Using the the dependently-typed programming language Agda, we formalise orders, with attention to the theory of Galois Connections, and showcase it by formalising a few results of the category of algebraic contexts with relational homomorphisms presented by Jipsen (2012) and Moshier (2013). We aim to exhibit an internal theory of Galois Connections and Closure operators where the ambient space need not have a notion of meets (intersections), which are the usual medium in presenting antisymmetry of partial orders. Instead we consider `symmetric quotients' as being the relational counterpart of propositional calculus' primitive connective: equivalence. We argue that it as a more natural primitive than meet --- especially its connection with certain proof heuristics regarding posets. Moreover, not only do we constrain ourselves to an unconventional set of primitive operators, but in fact we discard the familiar setting of relations and sets in favour of the more general setting of ordered categories with converse (OCCs) --- in fact, a large portion does not require identities and so semigroupoids may be used instead. / Thesis / Master of Science (MSc)

<p> A finiteness criterion is given for finitely generated positively ordered semigroups and this is used to show that various semigroups of operators in universal algebra are finite.</p> / Thesis / Master of Science (MSc)

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Potato farmers in Ecuador rely on chemical inputs to manage pests and optimize yields. IPM techniques are recommended to lower production costs, reduce exposure to pesticides, and improve the long-term sustainability of the agriculture system. We conducted a survey of 109 potato farmers in Carchi, Ecuador that included 30 Farmer Field School (FFS) participants, 28 farmers who had been exposed to FFS-participants, and 51 randomly selected farmers. Using an ordered probit model, the data were analyzed to identify determinants and constraints of adoption. Access to information through FFS was the main determinant of adoption of IPM, followed by field days, pamphlets, and exposure to FFS-participants. The study looked at the relative cost-effectiveness of information dissemination methods and found that field days and pamphlets have strong impacts on adoption considering their low cost of implementation. The only significant household variable was household size, where larger households adopted less IPM. Per capita land holdings were not significant in the model. There is evidence of farmer-to-farmer diffusion from FFS to non-FFS farmers. Further research is necessary to evaluate the nature and quality of information transfer between farmers. The study was limited by the small sample size and non-random selection of farmer respondents. / Master of Science

Yes / Measurement of molecular weight is an integral part of macromolecular and polymer characterization which usually has limitations. Herein, we present the use of a bench-top 80 MHz NMR spectrometer for diffusion-ordered spectroscopy as a practical and rapid approach for the determination of molecular weight/size using a novel solvent and polymer-independent universal calibration. / Royal Society. Grant Number: URF∖R1∖180274. Engineering and Physical Sciences Research Council. Grant Numbers: EP/V037943/1, EP/V007688/1, EP/V036211/1