abstract optimal management of water and nutrient could consider as effective on farm method to reduce pollution because agriculture is none point pollution. in this research, an optimal model was presented to reduce nitrate loss in furrow fertigation. the optimal model contains four simulation models for predicting runoff, deep percolation, nitrate concentration in runoff and nitrate concentra...

This paper suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove new versions of the Pontryagin maximum principle. Special attention is paid to the behavior of the adjoint var...

We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optimal control are proved, as well as necessary optimality conditions. Mathematics ...

Problems of optimal control of movable lumped sources in distributed systems when controls belong to the classes of impulsive, piecewise constant, and Heaviside functions are considered in the paper. The optimal control problems are investigated for various cases, according to the position of the sources. Necessary optimality conditions are obtained for optimal control problems considered on al...

Optimal control problems in measure spaces governed by semilinear elliptic equations are considered. First order optimality conditions are derived and structural properties of their solutions, in particular sparsity, are discussed. Necessary and sufficient second order optimality conditions are obtained as well. On the basis of the sufficient conditions, stability of the solutions is analyzed. ...

Let Dv,b,k denote the family of all connected block designs with v treatments and b blocks of size k. Let d ∈ Dv,b,k. The replication of a treatment is the number of times it appears in the blocks of d. The matrix C(d) = R(d) − 1 kN(d)N(d) > is called the information matrix of d where N(d) is the incidence matrix of d and R(d) is a diagonal matrix of the replications. Since d is connected, C(d)...