal delayed diffusion equation in r 2 and r 3 are also established respectively moreover we also extend our results to generally nonlocal delayed reaction diffusion equation

spreading speeds and traveling wavefronts for second order integrodifference equations this paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations by introducing an auxiliary integrodifference system the spreading speed is established for the integrodifference equation it is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts furthermore we prove that the traveling wavefronts are stable by applying the squeezing technique finally we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology

existence of travelling wave solutions of predator prey systems via the connection index we consider a reaction diffusion system which arises as a model of predator prey interactions in mathematical ecology the system admits four constant equilibria two of which are stable the main result is an existence theorem for travelling wave solutions which connect the two stable equilibria most previous efforts with regard to travelling waves for systems employ singular perturbations to locate the connecting orbit the new aspect of the present discussion lies in devising some novel methods for locating the connecting solution in phase space which do not require that the equations be singularly perturbed in certain cases the main result holds for an arbitrary choice of diffusion coefficients

asymptotic stability of traveling wave fronts in nonlocal reaction diffusion equations with delay abstract this paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction diffusion equations with delay under monostable assumption we prove that the traveling wave front is exponentially stable by means of the technical weighted energy method when the initial perturbation around the wave is suitable small in a weighted norm the exponential convergent rate is also obtained finally we apply our results to some population models and obtain some new results which recover complement and or improve a number of existing ones

a phase plane discussion of convergence to travelling fronts for nonlinear diffusion the paper is concerned with the asymptotic behavior as t of solutions u x t of the equation u t u xx f left u right 0 x in left infty infty right in the case f 0 f 1 0 with f u non positive for u 0 sufficiently close to zero and f u non negative for u 1 sufficiently close to 1 this guarantees the uniqueness but not the existence of a travelling front solution u u x ct u 0 u and it is shown in essence that solutions with monotonic initial data converge to a translate of this travelling front if it exists and to a stacked combination of travelling fronts if it does not the approach is to use the monotonicity to take u and t as independent variables and p ux as the dependent variable and to apply ideas of sub and super solutions to the diffusion equation for p

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

bistable wavefronts in a diffusive and competitive lotka volterra type system with nonlocal delays abstract a diffusive lotka volterra type model with nonlocal delays for two competitive species is considered the existence of a traveling wavefront analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays to a four dimensional system without delay furthermore in order to prove the asymptotic stability up to translation of bistable wavefronts of the system the existence regularity and comparison theorem of solutions of the corresponding cauchy problem are first established for the systems on r by appealing to the theory of abstract functional differential equations the asymptotic stability up to translation of bistable wavefronts are then proved by spectral methods in particular we also prove that the spreading speed is unique by upper and lower solutions technique from the point of view of ecology our results indicate that the nonlocal delays appeared in the interaction terms are not sensitive to the invasion of species of spatial isolation

traveling wave solutions in n dimensional delayed reaction diffusion systems with mixed monotonicity this paper deals with the existence of traveling wave solutions for n components delayed reaction diffusion systems with mixed monotonicity based on a certain kind of mixed quasimonotonicity reaction terms of higher dimension we propose new conditions on the reaction terms and new definitions of upper and lower solutions by using schauder s fixed point theorem and a cross iteration scheme we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions the general results obtained will be applied to type k monotone diffusive lotka volterra systems of higher dimension

trimmed lad and least squares estimation of truncated and censored regression models with fixed effects this paper considers estimation of truncated and censored regression models with fixed effects up until now no estimator has been shown to be consistent as the cross section dimension increases with the time dimension fixed trimmed least absolute deviations and trimmed least squares estimators are proposed for the case where the panel is of length two and it is proven that they are consistent and asymptotically normal it is not necessary to maintain parametric assumptions on the error terms to obtain this result a small scale monte carlo study demonstrates that these estimators can perform well in small samples copyright 1992 by the econometric society

traveling waves for time delayed reaction diffusion equations with degenerate diffusion abstract this paper is concerned with time delayed reaction diffusion equations with degenerate diffusion when the term for birth rate is a nonlocal integral with a heat kernel the family of minimum wave speeds corresponding to all the degenerate diffusion coefficients is proved to admit a uniform positive infimum however when the term for birth rate is local there is no positive infimum of all the minimum wave speeds this difference indicates that the nonlocal effect plays a role as laplacian such that a positive lower bound independent of the degenerate diffusion exists for the minimum wave speeds the approach adopted for the proof is the monotone technique with the viscosity vanishing method the degeneracy of diffusion for the equation causes us essential difficulty in the proof a number of numerical simulations are also carried out at the end of the paper which further numerically confirm our theoretical results