Harmonic Analysis – I

Stein-Tomas restriction theorem and Stricharz estimate for SchrÃ¶dinger equation

Stricharz estimate for wave equation

As taught by Steve Hofmann in University of Missouri, Fall 2019. Extra notes (Hofmann’s, not mine) added.

Thank you to John Hoffman, Tom Hogancamp, and Konstantinos Tselios for the corrections.

Harmonic Analysis – II

As taught by Steve Hofmann in University of Missouri, Spring 2020.

Analysis Qualifying Problems Collection

chosen for University of Missouri quals. Mostly based on Folland’s *Real Analysis*. Topics include:

- Measure & construction of Lebesgue measure
- Integration theorems (Dominated convergence, etc.)
- Modes of convergence (a.e., in norm, in measure)
- \(L^p\) space (inequalities, duality, etc.)
- Hilbert space (basis, projection, operator representation, weak convergence, extension theorem)

Potential Development for Al-TiN Nanolayers

My masters thesis at MSU. Not very interesting mathematically (except for showing theoretical construct such as simulated annealing works), but the pictures are nice to look at. Upshot: the best non-ceramic (i.e. not too disordered) material with respect to mechanical strength is the soft (Al) – hard (TiN) ‘sandwiches’.

This final version looks a bit weird, because I had to fit my Latex-typesetted draft to the school’s standard format.