There are two main tools for determining the stability of nonlinear partial differential equations (PDEs): Lyapunov Theory and linearization. The former has the advantage of providing stability results for nonlinear equations directly, while the latter considers the stability of linear equations and then further justification is needed to show the linear stability implies local stability of the nonlinear equation. Linearization has the advantage of investigating stability on a simpler equation; however, the justification can be difficult to prove. Both Lyapunov Theory and linearization are applied to the Landau--Lifshitz equation, a nonlinear PDE that describes the behaviour of magnetization inside a magnetic object. It is known that the Landau-Lifshitz equation has an infinite number of stable equilibrium points. We present a control that forces the system from one equilibrium to another. This is proved using Lyapunov Theory. The linear Landau--Lifshitz equation is also investigated because it provides insight to the nonlinear equation. The linear model is shown to be well--posed and its eigenvalue problem is solved. The resulting eigenvalues suggest an appropriate control for the nonlinear Landau--Lifshitz equation. Mathematically, the control causes the initial equilibrium to no longer be an equilibrium and the second point to be an asymptotically stable equilibrium point. This implies the magnetization has moved to the second equilibrium and hence the control objective is successfully achieved. The existence of multiple stable equilibria is closely related to hysteresis. This is a phenomenon that is often characterized by a looping behaviour; however, the existence of a loop is not sufficient to identify hysteretic systems. A more precise definition is required, which is presented, and applied to the Landau--Lifshitz equation (both linear and nonlinear) to establish the presence of hysteresis.

We study the (strong-)Gibbsian character on R Z d of the law at time t of an infinitedimensional gradient Brownian diffusion / when the initial distribution is Gibbsian.

Thesis (M.S.)--State University of New York at Binghamton, Computer Science Department, 2006. / Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 51-52).

Dan Kiley (American, 1912-2004) is one of the most highly regarded modernist landscape architects of the 20th century. As described in Kiley scholarship to-date, his decades-long practice exhibits a commitment to modernism inspired by classical landscape elements and modernist spatial techniques as a means of recreating the experience of a “walk in nature”. An unexamined aspect of Kiley scholarship is his consistent references to infinity in published writing and interviews, references which date as far back as the 1960s and continue into the 1990s, and therefore span much of his professional career. These references to infinity are often used to describe a personal appreciation of nature as well as an intentional approach to design. Through an analysis of these references, literature review of Kiley scholarship, interviews with selected Kiley colleagues, and archival research and site visits of five case studies (Miller Garden, North Christian Church, Fountain Place, Kiley Garden, and Donald J. Hall Sculpture Garden), this thesis examines the way in which Kiley referred to infinity and how he may have expressed infinity in his designed landscapes. This examination is contextualised within the histories of the ideas of infinity and artificial infinity in mathematics, theology, cosmology, art, and design. The history of the artificial infinite is synthesised into an updated taxonomy of expressions of the artificial infinite which is applied for an analysis of the case studies. The five case studies illustrate varying levels of richness and clarity, where expressions of the artificial infinite are spatially distributed and/or layered, connective and/or isolated (horizontally and/or vertically), and clearly expressed and/or interrupted. This analysis of the artificial infinite in the landscape architecture of Dan Kiley deepens our understanding of his design approach, connects Kiley to a longer and broader history of cultural ideas and expression, leads to a more nuanced understanding of modernist landscape architecture in the USA, broadens our understanding of the expression of infinity in landscape architecture, and demonstrates the applicability of an interpretive technique grounded in aesthetic analysis that could be applied to both art and design.

In a world where technology advances, it is important that the human-computer interface follows in the same pace, to maximize the user experience. This means that when the machines become more powerful and the services become more comprehensive, it is important that they still are adapted to the users.In the web browsing world, a concept called infinite-scroll has become popular when trying to maximise the user experience. This technique uses JavaScript to dynamically load more content to a webpage whilst the user is scrolling without ever reloading the page, to achieve a more fluid experience. This technique is used widely in social media websites such as Facebook and Twitter among others.However, this technique have been used very rarely on other types of websites. Why this could be the case and how infinite-scroll performs on an intranet will be described in this report. A quantitative study on how the user behaviour differs between a website with pagination and infinite-scroll has been conducted and analysed by gathering statistics through Google Analytics about how users interacts with the website in question. The study indicates that infinite-scroll can be useful on an intranet when adapted according to usability guidelines.

In the present paper, an attempt is made to obtain the potential distribution in the case of two such charges, a source-sink combination, located on the axis of a bore hole drilled through an infinite, homogeneous medium.

This work provides a detailed account of the historical role of the distinction between the potential and actual infinite in a variety of debates within natural philosophy and mathematics. It then connects these historical positions to modern debates over the possibility of pluralism within philosophy of logic and mathematics. In particular, it defends a view under which theories of the infinite and logic are justified abductively, and it argues that this abductive methodology provides space for an interesting pluralism about both the infinite and logical consequence. This argument relies on a detailed and thorough historical investigation into ancient, medieval, early modern, and modern views of the infinite, revealing a range of background metaphysical and epistemological commitments that motivate different abductive criteria for sophisticated philosophical positions on the infinite. It then suggests that charitable interpretations of the historical positions on the infinite should lead one to endorse a logical pluralism.

Reliable operation of every day use computing system, from simple coffee machines to complex flight controller system in an aircraft, is necessary to save time, money, and in some cases lives. System testing can check for the presence of unwanted execution but cannot guarantee the absence of such. Probabilistic model checking techniques have demonstrated significant potential in verifying performance and reliability of various systems whose execution are defined with likelihood. However, its inability to scale limits its applicability in practice. This thesis presents a new model checker, STAMINA, with efficient and scalable model truncation for probabilistic verification. STAMINA uses a novel model reduction technique generating a finite state representations of large systems that are amenable to existing probabilistic model checking techniques. The proposed method is evaluated on several benchmark examples. Comparisons with another state-of-art tool demonstrates both accuracy and efficiency of the presented method.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18402号 / 情博第517号 / 新制||情||91(附属図書館) / 31260 / 京都大学大学院情報学研究科複雑系科学専攻 / (主査)教授 山本 裕, 教授 西村 直志, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM