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#### Finite point configurations and projection theorems in vector spaces over finite fields

(University of Missouri--Columbia, 2010)

We study a variety of combinatorial distance and dot product related problems in vector spaces over finite fields. First, we focus on the generation of the Special Linear Group whose elements belong to a finite field with ...

#### Limit of many molecules dynamics with rigorous macroscopic results

(University of Missouri--Columbia, 2013)

. al.

**2005**). In particular, it is shown that sufficient assumptions for rigorous, non phenomenological, macroscopic equations for mass and momentum as the limit of Hamiltonian dynamics are indeed satisfied by a class of initial conditions and rescalings...#### A transition matrix for two bases of the integral cohomology of the Hilbert scheme of points in the projective plane

(University of Missouri--Columbia, 2010)

This work is devoted to comparing two integral bases for the integral cohomology of the Hilbert scheme of points in the projective plane. Let X be a smooth complex projective surface. One of the more interesting moduli ...

#### Mathematical problems from cryobiology

(University of Missouri--Columbia, 2009)

Cryobiology is the study of life anddeath at low temperatures and provides a fascinating setting for applied mathematics. The interdisciplinary nature of cryobiology mirrors the diversity of applications ranging from animal ...

#### Trace formulae in finite von Neumann algebras

(University of Missouri--Columbia, 2007)

The

**dissertation**is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for the [xi]-index, a spectral...#### Seiberg-Witten invariants on 3-manifolds with an orientation reversing involution

(University of Missouri--Columbia, 2009)

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This work is devoted to the study of Seiberg-Witten theory for three dimensional manifolds in the presence of involutions. G. Tian and S.Wang explored ...

#### Volatility estimation and price prediction using a hidden Markov model with empirical study

(University of Missouri--Columbia, 2007)

This work provides a solid development of a hidden Markov model (HMM) from the economic insight to the mathematic formulation. In this model, we assume both drift and volatility of the security return process are driven ...