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  • Pseudotsuga menziesii  (2)
  • Volterra integral equations  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Direct impacts of sheep upon Douglas-fir trees in two agrosilvopastoral systems (1992)
    Springer
    Agroforestry systems 19 (1992), S. 223-232 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00118780
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Productivity of two Douglas fir/subclover/sheep agroforests compared to pasture and forest monocultures (1996)
    Springer
    Agroforestry systems 34 (1996), S. 305-313 
    Details
    ISSN: 1572-9680
    Keywords: spatial pattern ; silvopastoral ; intercropping ; polyculture ; Pseudotsuga menziesii ; Trifolium subterraneum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Resource sharing between tree and forage plant components in silvopastoral systems includes a complex set of facilitative and competitive interactions. To the extent that facilitation exceeds competition, agroforests are expected to outyield monocultures of their components. Pasture and Douglas fir (Pseudotsuga menziesii) tree production of young agroforests was compared to pasture and forest monocultures under both grid and cluster patterns of tree planting near Corvallis, Oregon, USA, during 1983–1987. The height and diameter growth of forest and agroforest trees was similar, regardless of tree planting pattern. Five-year average annual forage production was 6500, 5800, and 2800 kg ha−1 on pasture, agroforest, and forest plots, respectively. The total cumulative 1982–1987 above-ground phytomass yield of forage plus trees was similar for pasture and conventional grid forest monocultures. The total productivity of agroforests, however, was over 30% greater than either pasture or forest components grown in monoculture. Approximately 1.6 ha (0.96 ha forest + 0.64 ha pasture) of monocultures would be needed to equal the productivity of 1 ha of agroforest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046930
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    An elementary proof of the maximum principle for optimal control problems governed by a Volterra integral equation (1987)
    Springer
    Journal of optimization theory and applications 54 (1987), S. 43-61 
    Details
    ISSN: 1573-2878
    Keywords: Control theory ; maximum principle ; Volterra integral equations ; necessary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An elementary proof of the maximum principle for optimal control problems whose states are governed by Volterra integral equations is given. Our proof is motivated by the work of Michel (Ref. 7) and utilizes only elementary results from analysis and mathematical programming. By appealing to Pontryagin-type perturbations of the controls, the above optimal control problem is effectively reduced to a mathematical programming problem. The results are then obtained by appealing to well-known mathematical programming results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940404
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  • 4
    Electronic Resource
    Electronic Resource
    Infinite-horizon optimal controls for problems governed by a volterra integral equation with state-and-control-dependent discount factor (1990)
    Springer
    Journal of optimization theory and applications 66 (1990), S. 311-336 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00939541
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