The purpose of this study was to investigate analytical approaches for estimating the optimum (profit maximizing) rate of initial overstory kill for increasing seasonal forage availability on a specific ranch. The models were developed using the big sagebrush (Artemisia tridentata) - crested wheatgrass (Agropyron cristatum, A. desertorum) vegetation type on a Utah cow-calf-yearling operation as an example. The models should be applicable on any ranching situation where understory forage production is constrained by the establishment and growth of undesirable overstory vegetation. Three model forms were developed and compared for their applicability to on-the-ground investment decision making. Single treatment period (STP) static and dynamic models and a multiple treatment period (MTP) dyne.mic model were theoretically developed. Ee.ch model we.s formulated using e. biological production function relating under story production to ini tie.l kill percentage, e. cost of overstory kill function fore. specific overstory reduction method, and a derived demand function for seasonal forage availability. The production function was estimated in both static and dynamic forms for use in the different models. The remaining functions were used in the same form for a11 model applications. Results indicated that the STP static optimization model holds the most promise for an on-the-ground decision making tool at the present time. Data to estimate dynamic production functions over a variety of vegetation types and grazing management situations essentially do not exist. This deficiency makes the use of long-term dynamic models less feasible for current decisions. It does not, however, alleviate the need to recognize long-term biological and economic relationships in making such decisions. The STP static model indicated that for the example Utah ranch a target big sagebrush kill rate between 89 and 100 percent would be optimal depending on the derived demand and cost of kill functions used. Target kill rates other than the optimum would represent potentially significant opportunity costs to this particular operation. The optimal solution obtained by this method is expected to change depending on the situation being analyzed. The model must be applied on a specific ranch basis and was not designed to make general recommendations.

Over the years, Utah has enjoyed the advantage of having natural agricultural resources that favor the production of livestock. Sheep and beef cattle do well on the desert and high mountain ranges that cover much of the state, Dairy cattle and wintering beef cattle use the alfalfa and native hay along with some corn silage that is grown in the irrigated valleys. Feed grains are grown in rotation with forage crops on irrigated land and also on dry land. Before 1950, the quantities of feed grains produced had been sufficient to meet the needs of dairy, range livestock and poultry. However, with the realization that Utah had a natural market position in relation to the coast markets, there developed an extensive poultry and livestock fattening business. Since that time Utah has been in the position of a feed grain deficit state. This has tended to raise the cost of feed grain by $10 to $12 per ton due to the transportation factor. Also, Utah's poultry industry relied partially upon feed wheat from northern Utah and southern Idaho, but with acreage allotments and price controls, the price of wheat increased to the point where it was no longer used as a poultry feed. As a consequence, poultry and egg producers also had to turn to importing more of their feed grains, which put them into a higher feed cost position along with the livestock feeder. In the past year, however, the price of feed wheat declined to the point where wheat was used extensively in livestock feed stuffs for the first time in years.

Resources available for agricultural production were ascertained and trends in their use were studied for seven counties of southwestern Utah. Special consideration was given to cropland, irrigation water, and operating capital as resource restrictions for a linear programming model. Budget data were obtained for crop and livestock enterprises by interviewing farmers and ranchers in the area. Budgets for four representative farm types representing climatic and irrigation differences were made to study crop possibilities. Acreage minimums or maximums for selected crops were established as conservation measures. Budgets were prepared for farm livestock enterprises to use with crop budgets for each representative farm. Results provided profit maximizing enterprise combinations for each representative farm.

<p> The realization of inductorless filters by means of RC-gyrator structures has been investigated, and the sensitivity of their response characteristics with respect to supply voltage variations has been measured. A critical appraisal is made of the various multiparameter sensitivity functions which have already been proposed in the literature, and the methods by which these sensitivity criteria may be computed are surveyed. A new index of performance, by which the multiparameter sensitivity of a linear, time-invariant network may be evaluated, is proposed. Furthermore, a new method of computing sensitivity indices is described and is shown to be highly efficient from a computational point of view. The index has been used to investigate the sensitivity performance of a wide range of passive and active filter structures. It has also been used to generate a so called "optimum tolerance set" for the elements of such filters and the effect of employing these optimum tolerance sets has been investigated.</p> <p> The index of perfonnance and the concept of the optimum tolerance set is extended to the case of RC active filters. A "two-level" optimization procedure is proposed, whereby an optimum nominal element value set may be combined with the corresponding optimum tolerance set to obtain a marked improvement in the sensitivity performance of the network. Finally, the synthesis of a highly selective RC-active filter is considered, and it is shown how an optimal structure and tolerance set can be obtained for such a network.</p> / Thesis / Doctor of Philosophy (PhD)

<p> A study of gradient optimization techniques, in particular as applied to system modelling problems, is made. Three efficient techniques are used to derive optimum second-order and third-order models for a seventh-order system. The optimization techniques are the Fletcher-Powell method, a more recent method proposed by Fletcher and a method based on a more general objective function proposed by Jacobson and Oksman.</p> <p> The approximation is carried out in the time domain. Least squares and least pth criteria are used, and almost minimax results are obtained for large values of p. Values of p up to 10^12 are successfully used. The results are compared with other minimax type algorithms.</p> / Thesis / Master of Engineering (MEngr)

<p> The Objective of this study is to investigate analytically the impact of certain technological and market conditions on the optimum location of the firm. The existing location models may be divided into those which consider both supply and demand aspects and those which concentrate on supply factors alone. Traditionally, the former group of models define equilibrium as the profit maximizing location and assume both a linear-homogeneous production function and a linear demand function. The latter class of models assume only the linear-homogeneity of production, and equilibrium is found at the cost-minimizing site.</p> <p> In this paper two cases are examined. Firstly, the influence of a general non-linear homogeneous production function on a simple cost minimizing model is considered. Secondly, the effect of non-linear demand functions and non-linear homogeneous technology on a profit maximizing model are assessed. The results indicate that the optimum location in the cost minimizing situation does not vary with the level of output, whatever the degree of homogeneity of the production function. This directly contradicts the common belief regarding the effects of production. Furthermore, in the profit-maximizing problem, and with non-linear homogeneous production, the solution is unaffected by the shape of the demand function.</p> <p> Suggestions for refining and extending this analysis include the use of general rather than specific demand, transportation and production functions: the employment of exhaustible inputs, and generalization to the three-dimensional situation.</p> / Thesis / Master of Arts (MA)

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Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin’s Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a logarithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the Steger-Warming flux-vector-splitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A non-uniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green’s function approach for the purpose of comparing the numerical results. The pressure-matching inverse design is then conducted for a nozzle parameterized by a single geometric parameter. In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2-D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the far-field boundary. A super-reduced design formulation is also explored by treating the angle of attack as an additional state; super-reduced gradients can be constructed either by solving adjoint equations with non-local boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson’s finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (super-reduced) gradients. / Ph. D.

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