<p>This dissertation refines and extends the theory of mesoprimary decomposition, as introduced by Kahle and Miller. We begin with an overview of the existing theory of mesoprimary decomposition </p><p>in both the combinatorial setting of monoid congruences and the arithmetic setting of binomial ideals. We state all definitions and results that are relevant for subsequent chapters. </p><p>We classify redundant mesoprimary components in both the combinatorial and arithmetic settings. Kahle and Miller give a class of redundant components in each setting that are redundant in every mesoprimary decomposition. After identifying a further class of redundant components at the level of congruences, we give a condition on the associated monoid primes that guarantees the existence of unique irredundant mesoprimary decompositions in both settings. </p><p>We introduce soccular congruences as combinatorial approximations of irreducible binomial quotients and use the theory of mesoprimary decomposition to give a combinatorial method of constructing irreducible decompositions of binomial ideals. We also demonstrate a binomial ideal which does not admit a binomial irreducible decomposition, answering a long-standing problem of Eisenbud and Sturmfels. </p><p>We extend mesoprimary decomposition of monoid congruences to congruences on monoid modules. Much of the theory for monoid congruences extends to this new setting, including a characterization of mesoprimary monoid module congruences in terms of associated prime monoid congruences and a method for constructing coprincipal decompositions of monoid module congruences using key witnesses. </p><p>We conclude with a collection of open problems for future study.</p> / Dissertation

The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. / Determining the best base stationing for military units can be modeled as a capacitated facility location problem with sole sourcing and multiple resource categories. Computational experience suggests that cross decomposition, a unification of Benders Decomposition and Lagrangean relaxation, is superior to other contemporary methods for solving capacitated facility location problems. Recent research extends cross decomposition to pure integer prograrnming problems with explicit application to capacitated facility location problems with sole sourcing; however, this research offers no computational experience. This thesis implements two cross decomposition algorithms for the capacitated facility location problem with sole sourcing and compares these decomposition algorithms with branch and bound methods. For some problems tested, cross decomposition obtains better solutions in less time; however, cross decomposition does not always perform better man branch and bound due to the time required to obtain the cross decomposition bound that is theoretically superior to other decomposition bounds.

No description available.

A novel decomposition method that is referred to as Contribution-based Decomposition is presented in this thesis. The influence of variables on the values of objective functions and/ or constraints is interpreted as their contributions. Based on contributions of variables, a design problem is decomposed into a number of sub-problems so that variables have similar relative contributions within each sub-problem. The similarity in contributions among variables will lead to an even pressure on the variables when they are driven to better solutions during an optimisation process and, as a result, better solutions can be obtained. Due to nonlinearity of objectives and/ or constrains, variables??? contributions may vary significantly during the solution process. To cope with such variations, a Dynamic Contribution-based Decomposition (DCD) is proposed. By employing DCD, decomposition of system problems is carried out not only at the beginning, but also during the optimisation process, and as a result, the decomposition will always be consistent with the contributions of the current solutions. Further more, a random decomposition is also developed and presented to work in conjunction with the Dynamic Contribution-based Decomposition to introduce re-decompositions when it is required, aiming to increase the global exploring ability. To solve multidisciplinary engineering optimisation problems more efficiently, new solvers are also developed. These include a mixed discrete variable Pattern Search (MDVPS) algorithm and a mixed discrete variable Genetic Algorithm (MDVGA). Inside the MDVGA, new techniques including a flexible floating-point encoding method, a non-dominance ranking strategy and heuristic crossover and mutation operators are also developed to avoid premature convergence and enhance the GA???s search ability. Both MDVPS and MDVGA are able to handle optimisation problems having mixed discrete variables. The former algorithm is more capable of local searching and the latter has better global search ability. A hybrid solver is proposed, which incorporates the MDVPS and the MDVGA and takes advantage of both their strengths. Lastly, a Dynamic Sub-space Optimisation (DSO) method is developed by employing the proposed Dynamic Contribution-based Decomposition methods and the hybrid solver. By employing DSO, decomposed sub-problems can be solved without explicit coordination. To demonstrate the capability of the proposed methods and algorithms, a range of test problems have been exercised and the results are documented. Collectively the results show significant improvements over other published popular approaches.

This thesis investigated the final products from the current effluent treatment system for woolscouring (wool washing) plants, namely, (i) sludge produced from the chemical flocculation of solids in the wastewater from the wash bowls, and (ii) concentrated suint (sheep sweat) produced from evaporation of the liquid phase separated from the sludge. In addition, fibrous wastes from the woolscouring process were studied. The aims of the study were to (i) investigate whether suint could be applied in a sustainable way to arable land as a potassium fertiliser, and (ii) assess the conditions under which the sludge could be composted for use as a soil conditioner to return organic matter to soil. Experiments involving suint were performed at both laboratory and glasshouse scales, while experiments involving the solid woolscour wastes were based both in the laboratory and using a small-scale (4.5 m3 total capacity) in-vessel composting unit established at a New Zealand woolscour. Decomposition was measured using net-nitrogen mineralisation and weight loss methods. Suint, the water-soluble contaminants on the fleece, contained high levels of potassium (20% on a dry weight basis) and also appreciable quantities of sulphur, sodium, and chlorine. Biological treatment before evaporation stabilised the resulting suint and improved the consistency of its composition. Suint did not affect the soil processes examined, in that it partly decomposed in soil, did not inhibit the turnover of model organic compounds, did not affect soil properties such as pH and electrical conductivity, and did not lead to increased leaching of mineral nitrogen. Suint was either neutral or positive towards plant performance when applied to soil at a rate of 100 kg potassium per hectare. Suint was therefore judged to be suitable for application to land and could be targeted to soils known to be deficient in potassium or to areas where crops with a high potassium demand are grown. Sludge, composed of dirt (soil particles, faecal matter, and skin and fibre debris) and wool grease, was highly variable in terms of its rate of decomposition, ranging from 0.8 to 27.8% of the initial total nitrogen mineralised over 30 days at 37℃. Fibrous wastes, such as opener (fibre and contaminants removed from the wool by agitation prior to scouring) and scoured wool cleaner (wool fibre and dust removed from scoured and dried wool) wastes, also showed variability in decomposition rates. Sludge decomposition was improved by as much as threefold when co-incubated with fibrous wastes. Although it was shown that the polyacrylamide and pesticide content of sludge did not inhibit its decomposition, the effect of the grease content was not fully understood. Chemical properties of woolscour sludge, such as the carbon to nitrogen ratio, suggested that sludge was a substrate of good resource quality. From a biological perspective, however, the data suggested that woolscour sludge was limited in available nutrients; sludge nitrogen was derived principally from keratin, which decomposed at a low rate resulting in the slow release of mineral nitrogen and low levels of microbial activity. Thus, sludge appeared a poor substrate for composting. However, the results from composting trials indicated that the sludge could be successfully processed after blending with a bulking agent such as sawdust. The blended material showed a 90% reduction in wool grease over 21 days of composting when the moisture content of the composting mass was kept optimal. Compost temperature exceeded 55℃ when wool fibre was added to the blend. Initial results from a case study involving the commercial composting of the entire sludge production (16 tonnes per day) from a New Zealand woolscour indicated that a saleable compost could be produced from a material that would otherwise go to landfill, and served to illustrate the commercial significance of these research results.

Thesis (Ph.D.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (ℓ.42-43)

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: Jochen A. Lauterbach, Dept. of Chemical Engineering. Includes bibliographical references.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 82-91). Also available via the Internet.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 99-105). Also available via the Internet.

Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 121-125). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.