Local Improvements to Reduced-Order Approximations of Optimal Control Problems Governed by Diffusion-Convection-Reaction Equation

We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be lack of accuracy if the POD basis depending on a set of parameters is used to approximate the problem depending on a different set of parameters. We are interested in the perturbation of diffusion term. To increase the accuracy and robustness of the basis, we compute three bases additional to the baseline POD. The first two of them use the sensitivity information to extrapolate and expand the POD basis. The other one is based on the subspace angle interpolation method. We compare these different bases in terms of accuracy and complexity and investigate the advantages and main drawbacks of them.Comment: 19 pages, 5 figures, 2 table

Ambiguities of modernist nationalism: architectural culture and nation-building in early Republican Turkey

Reviews the book "Modernism and Nation Building: Turkish Architectural Culture in the Early Republic," by Sibel Bozdogan

Focusing for Pronoun Resolution in English Discourse: An Implementation

Anaphora resolution is one of the most active research areas in natural language processing. This study examines focusing as a tool for the resolution of pronouns which are a kind of anaphora. Focusing is a discourse phenomenon like anaphora. Candy Sidner formalized focusing in her 1979 MIT PhD thesis and devised several algorithms to resolve definite anaphora including pronouns. She presented her theory in a computational framework but did not generally implement the algorithms. Her algorithms related to focusing and pronoun resolution are implemented in this thesis. This implementation provides a better comprehension of the theory both from a conceptual and a computational point of view. The resulting program is tested on different discourse segments, and evaluation and analysis of the experiments are presented together with the statistical results.Comment: iii + 49 pages, compressed, uuencoded Postscript file; revised version of the first author's Bilkent M.S. thesis, written under the supervision of the second author; notify Akman via e-mail ([email protected]) or fax (+90-312-266-4126) if you are unable to obtain hardcopy, he'll work out somethin

On the dimension of a certain measure in the plane

We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane. Our work generalizes work of Lewis and coauthors when the measure is $p$ harmonic and also for $p=2$, the well known theorem of Makarov regarding the Hausdorff dimension of harmonic measure relative to a point in a simply connected domain.Comment: 26 page