PERCEPTIONS OF THE PREPARATION OF EFFECTIVE MIDDLE SCHOOL PRINCIPALS

The primary purpose of this quantitative study was to examine middle school administrators’ perceptions of their preparation programs. The following research questions were addressed as a part of the study: 1. What skills, behaviors, and attitudes do middle school principals perceive to be important to be an effective middle school principal? 2. How do middle school principals perceive their level of preparedness in relation to the specific skills, behaviors, and attitudes? 3. To what degree do middle school principals believe that their level of preparation has influenced them to stay in their current role? 4. Which components of their preparation program do middle principals perceive to be the most valuable? 5. To what extent do middle school principals believe that the school district should design a program specifically to develop middle school principals? Middle school principals were selected to participate in this study. Quantitative data were gathered via online questionnaires. The research questions were addressed through analysis of the questionnaire data, using descriptive and inferential statistics. This study resulted in recommendations to provide a framework for the development of a principal preparation program designed to train effective middle school principals.

Quantitative Derivation of Effective Evolution Equations for the Dynamics of Bose-Einstein Condensates

This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.