In this paper we prove that the conjectures of Frisch and Parisi and Arneodo et al. (called the multifractal formalism for functions) may fail for some non-homogeneous selfsimilar functions on ℝ2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modified.
Summary The aim of this thesis is the multifractai analysis of selfsimilar functions and the study of the validity of the multifractai formalism. First, we determine the exact pointwise Holder regularity for functions such that locally the graph is roughly a contraction of the global graph, modulo an error; then we compute the Hausdorff dimensions of the sets of points which have the same Holder exponent; and finally we verify the conjectures of Frish and Parisi and the one of Arneodo, Bacry and Muzy, which relate these dimensions to some averaged quantities extracted from the function.
The course covers requirements engineering in depth including the followings: requirements Engineering Process - Elicitation of requirements - Functional and non-functional requirements - System services and constraints – Quality of Requirements - Requirements traceability matrix - Metrics for non-functional requirements - Use case description - Use case and context diagrams - Software Requirements Specification -IEEE Standard - Requirements for agile developments - Requirements for various systems: embedded systems, web-based systems, business systems, etc. – Requirements management.
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