An Investigation in Negative Transfer: Theory of Inhibition

Campbell and Robert (2012) found that numerical addition practice led to negative transfer on a subsequent test of numerical multiplication. Alternatively Rickard et al (2011) found negative transfer for numerical addition when participants were tested on an intermixed set of addition and subtractions problems after first practicing addition and then practicing subtraction. The present study sought to assess negative transfer by practicing participants with alphabet addition verification problems and testing the performance on alphabet multiplication verification. Ninety-five participants were split into 4 groups and given varying number of days of practice. During the test phase some multiplication verification problems included the same components as the practiced addition problems (e.g. B+3=E and Bx3=E). The results suggest that participants demonstrated significant learning of alphabet addition as well as negative transfer occurring for the alphabet multiplication problems when looking at an overall analysis. When looking at individual groups negative transfer was not seen

Characterization of Electrical Performance of Aluminum-Doped Zinc Oxide Pellets

Recently, the electronic industry has been shifting towards devices that can be controlled by touching the screen with one or more fingers. This technology is made possible by using transparent conducting oxides (TCOs). Zinc oxide (ZnO) is a potential replacement for the most currently used TCO (indium-tin oxide) due to its comparable optical properties. However, the doping mechanisms of zinc oxide need to be understood and improved. The goal of this research was to prepare n-type, aluminum-doped ZnO. Several dopant percentages were studied to investigate the optimum concentration. The electrical properties for all doping levels improved compared to undoped ZnO

Rigorous Results In Fluid And Kinetic Models

In the following, we will consider two different physical systems and their respective PDE models. In the first chapter, we prove time decay of solutions to the Muskat equation, which describes a fluid interface between two incompressible, immiscible fluids with different densities. In \cite{JEMS} and \cite{CCGRPS}, the authors introduce the norms \|f\|_{s}\eqdef \int_{\mathbb{R}^{2}} |\xi|^{s}|\hat{f}(\xi)| \ d\xi in order to prove global existence of solutions to the Muskat problem. In this paper, for the 3D Muskat problem, given initial data $f_{0}\in H^{l}(\mathbb{R}^{2})$ for some $l\geq 3$ such that $\|f_{0}\|_{1} \u3c k_{0}$ for a constant $k_{0} \approx 1/5$, we prove uniform in time bounds of $\|f\|_{s}(t)$ for $-2 \u3c s \u3c l-1$ and assuming $\|f_{0}\|_{\nu} \u3c \infty$ we prove time decay estimates of the form $\|f\|_{s}(t) \lesssim (1+t)^{-s+\nu}$ for $0 \leq s \leq l-1$ and $-2 \leq \nu \u3c s$. These large time decay rates are the same as the optimal rate for the linear Muskat equation. We prove analogous results in 2D. In the remaining chapters, we consider sufficient conditions, called continuation criteria, for global existence and uniqueness of classical solutions to the three-dimensional relativistic Vlasov-Maxwell system. In the compact momentum support setting, we prove that $\|p_{0}^{\frac{18}{5r} - 1+\beta}f\|_{L^{\infty}_{t}L^{r}_{x}L^{1}_{p}} \lesssim 1$ where $1\leq r \leq 2$ and $\beta \u3e0$ is arbitrarily small, is a continuation criteria. The previously best known continuation criteria in the compact setting is $\|p_{0}^{\frac{4}{r} - 1+\beta}f\|_{L^{\infty}_{t}L^{r}_{x}L^{1}_{p}} \lesssim 1$, where $1\leq r \u3c \infty$ and $\beta \u3e0$ is arbitrarily small, due to Kunze \cite{Kunze}. Our continuation criteria is an improvement in the $1\leq r \leq 2$ range. We also consider sufficient conditions for a global existence result to the three-dimensional relativistic Vlasov-Maxwell system without compact support in momentum space. In Luk-Strain \cite{Luk-Strain}, it was shown that $\|p_{0}^{\theta}f\|_{L^{1}_{x}L^{1}_{p}} \lesssim 1$ is a continuation criteria for the relativistic Vlasov-Maxwell system without compact support in momentum space for $\theta \u3e 5$. We improve this result to $\theta \u3e 3$. We also build on another result by Luk-Strain in \cite{L-S}, in which the authors proved the existence of a global classical solution in the compact regime if there exists a fixed two-dimensional plane on which the momentum support of the particle density remains bounded. We prove well-posedness even if the plane varies continuously in time

On fiber diameters of continuous maps

We present a surprisingly short proof that for any continuous map $f : \mathbb{R}^n \rightarrow \mathbb{R}^m$, if $n>m$, then there exists no bound on the diameter of fibers of $f$. Moreover, we show that when $m=1$, the union of small fibers of $f$ is bounded; when $m>1$, the union of small fibers need not be bounded. Applications to data analysis are considered.Comment: 6 pages, 2 figure

Combinatorial Stationary Prophet Inequalities

Numerous recent papers have studied the tension between thickening and clearing a market in (uncertain, online) long-time horizon Markovian settings. In particular, (Aouad and Sarita{\c{c}} EC'20, Collina et al. WINE'20, Kessel et al. EC'22) studied what the latter referred to as the Stationary Prophet Inequality Problem, due to its similarity to the classic finite-time horizon prophet inequality problem. These works all consider unit-demand buyers. Mirroring the long line of work on the classic prophet inequality problem subject to combinatorial constraints, we initiate the study of the stationary prophet inequality problem subject to combinatorially-constrained buyers. Our results can be summarized succinctly as unearthing an algorithmic connection between contention resolution schemes (CRS) and stationary prophet inequalities. While the classic prophet inequality problem has a tight connection to online CRS (Feldman et al. SODA'16, Lee and Singla ESA'18), we show that for the stationary prophet inequality problem, offline CRS play a similarly central role. We show that, up to small constant factors, the best (ex-ante) competitive ratio achievable for the combinatorial prophet inequality equals the best possible balancedness achievable by offline CRS for the same combinatorial constraints