The Asymptotic Couple of the Field of Logarithmic Transseries

The derivation on the differential-valued field $\mathbb{T}_{\log}$ of logarithmic transseries induces on its value group $\Gamma_{\log}$ a certain map $\psi$. The structure $(\Gamma_{\log},\psi)$ is a divisible asymptotic couple. We prove that the theory $T_{\log} = {\rm Th}(\Gamma_{\log},\psi)$ admits elimination of quantifiers in a natural first-order language. All models $(\Gamma,\psi)$ of $T_{\log}$ have an important discrete subset $\Psi:=\psi(\Gamma\setminus\{0\})$. We give explicit descriptions of all definable functions on $\Psi$ and prove that $\Psi$ is stably embedded in $\Gamma$.Comment: 24 page

The Influence of Instruction on Leadership

For decades, researchers have been studying leadership and have found it to be very difficult to fully understand. A basic knowledge of leadership is available, but the details are hard to specify. These details include the complexity of the construct of leadership (Bass & Stogdill, 1990), the difficulty of forming a single definition or theoretical perspective from many possible options (Edmunds & Yewchuk, 1996; Simonton, 1995), and the lack of valid and reliable measures of leadership ability (Edmunds, 1998; Jarosewich, Pfeiffer, & Morris, 2002). All of these issues make researching leadership difficult because it is hard to gain new knowledge and understanding of a topic when there is not a solid foundation to build upon. Leadership has been examined on multiple levels including gifted programs in primary schools and leadership development in business, but not a lot of research has specifically looked at the college student and how they view and develop leadership. This study will focus on college student leaders and how they define leadership. Specifically, it will compare student leaders who are in a program designed to enhance leadership development with student leaders who are not receiving formal leadership training

Advancing Cost-Effective Readiness by Improving the Supply Chain Management of Sparse, Intermittently-Demanded Parts

Many firms generate revenue by successfully operating machines such as welding robots, rental cars, aircraft, hotel rooms, amusement park attractions, etc. It is critical that these revenue-generating machines be operational according to the firm s target or requirement; thus, assuring sustained revenue generation for the firm. Machines can and do fail, and in many cases, restoring the downed machine requires spare part(s), which are typically managed by the supply chain. The scope of this research is on the supply chain management of the very sparse, intermittently-demanded spare parts. These parts are especially difficult to manage because they have little to no lead time demand; thus, modeling via a Poisson process is not viable. The first area of our research develops two new frameworks to improve the supply chain manager s stock policy on these parts. The stock polices are tested via case studies on the A-10C attack aircraft and B1 bomber fleets. Results show the AF could save $10M/year on the A10 and improve support to the B1 without increasing inventory. The second area of our research develops a framework to integrate the supply chain processes that generate these service parts. With the integrated framework, we establish two new forward-looking metrics. We show examples how these forward-looking metrics can advance the supply chain manager s desire to know what proactive decisions to make to improve his/her supply chain for the good of the firm

Distality in Valued Fields and Related Structures

We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian valued fields, and demonstrate that certain expansions of fields, e.g., the differential field of logarithmic-exponential transseries, are distal. As a new tool for analyzing valued fields we employ a relative quantifier elimination for pure short exact sequences of abelian groups.Comment: 58 p

Towards a model theory of logarithmic transseries

The ordered valued differential field $\mathbb{T}_{\log}$ of logarithmic transseries is conjectured to have good model theoretic properties. This thesis records our progress in this direction and describes a strategy moving forward. As a first step, we turn our attention to the value group of $\mathbb{T}_{\log}$. The derivation on $\mathbb{T}_{\log}$ induces on its value group $\Gamma_{\log}$ a certain map $\psi$; together forming the pair $(\Gamma_{\log},\psi)$, the \emph{asymptotic couple of $\mathbb{T}_{\log}$}. We study the asymptotic couple $(\Gamma_{\log},\psi)$ and show that it has a nice model theory. Among other things, we prove that \Th(\Gamma_{\log},\psi) has elimination of quantifiers in a natural language, is model complete, and has the non-independence property (NIP). As a byproduct of our work, we also give a complete characterization of when an $H$-field has exactly one or exactly two Liouville closures. Finally, we present an outline for proving a model completeness result for $\mathbb{T}_{\log}$ in a reasonable language. In particular, we introduce and study the notion of \emph{\LD-fields} and also the property of a differentially-valued field being \emph{$\Psi$-closed}