Um dos teoremas conhecidos de Poincaré afirma: Seja f um homeomorfismo do círculo que preserva orientação. Se p/q, com mdc(p, q) = 1, é o número de rotação de f, então f possui um ponto periódico de período q. Quando o conceito de número de rotação para um homeomorfismo do círculo é generalizado para um homeomorfismo f : T2 ? T2 homotópico à identidade, o resultado é um subconjunto convexo do plano R2, chamado conjunto de rotação e é denotado por ½(F) onde F é um levantamento de f. No caso que ½(F) tem interior não vazio, J. Franks obteve resultados análogos ao Teorema de Poincaré. Nesta dissertação estudamos um resultado análogo, obtido por Jonker e Zhang, quando ½(F) não tem interior. Mais precisamente: assumimos que ½(F) é um segmento de reta com inclinação irracional e mostramos que se 1 n(p1, p2) ? ½(F), com mdc(p1, p2, n) = 1, então f possui um ponto periódico de período n / One of the well know results of Poincaré state: Let f be an orientation preserving circle homeomorphism. If p/q, with mdc(p, q) = 1, is the rotation number of f, then there is a periodic point for f whose period is q. When the concept of rotations number, for orientation preserving circle homeomorphism, is generalized for torus homeomorphism f : T2 ? T2 that are homotopic to the identity, it results in a convex subset of R2, called rotation set and is denoted by ½(F) where F is a lifting of f. In the case that ½(F) has non-empty interior, J. Franks proved similar results to the Poincaré Theorem. In this work, when ½(F) has empty interior, we study an similar result obtained by Jonker and Zhang. More precisely: they suppose that the rotation set ½(F) is a line segment with irrational slope and demonstrate that if 1 n(p1, p2) ? ½(F), with mdc(p1, p2, n) = 1, then f has a periodic point of period n

by Aylwin Chung-Fai, Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 117-118). / Abstract --- p.i / Acknowledgement --- p.iii / List of Tables --- p.v / List of Figures --- p.vi / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- BLAS-3 Operations --- p.2 / Chapter 1.2 --- Organization of Thesis --- p.2 / Chapter 1.3 --- Contribution --- p.3 / Chapter 2 --- Background Studies --- p.4 / Chapter 2.1 --- Registers & Cache Memory --- p.4 / Chapter 2.2 --- Previous Research --- p.6 / Chapter 2.3 --- Problem of Register & Cache --- p.8 / Chapter 2.4 --- BLAS-3 Operations On RISC Microprocessor --- p.10 / Chapter 3 --- Compiler Optimization Techniques for BLAS-3 Operations --- p.12 / Chapter 3.1 --- One-Dimensional Q-Way J-Loop Unrolling --- p.13 / Chapter 3.2 --- Two-Dimensional P×Q -Ways I×J-Loops Unrolling --- p.15 / Chapter 3.3 --- Addition of Code to Remove Redundant Code --- p.17 / Chapter 3.4 --- Simulation Result --- p.17 / Chapter 3.5 --- Summary --- p.23 / Chapter 4 --- Architectural Model of Very Large Register File --- p.25 / Chapter 4.1 --- Architectural Model --- p.26 / Chapter 4.2 --- Traditional Register File vs. Very Large Register File --- p.32 / Chapter 5 --- Ideal Case Study of Very Large Register File --- p.35 / Chapter 5.1 --- Matrix Multiply --- p.36 / Chapter 5.2 --- LU Decomposition --- p.41 / Chapter 5.3 --- Convolution --- p.50 / Chapter 6 --- Worst Case Study of Very Large Register File --- p.58 / Chapter 6.1 --- Matrix Multiply --- p.59 / Chapter 6.2 --- LU Decomposition --- p.65 / Chapter 6.3 --- Convolution --- p.74 / Chapter 7 --- Proposed Case Study of Very Large Register File --- p.81 / Chapter 7.1 --- Matrix Multiply --- p.82 / Chapter 7.2 --- LU Decomposition --- p.91 / Chapter 7.3 --- Convolution --- p.102 / Chapter 7.4 --- Comparison --- p.111 / Chapter 8 --- Conclusion & Future Work --- p.114 / Chapter 8.1 --- Summary --- p.114 / Chapter 8.2 --- Future Work --- p.115 / Bibliography --- p.117

It is recognised that normative systems, and in particular electronic institutions and contracts are a potentially powerful means for making agent interactions in multi-agent systems effective and efficient. However, correctly specifying the behaviour of such systems is a difficult problem. Designers are faced with two concurrent, complex tasks: firstly they must specify the relationships (over time) between agents’ actions and their effects, and secondly they must also consider how agents’ actions are to be regulated through the definition of agents’ permissions and obligations. Such systems are typi- cally complex, and given this complexity it may be difficult for a designer to determine whether their original objectives have been captured by the specification of the system. In this dissertation we seek to address some of the problems associated with institu- tional specification. In order to do this we present a model for specifying institutions based on the notion of socially constructed reality that accounts not only for how the action and events which constitute the institution are described, but also how they are regulated. Institutions may be used in a number of ways, and may account for concepts at varying levels of abstraction. Recognising this we also investigate how several insti- tutions, each accounting for a particular aspect of a society may be composed and how the relationships between these institutions may be expressed. Given this model, we then demonstrate how, using the answer set programming paradigm institutional spec- ifications based on our model may be checked for the absence or presence of certain (un)desirable properties.

No description available.

Numerical simulation of cell motility is one of the difficult problems in computational science. It belongs to a class of problems which involve moving interfaces between flowing or deforming media. Different numerical techniques are being developed for different application areas and in this work an attempt is made to apply two popular numerical techniques used in the field of computational multiphase flows to a cell motility problem. An unsteady cell motility problem is considered to simulate numerically based on a two-dimensional mathematical model. Two important numerical methods, the Level set method and the Front tracking methods are applied to the cell motility problem to study several cases and to verify the convergence of the solution. With the assumption of no mechanical or physical obstructions to the cell, the results of the numerical simulations show that the domain shapes converge to a circular shape as they reach the steady state condition. The final steady state velocities with which the domains move and the final steady state area to which they converge are observed to be independent of domain shapes. Moreover all shapes converge to exactly same radius of circle and move with same velocity after reaching steady state condition.

This thesis considers a novel problem of obtaining global channel state information (CSI) at every node in an ad-hoc wireless network. A class of protocols for dissemination and estimation are developed which attempt to minimize the staleness of the estimates throughout the network. This thesis also provides an optimal protocol for CSI dissemination in networks with complete graph topology and a near optimal protocol in networks having incomplete graph topology. In networks with complete graph topology, the protocol for CSI dissemination is shown to have a resemblance to finding Eulerian tours in complete graphs. For networks having incomplete graph topology, a lower bound on maximum staleness is given and a near optimal algorithm based on finding minimum connected dominating sets and proper scheduling is described in this thesis.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 100-102. / by Robert Alan Proctor. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: p. 135-138. / by James William Walker. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Bibliography: leaves 106-109. / by Rae Michael Andrew Shortt. / Ph.D.

Este trabalho está preocupado com o conceito de medida e dimensão de Hausdorff usando ferramentas matemáticas adequadas. Como, frequentemente, é importante e difícil determinar a dimensão Hausdorff 1 de um conjunto e ainda mais difícil de encontrar ou mesmo estimar a sua medida Hausdorff, por auto proteção é usado o conjunto ternário de Cantor. A construção ternária simplifica certas dificuldades técnicas sobre a teoria da dimensão. O conjunto de Cantor é um exemplo interessante de um conjunto magro, perfeito, compacto e não enumerável, cuja medida e dimensão topológica são nulas. A análise de muitas das suas propriedades e consequências interessantes nos campos da teoria dos conjuntos e da topologia nos oferece uma rota direta que leva à medida Hausdorff do conjunto Cantor e sua dimensão fractal que é igual à sua dimensão Hausdorff. Também é calculada a dimensão Hausdorff para alguns fractais clássicos, como o tapete Sierpinski e a curva de flocos de neve von Koch. / This work is concerned with the concept of Hausdorff measure and dimension using suitable mathematical tools. Since it is often important and dificult to determine the Hausdorff dimension2 of a set and even harder to find or even to estimate its Hausdorff measure, by self-protection choices, it is used the ternary Cantor set. The ternary construction reduces technical difficulties about dimension theory. Cantor set is an interesting example of a meager, perfect, compact, uncountable set whose measure and topologic dimension are zero. Analysis of many of its interesting properties and consequences in the fields of set theory and topology provides a direct route that leads to the Hausdorff measure of the Cantor set and its fractal dimension that is equal to its Hausdorff dimension. It is also computed the Hausdorff dimension for some classical fractals such as the Sierpinski carpet and the von Koch snowflake curve.