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201206
Replicated regular twolevel factorial experiments are very useful for industry. The basic purpose of this type of experiments is to identify active effects that affect the mean and variance of the response. Hypothesis testing procedures are widely used for this purpose. However, the existing...

On Multivariate Quantile Regression: Directional Approach and Application with Growth Charts
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In this thesis, we introduce a concept of directional quantile envelopes, the intersection of the halfspaces determined by directional quantiles, and show that they allow for explicit probabilistic interpretation, compared to other multivariate quantile concepts. Directional quantile envelopes...

201406
This thesis deals with the TrotterKato approximation in utility maximization. The TrotterKato approximation is a method to split a differential equation into two parts, which are then solved iteratively over small time intervals. In the context of utility maximization, this procedure was...

201406
Let G be a locally compact group. It is wellknown that G^LUC, the spectrum of the algebra of left uniformly continuous functions on G, the socalled LUCcompactification of G, is a semigroup with product restricted from the Arens product on LUC(G)^*. Now consider the algebra of weighted left...

Representability of Algebraic CHOW Groups of Complex Projective Complete Intersections and Applications to Motives
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In 1990 James D. Lewis made a conjecture on the representability of algebraic Chow groups of projective algebraic manifolds. We prove that his conjecture holds for smooth complex complete intersections satisfying a numerical condition and consider some applications to motives.

201311
Heegner points on modular curves play a key role in the solution of Hilbert’s twelfth problem for qua dratic imaginary fields, as well as the proof of the Birch and SwinnertonDyer conjecture for the case ords=1 L(E, s) ≤ 1. The relationship between Heegner points and Hilbert’s twelfth is...

201406
This thesis is mostly based on six papers on selected topics in Asymptotic Geometric Analysis, Wavelet Analysis and Applied Fourier Analysis. The first two papers are devoted to Ball's integral inequality. We prove this inequality via spline functions. We also provide a method for computing all...

201311
This thesis deals with the problem proposed by Ye and Zhou (2007): Is a Qoptimal minimax design still symmetric if the requirement of $\int_\chi xm(x)dx = 0$ is removed? We have shown that for the simple linear regression, considering only the variance, a Qoptimal minimax design is necessarily...