Browsing by Subject "Algebraic"
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Item Codebook ordering for vector quantization(Texas Tech University, 2003-12) Ye, Linning; Mitra, Sunanda; Nutter, Brian; Karp, TanjaAddress predictive vector quantization (APVQ) utilizes an ordered codebook to exploit the dependency among close input vectors. The Kohonen algorithm is often chosen in APVQ. However, the Kohonen algorithm is not applicable while a codebook already exists. In this thesis three methods of ordering an existing codebook have been developed. Theoretically these codebook ordering methods can be utilized in any vector quantization in order to reduce the output bit rate. Here we apply it to two types of vector quantization approaches, geometric vector quantization (GVQ) and vector quantization based on the LBG algorithm. The results of codebook ordering on vector quantization based on the LBG algorithm are quite good. However, codebook ordering does not have good performance on GVQ. Therefore, while applying codebook ordering to one specific VQ, we should consider the property of this VQ in order to achieve a satisfactory result.Item Generalized quadrilateral circle patterns(Texas Tech University, 2003-08) Hume, Casey R.Not availableItem Multiplicative and dynamical analysis on idèles and idèle class groups(2016-05) Hughes, Adam Miles; Vaaler, Jeffrey D.; Ciperiani, Mirela, 1976-; Mohammadi, Amir; Allcock, Daniel; Sinclair, Christopher; Widmer, MartinWe prove an extension of a result due to Allcock and Vaaler from 2009. In the main theorem we show that an idèle group associated to Q-bar is naturally dense in a Banach algebra normed by the Weil height. We establish bounds for the dynamics of generic idèlic points of a field modulo the diagonally-embedded multiplicative groups of the associated fields.Item On the classification of seventh degree M-curves with the maximum number of points of intersection of the odd branch with a line(Texas Tech University, 2001-12) Smith, Daniel EricWe will start the classification of 7 degree AZ-curves with the maximum number of points of intersections of the odd branch with a line. This is done in three steps. First, we enumerate all possible curves with the maximum number of points of intersections of the odd branch with a line. Next, we find some restrictions to those curves. Finally, we start the construction of curves with maximum number of points of intersection.Item The first fundamental theorem of invariant theory for the unimodular and orthogonal groups(Texas Tech University, 1996-12) Mouron, Christopher GNot available