Wong Sze Hon. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 88-91). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Preliminaries --- p.1 / Chapter 1.2 --- Motivations --- p.1 / Chapter 1.3 --- Contributions --- p.3 / Chapter 1.4 --- Organization of the Thesis --- p.4 / Chapter 2 --- VLSI Physical Design Automation --- p.5 / Chapter 2.1 --- Preliminaries --- p.5 / Chapter 2.2 --- VLSI Design Cycle [1] --- p.6 / Chapter 2.2.1 --- System Specification --- p.6 / Chapter 2.2.2 --- Architectural Design --- p.6 / Chapter 2.2.3 --- Functional Design --- p.6 / Chapter 2.2.4 --- Logic Design --- p.8 / Chapter 2.2.5 --- Circuit Design --- p.8 / Chapter 2.2.6 --- Physical Design --- p.8 / Chapter 2.2.7 --- Fabrication --- p.8 / Chapter 2.2.8 --- Packaging and Testing --- p.9 / Chapter 2.3 --- Physical Design Cycle [1] --- p.9 / Chapter 2.3.1 --- Partitioning --- p.9 / Chapter 2.3.2 --- Floorplanning and Placement --- p.11 / Chapter 2.3.3 --- Routing --- p.11 / Chapter 2.3.4 --- Compaction --- p.12 / Chapter 2.3.5 --- Extraction and Verification --- p.12 / Chapter 2.4 --- Chapter Summary --- p.12 / Chapter 3 --- Recent Approaches on Circuit Partitioning --- p.14 / Chapter 3.1 --- Preliminaries --- p.14 / Chapter 3.2 --- Circuit Representation --- p.15 / Chapter 3.3 --- Delay Modelling --- p.16 / Chapter 3.4 --- Partitioning Objectives --- p.19 / Chapter 3.4.1 --- Interconnections between Partitions --- p.19 / Chapter 3.4.2 --- Delay Minimization --- p.19 / Chapter 3.4.3 --- Area and Number of Partitions --- p.20 / Chapter 3.5 --- Partitioning Algorithms --- p.20 / Chapter 3.5.1 --- Cut-size Driven Partitioning Algorithm --- p.21 / Chapter 3.5.2 --- Delay Driven Partitioning Algorithm --- p.32 / Chapter 3.5.3 --- Acyclic Circuit Partitioning Algorithm --- p.33 / Chapter 4 --- Clustering Based Acyclic Multi-way Partitioning --- p.38 / Chapter 4.1 --- Preliminaries --- p.38 / Chapter 4.2 --- Previous Works on Clustering Based Partitioning --- p.39 / Chapter 4.2.1 --- Multilevel Circuit Partitioning [2] --- p.40 / Chapter 4.2.2 --- Cluster-Oriented Iterative-Improvement Partitioner [3] --- p.42 / Chapter 4.2.3 --- Section Summary --- p.44 / Chapter 4.3 --- Problem Formulation --- p.45 / Chapter 4.4 --- Clustering Based Acyclic Multi-Way Partitioning --- p.46 / Chapter 4.5 --- Modified Fan-out Free Cone Decomposition --- p.47 / Chapter 4.6 --- Clustering Phase --- p.48 / Chapter 4.7 --- Partitioning Phase --- p.51 / Chapter 4.8 --- The Acyclic Constraint --- p.52 / Chapter 4.9 --- Experimental Results --- p.57 / Chapter 4.10 --- Chapter Summary --- p.58 / Chapter 5 --- Network Flow Based Multi-way Partitioning --- p.61 / Chapter 5.1 --- Preliminaries --- p.61 / Chapter 5.2 --- Notations and Definitions --- p.62 / Chapter 5.3 --- Net Modelling --- p.63 / Chapter 5.4 --- Previous Works on Network Flow Based Partitioning --- p.64 / Chapter 5.4.1 --- Network Flow Based Min-Cut Balanced Partitioning [4] --- p.65 / Chapter 5.4.2 --- Network Flow Based Circuit Partitioning for Time-multiplexed FPGAs [5] --- p.66 / Chapter 5.5 --- Proposed Net Modelling --- p.70 / Chapter 5.6 --- Partitioning Properties Based on the Proposed Net Modelling --- p.73 / Chapter 5.7 --- Partitioning Step --- p.75 / Chapter 5.8 --- Constrained FM Post Processing Step --- p.79 / Chapter 5.9 --- Experiment Results --- p.81 / Chapter 6 --- Conclusion --- p.86 / Bibliography --- p.88

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Gary L. Ebert, Dept. of Mathematical Sciences. Includes bibliographical references.

Thesis (M. Sc.)--Carleton University, 2004. / Includes bibliographical references (p. 38-39). Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 111-116). Available also in a digital version from Dissertation Abstracts.

Orientador: Jose Plinio de Oliveira Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T04:49:07Z (GMT). No. of bitstreams: 1 Andrade_CeciliaPereirade_M.pdf: 439122 bytes, checksum: 1ebde938fe2e698dd7e6b405a6324c2c (MD5) Previous issue date: 2009 / Resumo: Este trabalho está dividido em duas partes. A primeira refere-se a partições, constando dos principais resultados, algumas representações das partições e uma importante ferramenta que são as funções geradoras. A segunda parte apresenta os polinômios gaussianos e alguns teoremas importantes, bem como as identidades de Rogers-Ramanujan. / Abstract: This work is divided into two parts. The rest refers to partitions, consisting of the main results, some representations of the partitions and an important tool that are the generating functions. The second part presents the Gaussian polynomials and some important theorems as well as the identities of Rogers-Ramanujan. / Mestrado / Combinatoria / Mestre em Matemática Aplicada

The counting of fuzzy subsets of a finite set is of great interest in both practical and theoretical contexts in Mathematics. We have used some counting techniques such as the principle of Inclusion-Exclusion and the Mõbius Inversion to enumerate the fuzzy subsets of a finite set satisfying different conditions. These two techniques are interdependent with the M¨obius inversion generalizing the principle of Inclusion-Exclusion. The enumeration is carried out each time we redefine new conditions on the set. In this study one of our aims is the recognition and identification of fuzzy subsets with same features, characteristics or conditions. To facilitate such a study, we use some ideas such as the Hamming distance, mid-point between two fuzzy subsets and cardinality of fuzzy subsets. Finally we introduce the fuzzy scanner of elements of a finite set. This is used to identify elements and fuzzy subsets of a set. The scanning process of identification and recognition facilitates the choice of entities with specified properties. We develop a procedure of selection under the fuzzy environment. This allows us a framework to resolve conflicting issues in the market place.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1979 / Vita. / Bibliography: leaves 96-98. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Mathematics

All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching/contraction and the smearing due to noise. My goal is to determine the `finest attainable' partition for a given hyperbolic dynamical system and a given weak additive white noise. That is achieved by computing the local eigenfunctions of the Fokker-Planck evolution operator in linearized neighborhoods of the periodic orbits of the corresponding deterministic system, and using overlaps of their widths as the criterion for an optimal partition. The Fokker-Planck evolution is then represented by a finite transition graph, whose spectral determinant yields time averages of dynamical observables. The method applies in principle to both continuous- and discrete-time dynamical systems. Numerical tests of such optimal partitions on unimodal maps support my hypothesis.

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Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xii, 97 p.; also includes graphics. Includes bibliographical references (p. 94-97). Available online via OhioLINK's ETD Center