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The purpose of this thesis is to study the concept of measure and associated concepts. The study is general in nature; that is, no particular examples of a measure are given.

Approved for public release; distribution is unlimited / The United States Government and private industry are facing challenges in attempting to secure their computer network infrastructure. The purpose of this research was to capture current lessons learned from Government and Industry with respect to solving particular problems associated with the secure management of large networks. Nine thesis questions were generated to look at common security problems faced by enterprises in large networks. Research was predominantly gathered through personal interviews with professionals in the computer security area from both the public and private sector. The data was then analyzed to compile a set of lessons learned by both the public and private sector regarding several leading computer security issues. Some of the problems were challenges such as maintaining and improving security during operating systems upgrades, analyzing lessons learned in configurations management, employee education with regards to following policy and several other challenging issues. The results of this thesis were lessons learned in the areas of employee education, Government involvement in the computer security area and other key security areas. An additional result was the development of case studies based upon the lessons learned. / Naval Postgraduate School author (civilian).

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In the first chapter; we consider the invariant measure mu generated by an integral self-affine IFS. We prove that any integral self-affine measure with a common contracting matrix can be expressed as a vector-valued self-affine measure with an IFS satisfying the open set condition (OSC). The same idea can also be applied to scaling functions of refinement equations, we extended a well known necessary and sufficient condition for the existence of L1-solutions of lattice refinement equations. We then apply this vector-valued form to study the integral self-affine sets, we obtain an algorithm for the Lebesgue measure of integral self-affine region and an algorithm for the Hausdorff dimension of a class of self-affine sets. The vector-value setup also provides an easy way to consider the L q-spectrum and the multifractal formulism for self-similar measures. As an application we can conclude the differentiability of the Lq spectrum (for q > 0) of any integral self-similar measure with a common contracting matrix. / In this thesis, we study the invariant measures and sets generated by iterated function systems (IFS). The systems have been extensively studied in the frame work of Hutchinson [Hut]. For the iteration, it is often assumed that the IFS satisfies the open set condition (OSC), a non-overlap condition in the iteration. One of the advantage of the OSC is that the point in K can be uniquely represented in a symbolic space except for a mu-zero set and many important results have been obtained. Our special interest in this thesis is to transform an invariant measure with overlaps to a vector-valued form with non overlaps. The advantage of this vector-valued form is that locally the measure can be expressed as a product of matrices. / The problem considered in the third chapter is on the choice of the invariant open set in the finite type condition (FTC). From definition, the FTC depends on the choice of the invariant open set. We show that, in one dimensional case, if the IFS satisfies the FTC for some invariant open interval then it satisfies the FTC with all invariant open sets. To our surprising, we find a counter-example to show that, in high dimensional case, the invariant open set can not be chosen arbitrarily even if the IFS satisfies the OSC and generates a tile. / The second chapter is devoted to the absolute continuity of self-affine (real-valued or vector-valued) measures and some properties of the boundary of the invariant set. For self-similar IFS with a common contracting ratio, there is a necessary and sufficient condition for the self-similar measure to be absolutely continuous with respect to the Lebesgue measure (under the weak separation condition (WSC)). In our consideration we first extend the definition of WSC to self-affine IFS. Then we generalize the previous condition to obtain a necessary and sufficient condition for the self-affine vector-valued measures to be absolutely continuous with respect to the Lebesgue measure. As an application, we prove that the boundary of all integral self-affine set has zero Lebesgue measure. In addition, we prove that, for any IFS and any invariant open set V, the corresponding invariant (real-valued or vector-valued) measure is supported either in V or in ∂ V. / by Deng Qirong. / "March 2005." / Adviser: Ka-Sing Lau. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0301. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 87-91). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

by Wang Xiang-Yang. / "May 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 95-99). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

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This dissertation is in the area of complex dynamics, more specifically focused on the iteration of rational functions. Given a well-chosen family of rational functions, parameterized by a complex parameter, we are especially interested in regularity properties of the Hausdorff dimension of Julia sets of these polynomials considered as a function of the parameters. In this dissertation I deal with a family of polynomials of degree at least 3 depending in a holomorphic way on a parameter, focusing on the point where the dynamics and topology of the polynomials drastically change. In such a context proving continuity is quite challenging while real analyticity will most likely break. Our approach will, on the one hand, build on the existing methods of proving continuity of Hausdorff dimension, primarily based on proving continuity, in the weak* topology of measures on the Riemann sphere, of canonical conformal measures, but will also require methods which, up to my best knowledge, have not been implemented anywhere yet. Our main result gives a surprising example where the Hausdorff dimension of the Julia set is continuous in the parameter, but where the Julia set itself is not.

The purpose of this study was to develop a conceptual framework to enhance the redesign of a safety system. To identify the limitations of the current safety system, the concepts of congruency and integration of the safety function within a specific university environment were examined through a case study methodology. An emphasis was placed on the use of models from business and management literature for both the examination of the concepts and the subsequent development of the conceptual framework for the redesign. The researcher emphasized the use of multiple data sources in this study. These sources included: observations, documents, and interviews. A model from French and Bell (1990) was used to examine congruency which included interviewing two stakeholders associated with executive driven planned organizational change processes as well as the safety manager. A perception survey, as suggested by Petersen (1994), was developed and used as part of the examination of safety system integration and administered to twenty interviewees along with the safety manager. The findings provided evidence of gaps which may be hindering the success of the safety function within the organization. By examining organizational direction and comparing those findings to the findings representing the direction of the safety function, gaps in congruency were found. Integration gaps were discovered, in part, through examination of the safety process input, as described by the safety manager, as well as the safety process output as viewed by "customers" of the safety process. Countermeasures to close gaps were discovered in the research and later synthesized into a redesigned conceptual framework. The framework emphasized customer service, a systems approach, and a process perspective as an alternative to the legacy of a traditional, compliance driven safety system found to be in current use. / Graduation date: 1998

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