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In dieser Dissertation geht es um Schwinger-parametrische Feynmanintegrale in der Quantenelektrodynamik. Mittels einer Vielzahl von Methoden aus der Kombinatorik und Graphentheorie wird eine signifikante Vereinfachung des Integranden erreicht. Nach einer größtenteils in sich geschlossenen Einführung zu Feynmangraphen und -integralen wird die Herleitung der Schwinger-parametrischen Darstellung aus den klassischen Impulsraumintegralen ausführlich erläutert, sowohl für skalare Theorien als auch Quantenelektrodynamik. Es stellt sich heraus, dass die Ableitungen, die benötigt werden um Integrale aus der Quantenelektrodynamik in ihrer parametrischen Version zu formulieren, neue Graphpolynome enthalten, die auf Zykeln und minimalen Schnitten (engl. "bonds") basieren. Danach wird die Tensorstruktur der Quantenelektrodynamik, bestehend aus Dirac-Matrizen und ihren Spuren, durch eine diagrammatische Interpretation ihrer Kontraktion zu ganzzahligen Faktoren reduziert. Dabei werden insbesondere gefärbte Sehnendiagramme benutzt. Dies liefert einen parametrischen Integranden, der über bestimmte Teilmengen solcher Diagramme summierte Produkte von Zykel- und Bondpolynomen enthält. Weitere Untersuchungen der im Integranden auftauchenden Polynome decken Verbindungen zu Dodgson- und Spannwaldpolynomen auf. Dies wird benutzt um eine Identität zu beweisen, mit der sehr große Summen von Sehnendiagrammen in einer kurzen Form ausgedrückt werden können. Insbesondere führt dies zu Aufhebungen, die den Integranden massiv vereinfachen. / This thesis is concerned with the study of Schwinger parametric Feynman integrals in quantum electrodynamics. Using a variety of tools from combinatorics and graph theory, significant simplification of the integrand is achieved. After a largely self-contained introduction to Feynman graphs and integrals, the derivation of the Schwinger parametric representation from the standard momentum space integrals is reviewed in full detail for both scalar theories and quantum electrodynamics. The derivatives needed to express Feynman integrals in quantum electrodynamics in their parametric version are found to contain new types of graph polynomials based on cycle and bond subgraphs. Then the tensor structure of quantum electrodynamics, products of Dirac matrices and their traces, is reduced to integer factors with a diagrammatic interpretation of their contraction. Specifically, chord diagrams with a particular colouring are used. This results in a parametric integrand that contains sums of products of cycle and bond polynomials over certain subsets of such chord diagrams. Further study of the polynomials occurring in the integrand reveals connections to other well-known graph polynomials, the Dodgson and spanning forest polynomials. This is used to prove an identity that expresses some of the very large sums over chord diagrams in a very concise form. In particular, this leads to cancellations that massively simplify the integrand.

Thesis (MScEng (Civil Engineering))--Stellenbosch University, 2008. / The Southern African Institute of Steel Construction expressed concern with regard to the unit definition of the effective length factor, K, stipulated for compressive elements of parallel chord trusses in Clause 15 of SANS 10162-1:2005 - Limit state design of hot-rolled steelwork. The simplified method for truss design specified in the code assumes all compression members are pin-connected, which allows for greater design simplicity and reduces the amount of code interpretation required by the designer. In addition to this, Clause 15 requires the additional reduction in resistance of the first web compression members by a factor of 0.85. However, this approach may be considered overly conservative and in current design practice the effective length factor is often reduced to less than 1.0. This research investigates the effective length factor of web compression members in parallel chord trusses, by means of investigative structural analyses of representative trusses using ANGELINE and Prokon analytical programs, and by designing, constructing and testing six representative trusses, using current design practices. A comparative study of a number of different countries’ codified approaches to truss design is also included. The structural analyses revealed that in-plane buckling of the web compression members was the consistent mode of failure, however at a much greater applied load than the design load determined according to SANS 10162-1:2005. Contrary to the expected mode of failure, all six tests performed on the representative trusses exhibited elastic out-of-plane buckling, or strongaxis buckling, of the web compression members, but still at a much greater applied load than the design load. The unexpected out-of-plane buckling of the web members is due to the inplane stiffness of the end connections used. In order to stay true to current design practice, gusset plates and longitudinal welds were used to join the web members to the chords. The stiffness of the gusset plates therefore significantly reduced the effective length of the web compression members in-plane, but did not reduce the effective length out-of-plane. Despite the unanticipated behaviour of the tests performed, certain conclusions can still be drawn from the results. The unit definition of the effective length factor for in-plane buckling of web compression members is too conservative and a K factor of 0.8 is recommended. In addition to this an effective length factor for out-plane-buckling of web compression members of 1.1 is recommended for trusses with welded connections. The necessity of the reduction in resistance of 0.85 of the first web compression members requires further investigation. The most important conclusion to be drawn is that out-of-plane buckling of web compression members can be the dominant failure mode, which is not taken into consideration in current design practice.

The purpose of this thesis is to contrast Wagner's usages of the ninth, eleventh, and thirteenth intervals and chords, as found in Die Walküre, Act I and Götterdämmerung, Act I.

The aim of my diploma thesis is to summarize my knowledge of the guitar chord playing during working in the institution Dům dětí a mládeže in České Budějovice where I have been teaching for four years. It is focused on readers who teach guitar chord playing as an after-school activity or who learn how to play on their own. In the first part of the thesis there is a concept about the lector's theoretical knowledge. The second part (containing particular lessons) deals with the methodology of teaching the very beginners with no musical education.

[pt] A extração de parâmetros musicais de gravações de áudio a partir do processamento do sinal musical viabiliza uma série de aplicações importantes no campo de análise e classificação de peças musicais. A Harmonia é um importante aspecto da estrutura musical, fazendo da seqüência de acordes de uma peça uma informação extremamente relevante em sua análise e parte fundamental do próprio registro gráfico da música. Este trabalho discute os elementos envolvidos na transcrição de harmonia musical assim como as ferramentas matemáticas e de processamento de sinais adequadas a um método automático de análise e identificação de acordes, propondo um modelo para um sistema capaz de transcrever seqüências de acordes a partir de gravações de áudio comerciais. O sistema proposto analisa um sinal de áudio e retorna as cifras correspondentes aos acordes que melhor representam o sinal / [en] The extraction of musical parameters from audio recordings enables a series of important applications in the field of musical analysis and classification. Harmony is a major issue on music structure, making the chord sequence of a musical piece an extremely relevant information on its analysis and a fundamental part of the musical graphic register. This work discusses the elements involved in musical harmony transcription as well as the mathematical and signal processing tools suitable to build an automatic method for the analysis and identification of chords, proposing a model capable of transcribing chord sequences from commercial audio recordings. The proposed system analyzes an audio signal and returns the symbols corresponding to the chords that best fit the signal.

Freedom of speech and the right to privacy are maybe the most important elements of a modern society, yet the rights are often violated. This fact was the main reason for writing this thesis covering P2P network models, anonymity, censorship resistance and their use in real P2P networks and publishing systems. We discuss their effectiveness and suitability for specific purposes, but also the security considerations of their use. The second part of this thesis presents the LSPP publishing protocol, which is an library implementation of an anonymous censorship resistant P2P network. Finally, we analyze the proposed protocol and compare it with existing solutions.

This work deals with automatic chord recognition using neural networks. The problem was separated into two subproblems. The first subproblem aims to experimental finding of most suitable solution for a acoustic model and the second one aims to experimental finding of most suitable solution for a language model. The problem was solved by iterative method. First a suboptimal solution of the first subproblem was found and then the second one. A total of 19 acoustic and 12 language models were made. Ten training datasets was created for acoustic models and three for language models. In total, over 200 models were trained. The best results were achieved on acoustic models represented by convolutional networks together with language models represented by recurent networks with LSTM modules.

Today Moblity Management is one of the most important tasks that need to be accomplished to secure availability and performance of communication between people. This paper explains how moblity management is currently structured and what algorithms and approaches from Peer-To-Peer technology could be used to increase availability and performance.

A partir d'une interprétation musicologique de la notion scientifique de "modélisation et simulation'', cette thèse présente une approche d'analyse assistée par ordinateur où les partitions musicales sont reconstruites à partir de processus algorithmiques et simulées avec différents paramètres à partir desquels des variantes, appelés instances, sont générés. L'étude d'une pièce musicale par modélisation et simulation signifie comprendre l'oeuvre en la (re) composant de nouveau, en brouillant les limites entre le travail analytique et créatif. Cette approche est appliquée à trois études de cas: 1. une technique isolée, la "multiplication d'accords'', utilisé par Pierre Boulez (1925- 2016), qui a été explorée à travers le prisme formé par les théories de H. Hanson, S. Heinemann et L. Koblyakov; 2. La pièce "Spectral Canon pour Conlon Nancarrow" (1974) du compositeur américain James Tenney (1934-2006) à laquelle la simulation computationnelle à partir de différents paramètres a été prise à ses conséquences ultimes quand un "espace d'instances" est explorée a partir de stratégies de visualisation graphique; 3. Et enfin "Désordre" (1985), le première étude pour piano de l'austro-hongrois György Ligeti (1923-2006) dans laquelle les concepts de "tonalité combinatoire" et "décomposition en nombres premiers'', appliqué aux durées, ont été utilisés pour maximiser le potentiel de production d'instances. / From a musicological interpretation of the scientific notion of “modeling and simulation”, this thesis presents an approach for computer-aided analysis where musical scores are reconstructed from algorithmic processes and then simulated with different sets of parameters from which neighbouring variants, called instances, are generated. Studying a musical piece by modelling and simulation means to understand the work by (re)composing it again, blurring boundaries between analytical and creative work. This approach is applied to three case studies: an isolated technique, Pierre Boulez Chord Multiplication, which is explored through the prism formed by the theories of H. Hanson, S. Heinemann and L. Koblyakov; the piece Spectral Canon for Conlon Nancarrow (1974) by the american James Tenney (1934-2006) to which the computational simulation from different sets of parameters was taken to its ultimate consequences when a “space of instances” is created and strategies of visualisation and exploration are devised; and finally “Disorder”, the first piano study written by austro-hungarian György Ligeti in which the concepts of “combinatorial tonality” and “decomposition prime numbers”, applied to durations, are used to maximize the potential that a model has to produce different variations of the original piece.