Memento

School of Art and Design: Integrative Project ThesisArt and Design, School ofUniversity of MichiganUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/60498/1/IPThesis_Kim.pd

Unit-sphere preserving mappings

We prove that if a one-to-one mapping f : (n ≥ 2) preserves the unit n - 1 spheres (Sn -1), then f is a linear isometry up to translation

Bessel's Differential Equation and Its Hyers-Ulam Stability

We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation

Preparation and characterization of Artemisia Capillaris Thunb Extracts Embedded Electrospun PVA Nanofiber

This study seeks to use the Artemisia capillaris Thunb extracts, which has anti-inflammatory and antioxidation effects, to manufacture a nanoweb and seeks to contemplate the form and change of characteristics of the nanofiber according to the content of Artemisia capillaris Thunb extracts

Current-induced domain wall motion in a nanowire with perpendicular magnetic anisotropy

We study theoretically the current-induced magnetic domain wall motion in a metallic nanowire with perpendicular magnetic anisotropy. The anisotropy can reduce the critical current density of the domain wall motion. We explain the reduction mechanism and identify the maximal reduction conditions. This result facilitates both fundamental studies and device applications of the current- induced domain wall motion

Fourier Transform and Heat Equation in White Noise Analysis.

In this dissertation, we study the Fourier transform and heat equation in the white noise set-up. It is known that the Fourier transform ${\cal F}$ can be defined on the space (${\cal S}$)* of generalized white noise functionals. We prove that ${\cal F}$ is the adjoint of a certain linear operator on the space (${\cal S}$) of test functionals. On the other hand, it is known that if f is a bounded Lip-1 function on an abstract Wiener space with Gaussian measures P\sb{t}, then u(t)=P\sb{t}f solves the heat equation {d\over dt}u(t)={1\over2}\Delta\sb{G}u(t) with initial condition u(0) = f where \Delta\sb{G} is the Gross\u27 Laplacian. We show that if $\varphi$ is in (${\cal S}$), then u(t)=P\sb{t}\varphi is also in (${\cal S}$) and satisfies {d\over dt}u(t)={1\over2}\Delta\sb{G}u(t) with u(0) = f. The properties of some operators are also discussed

Notch1 intracellular domain suppresses APP intracellular domain—Tip60–Fe65 complex mediated signaling through physical interaction

AbstractThe amyloid beta-precursor protein (APP) and the Notch receptor are both type 1 integral transmembrane proteins, and both are cleaved by presenilin-dependent gamma-secretase activity. In this study, we have demonstrated that the Notch intracellular domain (Notch1-IC) suppresses APP-intracellular domain (AICD)-mediated ROS generation and cell death after being processed by gamma secretase. Notch1-IC physically interacts with AICD, Fe65, and Tip60, thereby disrupting the association of the AICD–Fe65–Tip60 trimeric transcription activator complex in AICD signaling. AICD–Fe65–Tip60 mediated reactive oxygen species generation was found to be suppressed by Notch1-IC. Furthermore, AICD–Fe65–Tip60 was shown to mediate cell death in human neuroblastoma cells, and the overexpression of Notch1-IC inhibited cell death induced by AICD–Fe65–Tip60. Collectively, our findings indicate that Notch1-IC plays the role of a negative regulator in AICD signaling via the disruption of the AICD–Fe65–Tip60 trimeric complex