Water management addresses the problem of optimal allocation of reusable water among different waterusing operations. Wastewater management deals with optimal design of effluent treatment units to respect environmental norms. However, optimal design of effluent treatment units should be solved in conjunction with the problem of optimal allocation of water among different processes that use water. A new methodology for targeting minimum effluent treatment flow rate satisfying minimum freshwater requirement is proposed in this paper. The proposed methodology can be applied to fixed-flow-rate as well as fixed-contaminant-load problems having a single contaminant. A source composite curve is proposed for directly targeting generation of wastewater. Freshwater can be indirectly targeted using overall mass balance. To target distributed generation of wastewater, wastewater composite curve is proposed. On the basis of this wastewater composite curve, targets for effluent systems can be set. All these targets can be set on a single concentration-contaminant load diagram before designing the detailed water-allocation network. Analytical algorithms are proposed to solve the integrated water and wastewater management problem. The minimum contaminant removal ratio of the effluent treatment system and the minimum number of required effluent treatment units are also reported in this paper.

This paper develops a theory of control for distributed systems (i.e., those defined by systems of constant coefficient partial differential operators) via the behavioral approach of Willems. The study here is algebraic in the sense that it relates behaviors of distributed systems to submodules of free modules over the polynomial ring in several indeterminates. As in the lumped case, behaviors of distributed ARMA systems can be reduced to AR behaviors. This paper first studies the notion of AR controllable distributed systems following the corresponding definition for lumped systems due to Willems. It shows that, as in the lumped case, the class of controllable AR systems is precisely the class of MA systems. It then shows that controllable 2-D distributed systems are necessarily given by free submodules, whereas this is not the case for n-D distributed systems, n ≥ 3. This therefore points out an important difference between these two cases. This paper then defines two notions of autonomous distributed systems which mimic different properties of lumped autonomous systems. Control is the process of restricting a behavior to a specific desirable autonomous subbehavior. A notion of stability generalizing bounded input-bounded output stability of lumped systems is proposed and the pole placement problem is defined for distributed systems. This paper then solves this problem for a class of distributed behaviors.

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We consider the question of determining the maximum number of points on sections of Grassmannians over finite fields by linear subvarieties of the Plücker projective space of a fixed codimension. This corresponds to a known open problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties. We recover most of the known results as well as prove some new results. A basic tool used is a characterization of decomposable subspaces of exterior powers, that is, subspaces in which every nonzero element is decomposable. Also, we use a generalization of the Griesmer-Wei bound that is proved here for arbitrary linear codes.