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1 
A Presentation of Current Research on Partitions of Lines and SpaceNugen, Frederick T. 12 1900 (has links)
We present the results from three papers concerning partitions of vector spaces V over the set R of reals and of the set of lines in V.

2 
Topics in optimization and vector optimization.January 1999 (has links)
by Peter Au. / Thesis (M.Phil.)Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 8788). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.5 / Chapter 2  Preliminaries  p.7 / Chapter 2.1  Recession and Conjugate Functions  p.7 / Chapter 2.2  Directional derivative and Subgradient  p.10 / Chapter 2.3  WellPosedness and Esubgradient  p.15 / Chapter 2.4  Exact Penalization  p.17 / Chapter 3  Some Recent Results on Error Bounds  p.20 / Chapter 3.1  Hoffman's Error Bound  p.20 / Chapter 3.2  Extension of Hoffman's Error Bound to Polynomial Systems  p.26 / Chapter 3.2.1  An Error Bound to Polynomial Systems  p.28 / Chapter 3.2.2  Error Bound for Convex Quadratic Inequali ties Systems  p.30 / Chapter 3.3  Error Bounds for a Convex Inequality  p.41 / Chapter 3.3.1  Unconstrained Case  p.42 / Chapter 3.3.2  Constrained Case  p.47 / Chapter 3.4  Error Bounds for System of Convex Inequalities  p.55 / Chapter 3.4.1  Unconstrained Case  p.56 / Chapter 3.4.2  Constrained Case  p.60 / Chapter 4  Some Recent Results on Certain Proper Efficient Points  p.63 / Chapter 4.1  Scalarization of Henig Proper Efficient Points  p.63 / Chapter 4.1.1  Preliminaries  p.64 / Chapter 4.1.2  Scalarization by Monotone Minkowski Func tionals  p.68 / Chapter 4.1.3  Scalarization by Continuous Norms  p.73 / Chapter 4.2  Pareto Optimizing and Scalarly Stationary Sequence  p.75 / Bibliography

3 
Recent developments in optimality notions, scalarizations and optimality conditions in vector optimization. / Recent developments in vector optimizationJanuary 2011 (has links)
Lee, Hon Leung. / "August 2011." / Thesis (M.Phil.)Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 98101) and index. / Abstracts in English and Chinese. / Chapter 1  Introduction  p.6 / Chapter 2  Preliminaries  p.11 / Chapter 2.1  Functional analysis  p.11 / Chapter 2.2  Convex analysis  p.14 / Chapter 2.3  Relative interiors  p.19 / Chapter 2.4  Multifunctions  p.21 / Chapter 2.5  Variational analysis  p.22 / Chapter 3  A unified notion of optimality  p.29 / Chapter 3.1  Basic notions of minimality  p.29 / Chapter 3.2  A unified notion  p.32 / Chapter 4  Separation theorems  p.38 / Chapter 4.1  Zheng and Ng fuzzy separation theorem  p.38 / Chapter 4.2  Extremal principles and other consequences  p.43 / Chapter 5  Necessary conditions for the unified notion of optimality  p.49 / Chapter 5.1  Local asymptotic closedness  p.49 / Chapter 5.2  First order necessary conditions  p.56 / Chapter 5.2.1  Introductory remark  p.56 / Chapter 5.2.2  Without operator constraints  p.59 / Chapter 5.2.3  With operator constraints  p.66 / Chapter 5.3  Comparisons with known necessary conditions  p.74 / Chapter 5.3.1  Finitedimensional setting  p.74 / Chapter 5.3.2  Zheng and Ng's work  p.76 / Chapter 5.3.3  Dutta and Tammer's work  p.80 / Chapter 5.3.4  Bao and Mordukhovich's previous work  p.81 / Chapter 6  A weak notion: approximate efficiency  p.84 / Chapter 6.1  Approximate minimality  p.85 / Chapter 6.2  A scalarization result  p.86 / Chapter 6.3  Variational approach  p.94 / Bibliography  p.98 / Index  p.102

4 
Vector optimization and vector variational principle. / CUHK electronic theses & dissertations collectionJanuary 2006 (has links)
In this thesis we study two important issues in vector optimization problem (VOP). The first is on the scalarization; here we provide some merit functions for VOP and analyze their error bound property. The second is on generalization of Ekeland's variational principle; here this famous result in variational analysis is now extended from the original setting for scalarvalued functions to that of vectorvalued functions. This generalization enable us to study the error bound property for systems of functions instead of that for a single function. / Liu Chunguang. / "June 2006." / Adviser: Kungfu Ng. / Source: Dissertation Abstracts International, Volume: 6711, Section: B, page: 6440. / Thesis (Ph.D.)Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 9294). / 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. / Abstracts in English and Chinese. / School code: 1307.

5 
Vector and plane fields on manifoldsLee, KonYing January 1977 (has links)
No description available.

6 
Dual linear spaces generated by a nonDesarguesian configurationSeffrood, Jiajia Yang Garcia January 2005 (has links)
Mode of access: World Wide Web. / Thesis (Ph. D.)University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 160161). / Electronic reproduction. / Also available by subscription via World Wide Web / viii, 161 leaves, bound ill. 29 cm

7 
On the existence of almost uniform linear spaces.Oravas, Monica Anette. Rosa, Alexander. Unknown Date (has links)
Thesis (Ph.D.)McMaster University (Canada), 1993. / Source: Dissertation Abstracts International, Volume: 5506, Section: B, page: 2239. Adviser: A. Rosa.

8 
Dual linear spaces generated by a nonDesarguesian configurationSeffrood, Jiajia Yang Garcia. January 2005 (has links)
Thesis (Ph. D.)University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 160161).

9 
The normality of products with a compact or a metric factorStarbird, Michael P. January 1974 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1974. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 8283).

10 
Semigroups of singular endomorphisms of vector spaceDawlings, Robert J. H. January 1980 (has links)
In 1967, J. A. Erdős showed, using a matrix theory approach that the semigroup Sing[sub]n of singular endomorphisms of an ndimensional vector space is generated by the set E of idempotent endomorphisms of rank n  1. This thesis gives an alternative proof using a linear algebra and semigroup theory approach. It is also shown that not all the elements of E are needed to generate Sing[sub]n. Necessary conditions for a subset of E to generate found; these conditions are shown to be sufficient if the vector space is defined over a finite field. In this case, the minimum order of all subsets of E that generate Sing[sub]n is found. The problem of determining the number of subsets of E that generate Sing[sub]n and have this minimum order is considered; it is completely solved when the vector space is twodimensional. From the proof given by Erdős, it could be deduced that any element of Sing[sub]n could be expressed as the product of, at most, 2n elements of E. It is shown here that this bound may be reduced to n, and that this is best possible. It is also shown that, if E+ is the set of all idempotent of Singn, then (E+)n−1 is strictly contained in Sing[sub]n. Finally, it is shown that Erdős's result cannot be extended to the semigroup Sing of continuous singular endomorphisms of a separable Hilbert space. The sub semigroup of Sing generated by the idempotent of Sing is determined and is, clearly, strictly contained in Sing.

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