necessary and sufficient conditions for near optimal harvesting control problem of stochastic age dependent system in this paper we consider a near optimal harvesting control problems for stochastic age structured population system we establish necessary and sufficient conditions for near optimality these conditions are described by adjoint equations and a nearly maximum condition on the hamiltonian the proof of the main result is based on ekeland s variational principle and the adjoint processes with respect to the control variable as is well known optimal controls may fail to exist even in simple cases this justifies the use of near optimal controls which exist under minimal assumptions and are sufficient in most practical cases at last an example is given for illustrating our results

some properties of exact tests for unit roots summary this paper is concerned with the null hypothesis that errors in a regression equation for time series data follow a random walk we examine the power properties of most powerful invariant tests for the unit root null hypotheses against exact stationary and nonstationary first order autoregressive models the analysis shows the importance of a constant term and a linear trend variable in certain cases the implications of the results for models estimated using seasonal data are briefly discussed

optimal birth control for an age dependent n dimensional food chain model abstract in this paper we investigate optimal policies for an age dependent n dimensional food chain model 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 control problem for linear periodic age dependent population dynamics in this paper we investigate an optimal harvesting problem for linear periodic age dependent population dynamics namely we consider the lotka mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations by mazur s theorem we demonstrate existence of solutions of the optimal control problem oh and by the conception of normal cone we also obtain the first order necessary conditions of optimality for problem oh finally under suitable assumptions we give uniqueness of solutions of the optimal control problem oh our results extend some known criteria

behavioral analysis of a nonlinear three staged population model with age size structure we present and analyze a nonlinear egg juvenile adult model in which eggs and juveniles are structured by age while adults by size the model consists of three first order partial differential equations with initial and boundary conditions existence and uniqueness of nonnegative solutions to the state system are investigated by the method of characteristics and a comparison principle extinction or persistence conditions of the population are obtained via the upper lower solution technique our investigation extends some results in the literature

optimal harvesting problems for age dependent interacting species with diffusion we investigate the optimal harvesting problems of a predator prey system for two age dependent populations with diffusion the existence and uniqueness of solutions for the system are proven using the fixed point theorem the existence of optimal control and maximum principles for problems are obtained

additional critical values and asymptotic representations for seasonal unit root tests this paper is concerned with tests for seasonal unit roots in a univariate time series process the paper extends the procedures and tables of critical values due to hylleberg et al 1990 and ghysels et al 1994 to obtain tests which are similar exactly and asymptotically with respect to both the initial values of the process and the possibility of differential seasonal drift under the null hypothesis of a seasonal unit root representations are derived for the limiting distributions of the test statistics in this and other cases of interest these representations provide an explanation for the similarity between critical values for the statistics in different scenarios the seasonal unit root properties of real seasonally unadjusted uk non durable consumption expenditure are re examined

proper fredholm submanifolds of hilbert space on considere des varietes et des sous varietes de hilbert riemanniennes on demontre qu une sous variete de fredholm propre a une structure de fredholm naturelle et on montre que les operateurs de forme sont compacts et que chaque fonction distance euclidienne fa satisfait la condition c de palais et smale on etudie la geometrie des sous varietes de fredholm propre a fibre normal plat

seasonal integration and cointegration this paper develops tests for roots in linear time series which have a modulus of one but which correspond to seasonal frequencies critical values for the tests are generated by monte carlo methods or are shown to be available from dickey fuller or dickey hasza fuller critical values representations for multivariate processes with combinations of seasonal and zero frequency unit roots are developed leading to a variety of autoregressive and error correction representations the techniques are used to examine cointegration at different frequencies between consumption and income in the u k

on a distributed control problem arising in dynamic optimization of a fixed size population the practical motivation for this paper is provided by the recruitment problem faced by many organizations of fixed size to keep the average age young and thus keep innovation and productivity high while at the same time keeping levels of recruitment high a typical example is an academy of sciences the problem is formalized by an infinite horizon optimal control model for a first order pde with nonlocal dynamics a mckendrick type equation based on the nonstandard necessary optimality condition proved in the paper the following results are established i stationarity of the optimal recruitment density ii strong ergodicity of the optimal solution iii principle of bipolar recruitment in the case where the productivity of the organization is measured by the average age of the members the analysis involves a new type of transversality condition for the costate system the stability with respect to perturbations of the optimal solution of a noncoercive bang bang type problem boundedness and stability of the solution of a specific volterra integral equation of the second kind

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

tests for seasonal moving average unit root in arima models abstract procedures to test for a unit root in the seasonal moving average ma operator for seasonal autoregressive integrated moving average arima models are examined such procedures are useful to distinguish deterministic from stochastic seasonal patterns the simple integrated seasonal ma 1 model z t y t yt s 1 b s t where y t is the observed seasonal series and t is a white noise sequence is considered and tests for h 0 1 versus h 1 1 are studied the locally best invariant unbiased and point optimal invariant tests are investigated the finite sample and asymptotic distributions of the test statistics under both the null hypothesis and local alternatives are derived quantiles of the null distributions are tabulated for quarterly and monthly data cases and a limited study of the powers of the tests is reported the test procedures are extended to more general seasonal arma models of the form z t 1 b s nt where n t follows a general stationary and invertible

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

gaussian tests for seasonal unit roots based on cauchy estimation and recursive mean adjustments abstract we propose tests for seasonal unit roots whose limiting null distributions are always standard normal regardless of the period of seasonality and types of mean adjustments the seasonal models of dickey hasza and fuller 1984 journal of american statistical association 79 355 367 dhf and hylleberg engle granger and yoo 1990 journal of econometrics 44 215 238 hegy are considered for estimating parameters related to the seasonal unit roots regressor signs are used as instrumental variables while recursive sample means are used for adjusting the seasonal means in addition to normality of the limiting null distributions in seasonal mean models the recursive mean adjustment provides the new tests with locally higher powers than those of the existing tests of dhf and hegy based on the ordinary least squares estimators if data have a strong linear time trend the recursive mean adjustment is a source of both power gains of some tests for local alternatives and power losses of all tests for other alternatives limiting normality allow evaluation of p values and testing joint significance of subsets of seasonal unit roots

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

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

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

optimal birth control of population dynamics abstract we study optimal birth control policies for an age structured population of mckendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control the functional analytic approach of dubovitskii and milyutin is adopted in the investigation maximum principles for problems with a free end condition a fixed final horizon are developed and the time optimal control problem the problem with target sets and the infinite planning horizon case are investigated

asymmetry and nonstationarity for a seasonal time series model abstract tests for symmetry and seasonal unit roots are developed for an extended model of hylleberg et al 1990 seasonal integration and cointegration journal econometrics 44 215 238 which can represent both partial seasonal unit roots and threshold effects methods based on ordinary least squares ols estimation and instrumental variable iv estimation are proposed and compared for adjusting mean functions ordinary mean adjustment and recursive mean adjustment are both considered several tests are constructed from various combination of estimation schemes and mean adjustment schemes among the tests the tests based on iv estimation are recommended because they have very simple limiting null distributions and have finite sample power properties comparable to those based on the olse the recommended tests are applied to a us unemployment rate data set and find evidences for both nonstationarities associated with zero frequency and threshold effects

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

optimal control for an age dependent competitive species model in a polluted environment in this paper a new age dependent toxicant population model in an environment with small toxicant capacity is formulated and the optimal control problem for this kind hybrid system is investigated the existence and uniqueness of nonnegative solution of this model is obtained by using a fixed point theorem the optimality conditions for the control problem are given by means of tangent normal cone techniques in nonlinear functional analysis the existence of optimal control policy is carefully verified by using of ekeland s variational principle

optimal harvesting problems for an age dependent n dimensional food chain model with diffusion we investigate the optimal harvesting problems of an age dependent n dimensional food chain model with spartially structured which is controlled by harvesting the existence and uniqueness of solution for the system are proven using banach fixed point theorem we establish existence result of optimal control and necessary optimality conditions

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

optimal birth control problems for a nonlinear vermin population model with size structure abstract in this paper we investigate theoretically the least cost size problem and the least cost deviation problem for a nonlinear size structured vermin population model with separable mortality which takes fertility rate as the control variable we obtain the existence of a unique non negative solution by considering the separable solution of the model which is crucial to obtain the optimal control strategy we also illustrate the continuous dependence of the population density on initial value and control parameter finally we study the least cost size problem and the least cost deviation problem our conclusion would be useful for managing the vermin

polar coordinates induced by actions of compact lie groups let g be a connected lie subgroup of the real orthogonal group 0 n for the action of g on r we construct linear subspaces a that intersect all orbits we determine for which g there exists such an a meeting all the g orbits orthogo nally groups that act transitively on spheres are obvious examples with few exceptions all possible g arise as the isotropy subgroups of riemannian symmetric spaces introduction let g be a compact lie group acting on a real vectorspace v and let k be a g invariant inner product on v having a linear cross section a c v of

testing for nonstationary parameter specifications in seasonal time series models let yt be an autoregressive process satisfying yt aiyt a2yt d a3yt d i et where et t o is a sequence of iid o u2 random variables and d 2 such processes have been used as parametric models for seasonal time series typical values of d are 2 4 and 12 corresponding to time series observed semi annually quarterly and monthly respectively if a 1 2 1 a 3 1 then aladyt et where a yt denotes yt yt r if a 12 3 1 1 1 the process is nonstationary and the theory for stationary autoregressive processes does not apply a methodology for testing the hypothesis as 2 13 1 1 1 is presented and percentiles for test statistics are obtained extensions are presented for multiplicative processes for higher order processes and for processes containing deterministic trend and seasonal components

optimal control of heterogeneous systems basic theory a general model of a heterogeneous control system is introduced in the form of a first order distributed system with nonlocal dynamics and exogenous side conditions the heterogeneity is represented by a parameter taking values in an abstract measurable space so that both continuous and discrete heterogeneity as well as probabilistic heterogeneity without density are included a distributed and a lumped controls are involved the latter appearing also in the side conditions an existence theorem is proved for the uncontrolled system and the sensitivity of the solution with respect to the control variables is estimated the main result is an optimality condition in the form of the pontryagin local maximum principle a global maximum principle holds for the distributed control under an additional condition that rules out discrete measurable heterogeneity spaces a number of possible applications are outlined age structured systems size structured systems nonlocal advection reaction equations static parametric heterogeneity in epidemiology and two stage control systems with uncertain switching time

optimal control of a nonlinear population dynamics with diffusion abstract in this paper we study the optimal control for some population dynamics problems we determine the necessary conditions and present an iterative scheme for the optimal control problems

age time continuous galerkin methods for a model of population dynamics continuous galerkin finite element methods in the age time domain are proposed to approximate the solution to the model of population dynamics with unbounded mortality coefficient function stability of the method is established and a priori l 2 error estimates are obtained treatment of the nonlocal boundary condition is straightforward in this framework the approximate solution is computed strip by strip marching in time some numerical examples are presented

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

unitary structure in representations of infinite dimensional groups and a convexity theorem in this paper we show that a kac moody algebra fl a associated to a symmetrizable generalized cartan matrix a carries a contravariant hermitian form which is positive definite on all root spaces we deduce that every integrable highest weight g a module l a carries a contravariant positivedefinite hermitian form this allows us to define the moment map and prove a generalization of the schur horn kosta nt heckman atiya h pressley convexity theorem the proofs are based on an identity which also gives estimates for the action of 9 a on fl a and l a we hope that the main idea behind the paper is apparent it is to use the interplay between the coadjoint and the highest weight representations we are grateful to v guillemin for an introduction to the moment map

the energy function and homogeneous harmonic maps for equivariant maps from a compact homogeneous space into an adjoint orbit of a compact lie group it is shown that the energy function is the restriction of a quadratic function on the lie algebra providing the orbit has the metric induced from the lie algebra one obtains a simple version of the harmonic map equation and an identity relating the energy and the square of the norm of the moment map several applications are given including an example which illustrates how a change of metric in a flag manifold affects the harmonicity of equivariant maps from the two sphere to the flag manifold

existence of overtaking solutions to infinite dimensional control problems on unbounded time intervals the optimal control of an infinite dimensional linear control system with unbounded time interval is considered the results obtained are an extension to a hilbert space setting of the results reported in brock and haurie math oper res 1 1976 pp 337 346 in particular it is shown that under appropriate conditions overtaking optimal trajectories asymptotically approach a unique optimal steady state this is the so called turnpike property found in the economics literature when this condition is combined with an associated optimal control problem results concerning the existence of overtaking optimal solutions are obtained both distributed and boundary controls are considered finally we demonstrate the applicability of our results by considering several examples arising in the context of economics and resources management

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

optimal harvesting for periodic age dependent population dynamics with logistic term we prove an asymptotic behavior result for an age dependent population dynamics with logistic term and periodic vital rates we investigate next an optimal harvesting problem related to a periodic age structured model with logistic term existence of an optimal control and necessary optimality conditions are established a conceptual algorithm to approximate the optimal pair is derived and some numerical experiments are presented

exact null controllability of the lobesia botrana model with diffusion abstract this paper is devoted to analyze the exact null controllability of the diffusive lobesia botrana model with nonlocal boundary condition we study the null controllability of butterfly population by acting on eggs larvas and female moths in a small age interval we assume that the control of female moths is in a certain given region of the vineyard the main result is established by combining some estimations and the carleman inequality for the backward system related to an optimal control problem a fixed point theorem is then used to draw the conclusion

size structured plant population models and harvesting problems harvesting problems for plants are discussed through a nonlinear size structured population model solvability of the harvesting model is verified and results of numerical simulations are presented to validate our approach to the harvesting problems

testing for unit roots in seasonal time series abstract regression estimators of coefficients in seasonal autoregressive models are described the percentiles of the distributions for time series that have unit roots at the seasonal lag are computed by monte carlo integration for finite samples and by analytic techniques and monte carlo integration for the limit case the tabled distributions may be used to test the hypothesis that a time series has a seasonal unit root

an instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models the unit root tests of caner and hansen econometrica 69 2001 1555 for asymmetric time series models based on the ordinary least squares estimator olse have asymptotic null distributions that depend on parameters of asymmetry we resolve this parameter dependency by adopting the instrumental variable estimation of shin and lee j business economic statist 19 2001 233 and the recursive mean adjustment of shin and so j time series anal 22 2001b 595 if the threshold parameter is known the limiting null distribution of the proposed wald test does not depend on any nuisance parameter and is chi squared if the threshold parameter is unknown and is estimated from data then under threshold effect the limiting null distributions of the proposed wald tests are chi squared as those for model with known threshold parameter whereas under no threshold effect they are chi squared only conditionally on the weak limit of the estimated threshold parameter our wald tests extend to seasonal models retaining the chi square asymptotics regardless of the parameter of seasonality which is not the case of the olse based tests moreover the proposed tests can be modified into one sided wald tests which are significantly more powerful than the tests of caner and hansen 2001 we apply our method to the monthly us unemployment rate and find some evidences of seasonal unit roots suggesting nonstationarity rather than the strong stationarity of caner and hansen 2001

a pontryagin maximum principle for infinite dimensional problems a basic idea of the classical approach for obtaining necessary optimality conditions in optimal control is to construct suitable needle like control variations we use this idea to prove the main result of the present paper a pontryagin maximum principle for infinite dimensional optimal control problems with pointwise terminal constraints in arbitrary banach state space by refining the classical variational technique we are able to replace the differentiability of the norm of the state space guaranteed by the strict convexity of its dual norm which is assumed in the known results by a separation argument we also drop another key assumption which is common in the existing literature on infinite dimensional control problems that the set of variations in the state space of the state trajectory s endpoint resulting from the control variations be finite codimensional instead we require only that it has nonempty interior in its closed affine hull as an application of the abstract result we present an illustrative example an optimal control problem for an age structured system with pointwise terminal state constraints

optimal control for age dependent population hybrid system in a polluted environment in this paper we study an optimal control problem for an age dependent population hybrid system in a polluted environment namely we establish a new toxicant population model with age dependence in a small content of the environment by fixed point theorem we obtain the existence and uniqueness of nonnegative solution of the toxicant population model with age dependence we employ tangent normal cone techniques in nonlinear functional analysis to deduct the optimality conditions for control problem the existence of optimal control policy is carefully verified by means of ekeland s variational principle

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

note on some periodic optimal harvesting problems for age structured population dynamics we consider two optimal harvesting problems related to age structured population dynamics with logistic term and time periodic of period t control and vital rates we derive the first order necessary optimality conditions for both problems we prove that in the particular case of time independent vital rates and under a natural hypothesis on the logistic term the optimal control for the first problem is constant the second problem concerns the constant harvesting efforts which act on subintervals of 0 t the maximizing here is treated with respect to the subinterval where the control acts we find the directional derivative of the cost functional some final comments concerning the population dynamics with diffusion are given as well

optimal harvesting for age distribution and weighted size competitive species with diffusion abstract in this paper the optimal harvesting problem for age distribution and weighted size competitive species with diffusion has been studied the existence and uniqueness of solution for the system are proven using the banach fixed point theorem the existence of optimal control is demonstrated and necessary optimality conditions are obtained via tangent normal cone technique in nonlinear functional analysis

on regression based tests for seasonal unit roots in the presence of periodic heteroscedasticity we analyse regression based tests for seasonal unit roots when the shocks are periodically heteroscedastic we show using the case of quarterly data to illustrate that the limiting marginal null distributions of tests for unit roots at the zero and nyquist frequencies are unaffected by the periodic heteroscedasticity however tests at the harmonic seasonal frequencies are shown to be either unaffected or to display a shift in their limiting distribution depending on the specific nature of the periodic heteroscedasticity in extreme cases certain of these limiting distributions are degenerate while others are simple functions of the well known dickey fuller distributions monte carlo evidence shows that the asymptotic theory provides a very good prediction for the finite sample behaviour of the unit root test statistics we show that tests with approximately correct size may be obtained by simulating their sampling distributions using periodic variance parameters estimated from the data in hand though laborious this procedure seems to be the best available since more conservative approaches sacrifice significant power

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

bootstrapping the hegy seasonal unit root tests this paper proposes bootstrap versions of the seasonal unit root tests of inter alia hylleberg engle granger and yoo j econometrics 44 1990 215 238 hegy we report a simulation study of the properties of both the conventional and bootstrapped seasonal unit root tests when applied to series having higher order serial correlation and or periodic heteroscedasticity both of which are known to severely distort the significance level of the conventional tests our results demonstrate that the bootstrap provides good approximations to the statistics null distributions moreover the bootstrap corrects the adverse effects of data dependent lag selection seen in the conventional augmented hegy tests the bootstrapped tests have comparable power to infeasible exactly significance level corrected lag augmented hegy tests and their use is recommended

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

on a population dynamics control problem with age dependence and spatial structure we consider the control problem for a population dynamics model with age dependence spatial structure and a nonlocal birth process arising as a boundary condition we examine the controllability at a given time t and show that approximate controllability holds for every fixed finite time t as a consequence a new uniqueness condition continuation result is proved

regional control in optimal harvesting of population dynamics abstract here we investigate the regional control for some optimal harvesting problems related to population dynamics namely we consider the problem of maximizing the profit for spatially structured harvesting problems with respect to both the harvesting effort and the selected subregion of the whole domain where the effort is localized for a fixed subregion we state necessary optimality conditions and use them to get the structure of the optimal effort and to reformulate the maximization problem with respect to the subregion where the harvesting effort is localized in a more convenient way we derive an iterative algorithm to increase at each iteration the profit by changing the subregion where the effort is localized some numerical tests are given to illustrate the effectiveness of the results for a particular optimal harvesting problem final comments are given as well concerning further directions to extend the results and methods presented here

overtaking optimal control problem of age dependent populations with infinite horizon abstract the optimal birth control of an age dependent population model with unbounded time interval is considered the minimum principle which must be satisfied by the overtaking optimal control is established large time behaviour and the turnpike property of the overtaking optimal trajectory are studied existence results are also presented

a product formula approach to nonlinear optimal control problems in this paper we prove the convergence of an iterative scheme of lie trotter type for optimal control problems governed by nonlinear systems the numerical implementation of the resulting algorithm is also discussed

optimal immigration age patterns in populations of fixed size a b s t r a c t due to a low birth rate many countries need immigration to sustain a given population size the resulting model consists of specific non standard age structured control systems on an infinite horizon this paper investigates the question of optimal choice of the immigration age profile within certain bounds the main qualitative result is that under certain conditions the optimal control the immigration age profile is time invariant although a dynamic framework is used this makes it possible to give a detailed description of the optimal immigration policy and to obtain numerical solutions for the austrian case the analysis requires a number of new results obtained in the paper a new type of transversality condition for the adjoint equation involved in the optimality conditions generic conditions for well posedness of the problem and appropriate stability conditions

exact tests in single equation autoregressive distributed lag models abstract for hypotheses on the coefficient values of the lagged dependent variables in the arx class of dynamic regression models test procedures are developed which yield exact inference for given up to an unknown scale factor distribution of the innovation errors they include exact tests on the maximum lag length for structural change and on the presence of seasonal or multiple unit roots i e they cover situations where usually asymptotic and non exact t f aoc adf or hegy tests are employed the various procedures are demonstrated and compared in illustrative empirical models and the approach is critically discussed

existence of periodic solutions in abstract semilinear equations and applications to biological models abstract in this paper we study the existence of mild periodic solutions of abstract semilinear equations in a setting that includes several other types of equations such as delay differential equations first order hyperbolic partial differential equations and reaction diffusion equations under different assumptions on the linear operator and the nonhomogeneous function sufficient conditions are derived to ensure the existence of mild periodic solutions in the abstract semilinear equations when the semigroup generated by the linear operator is not compact banach fixed point theorem is used whereas when the semigroup generated by the linear operator is compact schauder fixed point theorem is employed in applications we apply the main results to establish the existence of periodic solutions in delayed red blood cell models age structured models with periodic harvesting and the diffusive logistic equation with periodic coefficients

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

optimal birth control of age dependent competitive species iii overtaking problem a study is made of an overtaking optimal problem for a population system consisting of two competing species which is controlled by fertilities the existence of 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

a nonlinear model for human population dynamics a nonlinear model for birth dynamics an integral equation is formulated in which the current maternity behavior of a population is determined by birth levels in the past it is shown that certain values of a parameter yield a positive asymptotically stable equilibrium birth level which bifurcates to a periodic solution at a certain point the principal techniques used are integral inequalities and a hopf bifurcation

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

optimal control of free horizon problems for an age dependent n dimensional food chain model this paper is concerned with optimal birth policies for an age dependent n dimensional food chain model new results on problems with free final time and integral phase constraints are presented the approximate controllability of system is discussed

oscillation free solutions to volterra integral and integro differential equations with periodic force terms volterra equations governed by oscillatory functions arise frequently in applied fields to construct efficient algorithms for solving these equations oscillatory properties of their solutions should be studied in this paper oscillatory orders of solutions to a class of highly oscillatory volterra integral equations are presented then some modified solutions are given with the help of asymptotic expansions of highly oscillatory integrals finally theoretical analysis verifies these modified solutions enjoy less oscillation than the original one and extensions to highly oscillatory volterra integro differential equations are considered

optimal birth control of population dynamics ii problems with free final time phase constraints and mini max costs abstract we study optimal birth control of population systems of mckendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control new results on problems with free final time phase constraints and mini max costs are presented

optimal control of a competitive system with age structure we investigate optimal control of a first order partial differential equation pde system representing a competitive population model with age structure the controls are the proportions of the populations to be harvested and the objective functional represents the profit from harvesting the existence and unique characterization of the optimal control pair are established

optimality conditions for age structured control systems abstract we consider a fairly general model extension of the gurtin maccamy model of population dynamics of an age structured control system with nonlocal dynamics and nonlocal boundary conditions a necessary optimality condition is obtained in the form of pontryagin s maximum principle which is applicable to a number of practically meaningful models where the previously known results fail we discuss such models an epidemic control and a capital accumulation model as illustrations

a general theory of canonical forms si g est un groupe de lie compact et m une g variete riemannienne d orbites principales de codimension k alors une section ou une forme canonique pour m est une sous variete fermee lisse a k dimensions de m qui rencontre toutes les orbites de m orthogonalement

on periodic structures and testing for seasonal unit roots abstract the standard testing procedures for seasonal unit roots developed so far have been based mainly on time invariant autoregressive integrated moving average arima processes with ar polynomials involving seasonal differencing one attractive alternative is to use periodic arma models convenient procedures are presented for testing for the presence of unit roots at the zero and seasonal frequencies in periodic time series the limiting distributions are derived and tabulated simulation evidence illustrates the advantages of allowing for periodicity the tests are illustrated via applications to macroeconomic and ozone level data