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  • Infinite-horizon optimal control  (3)
  • sheep  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Agroforestry systems 25 (1994), S. 1-12 
    ISSN: 1572-9680
    Keywords: agroforestry ; grazing ; sheep ; Douglas-fir ; moisture stress
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Plant-soil-water relations of a silvopastoral system composed of a Douglas-fir (Pseudotsuga menziesii) timber crop, subterranean clover (Trifolium subterraneum) as a nitrogen-fixing forage, and tall fescue (Festuca arundinacea) as a forage crop were investigated near Corvallis, Oregon, during 1983–1986. Treatments included all possible combinations of two tree-planting patterns (trees planted 2.4 m apart in a grid, and groups of five trees spaced 7.6 m between clusters) and two grazing/understory management systems (agroforests were seeded to subclover and grazed by sheep; forests were unseeded and ungrazed). Mean twig xylem water potential (XWP) for Douglas-fir trees ranged from −0.3 to −1.5 MPa on forest plots and from −0.3 to −1.2 MPa on agroforest sites. Pre-dawn and sunset XWP were more negative for forest than for agroforest plots during dry summer periods. Midday XWP was similar for both agroforest and forest plots on all dates. Soil water content at 50–100 cm depth was greater under agroforest plots as compared to forest plots in 1984, but not in 1985 (unusually dry spring). Average foliage nitrogen content of tree needles was 1.54% vs. 1.43% for agroforests vs. forests, respectively. Our data are consistent with the hypotheses that: (1) grazing of understory vegetation may reduce water stress of trees during dry periods by reducing transpirational water use by the forage plants; and (2) nitrogen-fixing vegetation combined with grazing increases nitrogen uptake of associated trees. However, neither mean foliar N nor average XWP differences experienced by trees in agroforest versus forest plantations were sufficient to have an effect on tree growth. Our data demonstrate that it is possible to produce a second crop (i.e. forage grazed by sheep) in timber plantations without reducing the growth of the main tree crop.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Agroforestry systems 19 (1992), S. 223-232 
    ISSN: 1572-9680
    Keywords: agroforestry ; browsing ; debarking ; sheep ; deer ; Pseudotsuga menziesii
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Livestock may provide important service and production functions in agroforestry systems. However, use of livestock in conifer/improved pasture agrosilvopastoral systems is currently limited by concerns about potential damage to trees by livestock. Effects of sheep grazing on Douglas-fir (Pseudotsuga menziesii) trees in two patterns of sheep/pasture/conifer agroforest (cluster and grid plantations) were studied from 4 years after planting (1983) until the first precommercial thinning at age 10 years (1988). Trees averaged over 1 m in height when grazing began in summer 1983. Some browsing of tree lateral branches by sheep occurred regardless of grazing season in 1983–1985. However, the 2 to 10% of current year's lateral branch growth removed by grazing sheep was too low to impact tree growth. Sheep removed the terminal leaders from only 3 to 9% of trees each year during 1983–1985. Most browsing of terminals occurred in the summer when other forages had become mature and were relatively unpalatable to sheep. Less than 13% of agroforest trees were debarked by sheep each year during 1983–1987. By the end of grazing in 1987, less than 8% of agroforest trees had sustained a level of debarking likely to impact future growth (〉50% of tree circumference debarked). Grazing had no discernible effect upon tree diameter or height in any year (P 〉 0.05). Total tree mortality attributable to sheep grazing during 1983–1987 was only 0.9%, including three trees girdled by sheep and two debarked trees which were subsequently attacked by insects. Overall, grazing had no detrimental impact on timber stand growth or mortality.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 64 (1990), S. 55-69 
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; overtaking optimal solutions ; decision-horizon optimal solutions ; agreeable plans ; sufficient conditions for optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we investigate the relationship between two classes of optimality which have arisen in the study of dynamic optimization problems defined on an infinite-time domain. We utilize an optimal control framework to discuss our results. In particular, we establish relationships between limiting objective functional type optimality concepts, commonly known as overtaking optimality and weakly overtaking optimality, and the finite-horizon solution concepts of decision-horizon optimality and agreeable plans. Our results show that both classes of optimality are implied by corresponding uniform limiting objective functional type optimality concepts, referred to here as uniformly overtaking optimality and uniformly weakly overtaking optimality. This observation permits us to extract sufficient conditions for optimality from known sufficient conditions for overtaking and weakly overtaking optimality by strengthening their hypotheses. These results take the form of a strengthened maximum principle. Examples are given to show that the hypotheses of these results can be realized.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 66 (1990), S. 311-336 
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; Volterra integral equations ; recursive objective functionals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this work, we concern ourselves with the existence of optimal solutions to optimal control problems defined on an unbounded time interval with states governed by a nonlinear Volterra integral equation. These results extend both the work of Baum and others in infinite-horizon control of ordinary differential equations as well as the work of Angell concerning integral equations. In addition, we incorporate into the objective functional (described by an improper integral) a discount factor which reflects a hereditary dependence on both state and control. In this manner, we are able to generalize the recent results of Becker, Boyd, and Sung in which they establish an existence theorem in the calculus of variations with objective functionals of the so-called recursive type. Our results are obtained through the use of appropriate lower-closure theorems and compactness conditions. Examples are presented in which the applicability of our results is demonstrated.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 78 (1993), S. 465-491 
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; overtaking optimality ; economic growth ; chattering states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the Lagrange problem of optimal control defined on an unbounded time interval in which the traditional convexity hypotheses are not met. Models of this form have been introduced into the economics literature to investigate the exploitation of a renewable resource and to treat various aspects of continuous-time investment. An additional distinguishing feature in the models considered is that we do not assume a priori that the objective functional (described by an improper integral) is finite, and so we are led to consider the weaker notions of overtaking and weakly overtaking optimality. To treat these models, we introduce a relaxed optimal control problem through the introduction of chattering controls. This leads us naturally to consider the relationship between the original problem and the convexified relaxed problem. In particular, we show that the relaxed problem may be viewed as a limiting case for the original problem. We also present several examples demonstrating the applicability of our results.
    Type of Medium: Electronic Resource
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