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Skip to Search Results- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Hillen, Thomas (Mathematical and Statistical Sciences)
- 6Mizera, Ivan (Mathematical and Statistical Sciences)
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Fall 2012
In this thesis, we develop a novel method of generating CAPTCHAs, which are used to protect online resources from abuse by computer agents. We view CAPTCHA generation as random field simulation and construct a CAPTCHA by evolving an initial state via resimulating pixels until the image becomes...
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Fall 2015
The Busemann-Petty problem asks the following: if 𝐾,𝐿 ⊂ ℝⁿ are origin-symmetric convex bodies such that volₙ₋₁(𝐾 ∩ ξ^⊥)) ≤ volₙ₋₁(𝐿 ∩ ξ^⊥) ∀ ξ ∈ Sⁿ⁻¹, is it necessary that volₙ(𝐾) ≤ volₙ(𝐿)? This problem received a lot of attention, and many analogues have been considered. For origin-symmetric...
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Fall 2015
Riveros Pacheco, David Ricardo
For K/k a finite Galois extension of number fields with G=Gal(K/k) and S a finite G-stable set of primes of K which is "large", Gruenberg and Weiss proved that the ZG-module structure of the S-units of K is completely determined up to stable isomorphism by: its torsion submodule, the set S, a...
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Spring 2016
Optional processes including optional semimartingales are not necessarily right or left continuous. However, optional semimartingales have right and left limits. Moreover, optional processes may exist on ”un-usual” stochastic basis where the increasing information-filtrations are not complete or...
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Spring 2017
The importance of simulating fluid flow is indisputable. From weather forecasting to aviation to the blood flow inside our arteries, fluid flow significantly influences our everyday life. Among all possible fluid regimes, one is dominant in many physical applications. Turbulence, sometimes...