"Definition 1. A group G is an extension of a group A by a group B if and only if A is a normal subgroup of G and the factor group G/A is isomorphic to B. Definition 2. Two extensions G and H of A by B are called equivalent if and only if there exists an isomorphism between G and H that on A coincides with the identity automorphism and that maps onto each other the cosets of A corresponding to one and the same element of B. Consider the following example: let G be the cyclic group of order 4, that is G = {1, a, a², a³} and let H[subscript G] = {1, a²} be a normal subgroup of G. Now let V be the Klein four-group, that is, V = {1, a, b, c : a²=b²=c²=1} and H[subscript V] = {1, b} a normal subgroup of V. Since H[subscript G] and H[subscript V] are cyclic groups of order 2, set H[subscript V] = H[subscript G] = H. G and V are extensions of H by itself but are not equivalent extensions since no isomorphism exists between G and V. So the question arises: what are the necessary and sufficient conditions that two extensions G and G' of a group A by a group B be equivalent?"--Introduction. / Typescript. / "January 1960." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: Paul J. McCarthy, Professor Directing Paper. / Includes bibliographical references (leaf 37).

Aquesta memona està dedicada a l'estudi dels nombres d'extensions abelianes en dos casos importants. En el primer capítol treballem en el cas local. Sigui K una extensió finita de Q(p); M. Krasner el 1.966 i J-P. Serre el 1.978 varen obtenir el nombre de totes les extensions de K de grau donat. En aquesta memòria estudiem els següents problemes:Problema 1.- Donats enters positius e,n:a) caracteritzar en quins casos és no buit el conjunt M(ab)(n,e;K) de totes les extensions abelianes de grau "n" de K amb índex de ramificació e;b) calcular el cardinal a(n,e;K) de M(ab)(n,e;K), per a totes les parelles (n,e);c) calcular el nombre a(n;K) de totes les extensions abelianes de grau "n" de K.Seguidament introduïm la funció generatriu de tots els nombres a(n;K), nombres que posem com a coeficients d'una sèrie de Dirichlet.Problema 2.- Estudiar aquesta funció generatriu; especialment, la seva extensió meromorfa a tot el pla complex i els seus pols.En els capítols II i III treballem en el cas en què el cos base és el cos Q dels nombres racionals. Fixem un conjunt finit P = {p(1),p(2),...,p(k)} d'enters primers p(i) <p(i+1) i definim els conjuntsM(ab)(n;P) = {K/Q:K/Q abeliana, [K:Q] = n i K/Q no ramificada fora de P},iM(ab)(n, e, P)={K pertany a (M)(ab)(n;P): e(pi)(K/Q)=e(i, 1 -/= i -/= k}, on e = (e(1),e(2),...,e(k)) és un vector format per enters e(1)> 1.Estudiem, aleshores, els següents problemes:Problema 1'.- Donats P, e, n:a) caracteritzar quan> (M)ab(n, e, P) és no buit;b) calcular el cardinal de M(ab)(n, e, P);c) caracteritzar quan M(ab)(n;P) és no buit;d) calcular el cardinal, a(n;P) de M(ab)(n;P).Introduïm també la funció generatriu dels nombres a(n;P).Problema 2'.- Estudiar aquesta funció generatriu, com en el cas local.Tots els resultats de teoria de grups que necessitem s'inclouen en un apèndix. Tracten del nombre de subgrups d'un p-grup abelià finit que satisfan certes condicions. Tot i que les solucions d'alguns d'aquests problemes són conegudes, en donem aquí una solució completa de manera que els resultats es puguin aplicar directament als problemes de cossos plantejats. / This memory is devoted to the study of the number of abelian extensions in two important cases. In the first chapter we work in the local case. Let K be a finite extension of Q(p); M. Krasner in 1.966 and J.P. Serre in 1.978 have obtained the number of all extensions of K with given degree.

The Frobenius group is an example of a split extension. In this dissertation we study and describe the properties and structure of the group. We also describe the properties and structure of the kernel and complement, two non-trivial subgroups of every Frobenius group. Examples of Frobenius groups are included and we also describe the characters of the group. Finally we construct the Frobenius group 292 : SL(2, 5) and then compute it's Fischer matrices and character table. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

Customization of processors with instruction set extensions (ISEs) is a technique that improves performance through parallelization with a reasonable area overhead, in exchange for additional design effort. This thesis presents a collection of novel techniques that reduce the design effort and cost of generating ISEs by advancing automation and reconfigurability. In addition, these techniques maximize the perfomance gained as a function of the additional commited resources. Including ISEs into a processor design implies development at many levels. Most prior works on ISEs solve separate stages of the design: identification, selection, and implementation. However, the interations between these stages also hold important design trade-offs. In particular, this thesis addresses the lack of interaction between the hardware implementation stage and the two previous stages. Interaction with the implementation stage has been mostly limited to accurately measuring the area and timing requirements of the implementation of each ISE candidate as a separate hardware module. However, the need to independently generate a hardware datapath for each ISE limits the flexibility of the design and the performance gains. Hence, resource sharing is essential in order to create a customized unit with multi-function capabilities. Previously proposed resource-sharing techniques aggressively share resources amongst the ISEs, thus minimizing the area of the solution at any cost. However, it is shown that aggressively sharing resources leads to large ISE datapath latency. Thus, this thesis presents an original heuristic that can be parameterized in order to control the degree of resource sharing amongst a given set of ISEs, thereby permitting the exploration of the existing implementation trade-offs between instruction latency and area savings. In addition, this thesis introduces an innovative predictive model that is able to quickly expose the optimal trade-offs of this design space. Compared to an exhaustive exploration of the design space, the predictive model is shown to reduce by two orders of magnitude the number of executions of the resource-sharing algorithm that are required in order to find the optimal trade-offs. This thesis presents a technique that is the first one to combine the design spaces of ISE selection and resource sharing in ISE datapath synthesis, in order to offer the designer solutions that achieve maximum speedup and maximum resource utilization using the available area. Optimal trade-offs in the design space are found by guiding the selection process to favour ISE combinations that are likely to share resources with low speedup losses. Experimental results show that this combined approach unveils new trade-offs between speedup and area that are not identified by previous selection techniques; speedups of up to 238% over previous selection thecniques were obtained. Finally, multi-cycle ISEs can be pipelined in order to increase their throughput. However, it is shown that traditional ISE identification techniques do not allow this optimization due to control flow overhead. In order to obtain the benefits of overlapping loop executions, this thesis proposes to carefully insert loop control flow statements into the ISEs, thus allowing the ISE to control the iterations of the loop. The proposed ISEs broaden the scope of instruction-level parallelism and obtain higher speedups compared to traditional ISEs, primarily through pipelining, the exploitation of spatial parallelism, and reducing the overhead of control flow statements and branches. A detailed case study of a real application shows that the proposed method achieves 91% higher speedups than the state-of-the-art, with an area overhead of less than 8% in hardware implementation.

A current group GX is an infinite-dimensional Lie group of smooth maps from a smooth manifold X to a finite-dimensional Lie group G, endowed with pointwise multiplication. This thesis concerns current groups G§ for compact Riemann surfaces §. We extend some results in the literature to discuss the topology of G§ where G has non-trivial fundamental group, and use these results to discuss the theory of central extensions of G§. The second object of interest in the thesis is the Jacobi group, which we think of as being associated to a compact Riemann surface of genus one. A connection is made between the Jacobi group and a certain central extension of G§. Finally, we define a generalisation of the Jacobi group that may be thought of as being associated to a compact Riemann surface of genus g ≥ 1.

Thesis (M.S.)--University of North Carolina at Wilmington, 2005. / Includes bibliographical references (Leaf: [104])

Thesis (Doctoral)--Universität Bonn, 1991. / Includes bibliographical references.

Th. 3e cycle--Math. pures--Lille 1, 1978. N°: 715.

Only a few industries face challenges regarding sustainability to the same extent as the fashion industry being one of the largest consumer industries and the second most polluting industry in the world. These challenges are encouraged by the fast fashion business model, which is dominant in the sector and relies on the quick responsiveness to latest fashion trends while maintaining low prices, encouraging more consumption and shorter product life cycles. On the other side, a consumer shift towards more environmental consciousness can be observed leading to most fast fashion brands integrating sustainability in various forms into their products and services. A path that many fast fashion brands take in order to become more sustainable is the strategy of green branding through green brand extensions. Green brand extensions (GBEs) involve the application of an established brand name to new and greener products due to environmental considerations of the brand and can be divided into green line extensions (GLEs) and green category extensions (GCEs). Due to identified research gaps concerning how green brand extensions change consumer attitudes as well as the relationship between brand loyalty and the green image of brands, the following research question got developed to gain in-depth in consumer behavior in the fast fashion industry related to green brand extensions: RQ: How do green brand extensions of fast fashion brands affect the consumers’ parent brand attitude and brand loyalty? This primary study that aims to answer the research question was conducted following a deductive research approach and adopting a quantitative research design through collecting data by means of a web questionnaire. Thereby, the brand attitude of fashion consumers on green line and green category extensions as well as the relationship to brand loyalty got investigated focusing on Generation Y and Z as largest consumer groups of fast fashion. The main results of the study are that the introduction of a GLE by a fast fashion brand generally leads to a more positive brand attitude and a slightly improved brand loyalty of consumers towards the parent brand. However, when introducing a GCE, the launch has rarely a positive effect on the brand attitude and brand loyalty of consumers towards the parent brand. The relationship of GLEs and brand attitude is thereby moderated by the environmental concern of consumers as well as their friends and by the initial brand attitude towards the fast fashion brand. The relationship of GLEs and brand loyalty on the other hand is only moderated by environmental concern of consumers and the initial brand attitude. Looking at GCEs and their relationship with brand attitude as well as brand loyalty, it is influenced and moderated by the age of consumers, the environmental concern of their friends as well as consumers’ initial brand loyalty towards the parent brand.

The motivation of my dissertation is to improve two weaknesses of Random Forests. One, the failure to detect genetic interactions between two single nucleotide polymorphisms (SNPs) in higher dimensions when the interacting SNPs both have weak main effects and two, the difficulty of interpretation in comparison to parametric methods such as logistic regression, linear discriminant analysis, and linear regression. We focus on detecting pairwise SNP interactions in genome case-control studies. We determine the best parameter settings to optimize the detection of SNP interactions and improve the efficiency of Random Forests and present an efficient filtering method. The filtering method is compared to leading methods and is shown that it is computationally faster with good detection power. Random Forests allows us to identify clusters, outliers, and important features for subgroups of observations through the visualization of the proximities. We improve the interpretation of Random Forests through the proximities. The result of the new proximities are asymmetric, and the appropriate visualization requires an asymmetric model for interpretation. We propose a new visualization technique for asymmetric data and compare it to existing approaches.