global stabilization of the generalized korteweg de vries equation posed on a finite domain this paper is concerned with the internal stabilization of the generalized korteweg de vries equation on a bounded domain the global well posedness and the exponential stability are investigated when the exponent in the nonlinear term ranges over the interval 1 4 the global exponential stability is obtained whatever the location where the damping is active confirming positively a conjecture of perla menzala vasconcellos and zuazua quart appl math 60 2002 pp 111 129

on the controllability of the lotka mckendrick model of population dynamics abstract in this work we consider the problem of exact controllability of the linear lotka mckendrick model of population dynamics we establish an observability inequality and show that any initial condition can be steered into any quasi steady state by a distributed control except for a small interval of ages near zero in contrast with that we observe that the boundary control is more efficient in the sense that it controls the entire population the biological implication of our conclusions is that a closed population is more efficiently controlled through birth control as opposed to migration and eradication in particular this supports the trap alter release method for controlling a population of stray cats as opposed to the trap and kill method

exact boundary controllability for the linear korteweg de vries equation on the half line this paper is concerned with the controllability of the linear korteweg de vries equation on the domain o 0 infty the control being applied at the left endpoint x 0 it is shown that the em exact boundary controllability holds true in l 2 0 infty provided that the solutions are not required to be in l infty 0 t l 2 0 infty the proof rests on a carleman s estimate and an approximation theorem a similar result is obtained for the heat equation and for the schrodinger equation

boundary control of the korteweg de vries burgers equation further results on stabilization and well posedness with numerical demonstration we consider the korteweg de vries burgers equation on the interval 0 1 motivated by simulations resulting in modest decay rates with recently proposed control laws by liu and krstic which keeps some of the boundary conditions as homogeneous we propose a strengthened set of feedback boundary conditions we establish stability properties of the closed loop system prove well posedness and illustrate the performance improvement by a simulation example

optimal harvesting for nonlinear size structured population dynamics a harvesting problem is considered for a size structured population model with separable mortality rate and nonlinear fertility rate we transform the model to a system of equations and show the existence of a unique solution we also establish the existence of an optimal harvesting rate which maximizes the total harvest in a given time interval

an item response model with internal restrictions on item difficulty an irt model based on the rasch model is proposed for composite tasks that is tasks that are decomposed into subtasks of different kinds there is one subtask for each component that is discerned in the composite tasks a component is a generic kind of subtask of which the subtasks resulting from the decomposition are specific instantiations with respect to the particular composite tasks under study the proposed model constrains the difficulties of the composite tasks to be linear combinations of the difficulties of the corresponding subtask items which are estimated together with the weights used in the linear combinations one weight for each kind of subtask although the model does not belong to the exponential family its parameters can be estimated using conditional maximum likelihood estimation the approach is demonstrated with an application to spelling tasks

logistic latent trait models with linear constraints two linearly constrained logistic models which are based on the well known dichotomous rasch model the linear logistic test model lltm and the linear logistic model with relaxed assumptions llra are discussed necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimates of the structural model parameters are derived methods for testing composite hypotheses within the framework of these models and a number of typical applications to real data are mentioned

optimal birth control of age dependent competitive species abstract this work is concerned with optimal policies for two age structured biological populations in a competing system which is controlled by fertilities the maximum principles for problems with free terminal infinite horizon and target sets are obtained respectively via dubovitskii milyutin s general extremal theory

decay of solutions of some nonlinear wave equations abstract we study the large time behaviour of solutions to the initial value problem for the korteweg de vries equation and for the regularized long wave equation with a dissipative term appended using energy estimates a maximum principle and a transformation of cole hopf type sharp rates of temporal decay of certain norms of the solution are obtained

optimal control for a class of nonlinear age distributed population systems this paper deals with an optimal control problem for a kind of age dependent biological population systems the well posedness of the state system is treated by means of characteristics line and fixed point principle necessary optimality conditions are obtained via tangent normal cone technique in nonlinear functional analysis the existence and uniqueness of the optimal controller are established by the use of ekeland s principle

exact boundary controllability of the korteweg de vries equation we consider boundary control of the distributed parameter system described by the korteweg de vries kdv equation posed on a finite interval alpha leq x leq beta left begin array l u t u x uu x u xxx 0 u alpha t h 1 t qquad u beta t h 2 t qquad u x beta t h 3 t u end array right qquad for t geq 0 it is shown that by choosing appropriate control inputs h j t j 1 2 3 one can always guide the system from a given initial state phi in h s alpha beta to a given terminal state psi in h s alpha beta in the time period 0 t so long as phi and psi satisfy phi cdot w cdot 0 h s alpha beta leq delta quad mbox and quad psi cdot w cdot t h s alpha beta leq delta for some delta 0 independent of phi and psi where s geq 0 and w equiv w x t is a given smooth solution of the kdv equation this exact boundary controllability is established by considering a related initial value control problem of the kdv equation posed on the whole line r various recently discovered smoothing properties of the kdv equation have played important roles in our approach

optimal harvesting control problem for an age dependent competing system of n species this paper is concerned with optimal harvesting policy for an age dependent n dimension competing species the existence and uniqueness of nonnegative solution of the system are proved using the fixed point theorem the existence of optimal control strategy is discussed optimality conditions are derived by means of normal cone and dubovitskii milyutin s general theory our results extend some known criteria

exact controllability of a nonlinear korteweg de vries equation on a critical spatial domain we consider the boundary controllability problem for a nonlinear korteweg de vries equation with the dirichlet boundary condition we study this problem for a spatial domain with a critical length for which the linearized control system is not controllable in order to deal with the nonlinearity we use a power series expansion of second order we prove that the nonlinear term gives the local exact controllability around the origin provided that the time of control is large enough

exact and approximate controllability of the age and space population dynamics structured model we prove exact and approximate controllability for a linear age dependent and spatially structured population dynamics problem the birth process is nonlocal and the demographic functions depends on age time and space our method relies on the derivation of a carleman inequality for the backward nonlocal adjoint system

equivalent linear logistic test models this paper is about the linear logistic test model lltm we demonstrate that there are infinitely many equivalent ways to specify a model an implication is that there may well be many ways to change the specification of a given lltm and achieve the same improvement in model fit to illustrate this phenomenon we analyze a real data set using a lagrange multiplier test for the specification of the model this lagrange multiplier test is similar to the modification index used in structural equation modeling

rapid stabilization for a korteweg de vries equation from the left dirichlet boundary condition this paper deals with the stabilization problem for the korteweg de vries equation posed on a bounded interval the control acts on the left dirichlet boundary condition at the right end point dirichlet and neumann homogeneous boundary conditions are considered the proposed feedback law forces the exponential decay of the system under a smallness condition on the initial data moreover the decay rate can be tuned to be as large as desired the feedback control law is designed by using the backstepping method

optimal harvesting problem for an age dependent n dimensional food chain diffusion model in this work optimal harvesting policy for an age dependent and spatial diffusion n dimensional food chain model is discussed the existence and uniqueness of non negative solution to the system are investigated by using the fixed point theorem the existence of optimal control strategy is discussed and optimality conditions are obtained our results extend some known criteria

nonlinear age dependent population growth under harvesting we consider the nonlinear age dependent population growth model introduced by gurtin maccamy arch rat mech anal 54 281 300 1974 to which is added a harvest of members at a rate which is constant in time but may depend on the age of members being harvested this partial differential equation may be transformed by the method of characteristics into a pair of functional equations for the total population size and the birth rate we discuss the behaviour of solutions when the birth and death moduli are functions of a single variable either the age or the total population size

a degenerate population system carleman estimates and controllability abstract in this paper we consider a system in non divergence form which models the interaction between two different species u and v both of them depend on time on age and on space moreover the diffusion coefficients degenerate at the boundary of domain we study in particular null controllability of the system via observability inequalities and carleman estimates for the associated non homogeneous adjoint problem

remarks on equivalent linear logistic test models by bechger verstralen and verhelst 2002 this paper discusses a new form of specifying and normalizing a linear logistic test model lltm as suggested by bechger verstralen and verhelst psychometrika 2002 it is shown that there are infinitely many ways to specify the same normalization moreover the relationship between some of their results and equivalent previous results in the literature is clarified and it is shown that the goals of estimating and testing a single element of the weight matrix for which they propose new methods can be reached by means of simple well known tools already implemented in published lltm software

identifiability of nonlinear logistic test models the linear logistic test model lltm specifies the item parameters as a weighted sum of basic parameters the lltm is a special case of a more general nonlinear logistic test model nltm where the weights are partially unknown this paper is about the identifiability of the nltm sufficient and necessary conditions for global identifiability are presented for a nltm where the weights are linear functions while conditions for local identifiability are shown to require a model with less restrictions it is also discussed how these conditions are checked using an algorithm due to bekker merckens and wansbeek 1994 several illustrations are given

equivalent mirid models it is shown that in the context of the model with internal restrictions on the item difficulties mirid different componential theories about an item set may lead to equivalent models furthermore we provide conditions for the identifiability of the mirid model parameters and it will be shown how the mirid model relates to the linear logistic test model lltm while it is known that the lltm is a special case of the mirid we show that it is possible to construct an lltm that encompasses the mirid the mirid model places a bilinear restriction on the item parameters of the rasch model it is explained how this fact is used to simplify the results of bechger verhelst and verstralen 2001 and bechger verstralen and verhelst 2002 and extend their scope to a wider class of models

boosting the decay of solutions of the linearised korteweg de vries burgers equation to a predetermined rate from the boundary abstractthe aim of this article is to extend recent results on the boundary feedback controllability of the korteweg de vries equation to the korteweg de vries burgers equation which is posed on a bounded domain in the first part of the paper it is proven that all the sufficiently small solutions can be steered to zero at any desired exponential rate by means of a suitably constructed boundary feedback controller in the second part an observer is proposed when a type of boundary measurement is available while there is no full access to the medium

optimal birth control of age dependent competitive species ii free horizon problems we study optimal birth policies for two age dependent populations in a competing system which is controlled by fertilities new results on problems with free final time and integral phase constraints are presented and the approximate controllability of system is discussed

optimal harvesting for a nonlinear age dependent population dynamics here we investigate an optimal harvesting problem for a nonlinear age dependent population dynamics existence and uniqueness of a positive solution for the model are demonstrated the structure of the solution is also investigated we establish the existence of the optimal control and the convergence of a certain fractional step scheme for some approximating problems we obtain the optimal controllers in feedback form via the dynamic programming method

overtaking optimal control problem for an age dependent competition system of n species abstract in this paper the overtaking optimal control problem for an age dependent competition model of n species with unbounded time interval is considered the existence of overtaking optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions weak and strong turnpike properties of optimal trajectories are established

identifiability of diagnostic classification models diagnostic classification models dcms are important statistical tools in cognitive diagnosis in this paper we consider the issue of their identifiability in particular we focus on one basic and popular model the dina model we propose sufficient and necessary conditions under which the model parameters are identifiable from the data the consequences in terms of the consistency of parameter estimates of fulfilling or failing to fulfill these conditions are illustrated via simulation the results can be easily extended to the dino model through the duality of the dina and dino models moreover the proposed theoretical framework could be applied to study the identifiability issue of other dcms

exact controllability and stabilizability of the korteweg de vries equation in this paper we consider distributed control of the system described by the korteweg de vries equation i atu uaxu e3 u f on the interval 0 0 with periodic boundary conditions ii au 27r t ku o t k 0 1 2 where the distributed control f f x t is restricted so that the volume f u x t dx of the solution is conserved both exact controllability and stabilizibility questions are studied for the system in the case of open loop control if the control f is allowed to act on the whole spatial domain 0 27r it is shown that the system is globally exactly controllable i e for given t 0 and functions q x x with the same volume one can alway find a control f so that the system i ii has a solution u x t satisfying u x 0 0 x u x t x if the control f is allowed to act on only a small subset of the domain 0 27r then the same result still holds if the initial and terminal states b and 0 have small amplitude in a certain sense in the case of closed loop control the distributed control f is assumed to be generated by a linear feedback law conserving the volume while monotonically reducing f u x t 2dx the solutions of the resulting closed loop system are shown to have uniform exponential decay to a constant state as in the open loop control case a small amplitude assumption is needed if the control is allowed to act on only a small subdomain the smoothing property of the periodic linear kdv equation discovered recently by bourgain has played an important role in establishing the exact controllability and stabilizability results presented in this paper

boundary feedback stabilization of the korteweg de vries burgers equation posed on a finite interval abstract this paper studies the boundary feedback stabilization problem of the korteweg de vries burgers equation posed on a finite interval a linear boundary feedback control law is proposed then the resulting closed loop nonlinear system is shown not only to be globally well posed but also to be exponentially stable in the space h s 0 l with s 0 3 the sharp kato smoothing property of the associated linear problem is revealed through the boundary integral operator which plays a key role in our analysis

identifiability and equivalence of gllirm models the generalized logit linear item response model gllirm is a linearly constrained nominal categories model ncm that computes the scale and intercept parameters for categories as a weighted sum of basic parameters this paper addresses the problems of the identifiability of the basic parameters and the equivalence between different gllirm models it is shown that the identifiability of the basic parameters depends on the size and rank of the coefficient matrix of the linear functions moreover two models are observationally equivalent if the product of the respective coefficient matrices has full column rank finally the paper also explores the relations between the parameters of nested models

optimal birth control for predator prey system of three species with age structure in this paper we investigate optimal policies for three age dependent populations in a predator prey system which is controlled by fertility by using dubovitskii milyutin s general theory the maximum principles are obtained for problems with free terminal states infinite horizon and target sets respectively

optimal harvesting for periodic age dependent population dynamics here we investigate the optimal harvesting problem for some periodic age dependent population dynamics namely we consider the linear lotka mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations existence and uniqueness of a positive periodic solution are demonstrated and the existence and uniqueness of the optimal control are established we also state necessary optimality conditions a numerical algorithm is developed to approximate the optimal control and the optimal harvest some numerical results are presented

on the bayesian nonparametric generalization of irt type models we study the identification and consistency of bayesian semiparametric irt type models where the uncertainty on the abilities distribution is modeled using a prior distribution on the space of probability measures we show that for the semiparametric rasch poisson counts model simple restrictions ensure the identification of a general distribution generating the abilities even for a finite number of probes for the semiparametric rasch model only a finite number of properties of the general abilities distribution can be identified by a finite number of items which are completely characterized the full identification of the semiparametric rasch model can be only achieved when an infinite number of items is available the results are illustrated using simulated data

linking item response model parameters with a few exceptions the problem of linking item response model parameters from different item calibrations has been conceptualized as an instance of the problem of test equating scores on different test forms this paper argues however that the use of item response models does not require any test score equating instead it involves the necessity of parameter linking due to a fundamental problem inherent in the formal nature of these models their general lack of identifiability more specifically item response model parameters need to be linked to adjust for the different effects of the identifiability restrictions used in separate item calibrations our main theorems characterize the formal nature of these linking functions for monotone continuous response models derive their specific shapes for different parameterizations of the 3pl model and show how to identify them from the parameter values of the common items or persons in different linking designs