In the thesis, there are two kinds of fuzzy linear programming problems, one of them is a linear programming problem with fuzzy technological coefficients and the second is linear programming problem in which both the right-hand side and the technological coefficients are fuzzy numbers. I solve the fuzzy linear programming problems with fuzzy decisive set method.

Eigen fuzzy sets of fuzzy relation can be used for the estimation of highest and lowest levels of involved variables when applying max-min composition on fuzzy relations. By the greatest eigen fuzzy sets (set which can be greater anymore) maximum membership degrees of any fuzzy set can be found, with the help of least eigen fuzzy set (set which can be less anymore) minimum membership degrees of any fuzzy sets can be found as well.The lowest and highest level, impact or e ffect of anything can be found by applying eigen fuzzy set theory. The implicational aspect of this research study is medical and customer satisfaction level measurement. By applying methods of eigen fuzzy set theory the e ffectiveness of medical cure and customer satisfaction can be found with high precision.

The practice of managing capital project delivery in America evolves. By proxy, the skillsets necessary to fulfill the requirements of this profession also evolve. This report attempts to identify sources that define which skillsets are most valuable for professionals managing capital project delivery today. The report will specifically explore professional certifications and organizations, Accreditation Board for Engineering and Technology (ABET) accredited education programs, and industry opinion. Included in the study is a discussion of valuable skillsets for future construction management professionals. / text

Pore-scale simulation has become increasingly important in recent years as a tool to understand multiphase flow behavior. Wettability affects aspects of flow such as capillary-pressure saturation curves, residual saturation of each phase, and relative permeability. Simulation of wettability at the pore-scale is still a non-trivial problem, and many different approaches exist to model it. In this work, we implement a variational level set formulation to impose different contact angles at the solid-fluid-fluid contact line for two-phase flow in simple rhomboidal pore geometries, and calculate the maximum mean curvature (equivalently capillary pressure) for each case. We compare our results with a detailed set of analytical and experimental results in a range of pore geometries of varying wettability from Mason and Morrow (1994), and demonstrate the accuracy of this method. While the simulations shown are for relatively simple geometries, the method has the ability to handle arbitrarily complex geometry (such as input from X-ray microtomography imaging). / text

This is a compilation of selected set and costume designs from my past three years as a MFA candidate in theatrical design at the University of Texas at Austin. I hope this portfolio will help launch my career as a theatrical designer. My primary focus is set design and my secondary interest is costume design. This portfolio represents my best work as a costume and set designer. Each design will include a number of images that range from production photographs to preliminary sketches. / text

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The study of combinatorial patterns of words has raised great interest since the early 20th century. In this master's thesis presentation we study two combinatorial patterns. The first pattern is “abelian k-th power free” and the second one is “representability of sets of words of equal length”. For the first pattern we study the context-freeness of non-abelian k-th powers. A word is a non-abelian k-th power if it cannot be factorized in the form w1w2...wk where the wi are permutations of w1 for 2 ≤ i ≤ k. We show that neither the language of non-abelian squares nor the language of non- abelian cubes is context-free. For the second pattern we study the representability of a set of words of fixed length. A set S of words of length n is representable if there exists some word w such that the set of length-n factors of w equals S. We will give lower and upper bounds for the number of such representable sets. Furthermore, we study a variation of the problem: we fix a length t, and try to evaluate the number of sets of words of length n such that there exists some word w of length t such that the set of length-n factors of w equals S. We give a closed-form formula in the case where n ≤ t < 2n. In particular, we give a characterization on two distinct words having the same subset of length-n factors.

Given two set systems $\mathscr{A}$ and $\mathscr{B}$ over an $n$-element set, we say that $(\mathscr{A,B})$ forms a recovering pair if the following conditions hold: \\ $ \forall A, A' \in \mathscr{A}$ and $ \forall B, B' \in \mathscr{B}$, $A \setminus B = A' \setminus B' \Rightarrow A=A'$ \\ $ \forall A, A' \in \mathscr{A}$ and $ \forall B, B' \in \mathscr {B}$, $B \setminus A = B' \setminus A' \Rightarrow B=B'$ \\ In 1989, G\'bor Simonyi conjectured that if $(\mathscr)$ forms a recovering pair, then $|\mathscr||\mathscr|\leq 2^n$. This conjecture is the focus of this thesis. This thesis contains a collection of proofs of special cases that together form a complete proof that the conjecture holds for all values of $n$ up to 8. Many of these special cases also verify the conjecture for certain recovering pairs when $n>8$. We also present a result describing the nature of the set of numbers over which the conjecture in fact holds. Lastly, we present a new problem in graph theory, and discuss a few cases of this problem.

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