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Notes of functional analysis

Comment: 60 pages

Nystuen/Dacey Nodal Analysis

"Foreword" by Nystuen: Graph theory is a mathematics of structure. Many years ago we (Nystuen and Dacey, 1961) used some theorems from graph theory in the analysis of the spatial structure of a nodal region. The application was novel. More commonly, Euclidean geometry had served as the means to formalize spatial aspects of geographical problems. Tinkler's work is an exception. Over the years he has developed graph theory methods of geographical analysis (involving nodal regions) that have gone well beyond our modest beginning. The present work shows the evolution of nodal analysis.

Electric circuit analysis

The contribution of Lausanne Polytechnic to the development of modern methods of analysis of power networks, in particular to the activities of a group of engineers constituting the `Electric Network Studies Centre', is described

Life Cycle Analysis (LCA)

Life cycle analysis (LCA) is the systematic approach of looking at a product’s complete life cycle, from raw materials to final disposal of the product. It offers a "cradle to grave" look at a product or process, considering environmental aspects and potential impacts. This fact sheet provides an overview of the LCA process.

Theories of Comparative Analysis

Comparative analysis is the problem of predicting how a system will react to perturbations in its parameters, and why. For example, comparative analysis could be asked to explain why the period of an oscillating spring/block system would increase if the mass of the block were larger. This thesis formalizes the task of comparative analysis and presents two solution techniques: differential qualitative (DQ) analysis and exaggeration. Both techniques solve many comparative analysis problems, providing explanations suitable for use by design systems, automated diagnosis, intelligent tutoring systems, and explanation based generalization. This thesis explains the theoretical basis for each technique, describes how they are implemented, and discusses the difference between the two. DQ analysis is sound; it never generates ...

Nonlinear Principal Component Analysis

Two quite different forms of nonlinear principal component analysis have been proposed in the literature. The first one is associated with the names of Guttman, Burt, Hayashi, Benzécri, McDonald, De Leeuw, Hill, Nishisato. We call it multiple correspondence analysis. The second form has been discussed by Kruskal, Shepard, Roskam, Takane, Young, De Leeuw, Winsberg, Ramsay. We call it nonmetric principal component analysis. The two forms have been related and combined, both geometrically and computationally, by Albert Gifi. In this paper we discuss the relationships in more detail, and propose an alternative algorithm for nonlinear principal component analysis which combines features of both previous approaches.

Nichtstandard-Analysis reellwertiger Funktionen

In this thesis we provide an introduction to nonstandard analysis of real functions with occasional comparison to classical analysis. In big parts of this thesis we follow [LR]. Several examples and aspects are taken from [WZ], [RB], [DL], and also [TL] is used. For the standard approach to analysis we use [OF] as a reference. This paper is divided into three parts, namely a historic and preparatory introduction, the main part consisting of chapters 3-7 and the subsequent résumé. The first chapter gives a brief review of the historical development of nonstandard analysis and a summary of the difference between classical analysis and nonstandard analysis. The second chapter then deals with the basic notions of nonstandard numbers. More details can be found in the thesis of [SC]. In the main part, we mainly deal with nonstand...

Practical Shape Analysis

Shape analysis is a program analysis technique used to prove thatimperative programs using manual memory management will not crash. Inthe past, shape analysis has been applied to data structures likelinked lists and binary trees. It has also been used onsimplified versions of Windows device drivers.We describe techniques that allow us to apply shape analysis to datastructures that occur commonly in systems code. These data structuresoften use arrays, hash tables, C strings, and buffers of a knownsize. Sometimes, memory in these data structures is managed by manualreference counting. Analyzing such code is difficult or impossiblewith existing shape analyses. Most difficult of all, many datastructures use several of these patterns at the same time, such as ahash table pointing to reference counted objects through which adoubly linked lis...

Analysis on disconnected sets

Comment: 4 pages, latex-2e

Elements of harmonic analysis

Comment: latex-2e, 22 pages