A major impediment to scientific progress in many fields is the inability to make sense of the huge amounts of data that have been collected via experiment or computer simulation. This dissertation provides tools to visualize, represent, and analyze the collection of sensors and data all at once in a single combinatorial geometric object. Encoding and translating heterogeneous data into common language are modeled by supporting objects. In this methodology, the behavior of the system based on the detection of noise in the system, possible failure in data exchange and recognition of the redundant or complimentary sensors are studied via some related geometric objects. Applications of the constructed methodology are described by two case studies: one from wildfire threat monitoring and the other from air traffic monitoring. Both cases are distributed (spatial and temporal) information systems. The systems deal with temporal and spatial fusion of heterogeneous data obtained from multiple sources, where the schema, availability and quality vary. The behavior of both systems is explained thoroughly in terms of the detection of the failure in the systems and the recognition of the redundant and complimentary sensors. A comparison between the methodology in this dissertation and the alternative methods is described to further verify the validity of the sheaf theory method. It is seen that the method has less computational complexity in both space and time.

Η διπλωματική εργασία έχει στόχο την εισαγωγή δύο θεμάτων της αντιμεταθετικής άλγεβρας, τον εντοπισμό και τη θεωρία φασμάτων,ειδικά για αντιμεταθετικούς δακτύλιους.Ως αναγκαίο συμπλήρωμα παρουσιάσαμε μια εισαγωγή στη θεωρία δραγμάτων και δώσαμε μια έκταση στον δακτύλιο των συνεχών συναρτήσεων.Στο τελευταίο κεφάλαιο παρουσιάζουμε κάποιες εφαρμογές στη θεωρία φασμάτων και δραγμάτων. / This master thesis is an introduction of two subjects in the commutative algebra,the localization and the spectrum theory,especially for commutative rings.We also present an introduction to the sheaf theory and we give an extend to the rings of continous functions.In the last chapter we give some examples of spectrums and sheafs in some algebraic structures.

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19393号 / 理博第4124号 / 新制||理||1593(附属図書館) / 32418 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 中島 啓, 教授 小野 薫, 教授 望月 拓郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Thesis (PhD (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Classical formulations model belief revision as a deterministic process. Under certain circumstances, the process may have more than one outcome, which suggests that belief revision is non-deterministic instead. Representations exist that model belief revision in either format, and for both formats there are axiom schemes that determine whether the representation is in fact a belief revision process. Although the axiom scheme for the non-deterministic case generalises that of the deterministic case, both schemes entail that all of the beliefs held by an agent are affected by new information, which is perhaps unintuitive. Rather, one may consider that belief revision should be local, with beliefs only affected if the new information is pertinent to them. We approach the problem of belief revision from the standpoint that it is local and non-deterministic, and the purpose and contribution of this dissertation is the development of a topological framework with which to model belief revision in this manner. / AFRIKAANSE OPSOMMING: Geloofshersiening word gewoonlik as ’n deterministiese proses voorgestel. Meer as een uitkoms mag bestaan vir verskeie omstandighede, wat aandui dat die proses liewer nie-deterministies van aard is. Beide die gevalle word deur aksiomaskemas gereguleer, en die aksiomas vir die nie-deterministiese geval veralgemeen dié van die deterministiese geval. Albei aksiomaskemas stipuleer, miskien onintuïtief, dat alle gelowe van ’n agent deur die nuwe informasie geaffekteer word. ’n Beter metode is dat net daardie gelowe waarvoor die nuwe informasie toepaslik is geaffekteer word. Ons benader die probleem van geloofshersiening uit die standpunt dat dit lokaal en nie-deterministies is, en die doel en bydrae van hierdie proefskrif is dus die ontwikkeling van ’n topologiese raamwerk waarmee ons geloofshersiening op hierdie manier kan voorstel.

We introduce the definition of 1-cotilting object in a Grothendieck category and investigate its relation to the analogue of the standard definition of 1-cotilting module. The 1-cotilting quasi-coherent sheaves on a Noetherian scheme are stud- ied in particular: using the classification of hereditary torsion pairs in the category of quasi-coherent sheaves on a Noetherian scheme X, to each hereditary torsion- free class F that is generating we assign a 1-cotilting quasi-coherent sheaf whose 1-cotilting class is F. This provides a family of pairwise non-equivalent 1-cotilting quasi-coherent sheaves which are parametrized by specialization closed subsets of X avoiding the set of associated points of a chosen generator of the category of quasi-coherent sheaves. In many cases (e.g. for separated schemes), this set of avoided points can be chosen as the set of associated points of the scheme. 1

No description available.

Univ., FB Mathematik, Habil.-Schr., 2001--Hamburg, 2001.

A key property of projective varieties is the very ampleness of line bundles as this provides embeddings into projective space and allows us to express the variety in equational terms. In this thesis we study the general version of this property which is k- very ampleness of line bundles. We introduce the notation of critical k-very ampleness and compute it for abelian surfaces. The property of k-very ampleness is usually discussed using tools from divisor theory but we take a different approach and use methods from derived algebraic geometry as part of program to use properties of the derived category of a variety to access the geometry of the variety. In particular, we use the Fourier-Mukai transform, moduli spaces of sheaves and properties of Bridgeland stability. We compute walls for certain Bridgeland stable spaces and certain Chern characters and to complete the picture we study the moduli spaces of torsion sheaves with minimal first Chern class and we go on to compute the walls for these as well building on tools developed earlier in the thesis.

No description available.