We study the scheduling problem for data collection from sensor nodes to the sink node in wireless sensor networks, also referred to as the convergecast problem. The convergecast problem in general network topology has been proven to be NP-hard. In this paper, we propose our heuristic algorithm (finding the minimum scheduling time for convergecast (FMSTC)) for general network topology and evaluate the performance by simulation. The results of the simulation showed that the number of time slots to reach the sink node decreased with an increase in the power. We compared the performance of the proposed algorithm to the optimal time slots in a linear network topology. The proposed algorithm for convergecast in a general network topology has 2.27 times more time slots than that of a linear network topology. To the best of our knowledge, the proposed method is the first attempt to apply the optimal algorithm in a linear network topology to a general network topology.

京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第19795号 / 人博第766号 / 新制||人||184(附属図書館) / 27||人博||766(吉田南総合図書館) / 32831 / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)教授 立木 秀樹, 准教授 櫻川 貴司, 教授 日置 尋久 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM

The aim of this thesis is twofold. First, we investigate spaces defined by asserting that their nowhere dense subsets have certain properties. Secondly, we develop some techniques for the construction of topological spaces. We consider spaces where the nowhere dense sets are asserted to have some property P, calling such spaces boundary-P. We show that if there are no Lusin spaces then every compact boundary-metrizable space is metrizable. Boundary-separability is also studied and we show that if there are no L-spaces then every boundary-separable space is separable. By adapting the absolute dimension function of Arhangel'skii, we define the new concept of cohesion. We show that every compact cohesive and every Hausdorff, sequential cohesive space is scattered. However, we construct regular, crowded spaces of all finite cohesions though there are no regular spaces of transfinite cohesion. We consider too the preservation of cohesion under various mappings and under the formation of products. Turning to construction, we consider the class of compact monotonically normal spaces. It is well-known that it contains the class of spaces which are the continuous images of compact ordered spaces but it is still open as to whether they are actually distinct classes. Using Watson's resolutions, we give a method for constructing monotonically normal spaces. Though this also preserves continuous images of arcs, we show that it is because of a powerful result of Cornette rather than any trivial observation. We also examine more closely monotone normality in images of compact ordered spaces using the Collins-Roscoe structuring mechanism. From this, we extract a strong instance of the mechanism, linear chain (F), which is held by all images of ordered compacta and all proto-metrizable spaces and implies Junnila's concept of utter normality. Elementary submodels are an important tool in the construction of topological spaces. We develop a general method for applying them in varying circumstances and illustrate it by constructing three examples: Balogh's Q-set space, Rudin's normal but not collectionwise Hausdorff space and Balogh's small Dowker space.

Minimal Walks are a method of demonstrations in set theory and general topology. Although the main work of this document will be the construction of the L space, we intend to explain walk\'s fundamentals in a bit more detail. / Passeios mínimos são um método de demonstrações em teoria dos conjuntos e topologia geral. Apesar do trabalho principal dessa dissertação ser a existência do L espaço, a intenção é explicar os fundamentos dos passeios mínimos um tanto detalhadamente.

Minimal Walks are a method of demonstrations in set theory and general topology. Although the main work of this document will be the construction of the L space, we intend to explain walk\'s fundamentals in a bit more detail. / Passeios mínimos são um método de demonstrações em teoria dos conjuntos e topologia geral. Apesar do trabalho principal dessa dissertação ser a existência do L espaço, a intenção é explicar os fundamentos dos passeios mínimos um tanto detalhadamente.

Dado um semigrupo S e a topologia discreta sobre ele, é possível estender a operação ao compactificado de Stone-Cech beta(S) de forma que seja contínua à direita. Diversas propriedades algébricas tais como cancelatividade, comutatividade e ser grupo implicam em propriedades algébrico-topológicas de beta(S). Em particular, o conjunto dos naturais com a soma e/ou o produto é o mais explorado: resultados tais como a existência de 2^c ideais á esquerda minimais e de cadeias decrescentes de idempotentes são mostrados e suas consequências discutidas. / Given a semigroup S and its discrete topology, it is possible to extend its operation to its Stone-Cech compactification beta(S) so that it is right-continuous. Several algebraic properties such as cancellativity, commutativity annd being a group influence topological-algebraic properties of beta(S). Most especially, the set of natural numbers with addition and/or multiplication is explored: results such as the existence of 2^c minimal left ideals or of decreasing chains of idempotents are shown and their consequences analysed.

On étudie les feuilletages transversalement affines des surfaces compactes, avec ou sans bord. On met en relation plusieurs méthodes de construction de tels feuilletages: application de premier retour et échanges d'intervalles affines (pour un feuilletage pas nécessairement orientable); mesure brisée sur un réseau ferroviaire; feuilletage mesuré sur le revêtement universel avec automorphismes du revêtement agissant de manière affine; recollement le long de leur bord de surfaces munies de feuilletages affines. On étudie l'injectivité des applications à image dans l'espace des classes d'équivalence des feuilletages transversalement affines qui résultent de ces diverses constructions.

Mathematics education is a constant topic of conversation in the United States. Many attempts have been made historically to reform teaching methods and improve student results. Particularly, past ideas have emphasized problem-solving to make math feel more applicable and enjoyable. Many have additionally tackled the widespread problem of “math anxiety” by creating lessons that are more discussion-based than drill-based to shift focus from speed and accuracy. In my project, I explored past reform goals and some added goals concerning students' perceptions of mathematics. To do so, I created and tested a pilot workshop in topology, a creative and intuitive field, for use in 4th-6th grade classrooms. Preliminary results suggest some success in altering student views on mathematics.

The work in this thesis contains some contributions to constructive point-free topology and the theory of apartness spaces. The first two papers deal with constructive domain theory using formal topology. In Paper I we focus on the notion of a domain representation of a formal space as a way to introduce generalized points of the represented space, whereas we in Paper II give a constructive and point-free treatment of the domain theoretic approach to differential calculus. The last two papers are of a slightly different nature but still concern constructive topology. In paper III we consider a measure theoretic covering theorem from various constructive angles in both point-set and point-free topology. We prove a point-free version of the theorem. In Paper IV we deal with issues of impredicativity in the theory of apartness spaces. We introduce a notion of set-presented apartness relation which enables a predicative treatment of basic constructions of point-set apartness spaces.

Thesis (M.A.)--Carleton University, 2001. / Includes bibliographical references (p. 230-240). Also available in electronic format on the Internet.