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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
61

Constructing a v2 Self Map at p=3

Reid, Benjamin 06 September 2017 (has links)
Working at the prime p = 3, we construct a stably finite spectrum, Z, with a v_2^1 self map f. Further, both Ext_A(H*(Z),Z_3) and Ext_A(H*(Z),H*(Z)) have a vanishing line of slope 1/16 in (t-s,s) coordinates, and the map f is represented by an element a of Ext where multiplication by a is parallel to the vanishing line. To accomplish this construction, we prove a result about the connection between particular self maps of spectra and their effect on the Margolis homology of related modules over the Steenrod Algebra.
62

Contributions to the theory of nearness in pointfree topology

Mugochi, Martin Mandirevesa 09 1900 (has links)
We investigate quotient-fine nearness frames, showing that they are reflective in the category of strong nearness frames, and that, in those with spatial completion, any near subset is contained in a near grill. We construct two categories, each of which is shown to be equivalent to that of quotient-fine nearness frames. We also consider some subcategories of the category of nearness frames, which are co-hereditary and closed under coproducts. We give due attention to relations between these subcategories. We introduce totally strong nearness frames, whose category we show to be closed under completions. We investigate N-homomorphisms and remote points in the context of totally bounded uniform frames, showing the role played by these uniform N-homomorphisms in the transfer of remote points, and their relationship with C -quotient maps. A further study on grills enables us to establish, among other things, that grills are precisely unions of prime filters. We conclude the thesis by showing that the lattice of all nearnesses on a regular frame is a pseudo-frame, by which we mean a poset pretty much like a frame except for the possible absence of the bottom element. / Mathematical Sciences / Ph.D. (Mathematics)
63

Model theory of the universal covering spaces of complex algebraic varieties

Gavrilovich, Misha January 2006 (has links)
No description available.
64

Strong classification of [gamma]-structures

Bracho, Javier. January 1981 (has links)
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1981 / Bibliography: leaves 102-103. / by Javier Bracho. / Ph. D. / Ph.D. Massachusetts Institute of Technology, Department of Mathematics
65

Preconditioned sequential and parallel conjugate gradient algorithms for homotopy curve tracking

Irani, Kashmira M. 08 April 2009 (has links)
There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Variants of the conjugate gradient algorithm along with different preconditioners are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. In addition, a parallel version of Craig's method with incomplete LU factorization preconditioning is implemented on a shared memory parallel computer with various levels and degrees of parallelism (e.g., linear algebra, function and Jacobian matrix evaluation, etc.). An in-depth study is presented for each of these levels with respect to the speedup in execution time obtained with the parallelism, the time spent implementing the parallel code and the extra memory allocated by the parallel algorithm. / Master of Science
66

Hopf Invariants in Real and Rational Homotopy Theory

Wierstra, Felix January 2017 (has links)
In this thesis we use the theory of algebraic operads to define a complete invariant of real and rational homotopy classes of maps of topological spaces and manifolds. More precisely let f,g : M -&gt; N be two smooth maps between manifolds M and N. To construct the invariant, we define a homotopy Lie structure on the space of linear maps between the homology of M and the homotopy groups of N, and a map mc from the set of based maps from M to N, to the set of Maurer-Cartan elements in the convolution algebra between the homology and homotopy. Then we show that the maps f and g are real (rational) homotopic if and only if mc(f) is gauge equivalent to mc(g), in this homotopy Lie convolution algebra. In the last part we show that in the real case, the map mc can be computed by integrating certain differential forms over certain subspaces of M. We also give a method to determine in certain cases, if the Maurer-Cartan elements mc(f) and mc(g) are gauge equivalent or not. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 2: Manuscript. Paper 3: Manuscript.</p>
67

Categorical model structures

Williamson, Richard David January 2011 (has links)
We build a model structure from the simple point of departure of a structured interval in a monoidal category — more generally, a structured cylinder and a structured co-cylinder in a category.
68

Parallel schemes for global interative zero-finding.

January 1993 (has links)
by Luk Wai Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 44-45). / ABSTRACT --- p.i / ACKNOWLEDGMENTS --- p.ii / Chapter CHAPTER 1. --- INTRODUCTION --- p.1 / Chapter CHAPTER 2. --- DRAWBACKS OF CLASSICAL THEORY --- p.4 / Chapter 2.1 --- Review of Sequential Iterative Methods --- p.4 / Chapter 2.2 --- Visualization Techniques --- p.8 / Chapter 2.3 --- Review of Deflation --- p.10 / Chapter CHAPTER 3. --- THE IMPROVEMENT OF THE ABERTH METHOD --- p.11 / Chapter 3.1 --- The Durand-Kerner method and the Aberth method --- p.11 / Chapter 3.2 --- The generalized Aberth method --- p.13 / Chapter 3.3 --- The modified Aberth Method for multiple-zero --- p.13 / Chapter 3.4 --- Choosing the initial approximations --- p.15 / Chapter 3.5 --- Multiplicity estimation --- p.16 / Chapter CHAPTER 4. --- THE HIGHER-ORDER ITERATIVE METHODS --- p.18 / Chapter 4.1 --- Introduction --- p.18 / Chapter 4.2 --- Convergence analysis --- p.20 / Chapter 4.3 --- Numerical Results --- p.28 / Chapter CHAPTER 5. --- PARALLEL DEFLATION --- p.32 / Chapter 5.1 --- The Algorithm --- p.32 / Chapter 5.2 --- The Problem of Zero Component --- p.34 / Chapter 5.3 --- The Problem of Round-off Error --- p.35 / Chapter CHAPTER 6. --- HOMOTOPY ALGORITHM --- p.36 / Chapter 6.1 --- Introduction --- p.36 / Chapter 6.2 --- Choosing Q(z) --- p.37 / Chapter 6.3 --- The arclength continuation method --- p.38 / Chapter 6.4 --- The bifurcation problem --- p.40 / Chapter 6.5 --- The suggested improvement --- p.41 / Chapter CHAPTER 7. --- CONCLUSION --- p.42 / REFERENCES --- p.44 / APPENDIX A. PROGRAM LISTING --- p.A-l / APPENDIX B. COLOR PLATES --- p.B-l
69

Laguerre's method in global iterative zero-finding.

January 1993 (has links)
by Kwok, Wong-chuen Tony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves [85-86]). / Acknowledgement / Abstract / Chapter I --- Laguerre's Method in Polynomial Zero-finding / Chapter 1 --- Background --- p.1 / Chapter 2 --- Introduction and Problems of Laguerre´ةs Method --- p.3 / Chapter 2.1 --- Laguerre´ةs Method in Symmetrie-Cluster Problem / Chapter 2.2 --- Cyclic Behaviour / Chapter 2.3 --- Supercluster Problem / Chapter 3 --- Proposed Enhancement to Laguerre 's Method --- p.9 / Chapter 3.1 --- Analysis of Adding a Zero or Pole / Chapter 3.2 --- Proposed Algorithm / Chapter 4 --- Conclusion --- p.17 / Chapter II --- Homotopy Methods applied to Polynomial Zero-finding / Chapter 1 --- Introduction --- p.18 / Chapter 2 --- Overcoming Bifurcation --- p.22 / Chapter 3 --- Comparison of Homotopy Algorithms --- p.27 / Chapter 4 --- Conclusion --- p.29 / Appendices / Chapter I --- Laguerre's Method in Polynomial Zero-finding / Chapter 0 --- Naming of Testing Polynomials / Chapter 1 --- Finding All Zeros using Proposed Laguerre's Method / Chapter 2 --- Experiments: Selected Pictures of Comparison of Proposed Strategy with Other Strategy / Chapter 3 --- Experiments: Tables of Comparison of Proposed Strategy with Other Strategy / Chapter 4 --- Distance Colorations and Target Colorations / Chapter II --- Homotopy Methods applied to Polynomial Zero-finding / Chapter 1 --- Comparison of Algorithms using Homotopy Method / Chapter 2 --- Experiments: Selected Pictorial Comparison / Chapter III --- An Example Demonstrating Effect of Round-off Errors References
70

Homotopies and Deformation Retracts

Stark, William D. (William David) 12 1900 (has links)
This paper introduces the background concepts necessary to develop a detailed proof of a theorem by Ralph H. Fox which states that two topological spaces are the same homotopy type if and only if both are deformation retracts of a third space, the mapping cylinder. The concepts of homotopy and deformation are introduced in chapter 2, and retraction and deformation retract are defined in chapter 3. Chapter 4 develops the idea of the mapping cylinder, and the proof is completed. Three special cases are examined in chapter 5.

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