Spelling suggestions: "subject:"[een] SET THEORY"" "subject:"[enn] SET THEORY""
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On Mergelyan's theorem.Borghi, Gerald. January 1973 (has links)
No description available.
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Topological transversality of condensing set-valued mapsKaczynski, Tomasz. January 1986 (has links)
No description available.
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Counting Convex Sets on Products of Totally Ordered SetsBarnette, Brandy Amanda 01 May 2015 (has links)
The main purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the work presented in this thesis. Also, the definitions and notation used throughout the paper are introduced here The second chapter starts with examining the product spaces of the form {1; 2; : : : ;n} × {1; 2}. That is, we begin by analyzing a two-row by n-column space for n > N. Three separate approaches are discussed, and verified, to find the total number of convex sets on the space. A general formula is presented to obtain this total for all n. In the third chapter we take the same {1; 2; : : : ;n} × {1; 2} spaces from Chapter 2 and consider all the scenarios for adding a second disjoint convex set to the space. Adding a second convex set gives a collection of two mutually disjoint sets. Again, a general formula is presented to obtain this total number of such collections for all n. The fourth chapter takes the idea from Chapter 2 and expands it to product spaces {1; 2; : : : ;n} × {1; 2; : : : ;m} consisting of more than two rows. Here the creation of convex sets having z rows from those having z − 1 rows is exploited to obtain a model that will give the total number of z-row convex sets on any n × m space, provided the set occupies z adjacent rows. Finally, the fifth chapter describes all possible scenarios for convex sets to be placed in the {1; 2; : : : ;n}×{1; 2; : : : ;m} space. This chapter then explains the process needed to acquire a count of all convex sets on any such space as well. Chapter 5 ends by walking through this process with a concrete example, breaking it down into each scenario. We conclude by briefly summarizing the results and specifying future work we would like to further investigate, in Chapter 6.
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Covering Matrices, Squares, Scales, and Stationary ReflectionLambie-Hanson, Christopher 01 May 2014 (has links)
In this thesis, we present a number of results in set theory, particularly in the areas of forcing, large cardinals, and combinatorial set theory. Chapter 2 concerns covering matrices, combinatorial structures introduced by Viale in his proof that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. In the course of this proof and subsequent work with Sharon, Viale isolated two reflection principles, CP and S, which can hold of covering matrices. We investigate covering matrices for which CP and S fail and prove some results about the connections between such covering matrices and various square principles. In Chapter 3, motivated by the results of Chapter 2, we introduce a number of square principles intermediate between the classical and (+). We provide a detailed picture of the implications and independence results which exist between these principles when is regular. In Chapter 4, we address three questions raised by Cummings and Foreman regarding a model of Gitik and Sharon. We first analyze the PCF-theoretic structure of the Gitik-Sharon model, determining the extent of good and bad scales. We then classify the bad points of the bad scales existing in both the Gitik-Sharon model and various other models containing bad scales. Finally, we investigate the ideal of subsets of singular cardinals of countable cofinality carrying good scales. In Chapter 5, we prove that, assuming large cardinals, it is consistent that there are many singular cardinals such that every stationary subset of + reflects but there are stationary subsets of + that do not reflect at ordinals of arbitrarily high cofinality. This answers a question raised by Todd Eisworth and is joint work with James Cummings. In Chapter 6, we extend a result of Gitik, Kanovei, and Koepke regarding intermediate models of Prikry-generic forcing extensions to Radin generic forcing extensions. Specifically, we characterize intermediate models of forcing extensions by Radin forcing at a large cardinal using measure sequences of length less than. In the final brief chapter, we prove some results about iterations of w1-Cohen forcing with w1-support, answering a question of Justin Moore.
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Notes on a two cardinal theorem of ShelahBrubacher, Jeff. January 1983 (has links)
No description available.
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Distributed Random Set Theoretic Soft/Hard Data FusionKhaleghi, Bahador January 2012 (has links)
Research on multisensor data fusion aims at providing the enabling technology to combine
information from several sources in order to form a unifi ed picture. The literature
work on fusion of conventional data provided by non-human (hard) sensors is vast and
well-established. In comparison to conventional fusion systems where input data are generated
by calibrated electronic sensor systems with well-defi ned characteristics, research
on soft data fusion considers combining human-based data expressed preferably in unconstrained
natural language form. Fusion of soft and hard data is even more challenging, yet
necessary in some applications, and has received little attention in the past. Due to being
a rather new area of research, soft/hard data fusion is still in a
edging stage with even
its challenging problems yet to be adequately de fined and explored.
This dissertation develops a framework to enable fusion of both soft and hard data
with the Random Set (RS) theory as the underlying mathematical foundation. Random
set theory is an emerging theory within the data fusion community that, due to its powerful
representational and computational capabilities, is gaining more and more attention among
the data fusion researchers. Motivated by the unique characteristics of the random set
theory and the main challenge of soft/hard data fusion systems, i.e. the need for a unifying
framework capable of processing both unconventional soft data and conventional hard data,
this dissertation argues in favor of a random set theoretic approach as the first step towards
realizing a soft/hard data fusion framework.
Several challenging problems related to soft/hard fusion systems are addressed in the
proposed framework. First, an extension of the well-known Kalman lter within random
set theory, called Kalman evidential filter (KEF), is adopted as a common data processing
framework for both soft and hard data. Second, a novel ontology (syntax+semantics)
is developed to allow for modeling soft (human-generated) data assuming target tracking
as the application. Third, as soft/hard data fusion is mostly aimed at large networks of
information processing, a new approach is proposed to enable distributed estimation of
soft, as well as hard data, addressing the scalability requirement of such fusion systems.
Fourth, a method for modeling trust in the human agents is developed, which enables the
fusion system to protect itself from erroneous/misleading soft data through discounting
such data on-the-fly. Fifth, leveraging the recent developments in the RS theoretic data
fusion literature a novel soft data association algorithm is developed and deployed to extend
the proposed target tracking framework into multi-target tracking case. Finally, the
multi-target tracking framework is complemented by introducing a distributed classi fication
approach applicable to target classes described with soft human-generated data.
In addition, this dissertation presents a novel data-centric taxonomy of data fusion
methodologies. In particular, several categories of fusion algorithms have been identifi ed
and discussed based on the data-related challenging aspect(s) addressed. It is intended to
provide the reader with a generic and comprehensive view of the contemporary data fusion
literature, which could also serve as a reference for data fusion practitioners by providing
them with conducive design guidelines, in terms of algorithm choice, regarding the specifi c
data-related challenges expected in a given application.
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The Enhancement Of The Cell-based Gis Analyses With Fuzzy Processing CapabilitiesYanar, Tahsin Alp 01 January 2003 (has links) (PDF)
In order to store and process natural phenomena in Geographic Information
Systems (GIS) it is necessary to model the real world to form computational
representation. Since classical set theory is used in conventional GIS software systems to model uncertain real world, the natural variability in the environmental phenomena can not be modeled appropriately. Because, pervasive imprecision of the real world is unavoidably reduced to artificially precise spatial entities when the conventional crisp logic is used for modeling.
An alternative approach is the fuzzy set theory, which provides a formal
framework to represent and reason with uncertain information. In addition,
linguistic variable concept in a fuzzy logic system is useful for communicating
concepts and knowledge with human beings.
In this thesis, a system to enhance commercial GIS software, namely ArcGIS, with fuzzy set theory is designed and implemented. The proposed system allows users to (a) incorporate human knowledge and experience in the form of linguistically defined variables into GIS-based spatial analyses, (b) handle impreiii cision in the decision-making processes, and (c) approximate complex ill-defined
problems in decision-making processes and classification.
The operation of the proposed system is presented through case studies,
which demonstrate its application for classification and decision-making processes.
This thesis shows how fuzzy logic approach may contribute to a better
representation and reasoning with imprecise concepts, which are inherent characteristics of geographic data stored and processed in GIS.
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Badiou, political nihilism, and a small-scale solutionVizeau, Brent 11 1900 (has links)
In "Badiou, Political Nihilism, and a Small-Scale Solution", I argue that Badious presentation of politics, exclusively on a large scale that of the nation-state betrays his underlying set-theoretic ontology. The consequence of presenting politics on this scale is that political events, opportunities for genuine political engagement, are extremely rare. This leaves potential political actors with little reason to believe they will have the opportunity to engage in politics. The absence of meaningful engagement, along with Badious unique conception of truth, gives rise to the problem of political nihilism. But, just as sets are both composed of sets and couched within others, situations too should be viewed as scalable. Re-presenting politics on a multiplicity of scales overcomes the worry about nihilism, while better capturing the real complexity and texture of political commitments.
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Graph decompositions, theta graphs and related graph labelling techniquesBlinco, A. D. Unknown Date (has links)
No description available.
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A study of Polya's enumeration theoremWilliams, Elizabeth C., January 2005 (has links) (PDF)
Thesis(M.S.)--Auburn University, 2005. / Abstract. Vita. Includes bibliographic references.
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