Rezensionen

Uwe Kraeft

Goldbach's Conjecture and Structures of Primes in Number Theory

The author continues his activities known from earlier, apparently self-published, volumes. Apart from historical reproductions, many tables for small numbers are presented, followed by resulting ideas of the author for proof strategies. The style is probably best characterized by E. J. Barbeau´s review of the author´s _rst book of this type (see Zbl 977.11504). Olaf Teschke (Berlin)

Quelle: Zentralblatt MATH 1200 | 1

Jochen Gorski

Multiple Objective Optimization and Implications for Single Objective Optimization

This thesis deals with multiple objective optimization problems. The first chapter of Part I deals with the question of how multiple objective solution approaches can be used to solve single objective combinatorial optimization problems. The author concentrates on constrained versions of single objective problems as well as on algebraic sum problems. The remaining chapters of Part I are dedicated to the connectedness of the efficient set of multiple objective combinatorial optimization problems. The author focuses on problems with sum objectives and bottleneck objectives. Single objective knapsack problems with binary weights and biobjective matroid problems with binary costs are considered. Part II is devoted to biconvex minimization and biconvex maximization problems. Special attention is given to the connection location-allocation problem in the plane. Svetlana A. Kravchenko (Minsk)

Quelle: Zentralblatt MATH 1214 | 1

Georg Maier

Smooth Minimum Arc Paths

Contour Approximation with Smooth Arc Splines

The book is related to two domains, more precisely, to the frontier between computer aided design and approximation theory. The goal of the subject presented is to give a representation of the contour for a quasi-planar object by a planar (smooth) curve approximating the extracted point. This solution is presented as better than the solution given by a finite list of pixel coordinates which constitute the information from the border of an object captured by an optical sensor. The appropriate description of the contour is an important matter in practical domains related to subjects is vision metrology and quality assurance. One approach is to approximate the contour with smooth arc splines (composed with circular arcs and line segments which are linked at the break points by some smoothness conditions). This kind of approach can be viewed as a multi-criterial optimization among can be underlined the minimization of the approximation error which can be obtained by taking an increased number of pieces (arcs and segments) in the structure of the estimator. In order to solve this problem the author defines a start-destination channel having a source and a destination segment. Taking into account this approach, every smooth minimum arc path which is an arc spline being preserved inside the start-destination channel and connecting the source and destination segments with a minimum number of segments is an appropriate solution of the problem. More exactly, if we consider a start and an end point on a piecewise restricted analytic curve (particularly a polygon), the solution will be a smooth arc path composed by a minimum number of pieces, smoothly connected in the break points and preserved in the inside of the curve closure. The author presents a mathematical characterization of this kind of solution based on an algorithm of order equal to the square of the number of vertices. The book is structured in six chapters, having also a useful index of symbols, algorithms, notions and references based on both classical and recent works in the _eld. In the introductory chapter, the motivation of the work is given beginning with some practical example from reverse engineering. In the second chapter, basic de_nitions and notations are prepared, namely conics and circles, planar curves and arc splines, together with some results related to set-valued analysis and approximation theory, Hausdor_ metric and local Hausdor_ topology. The mathematical modeling for the outlined problem is presented in the third chapter, the algorithmic approach is the goal for the fourth chapter and various applications of minimum arc paths are described in the fifth chapter. Also, some open problems and possible future research directions are outlined in the last chapter. The book is well written taking into account both theoretical and practical issues. Nicoleta Breaz (Alba Iulia)

Quelle: Zentralblatt MATH 1216 | 1

Darko Pavic

Combining Raster- and Vector-Representations for Image and Geometry Processing Applications

Summary: Geometric information is omnipresent in any data used as input in computer graphics applications. While this is obvious for geometry processing applications, where 3D models are the objects of interest, it is not directly apparent in the case of image and video processing applications. However, there are at least two di_erent views for interpreting images as representations for geometric information. First, images can be seen as height _elds over spatial 2D domains and as such describe geometric shapes in the used color space. Second, images show projected 3D geometry, which we can describe or at least approximate and exploit. In order to take advantage of the provided geometric information in the input data, the key issue is to find the most appropriate geometry representation which is perfectly suited for specific application´s requirements. In this thesis we show that a combination of raster- and vector-representations of the geometric information contained in the input data provides novel opportunities and ways for solving very challenging tasks in the areas of image and geometry processing. By this we also draw parallels between these two, at first glance, completely different areas in computer graphics, and show a way to address problems posed in these areas in a uni_ed manner. We present a number of novel approaches which provide several improvements over previous works by appropriate recovery and exploitation of different geometry representations in the input data. In the first part of this thesis we show how to efficiently represent and exploit geometry in the color space for a number of image processing tasks. The standard raster-representation of an image is extended inside the concept of Two-Colored Pixels (TCPs) with an appropriate vectorization of the geometric information in the color space. We exploit the same TCP concept as a basic operator for an interactive brush tool, as a supporting data structure for retargeting applications and also as a feature/non-feature classifier for the computation of genuine image mosaics. In the context of our mosaicing algorithm, for matching we propose polynomial image descriptors as a very compact geometric representation of an image in the color space. In the second part of this thesis we interpret an image as a container for the projected 3D world space geometry. Under the assumption of existence of (nearly) planar structures in the underlying scene we de_ne a vectorization of an image through 2D projective transforms, so-called homographies. We propose a novel image completion method which exploits the perspective information provided by the homographies. Our approach is interactive since all the necessary computations are described as convolution operations and are done in the Fourier domain. In addition, we present a unifying framework for a 2D video editing system which allows for quite challenging application scenarios such as video enhancement, background replacement or perspectively correct video cut and paste. In the third and last part of this thesis we propose novel algorithms for two important geometric operations, namely for the computation of o_set surfaces and for Boolean operations. Our o_setting operation can handle arbitrary, maybe degenerated, polygonal meshes and is guaranteed to produce the geometrically correct output within a prescribed tolerance. We also introduce a simple but e_ective mesh operation which allows for detecting and including sharp features into the output o_set surface. Finally, the problem of limited voxel resolution, inherent to every volumetric method, is avoided by our volume tiling approach. Our hybrid Booleans not only exploit hybrid geometry representations but also compute the final output surface in a hybrid way, i.e., by stitching the appropriately clipped polygonal input geometry with the newly extracted output geometry, where a volumetric approach is used.

Quelle: Zentralblatt MATH 1209 | 1

Mahmood Alam

Cartan Subalgebras of Locally Finite Lie Algebras

In this dissertation, the author investigates the cohomology spaces of locally nilpotent Lie algebras with values in a weakly locally _nite module of a locally nilpotent Lie algebra, due to the natural importance of cohomology spaces in such a case. The work, which contains a dissertation of almost 80 pages, is divided into three Chapters. In the _rst of them the author deals with the basic notions of Lie algebras Theory and Cohomology of Lie algebras. He introduces a new concept which he calls ad-splittability of locally nilpotent Lie algebras. Chapter 2 is devoted to deal with the cohomology spaces of nilpotent and locally nilpotent Lie algebras. The author proves some results related to the vanishing of cohomology spaces of these algebras. Finally, in Chapter 3, the author investigates the conjugacy classes of splitting Cartan subalgebras and maximal toral subalgebras of ad-splittable locally solvable and those ad-splittable Lie algebras which are non-abelian extensions of locally nilpotent Lie algebras. Juan N_u~nez Vald_es (Sevilla)

Quelle: Zentralblatt MATH 1207 | 1

Uwe Kraeft

Challenges in Number Theory

The author continues his activities known from earlier, apparently self-published, volumes. There is nothing that the reviewer can add to E. J. Barbeau´s review of the author´s first book of this type (2000; Zbl 977.11504). Olaf Teschke (Berlin)

Quelle: Zentralblatt MATH 1200 | 1

Mohamed Amine Chatti

Personalization in Technology Enhanced Learning

A Social Software Perspective

There is a wide agreement that traditional Technology Enhanced Learning (TEL) models have failed to cope with the fast-paced change and critical challenges of the new knowledge era. In this thesis, the Learning as a Network (LaaN) theory is introduced as a response to the increasing complexity of the new learning environments. LaaN draws upon connectivism, complexity theory, and double-loop learning. It views knowledge as a personal network and represents a knowledge ecological approach to learning. Based on the LaaN theory, the 3P Learning Model is discussed as an alternative TEL model that represents a fundamental shift toward a more personalized, social, open, dynamic, emergent and knowledge-pull model for learning, as opposed to the one-size-fits-all, centralized, static, top-down, and knowledge-push paradigms of traditional TEL models. (DIPF/Orig.).; Traditionelle Technology Enhanced Learning (TEL) Modelle sind, wie heute allgemein anerkannt, nicht geeignet, um mit den rasanten Änderungen und den kritischen Herausforderungen der neuen Wissensära mithalten zu können. Als Antwort auf die steigende Komplexität von Lernumgebungen wird in der vorliegenden Dissertation die Theorie Learning as a Network (LaaN) vorgestellt, die auf Connectivism, Komplexitätstheorie und Double-Loop-Lernen basiert. Die LaaN-Theorie begreift Wissen als persönliches Netzwerk und zeigt einen wissensökologischen Ansatz zum Lernen auf. Basierend auf der LaaN-Theorie wird das 3P-Lernmodell als ein alternatives TEL-Modell vorgestellt, das einen Wechsel zu einem personalisierten, sozialen, offenen, dynamischen, aufstrebenden Knowledge-Pull-Modell fürs Lernen darstellt, im Gegensatz zu traditionellen, allgemeingültigen, zentralisierten, statischen, von oben herab definierten Knowledge-Push-TEL-Modellen. Abschließend wird das Social-Software-Supported-Learning-Rahmenwerk vorgestellt, welches die Anwendung des 3P-Lernmodells illustriert. Hierzu werden die Grundideen des Modells mit Hilfe von Social-Software-Technologien und Konzepten aus dem Web 2.0 umgesetzt. (DIPF/Orig.).

Quelle: fachportal-paedagogik.de