The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.

M.Ing. (Electrical and Electronic Engineering) / This dissertation deals with the mapping of an unknown environment. Mapping of an environment can be accomplished by asking the question “What is in my world?” whilst moving through the environment. Once the objects occupying the ‘world’ have been discovered, the locations of these objects are stored somewhere (for example on paper), so that the environment can be navigated at a later stage. In the context of robots, a map provides the robot with a certain degree of “intelligence”. Several different types of applications are available for robots with “intelligence”; ranging from mining applications, to search and rescue situations, to surveillance applications and recognisance applications. The research hypothesis posed by this dissertation is as follows: Produce a human readable map for an unknown defined structured environment using a single laser range finder (LRF). The focus was on mapping environments resembling mine tunnels. In mine tunnel environments sensors, such as wheel odometers, can fail. This failure makes it advantageous to be able to create a map of the environment with the data obtained solely from the LRF. For this dissertation, the following restrictions were placed on the environment being mapped. It had to be structured (i.e. the environment could be described by simple geometric primitives such as lines); it had to be static (the only entity allowed to move in the environment was the LRF to obtain data); and the environment had to be defined (i.e. have a starting and ending point). During the course of this Masters research, it was discovered that in order to create a human readable map, one has to determine the accurate localisation of the sensor in the environment whilst mapping. The described scenario is a typical problem in mapping and is referred to as the ‘simultaneous localisation and mapping (SLAM) problem’. This dissertation shows results when mapping was done with – and without – accurate localisation. The final approach used to create the human readable map consisted of determining scan matched odometry (based on a feature matching and ICP algorithm). The scan matched odometry is incorporated into a grid-based SLAM technique that utilises a particle filter to accurately determine the position of the sensor in the environment, in order to create a human readable map of the environment. The algorithm used (as described) was able to close loops (i.e. the mapping algorithm was able to handle the sensor returning to its starting point) and it produced satisfactory results for the types of environments as required by the scope of this dissertation.

Orientador: Jorge Tulio Mujica Ascui / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-07T16:44:31Z (GMT). No. of bitstreams: 1 Takatsuka_Paula_D.pdf: 3540981 bytes, checksum: 643e40ac81900cf042cfe1cfb3737b0d (MD5) Previous issue date: 2006 / Resumo: Este trabalho estende teoremas clássicos da teoria de funções holomorfas de uma variável complexa para espaços localmente convexos de dimensão infinita. Serão dadas várias caracterizações de famílias normais, n¿ao apenas com relação à topologia compacto-aberta, mas também para outras topologias naturais no espaço de aplicações holomorfas. Teoremas de tipo Montel e de tipo Schottky, bem como outros resultados correlatos, ser¿ao estabelecidos em dimensão infinita para as diferentes topologias. Teoremas de limita¸c¿ao universal sobre famílias de funções holomorfas que omitem dois valores distintos ser¿ao formulados para espaços de Banach / Abstract: The present work extends some classical theorems from the theory of holomorphic functions of one complex variable to infinite dimensional locally convex spaces. Several characterizations of normal families are given, not only for the compact-open topology, but also for other natural topologies on spaces of holomorphic mappings. Montel-type and Schottky-type theorems and various related results are established in infinite dimension for these different topologies. Universal boundedness theorems concerning families of holomorphic functions which omit two distinct values are formulated for Banach spaces / Doutorado / Mestre em Matemática

Every continuous convex function defined on a separable Banach space is Gateaux differentiable on a dense G^ subset of the space E [Mazur]. Suppose we are given a sequence (xn) that Is dense in E. Can we always find a Gateaux differentiable point x such that x = z^=^anxn.for some sequence (an) with infinitely many non-zero terms so that Ση∞=1||anxn|| < co ? According to this paper, such points are called of "simple type," and shown to be dense in E. Mazur's theorem follows directly from the result and Rybakov's theorem (A countably additive vector measure F: E -* X on a cr-field is absolutely continuous with respect to |x*F] for some x* e Xs) can be shown without deep measure theoretic Involvement.

This dissertation is a study of the dynamics of one-dimensional unimodal maps and is mainly concerned with those maps which are trapezoidal. The trapezoidal function, f_e, is defined for eΣ(0,1/2) by f_e(x)=x/e for xΣ[0,e], f_e(x)=1 for xΣ(e,1-e), and f_e(x)=(1-x)/e for xΣ[1-e,1]. We study the symbolic dynamics of the kneading sequences and relate them to the analytic dynamics of these maps. Chapter one is an overview of the present theory of Metropolis, Stein, and Stein (MSS). In Chapter two a formula is given that counts the number of MSS sequences of length n. Next, the number of distinct primitive colorings of n beads with two colors, as counted by Gilbert and Riordan, is shown to equal the number of MSS sequences of length n. An algorithm is given that produces a bisection between these two quantities for each n. Lastly, the number of negative orbits of size n for the function f(z)=z^2-2, as counted by P.J. Myrberg, is shown to equal the number of MSS sequences of length n. For an MSS sequence P, let H_ϖ(P) be the unique common extension of the harmonics of P. In Chapter three it is proved that there is exactly one J(P)Σ[0,1] such that the itinerary of λ(P) under the map is λ(P)f_e is H_ϖ(P). In Chapter four it is shown that only period doubling or period halving bifurcations can occur for the family λf_e, λΣ[0,1]. Results concerning how the size of a stable orbit changes as bifurcations of the family λf_e occur are given. Let λΣ[0,1] be such that 1/2 is a periodic point of λf_e. In this case 1/2 is superstable. Chapter five investigates the boundary of the basin of attraction of this stable orbit. An algorithm is given that yields a graph directed construction such that the object constructed is the basin boundary. From this we analyze the Hausdorff dimension and measure in that dimension of the boundary. The dimension is related to the simple β-numbers, as defined by Parry.

We present a new approach to information fusion of web data sources. It is based on peer-to-peer mappings between sources and utilizes correspondences between their instances. Such correspondences are already available between many sources, e.g. in the form of web links, and help combine the information about specific objects and support a high quality data fusion. Sources and mappings relate to a domain model to support a semantically focused information fusion. The iFuice architecture incorporates a mapping mediator offering both an interactive and a script-driven, workflow-like access to the sources and their mappings. The script programmer can use powerful generic operators to execute and manipulate mappings and their results. The paper motivates the new approach and outlines the architecture and its main components, in particular the domain model, source and mapping model, and the script operators and their usage.

Les équivalences sous-linéairement bilipschitziennes ont été introduites par Yves Cornulier afin de décrire les cônes asymptotiques des groupes de Lie. Elles généralisent les quasiisométries. Cette thèse construit des invariants pour l'équivalence sous-linéairement bilipschitzienne entre groupes et espaces hyperboliques au sens de Gromov, en utilisant l'analyse au bord de Gromov. Une classe d'application généralisant les homéomorphismes quasisymétriques, et une dimension conforme associée, sont introduites. Les espaces riemannien de type non-compact et de rang un, ainsi que certains espaces homogènes de courbure strictement négative, sont classifiés à équivalence sous-linéairement bilipschitzienne près. / Sublinearly biLipschitz equivalences have been introduced by Yves Cornulier as a means of describing the asymptotic cones of Lie groups; they include and generalize quasiisometries. This thesis provides invariants for sublinearly biLipschitz equivalence between Gromov-hyperbolic groups and spaces using analysis on the Gromov boundary. A class of applications generalizing quasisymmetric mappings, and a corresponding conformal dimension, are introduced as tools. Riemannian symmetric spaces of noncompact type as well as a subclass of homogeneous negatively curved Riemannian manifolds are classified up to sublinearly biLipschitz equivalence.

Since 2018, privacy notices are required by websites to inform users of their use of cookies where the users can choose whether or not they want to accept the cookies. While the use of privacy notices theoretically provides the ability for users to be in charge of their own privacy online, there are issues regarding privacy notices that lead to that they hardly ever work in practice. The reasons for this are many but center around that privacy notices are designed to manipulate users to accept cookies rather than to inform and encourage users to make deliberate choices. In light of this, the purpose of this study is to evaluate whether or not the two principles from choice architecture, defaults and mappings, are an appropriate approach to improve users' understanding and affect their decision-making process regarding privacy notices. The study used a combination of qualitative methods and contained a screening survey, prototype testing and interviews. The screening survey was used to select appropriate participants who later conducted the prototype testing and interviews. Four prototypes displaying four different privacy notices were designed and presented to the participants. Each participant was randomly assigned one of the prototypes and later asked questions regarding their interaction with and understanding of the privacy notice. The data collected was analyzed using a thematic analysis. The results derived from the analysis revealed that a majority of the participants did not read the privacy notice. Further, the factors that influenced participants’ interactions with the privacy notice were mainly habitual rather than affected by the specific prototype they were presented with. Based on the results, it can be concluded that defaults may impact the user’s decision due to visual cues. However, neither defaults nor mappings worked as an encouragement for the user to make a well-informed and deliberate choice.

The objective of this dissertation is to present a modeling and simulation methodology for MEMS devices and identify and understand the associated nonlinearities due to large deflections, electric actuation, impacts, and friction. In the first part of the dissertation, we introduce a reduced-order model of flexible microplates under electric excitation. The model utilizes the von Karman plate equations to account for geometric nonlinearities due to large plate deflections. The Galerkin approach is employed to reduce the partial-differential equations of motion and associated boundary conditions into a finite dimensional system of nonlinearly coupled ordinary-differential equations. We use the reduced-order model to analyze the mechanical behavior of a simply supported microplate and a fully clamped microplate. Effect of various design parameters on both the static and dynamic characteristics of microplates is studied. The second part of the dissertation presents comprehensive modeling and simulation tools for impact microactuators. Nonsmooth dynamics due to impacts and friction are studied, combining various approaches, including direct numerical integration, root-finding technique for periodic motions, continuation of grazing periodic orbits, and local analysis of the near grazing dynamics. The transition between nonimpacting and impacting long term motions, referred to as grazing bifurcations, indicates the transition between on and off states of an impact microactuator. Three different on-off switching mechanisms are identified for the Mita microactuator. These mechanisms also generalize to arbitrary impacting systems with a similar nonlinearity. A local map based on the concept of discontinuity mapping provides an effcient and accurate tool for the grazing bifurcation analysis. Nonlinear impacting dynamics of the microactuator are studied in detail to identify various bifurcations and parameter ranges corresponding to chaotic motions. We find that the frequency-response curves of the impacting dynamics are significantly different from those of the nonimpacting dynamics. / Ph. D.

京都大学 / 新制・課程博士 / 博士(人間・環境学) / 甲第24698号 / 人博第1071号 / 新制||人||251(附属図書館) / 2022||人博||1071(吉田南総合図書館) / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)准教授 木坂 正史, 教授 角 大輝, 教授 足立 匡義, 教授 諸澤 俊介 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM