asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

nonlinear boundary value problems for first order impulsive functional differential equations this paper is concerned with solutions of nonlinear boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid obviously we extend previous results

fixed points and approximate solutions for nonlinear operator equations we study a nonlinear operator equation and obtain a sequence of approximate solutions by extending the monotone iterative technique to new situations some examples and applications are presented

integration of thiele continued fractions and the method of fundamental solutions for solving unconfined seepage problems unconfined seepage through an earth dam or a levee is recognized as a challenging problem this complexity is mainly due to the fact that determination of the phreatic line through the dam levee body is not straightforward for simulation purposes mesh generation as well as accurate and smooth alteration of the phreatic line at the junction with the downstream slope referred to as exit point for an unconfined seepage problem with complex geometry generally makes cumbersome numerical solutions this study presents an innovative boundary type meshfree method to determine the phreatic line location in unconfined seepage problems the current study explicitly addresses the problem that alternative methods commonly face to deal with the exit point the method is developed based upon integrating the method of fundamental solutions mfs particle swarm optimization pso algorithm and thiele continued fractions tcf to accurately estimate the phreatic line location the proposed framework uses mfs to solve the flow continuity equation tcf to generate the phreatic line and pso to optimize the phreatic line location generated by tcf as a boundary method mfs only deals with the boundaries of the domain and consequently it only takes the exact position of phreatic line as a variable boundary the proposed approach employs tcf to guarantee that the phreatic line is tangent to the downstream slope at the exit point a characteristics which is important especially for the cases where abrupt changes occur in the phreatic line near the exit point for comparison and validation purposes the phreatic lines determined by the proposed approach for two unconfined seepage problems are compared and verified against those obtained from alternative analytical and numerical methods as well as a set of experimental results an excellent agreement is demonstrated upon comparison of the proposed method to the results attained from the analytical solutions and experimental tests

adjusted qmle for the spatial autoregressive parameter abstract one simple and often very effective way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter we apply this general principle to the quasi maximum likelihood estimator qmle of the autoregressive parameter in a spatial autoregression the resulting estimator for has better finite sample properties compared to the qmle for especially in the presence of a large number of covariates it can also solve the incidental parameter problem that arises for example in social interaction models with network fixed effects however spatial autoregressions present specific challenges for this type of adjustment because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for conditions for this to happen are given and implications are discussed for inference we propose confidence intervals based on a lugannani rice approximation to the distribution of the adjusted qmle of based on our simulations the coverage properties of these intervals are excellent even in models with a large number of covariates

antiperiodic boundary value problem for first order impulsive ordinary differential equations this paper discusses the antiperiodic boundary value problem for first order impulsive ordinary differential equations we establish several existence results by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique

finite sample properties of maximum likelihood estimator in spatial models we investigate the finite sample properties of the maximum likelihood estimator for the spatial autoregressive model a stochastic expansion of the score function is used to develop the second order bias and mean squared error of the maximum likelihood estimator we show that the results can be expressed in terms of the expectations of cross products of quadratic forms or ratios of quadratic forms in a normal vector which can be evaluated using the top order invariant polynomial our numerical calculations demonstrate that the second order behaviors of the maximum likelihood estimator depend on the degree of sparseness of the weights matrix

diagnostic tests for homoskedasticity in spatial cross sectional or panel models abstract we propose an adjusted quasi score aqs method for constructing tests for homoskedasticity in spatial econometric models we first obtain an aqs function by adjusting the score type function from the given model to achieve unbiasedness and then develop an outer product of martingale difference opmd estimate of its variance in standard problems where a genuine quasi score vector is available the aqs opmd method leads to finite sample improved tests over the usual methods more importantly in non standard problems where a genuine quasi score is not available and the usual methods fail the proposed aqs opmd method provides feasible solutions the aqs tests are formally derived and asymptotic properties examined for three representative models spatial cross sectional static and dynamic panel models monte carlo results show that the proposed aqs tests have good finite sample properties

periodic boundary value problems for a class of functional differential equations in this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part

boundary value problem for second order impulsive functional differential equations this paper is concerned with the existence of minimal and maximal solutions of boundary value problem for second order impulsive functional differential equations the method of upper and lower solutions and the monotone iterative technique are used

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems

numerical solutions to some free surface flows through nonhomogeneous media steady state free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique the problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel these ponds and channels may have variable shaped bottoms since the baiocchi transformation was used to define a new dependent variable the form of the permeability function was restricted to a product of functions of the independent variables herein the permeability was chosen to be a function of the depth only for certain forms of this function namely those having negative gradients part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory the governing differential equation which holds in the sense of distributions is derived for a fixed solution domain and a simple algorithm a finite difference successive over relaxation scheme with projection is given to obtain the solution to these free surface problems numerous comparisons are made with published results rigorous mathematical justification of the methods used herein can be found in the references cited

conditions for global attractivity of n patches predator prey dispersion delay models abstract in this paper a nonautonomous predator prey dispersion model with functional response and continuous time delay is studied where all parameters are time dependent in this system which consists of n patches the prey species can disperse among n patches but the predator species is confined to one patch and cannot disperse it is proved the system is uniformly persistent under any dispersion rate effect furthermore the sufficient conditions are established for global attractivity of a periodic solution of the system

global attractivity of positive periodic solutions for nonlinear impulsive systems abstract in this paper the existence uniqueness and global attractivity of positive periodic solutions for nonlinear impulsive systems are studied firstly existence conditions are established by the method of lower and upper solutions then uniqueness and global attractivity are obtained by developing the theories of monotone and concave operators and lastly the method and the results are applied to the impulsive n species cooperative lotka volterra system and a model of a single species dispersal among n patches

on the bootstrap for moran s i test for spatial dependence this paper is concerned with the use of the bootstrap for statistics in spatial econometric models with a focus on the test statistic for moran s i test for spatial dependence we show that for many statistics in spatial econometric models the bootstrap can be studied based on linear quadratic lq forms of disturbances by proving the uniform convergence of the cumulative distribution function for lq forms to that of a normal distribution we show that the bootstrap is generally consistent for test statistics that can be approximated by lq forms including moran s i possible asymptotic refinements of the bootstrap are most commonly studied using edgeworth expansions for spatial econometric models we may establish asymptotic refinements of the bootstrap based on asymptotic expansions of lq forms when the disturbances are normal we prove the existence of the usual edgeworth expansions for lq forms when the disturbances are not normal we establish an asymptotic expansion of lq forms based on martingales these results are applied to show the second order correctness of the bootstrap for moran s i test

isogeometric analysis in solution of unconfined seepage problems abstract this article investigates the numerical solution of saturated unconfined seepage problems in which a fluid with a free surface passes through a porous media in such cases the geometry of the wet region is unknown in advance and must be obtained through an iterative process such problems are known as variable domain problems since the use of traditional mesh based numerical methods is not straight forward due to remeshing difficulties the isogeometric analysis is proposed here which eliminates the meshing process and accordingly makes this method an attractive tool to deal with such problems on the other hand the use of isogeometric analysis accounts for other difficulties which this paper aims to address in the isogeometric analysis the boundary control points are not located on the domain boundary therefore in this article a new boundary updating formula is proposed to reconstruct the free surface for modifying the control net the transfinite interpolation is used in order to update the control net when the geometry undergoes any change the domain is considered inhomogeneous with spatially varied permeability three benchmark examples are solved to demonstrate the applicability of the proposed method finally the results are compared with those available in the literature

identification and estimation of econometric models with group interactions contextual factors and fixed effects this paper considers identification and estimation of structural interaction effects in a social interaction model the model allows unobservables in the group structure which may be correlated with included regressors we show that both the endogenous and exogenous interaction effects can be identified if there are sufficient variations in group sizes we consider the estimation of the model by the conditional maximum likelihood and instrumental variables methods for the case with large group sizes the possible identification can be weak in the sense that the estimates converge in distribution at low rates

on the asymptotic behavior of a class of deterministic models of cooperating species in this paper the global behavior of solutions of a class of ordinary differential equations modeling n cooperating biological species is determined the class of systems includes the classical lot

first order impulsive ordinary differential equations with anti periodic and nonlinear boundary conditions the monotone iterative technique is a powerful method that have been used to approximate the extremal solutions of several problems 1 2 on the other hand impulsive differential equations are a basic tool to study some problems of biology medicine engineering and physics 3 in this paper we deal with the following nonlinear boundary value problem for first order differential equation with impulses at fixed points

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

existence of positive periodic solutions of a neutral delay lotka volterra system with impulses sufficient conditions are obtained for the existence of periodic positive solutions of a class of neutral impulsive delay lotka volterra systems n i t n i t a i t j 1n b i j t n j t t i j t j 1nc i j t n j t c i j t n i t k n i t k b i kn i t k i 1 2 n k 1 2 by using some techniques of mawhin coincidence degree theory my results generalize some known results it is shown that under the appropriate linear periodic impulsive perturbations the neutral impulsive delay lotka volterra system preserves the original periodicity of the neutral nonimpulsive delay lotka volterra system

exact and higher order properties of the mle in spatial autoregressive models with applications to inference abstract the quasi maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data a rigorous analysis of the first order asymptotic properties of the estimator under some assumptions on the evolution of the spatial design matrix is available in lee 2004 but very little is known about its exact or higher order properties in this paper we first show that the exact cumulative distribution function of the estimator can under mild assumptions be written in terms of that of a particular quadratic form simple examples are used to illustrate important exact properties of the estimator that follow from this representation in general models a complete exact analysis is not possible but a higher order saddlepoint approximation is made available by the main result we use this approximation to construct confidence intervals for the autoregressive parameter coverage properties of the proposed confidence intervals are studied by monte carlo simulation and are found to be excellent in a variety of circumstances

further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations abstract this paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations x t a t x t f t x t x 1 t x n t t j t 1 t p x t k x t k i k x t k k 1 2 p x 0 x t we obtain sufficient conditions for the existence of at least one solution of problem at resonance and nonresonance cases respectively examples are presented to illustrate the main results

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

the second order bias and mean squared error of nonlinear estimators abstract despite the now widespread use of nonlinear estimators their finite sample properties have received very little attention in either the statistics or econometrics literature we partially redress this problem by deriving and examining the second order bias and mean squared error of a fairly wide class of nonlinear estimators which includes nonlinear least squares maximum likelihood and many generalized method of moments estimators as special cases a number of examples are provided the results from a monte carlo exercise demonstrate how the results can be applied for improved inferences

the second order bias and mean squared error of estimators in time series models we develop analytical results on the second order bias and mean squared error of estimators in time series models these results provide a unified approach to developing the properties of a large class of estimators in linear and nonlinear time series models and they are valid for both normal and nonnormal samples of observations and where the regressors are stochastic the estimators included are the generalized method of moments maximum likelihood least squares and other extremum estimators our general results are applied to four time series models we investigate the effects of nonnormality on the second order bias results for two of these models while for all four models the second order bias and mean squared error results are given under normality numerical results for some of these models are also presented

global attractivity of nonautonomous stage structured population models with dispersal and harvest the nonautonomous stage structured single species dispersal model with harvesting of mature individuals in an n patch environment is considered in which the individual members of the population have a life history that takes them through two stages immature and mature by using the theory of monotone and concave operators to functional differential equations we establish conditions under which this population dynamical system admits a positive periodic solution which attracts all positive solutions

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

a general method for third order bias and variance corrections on a nonlinear estimator motivated by a recent study of bao and ullah 2007a on finite sample properties of mle in the pure sar spatial autoregressive model a general method for third order bias and variance corrections on a nonlinear estimator is proposed based on stochastic expansion and bootstrap working with concentrated estimating equation simplifies greatly the high order expansions for bias and variance a simple bootstrap procedure overcomes a major difficulty in analytically evaluating expectations of various quantities in the expansions the method is then studied in detail using a more general sar model with its effectiveness in correcting bias and improving inference fully demonstrated by extensive monte carlo experiments compared with the analytical approach the proposed approach is much simpler and has a much wider applicability the validity of the bootstrap procedure is formally established the proposed method is then extended to the case of more than one nonlinear estimator

profile quasi maximum likelihood estimation of partially linear spatial autoregressive models abstract we propose profile quasi maximum likelihood estimation of spatial autoregressive models that are partially linear the rate of convergence of the spatial parameter estimator depends on some general features of the spatial weight matrix of the model the estimators of other finite dimensional parameters in the model have the regular n rate of convergence and the estimator of the nonparametric component is consistent but with different restrictions on the choice of bandwidth parameter associated with different natures of the spatial weights monte carlo simulations verify our theory and indicate that our estimators perform reasonably well in finite samples

boundary flows in general coset theories in this paper we study the boundary effects for off critical integrable field theories which have close analogues with integrable lattice models our models are the coset conformal field theories perturbed by an integrable boundary and bulk operators the boundary interactions are encoded into the boundary reflection matrix using the thermodynamic bethe ansatz tba method we verify the flows of the conformal bcs by computing the boundary entropies these flows of the bcs have direct interpretations for the fusion restricted solid on solid rsos lattice models for super conformal field theories cfts k 2 we show that these flows are possible only for the neveu schwarz sector and are consistent with the lattice results the models we consider cover a wide class of integrable models in particular we show how the impurity spin is screened by electrons for the k channel kondo model by taking the limit we also study the problem using an independent method based on the boundary roaming tba our numerical results are consistent with the boundary cfts and rsos tba analysis

periodic boundary value problems for second order impulsive integro differential equations by developing a new comparison result and using the monotone iterative technique we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for second order nonlinear impulsive integro differential equations of mixed type

nonlinear boundary problem of first order impulsive integro differential equations this paper focuses on first order impulsive integro differential equations with nonlinear boundary the lower and upper solutions combined with monotone iterative techniques are used to obtain the existence of extremal solutions of the problem numerical examples are given to prove its validity

boundary value problem of second order impulsive functional differential equations this paper discusses a kind of linear boundary value problem for a nonlinear second order impulsive functional differential equations we establish several existence results by using the lower and upper solutions and monotone iterative techniques an example is discussed to illustrate the efficiency of the obtained result

periodic boundary value problem for first order impulsive functional differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of minimal and maximal solutions of the periodic boundary value problem for first order impulsive functional differential equations is considered

anti periodic boundary value problems for first order impulsive functional differential equations this paper considers existence of solutions for a class of first order functional differential equation with anti periodic boundary value conditions we introduce new concept of lower and upper solutions which is quite different from the former one and we present that monotone iterative technique coupled with lower and upper solutions is still valid

functional determinants from wronski green functions a general technique is developed for calculating functional determinants of second order differential operators with dirichlet periodic and antiperiodic boundary conditions without the knowledge of spectral properties as an example we give explicit formulas for a harmonic oscillator with an arbitrary time dependent frequency where our result is a generalization of the gel fand yaglom famous formula for dirichlet boundary conditions our technique is based on the wronski s construction of green functions which does not require spectral knowledge our final formula expresses the ratios of functional determinants in terms of an ordinary 2 2 determinant of a constant matrix constructed from two linearly independent solutions of the homogeneous differential equations associated with second order differential operators for ratios of determinants encountered in semiclassical fluctuations around a classical solution the result can further be expressed in terms of the classical solution special properties of operators with a zero mode are exhibited

estimation of spatial autoregressive panel data models with fixed effects this paper establishes asymptotic properties of quasi maximum likelihood estimators for sar panel data models with fixed effects and sar disturbances a direct approach is to estimate all the parameters including the fixed effects because of the incidental parameter problem some parameter estimators may be inconsistent or their distributions are not properly centered we propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions for the model with individual effects only the direct approach does not yield a consistent estimator of the variance parameter unless t is large but the estimators for other common parameters are the same as those of the transformation approach we also consider the estimation of the model with both individual and time effects

existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti periodic boundary conditions this paper describes the method of quasilinearization for first order nonlinear impulsive functional differential equations with anti periodic boundary conditions a monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand 2007 elsevier ltd all rights reserved

efficient estimation of the semiparametric spatial autoregressive model efficient semiparametric and parametric estimates are developed for a spatial autoregressive model containing non stochastic explanatory variables and innovations suspected to be non normal the main stress is on the case of distribution of unknown nonparametric form where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest these estimates are as efficient as the ones based on a correct form in particular they are more efficient than pseudo gaussian maximum likelihood estimates at non gaussian distributions two different adaptive estimates are considered relying on somewhat different regularity conditions a monte carlo study of finite sample performance is included

boundary value problems for first order functional differential equations with impulsive integral conditions in this paper by using the method of lower and upper solutions coupled with the monotone iterative technique we give conditions for existence of extreme solutions for first order functional differential equations with a new impulsive integral condition some comparison results are also formulated

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

stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients abstract we consider the following nonlinear impulsive delay differential equation with variable coefficients and forcing term x t a t x t f t x e t t 0 t t k x t k x t k i k x t k k n using new methods different from those in tang et al appl math comput 131 2002 373 nieto j comput appl math lett 15 2002 489 franco and nieto j comput appl math 88 1998 144 nieto j math anal appl 205 1997 423 he and yu j math anal appl 272 2002 67 we establish stability theorems for when e t 0 under the assumption that there is bk such that bkx2 x x ik x x2 for k n and x r theorems 2 1 2 4 the existence results for three positive periodic solutions and nonexistence results for periodic solution of when e t 0 under the assumption exp 0 t a u d u 0 t k 1 b k and bk 1 for all k theorems 3 1 3 2 and the existence results for periodic solution of at resonance which is caused by impulses i e exp 0 t a u d u 0 t k 1 b k under the assumption bk 1 for all k theorems 4 2 4 3 some results obtained improve and generalize the known theorems and some other results are new examples are presented to illustrate the main results

global attractivity of periodic solutions of population models abstract this paper studies periodic solutions of two types of population models with time delays and periodic coefficients the first represents one species growth with delayed recruitments and the second models a single species despersal among the n patches by developing the theory of monotone and concave operators to functional differential equations we establish conditions under which each model admits a positive periodic solution which attracts all positive solutions

integral boundary value problems for first order integro differential equations with impulsive integral conditions this paper is concerned with the integral boundary value problems for first order integro differential equations with impulsive integral conditions sufficient conditions are obtained for the existence of extremal solutions

nonlinear boundary value problem of first order impulsive functional differential equations this paper discusses nonlinear boundary value problem for first order impulsive functional differential equations we establish several existence results by using the lower and upper solutions and monotone iterative techniques two examples are discussed to illustrate the efficiency of the obtained results

existence of solutions for anti periodic boundary value problems abstract by using schauder s fixed point theorem and the lower and upper solutions method we discuss the anti periodic boundary value problem for a class of second order differential equations some sufficient conditions for the existence of solutions are obtained

existence of solutions for second order impulsive differential equations with deviating arguments abstract this paper deals with impulsive second order differential equations with deviating arguments we investigate the existence of solutions of such problems with nonlinear boundary conditions to obtain corresponding results we discuss also second order impulsive differential inequalities with deviating arguments

monotone iterative techniques of v lakshmikantham for a boundary value problem for systems of impulsive differential difference equations by means of the monotone iterative techniques of v lakshmikantham a couple of minimal and maximal quasisolutions of a two point boundary value problem for a system of impulsive differential difference equations are constructed

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

impulsive anti periodic boundary value problem of first order integro differential equations this paper is concerned with the anti periodic boundary value problem of first order nonlinear impulsive integro differential equations we first establish a new comparison principle and then obtain the existence of extremal solutions by upper lower solution and monotone iterative techniques some examples are presented to illustrate the main results

a class of boundary value problems for first order impulsive integro differential equations with deviating arguments this paper is concerned with a class of boundary value problems for nonlinear mixed impulsive integro differential equations with deviating arguments we establish a new comparison principle and use the method of upper and lower solutions together with the monotone iterative technique under suitable conditions we obtain the existence results of extremal solutions for the problems an example is also given to illustrate our results

periodic solutions for ordinary differential equations with sublinear impulsive effects abstract the continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects the applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations for instance the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with landesman lazer conditions

the periodic solutions for general periodic impulsive population systems of functional differential equations and its applications in this paper the general periodic impulsive population systems of functional differential equations are investigated by using the method of poincare map and horn s fixed point theorem we prove that the ultimate boundedness of all solutions implies the existence of periodic solutions as applications of this result the existence of positive periodic solutions for the general periodic impulsive kolmogorov type population dynamical systems are discussed we further prove that as long as the system is permanent there must exist at least one positive periodic solution in addition the permanence and existence of positive periodic solutions are discussed for the periodic impulsive single species logistic models and the periodic impulsive n species lotka volterra competitive models with delays

unified m estimation of fixed effects spatial dynamic models with short panels abstract it is well known that quasi maximum likelihood qml estimation of dynamic panel data dpd models with short panels depends on the assumptions on the initial values and a wrong treatment of them will result in inconsistency and serious bias the same issues apply to spatial dpd sdpd models with short panels in this paper a unified m estimation method is proposed for estimating the fixed effects sdpd models containing three major types of spatial effects namely spatial lag spatial error and space time lag the method is free from the specification of the distribution of the initial observations and robust against nonnormality of the errors consistency and asymptotic normality of the proposed m estimator are established a martingale difference representation of the underlying estimating functions is developed which leads to an initial condition free estimate of the variance of the m estimators monte carlo results show that the proposed methods have excellent finite sample performance

existence of solutions to first order impulsive periodic boundary value problems abstract this paper is concerned with the solvability of periodic boundary value problems for first order impulsive ordinary differential equations by using schaeffer s theorem a sufficient condition for existence of solution of the problem is obtained which extends and improves some known results in the literature

anti periodic boundary value problems of second order impulsive differential equations this paper discusses anti periodic boundary value problems of second order impulsive differential equations by using the method of upper and lower solutions coupled with the monotone iterative technique new existence results of coupled solutions and uniqueness of problems are obtained

the sturm liouville operator on the space of functions with discontinuity conditions the sturm liouville differential operators defined on the space of discontinuous functions where the moments of discontinuity of the functions are interior points of the interval and the discontinuity conditions are linear have been studied auxiliary results concerning the green s formula boundary value and eigenvalue problems for impulsive differential equations are emphasized

semiparametric gmm estimation of spatial autoregressive models abstract we propose semiparametric gmm estimation of semiparametric spatial autoregressive sar models under weak moment conditions in comparison with the quasi maximum likelihood based semiparametric estimator of su and jin 2010 we allow for both heteroscedasticity and spatial dependence in the error terms we derive the limiting distributions of our estimators for both the parametric and nonparametric components in the model and demonstrate the estimator of the parametric component has the usual n asymptotics when the error term also follows an sar process we propose an estimator for the parameter in the sar error process and derive the joint asymptotic distribution for both spatial parameters consistent estimates for the asymptotic variance covariance matrices of both the parametric and nonparametric components are provided monte carlo simulations indicate that our estimators perform well in finite samples

gmm and 2sls estimation of mixed regressive spatial autoregressive models the gmm method and the classical 2sls method are considered for the estimation of mixed regressive spatial autoregressive models these methods have computational advantage over the conventional maximum likelihood method the proposed gmm estimators are shown to be consistent and asymptotically normal within certain classes of gmm estimators best ones are derived the proposed gmm estimators improve upon the 2sls estimators and are applicable even if all regressors are irrelevant a best gmm estimator may have the same limiting distribution as the ml estimator with normal disturbances

a study on quasi periodic boundary value problems for nonlinear higher order impulsive differential equations a study concerning the solvability of the quasi periodic boundary value problems for nonlinear higher order impulsive differential equations is made sufficient conditions for the existence of at least one solution to the problems are obtained examples are presented to illustrate the main results

on differential algebraic problems in this paper the existence of extremal or quasi solutions for differential algebraic problems with causal operators is investigated the case when such problems have a unique solution is also discussed to obtain existence results a monotone iterative technique is applied

maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods abstract a transformed likelihood approach is suggested to estimate fixed effects dynamic panel data models conditions on the data generating process of the exogenous variables are given to get around the issue of incidental parameters the maximum likelihood mle and minimum distance estimator mde are suggested both estimators are shown to be consistent and asymptotically normally distributed a hausman type specification test is suggested to test the fixed versus random effects specification or conditions on the data generating process of the exogenous variables monte carlo studies are conducted to evaluate the finite sample properties of the mle mde instrumental variable estimator iv and linear generalized method of moments estimator gmm it is shown that the likelihood approach appears to dominate the gmm approach both in terms of the bias and root mean square error of the estimators and the size and power of the test statistics

imposing dirichlet boundary conditions with nitsche s method and spline based finite elements a key challenge while employing non interpolatory basis functions in finite element methods is the robust imposition of dirichlet boundary conditions the current work studies the weak enforcement of such conditions for b spline basis functions with application to both second and fourth order problems this is achieved using concepts borrowed from nitsche s method which is a stabilized method for imposing constraints on surfaces conditions for the stability of the system of equations are derived for each class of problem stability parameters in the nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the dirichlet boundary the approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not through several numerical examples the approach is shown to yield optimal rates of convergence copyright 2010 john wiley sons ltd

an algorithm for approximate solving of differential equations with maxima an algorithm for constructing two sequences of successive approximations of the solution of the initial value problem for nonlinear differential equations with maxima is given this algorithm is based on the monotone iterative technique it is proved that both sequences are monotonically convergent each term of the constructed sequences is a solution of an initial value problem for linear differential equations with maxima and it is a lower upper solution of the given problem both the scalar case and the multidimensional case are studied an example solved by computer realization of the suggested algorithm illustrates the practical application of the method

on bias inconsistency and efficiency of various estimators in dynamic panel data models abstract when a model for panel data includes lagged dependent explanatory variables then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension t gets large usually however such datasets have substantial sample size in the cross section dimension n whereas t is often a single digit number results on the asymptotic bias n in this situation have been published a decade ago but hence far analytic small sample assessments of the actual bias have not been presented here we derive a formula for the bias of the least squares dummy variable lsdv estimator which has a o n 1 t 3 2 approximation error in a simulation study this is found to be remarkably accurate due to the small variance of the lsdv estimator which is usually much smaller than the variance of consistent generalized method of moments estimators a very efficient procedure results when we remove the bias from the lsdv estimator the simulations contain results for a particular operational corrected lsdv estimation procedure which in many situations proves to be much more efficient than various instrumental variable type estimators

on the asymptotic distribution of the moran i test statistic with applications by far the most popular test for spatial correlation is the one based on moran s 1950 i test statistic despite this the available results in the literature concerning the large sample distribution of this statistic are limited and have been derived under assumptions that do not cover many applications of interest in this paper we 3rst give a general result concerning the large sample distribution of moran i type test statistics we then apply this result to derive the large sample distribution of the moran i test statistic for a variety of important models in order to establishth ese results we also give a new central limit theorem for linear quadratic forms 2001 elsevier science s a all rights reserved jel classi cation c12 c21

existence of an anti periodic solution for the quasilinear wave equation with viscosity abstract we prove the existence of a strong anti periodic solution for the quasilinear wave equation with viscosity u tt mathop rm div bigl lbrace sigma bigl abla u 2 bigr abla u bigr rbrace delta u t f x t qquad hbox in omega times r under the dirichlet boundary conditionu t 0 where is a bounded domain inrnwith the boundary and v2 is a function like 1 sqrt 1 v 2