Interval-valued fuzzy graphs

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs

Institutional Structure in Corporate Agriculture

In this dissertation, a state-contingent, principal-agent model is developed to examine the institution of input provision by a corporate firm that contracts with agents for the production of a given commodity. "Input provision" entails not only the provision and delivery of key inputs by the principal but also their purchases (or in-house production), as well as contract design to ensure their optimal use. The provision of key inputs is modeled in the context of production contracts for poultry and pork, such as those offered by Perdue Farms, Smithfield Foods, and Tyson Foods in the United States. The decision in question is the levels of inputs (e.g. feed, medication) that the contracting company provides to the farmer. This decision is endogenous to the model, and facilitates comparison of production contracts (input provision) with marketing contracts (no input provision, with all inputs purchased and/or provided by the farmer himself). The theoretical model formalizes Coase's idea that an institutional arrangement emerges if the benefits associated with it exceed the costs. In particular, I characterize the case of no input provision as a corner solution for the optimal choice of inputs provided. The extent of input provision, in turn, reflects "limits to firm size". I also examine conditions under which incentives relating to one of two output dimensions (produced by the agent) tend to zero, when both dimensions are observable and verifiable. The state-contingent approach is used as it allows for a general production technology, and the inclusion of transaction costs in a general theoretical model. The possibility of reservation utility being endogenous in dyadic relationships is also examined. This is explored formally by incorporating pre-contract interactions in a contractual framework with the principal and the agent competing as independent producers prior to contracting. Investment decisions of the principal in this framework favorably impact his variable costs both as an independent producer and as the principal party to a contract. I show that the higher these benefits, the stronger is the incentive for the principal to decide in favor of higher initial investment levels and realize a more competitive position vis-à-vis the smaller producer

Numerical modelling of polydispersed flows using an adaptive-mesh finite element method with application to froth flotation

An efficient numerical framework for the macroscale simulation of three-phase polydispersed flows is presented in this thesis. The primary focus of this research is on modelling the polydispersity in multiphase flows ensuring the tractability of the solution framework. Fluidity, an open-source adaptive-mesh finite element code, has been used for solving the coupled equations efficiently. Froth flotation is one of the most widely used mineral processing operations. The multiphase, turbulent and polydispersed nature of flow in the pulp phase in froth flotation makes it all the more challenging to model this process. Considering that two of the three phases in froth flotation are polydispersed, modelling this polydispersity is particularly important for an accurate prediction of the overall process. The direct quadrature method of moments (DQMOM) is implemented in the Fluidity code to solve the population balance equation (PBE) for modelling the polydispersity of the gas bubbles. The PBE is coupled to the Eulerian--Eulerian flow equations for the liquid and gas phases. Polydispersed solids are modelled using separate transport equations for the free and attached mineral particles for each size class. The PBE has been solved using DQMOM in a finite element framework for the first time in this work. The behaviour of various finite element and control volume discretisation schemes in the solution of the PBE is analysed. Rigorous verification and benchmarking is presented along with model validation on turbulent gravity-driven flow in a bubble column. This research also establishes the importance of modelling the polydispersity of solids in flotation columns, which is undertaken for the first time, for an accurate prediction of the flotation rate. The application of fully-unstructured anisotropic mesh adaptivity to the polydispersed framework is also analysed for the first time. Significant improvement in the solution efficiency is reported through its use.Open Acces

Analyzing the Access to Unhealthy Food Sources in Relation to Obesity and Income Levels in Broome County

The relationship between income level, obesity, and fast-food restaurant availability can give us an insight into why people are more likely to choose food that is more readily available to them in terms of location, affordability, and general convenience. The consumption of fast food as an alternative to home-cooked meals is a common practice that is usually seen in mostly lower-income populations because of its affordability. In order to see if there was a correlation between the availability of fast-food restaurants and the obesity rates of various towns and cities of Broome County, especially within the lower-income town, I compiled data on the number of fast-food restaurants in each town with the town’s obesity rates to see if there was a correlation. I compared the data from nineteen different cities and towns of Broome County, including data about the obesity rates, income levels, and the number of fast-food restaurants in each region. I expect to find that the data collected will show that as the number of fast-food restaurants goes up, so will the obesity rates within each town or city. Additionally, as both of these variables go up, the income level of each town or city will go down. This study can help us understand why it might be important to create more low-price meal options that are as readily available, affordable, and yet more nutritious for lower-income families to choose in order to avoid the health risks that come with the fast-food industry.https://orb.binghamton.edu/research_days_posters_2022/1124/thumbnail.jp